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Advances in automating analysis of neural time series

M
Mainak Jas

This document describes advances in automating the analysis of neural time series data, specifically EEG and MEG data. It discusses challenges with manual analysis methods, including lack of reproducibility and scalability. It then summarizes the author's contributions to improving automation and reproducibility through tools like a Brain Imaging Data Structure validator, a tutorial on group analysis methods, and a method called Autoreject for automatically rejecting artifact-contaminated trials in EEG/MEG data. The goal of this work is to develop fully automated and reproducible analysis methods that can handle large datasets.

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Advances in automating analysis of neural time series Mainak Jas Advisor: Alexandre Gramfort Ph.D. defense April 12, 2018
Advances in automating analysis of neural time series 2 Where does the data come from?
Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG)
Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG)
Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG) Spontaneous brain activity
Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG) Earth’s magnetic field Spontaneous brain activity
Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG) Earth’s magnetic field Traffic, Electrical disturbance Spontaneous brain activity
Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG) Earth’s magnetic field Traffic, Electrical disturbance Spontaneous brain activity Sensor noise
Advances in automating analysis of neural time series 3 We will analyze multivariate time series
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trigger channel
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trials Trigger channel
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trials Trigger channel
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trials Trigger channel Evoked response
Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trials Trigger channel Evoked response N170: faces P300: surprise N400: words etc.
4 Manual analysis cannot be scaled and is not reproducible
4 Manual analysis cannot be scaled and is not reproducible 1http://biorxiv.org/content/biorxiv/early/2016/02/12/039354.full.pdf (A practical guide for improving transparency and reproducibility in neuroimaging research) “Quite often in the course of a project parameters are modified, list of subjects are changed, and processing steps need to be rerun … automating instead of manual interventions can really pay off” —Russel Poldrack1
4 Manual analysis cannot be scaled and is not reproducible 1http://biorxiv.org/content/biorxiv/early/2016/02/12/039354.full.pdf (A practical guide for improving transparency and reproducibility in neuroimaging research) “Quite often in the course of a project parameters are modified, list of subjects are changed, and processing steps need to be rerun … automating instead of manual interventions can really pay off” —Russel Poldrack1 Advances in automating analysis of neural time series
Advances in automating analysis of neural time series 5 Contributions
Advances in automating analysis of neural time series 5 Contributions Reproducibility • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Brain Imaging Methods) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data)
Advances in automating analysis of neural time series 5 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Brain Imaging Methods) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
Advances in automating analysis of neural time series 5 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Brain Imaging Methods) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
Advances in automating analysis of neural time series 6 Contribution I: Brain Imaging Data Structure (BIDS) validator
Advances in automating analysis of neural time series 6 Contribution I: Brain Imaging Data Structure (BIDS) validator - Automatic converter MNE-BIDS - BIDS compatible dataset ds000248
Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis code [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis code ? [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis code ? http://mne-tools.github.io/mne-biomag-group-demo/ [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis •Diagnostic plots code ? http://mne-tools.github.io/mne-biomag-group-demo/ [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis •Diagnostic plots •Alternatives code ? http://mne-tools.github.io/mne-biomag-group-demo/ [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis •Diagnostic plots •Alternatives •Statistics code ? http://mne-tools.github.io/mne-biomag-group-demo/ [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
Advances in automating analysis of neural time series 8 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Neuroscience) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
Advances in automating analysis of neural time series 9 Contribution III: Automatic rejection of artifactssensors Trials [Jas, Engemann, Raimondo, Bekhti, Gramfort. NeuroImage. 2017] Bad trial
Related work Riemannian Potato [Barachant, 2013] PREP (RANSAC) [Bigdely-Shamlo, 2015] FASTER [Nolan, 2010] 10 Robust regression [Diedrichsen, 2005] Sensor Noise Suppression [Cheveigné, 2008] Advances in automating analysis of neural time series
Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes
Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A
Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A
Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A
Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A A < threshold τ
Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A A < threshold τ Good data Yes?
Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A A < threshold τ Good data Bad data Yes? No?
Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12Advances in automating analysis of neural time series
Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12 Too few trials! Advances in automating analysis of neural time series
Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12 Too few trials! Advances in automating analysis of neural time series
Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12 Too few trials! Outliers not removed Advances in automating analysis of neural time series
Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12 Too few trials! Outliers not removedOptimal Advances in automating analysis of neural time series Evoked response
13 How do we measure data quality? Many trials for a single sensor
13 Artifact How do we measure data quality? Many trials for a single sensor
13 Artifact How do we measure data quality? Many trials for a single sensor
13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set
13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set XvalXtrain(τ)
13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set XvalXtrain(τ)
13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set Xval Fro RMSE = Xtrain(τ)
(lower error = cleaner training set) 13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set Xval Fro RMSE = Xtrain(τ)
14 But what if my validation data also has artifacts? Advances in automating analysis of neural time series
14 But what if my validation data also has artifacts? Validation set Advances in automating analysis of neural time series
14 But what if my validation data also has artifacts? Xval Validation set Advances in automating analysis of neural time series
14 But what if my validation data also has artifacts? Xval Xval ~ Validation set Advances in automating analysis of neural time series
14 But what if my validation data also has artifacts? Xval Xval ~ Answer: use the median instead of the mean RMSE= Xtrain(τ) Xval ~ Fro Validation set Advances in automating analysis of neural time series
Autoreject (global) vs. human threshold 15Advances in automating analysis of neural time series
Autoreject (global) vs. human threshold 15Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
Autoreject (global) vs. human threshold 1.85 1.95 2.05 2.15 2.25 2.35 40 57 73 90 106 123 139 156 172 189 RMSE(μV) Threshold (μV) RMSE Autoreject (global) Manual 15Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
Autoreject (global) vs. human threshold 1.85 1.95 2.05 2.15 2.25 2.35 40 57 73 90 106 123 139 156 172 189 RMSE(μV) Threshold (μV) RMSE Autoreject (global) Manual 15 Average with 5-fold cross-validation Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
Autoreject (global) vs. human threshold 1.85 1.95 2.05 2.15 2.25 2.35 40 57 73 90 106 123 139 156 172 189 RMSE(μV) Threshold (μV) RMSE Autoreject (global) Manual 15 Average with 5-fold cross-validation Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
Autoreject (global) vs. human threshold 1.85 1.95 2.05 2.15 2.25 2.35 40 57 73 90 106 123 139 156 172 189 RMSE(μV) Threshold (μV) RMSE Autoreject (global) Manual 15 Average with 5-fold cross-validation Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
How to sample the thresholds? 16
How to sample the thresholds? 16 error Thresholds
How to sample the thresholds? 16 error Thresholds
How to sample the thresholds? 16 Grid search error Thresholds
How to sample the thresholds? 16 Grid search Grid resolution error Thresholds
How to sample the thresholds? 16 Random search error Thresholds
17 Bayesian optimization: a more efficient approach Thresholds error
17 Bayesian optimization: a more efficient approach Thresholds error
17 Bayesian optimization: a more efficient approach Thresholds error Gaussian process
17 Bayesian optimization: a more efficient approach Thresholds error Exploration vs exploitation dilemma Gaussian process
17 Bayesian optimization: a more efficient approach Thresholds error Exploration vs exploitation dilemma Gaussian process Acquisition function
17 Bayesian optimization: a more efficient approach Thresholds error Exploration vs exploitation dilemma Gaussian process Acquisition function
18 Each sensor has a different threshold
18 0 5 10 15 20 25 123 225 327 430 532 634 736 839 Numberofsensors Threshold (fT/cm) Each sensor has a different threshold
18 0 5 10 15 20 25 123 225 327 430 532 634 736 839 Numberofsensors Threshold (fT/cm) Each sensor has a different threshold Sensors Trials
18 0 5 10 15 20 25 123 225 327 430 532 634 736 839 Numberofsensors Threshold (fT/cm) Each sensor has a different threshold Sensors Trials
18 0 5 10 15 20 25 123 225 327 430 532 634 736 839 Numberofsensors Threshold (fT/cm) Each sensor has a different threshold Sensors Trials
19 Schematic of the complexity of the problem Trials Sensors
19 Schematic of the complexity of the problem Trials Sensors Bad trial
19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor
19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor
19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
19 Schematic of the complexity of the problem Naïve solution: Drop bad trials and sensors Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts Naïve solution: Drop bad trials and sensors
19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts Naïve solution: Drop bad trials and sensors
19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial
19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial Interpolation Bad sensor Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial Interpolation • EEG: Spherical splines • MEG: MNE Bad sensor [Hamalainen et al., 1994] [Perrin et al., 1989] Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial Interpolation • EEG: Spherical splines • MEG: MNE Bad sensor [Hamalainen et al., 1994] [Perrin et al., 1989] Else: interpolate ρ (=2) worst bad sensors per trial Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial Else: interpolate ρ (=2) worst bad sensors per trial Interpolation • EEG: Spherical splines • MEG: MNE Bad sensor [Hamalainen et al., 1994] [Perrin et al., 1989] Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
Autoreject in action: MNE sample data (MEG) 20http://autoreject.github.io/auto_examples/plot_auto_repair.html
21 Autoreject in action (EEG data) Advances in automating analysis of neural time series Before autoreject After autoreject 19 subject Faces dataset [Wakeman and Henson, 2015]
22 Quantitative evaluation Advances in automating analysis of neural time series [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
22 Quantitative evaluation Advances in automating analysis of neural time series   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
22 Quantitative evaluation Advances in automating analysis of neural time series one subject   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
22 Quantitative evaluation Advances in automating analysis of neural time series Competing method better one subject   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
22 Quantitative evaluation Advances in automating analysis of neural time series Autoreject better Competing method better one subject   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
22 Quantitative evaluation Advances in automating analysis of neural time series Autoreject better Competing method better one subject   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
Transparency: an example diagnostic plot 23http://autoreject.github.io/auto_examples/plot_visualize_bad_epochs.html
Transparency: an example diagnostic plot 23 Sensor to be interpolated http://autoreject.github.io/auto_examples/plot_visualize_bad_epochs.html
Transparency: an example diagnostic plot 23 Sensor to be interpolated Bad sensor but not going to be interpolated http://autoreject.github.io/auto_examples/plot_visualize_bad_epochs.html
Transparency: an example diagnostic plot 23 Sensor to be interpolated Bad sensor but not going to be interpolated Bad trials http://autoreject.github.io/auto_examples/plot_visualize_bad_epochs.html
Advances in automating analysis of neural time series 24 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Neuroscience) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
Advances in automating analysis of neural time series 24 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Neuroscience) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
Contribution IV: Learn representations from neural data #1 Shape of brain rhythms matter 25Advances in automating analysis of neural time series [Cole and Voytek, 2017] μ rhythm [Jas, Dupré la Tour, Şimşekli, Gramfort. NIPS. 2017]
Contribution IV: Learn representations from neural data #1 Shape of brain rhythms matter 25Advances in automating analysis of neural time series [Cole and Voytek, 2017] μ rhythm [Jas, Dupré la Tour, Şimşekli, Gramfort. NIPS. 2017]
Contribution IV: Learn representations from neural data #2 Filtering #1 Shape of brain rhythms matter 25Advances in automating analysis of neural time series [Cole and Voytek, 2017] μ rhythm [Jas, Dupré la Tour, Şimşekli, Gramfort. NIPS. 2017]
Contribution IV: Learn representations from neural data #2 Filtering #1 Shape of brain rhythms matter 25Advances in automating analysis of neural time series [Cole and Voytek, 2017] μ rhythm asymmetry [Jas, Dupré la Tour, Şimşekli, Gramfort. NIPS. 2017]
Some attempts in the neuroscience community 26Advances in automating analysis of neural time series
Some attempts in the neuroscience community 26 Adaptive Waveform Learning [Hitziger, 2017] Template waveform Coefficient updates waveform updates Different durations Advances in automating analysis of neural time series
Some attempts in the neuroscience community Sliding Window Method [Gips et al., 2017] 26 Adaptive Waveform Learning [Hitziger, 2017] Template waveform Coefficient updates waveform updates Different durations Advances in automating analysis of neural time series
Some attempts in the neuroscience community Sliding Window Method [Gips et al., 2017] MoTIF [Jost et al., 2006] 26 Adaptive Waveform Learning [Hitziger, 2017] Template waveform Coefficient updates waveform updates Different durations Learning recurrent waveforms in EEG [Brockmeier & Principe, 2016] Multivariate temporal dictionary learning [Barthélemy et al., 2013] Advances in automating analysis of neural time series
The problem setup (simulation) 27Advances in automating analysis of neural time series
The problem setup (simulation) 27Advances in automating analysis of neural time series
The problem setup (simulation) 27Advances in automating analysis of neural time series
The problem setup (simulation) Two different atoms (can have more) 27Advances in automating analysis of neural time series
The problem setup (simulation) Different amplitudes Two different atoms (can have more) 27Advances in automating analysis of neural time series
The problem setup (simulation) Different locations Different amplitudes Two different atoms (can have more) 27Advances in automating analysis of neural time series
The problem setup (simulation) Different locations Different amplitudes Two different atoms (can have more) Atoms can even overlap 27Advances in automating analysis of neural time series
The problem setup (simulation) Different locations Different amplitudes Two different atoms (can have more) Small gaussian noise Atoms can even overlap 27Advances in automating analysis of neural time series
28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015]
28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] =nx
28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] *=nx k d k nz
28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] *=nx k d k nz 
28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
28 Convolutional Sparse Coding (CSC) formulation             n kn k n k k n k n zd zzdx , 2 2 , *min  Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
28 Convolutional Sparse Coding (CSC) formulation Penalty to enforce sparsity             n kn k n k k n k n zd zzdx , 2 2 , *min  Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
28 Convolutional Sparse Coding (CSC) formulation Penalty to enforce sparsity             n kn k n k k n k n zd zzdx , 2 2 , *min  s.t. 0k nz Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
28 Convolutional Sparse Coding (CSC) formulation d k 2 2 ≤ 1 Penalty to enforce sparsity             n kn k n k k n k n zd zzdx , 2 2 , *min  s.t. 0k nz Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  29Advances in automating analysis of neural time series
Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  29Advances in automating analysis of neural time series • Not jointly convex in both d and z
Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed
Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  d-step 29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  z-step 29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  d-step 29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  z-step 29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
z-step: The Toeplitz matrix trick 30Advances in automating analysis of neural time series
z-step: The Toeplitz matrix trick k n kk n k zDzd * 30Advances in automating analysis of neural time series
z-step: The Toeplitz matrix trick k n kk n k zDzd * k D 30Advances in automating analysis of neural time series
z-step: The Toeplitz matrix trick k n kk n k zDzd * k D k nz 30Advances in automating analysis of neural time series
z-step: The Toeplitz matrix trick k n kk n k zDzd * k D k nz    kn k n n k k n k n z zzDx , 2 2 min  30Advances in automating analysis of neural time series
z-step: The Toeplitz matrix trick 31Advances in automating analysis of neural time series
z-step: The Toeplitz matrix trick k k n k zD 31Advances in automating analysis of neural time series
z-step: The Toeplitz matrix trick 1 D k k n k zD 1 nz 31Advances in automating analysis of neural time series
z-step: The Toeplitz matrix trick 1 D k D k k n k zD 1 nz k nz 31Advances in automating analysis of neural time series
[ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz 31Advances in automating analysis of neural time series
[ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 31Advances in automating analysis of neural time series
        n nnn z zDzx  2 2 2 1 min [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 31Advances in automating analysis of neural time series
          n nnn n zDzx z  2 2 2 1 [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 31Advances in automating analysis of neural time series
          n nnn n zDzx z  2 2 2 1 [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 1 )( nn T DzxD 31Advances in automating analysis of neural time series
          n nnn n zDzx z  2 2 2 1 [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 1 )( nn T DzxD Now, we can feed the gradient to L-BFGS-B optimization algorithm 31Advances in automating analysis of neural time series
             n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 k nZ 32Advances in automating analysis of neural time series
             n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 k nZ 32Advances in automating analysis of neural time series
             n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 k nZ 32Advances in automating analysis of neural time series
             n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 k nZ 32Advances in automating analysis of neural time series
             n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 k nZ 32Advances in automating analysis of neural time series
             n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 0 .5 0 k nZ 32Advances in automating analysis of neural time series
             n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 0 .5 0 0 2 4 k nZ k d 32Advances in automating analysis of neural time series
             n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 0 .5 0 0 2 4 k nZ k d kk n k n k dZzd * 32Advances in automating analysis of neural time series
            n k kk nn d dZx 2 2 1 2 1 min2 2 k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 0 .5 0 0 2 4 k nZ k d kk n k n k dZzd * We remove the regularization term as it doesn’t depend on d 32Advances in automating analysis of neural time series Least square problem under unit norm constraint
33 d-step: The atoms are updated using LBFGS-B Advances in automating analysis of neural time series
33 d-step: The atoms are updated using LBFGS-B              n k kk nnk dZx d 2 2 2 1 Advances in automating analysis of neural time series
33 d-step: The atoms are updated using LBFGS-B              n k kk nnk dZx d 2 2 2 1          k kk nn Tk n dZxZ Advances in automating analysis of neural time series
33 d-step: The atoms are updated using LBFGS-B              n k kk nnk dZx d 2 2 2 1          2 ˆ 1 ,1minˆˆ k kk d dd 1. Gradient step 2. Projection step          k kk nn Tk n dZxZ Advances in automating analysis of neural time series Projected gradient descent
33 d-step: The atoms are updated using LBFGS-B              n k kk nnk dZx d 2 2 2 1          2 ˆ 1 ,1minˆˆ k kk d dd 1. Gradient step 2. Projection step          k kk nn Tk n dZxZ Advances in automating analysis of neural time series In practice, it is more complicated … LBFGS-B in the dual Projected gradient descent
Putting it all together 34Advances in automating analysis of neural time series
Putting it all together z update 34Advances in automating analysis of neural time series
Putting it all together z update Toeplitz D 34Advances in automating analysis of neural time series
Putting it all together z update d update Toeplitz D 34Advances in automating analysis of neural time series
Putting it all together z update d update Toeplitz D Strided Z 34Advances in automating analysis of neural time series
Putting it all together z update d update Toeplitz D Strided Z (L-BFGS-B) (L-BFGS-B) 34Advances in automating analysis of neural time series
Putting it all together z update d update Toeplitz D Strided Z (L-BFGS-B) (L-BFGS-B) Alternate minimization 34Advances in automating analysis of neural time series
35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom Advances in automating analysis of neural time series
35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom Advances in automating analysis of neural time series
35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes Advances in automating analysis of neural time series
35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes 1 hour Advances in automating analysis of neural time series
35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes 1 hour Advances in automating analysis of neural time series
35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes 1 hour 45 minutes Advances in automating analysis of neural time series
35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes 1 hour 45 minutes 2 hours Advances in automating analysis of neural time series
36 The quasi-Newton solver outperform ADMM solvers Advances in automating analysis of neural time series
36 The quasi-Newton solver outperform ADMM solvers ADMM solvers Advances in automating analysis of neural time series
36 The quasi-Newton solver outperform ADMM solvers Different random seeds ADMM solvers Advances in automating analysis of neural time series
Cross frequency coupling uncovered via CSC ~80 Hz 37Advances in automating analysis of neural time series [Canolty, 2006] [Dupré la Tour, 2017]
Challenge Neural data often contains transient artifacts 38Advances in automating analysis of neural time series
39 CSC in the presence of transient artifacts Advances in automating analysis of neural time series
39 CSC in the presence of transient artifacts Advances in automating analysis of neural time series
39 Neural signals CSC in the presence of transient artifacts Advances in automating analysis of neural time series
39 Transient artifacts Neural signals CSC in the presence of transient artifacts Advances in automating analysis of neural time series
A probabilistic interpretation 40Advances in automating analysis of neural time series
A probabilistic interpretation 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
A probabilistic interpretation          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
A probabilistic interpretation        1,*~,| 1 , K k k n k tn zdNdzx          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate Data likelihood 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
A probabilistic interpretation )(~, k tnz       1,*~,| 1 , K k k n k tn zdNdzx          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate PriorData likelihood 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
A probabilistic interpretation )(~, k tnz       1,*~,| 1 , K k k n k tn zdNdzx          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate PriorData likelihood 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
A probabilistic interpretation )(~, k tnz       1,*~,| 1 , K k k n k tn zdNdzx          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate PriorData likelihood 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min  Sparser activations
Alpha-stable distributions ),,,(~ SX 41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996]
Alpha-stable distributions ),,,(~ SX 41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent 41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),(  41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),0( Scale parameter ),(  41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),0( Scale parameter ),(  41 Special cases Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),0( Scale parameter ),(  41 Special cases Normal distribution ),,0,2(~  SX Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),0( Scale parameter ),(  41 Special cases Normal distribution ),,0,2(~  SX ),,0,1(~  SX Cauchy distribution Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
42        1,*~,| 1 , K k k n k tn zdNdzx From light tails to heavy tails         K k k n k tn zdSdzx 1 , *,2/1,0,~,|  2 Symmetric alpha-stable distributions Advances in automating analysis of neural time series
Symmetric α-stable distribution is conditionally Gaussian 43Advances in automating analysis of neural time series [Samorodnitsky et al., 1996]
Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|  Advances in automating analysis of neural time series [Samorodnitsky et al., 1996]
       tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|  Advances in automating analysis of neural time series [Samorodnitsky et al., 1996]
       tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|  Advances in automating analysis of neural time series from a positive stable distribution tn, [Samorodnitsky et al., 1996]
       tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|             n kn k n k k n k n n zd zzdx , 2 2 , * 1 min   Weighted CSC! Advances in automating analysis of neural time series from a positive stable distribution tn, [Samorodnitsky et al., 1996]
       tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|             n kn k n k k n k n n zd zzdx , 2 2 , * 1 min   Weighted CSC! Advances in automating analysis of neural time series But is not known …tn, from a positive stable distribution tn, [Samorodnitsky et al., 1996]
EM algorithm is used to estimate MAP when some variables are missing 44Advances in automating analysis of neural time series [Dempster et. al., 1977]
EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E Advances in automating analysis of neural time series [Dempster et. al., 1977]
EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E                  n kn k n k k n k n n i zzdxEzdB , 2 2 )( * 1 ),(   Advances in automating analysis of neural time series [Dempster et. al., 1977]
EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E                  n kn k n k k n k n n i zzdxEzdB , 2 2 )( * 1 ),(   Advances in automating analysis of neural time series [Dempster et. al., 1977] weights
EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step Maximization step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E ),(maxarg),( )( , )1()1( zdBzd i zd ii                   n kn k n k k n k n n i zzdxEzdB , 2 2 )( * 1 ),(   Advances in automating analysis of neural time series [Dempster et. al., 1977] weights
EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step Maximization step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E ),(maxarg),( )( , )1()1( zdBzd i zd ii                   n kn k n k k n k n n i zzdxEzdB , 2 2 )( * 1 ),(   Iterate until convergence Advances in automating analysis of neural time series [Dempster et. al., 1977] weights
45 For the E-step, we compute the expectation using sampling Advances in automating analysis of neural time series [Bishop, 2007]
45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E Advances in automating analysis of neural time series [Bishop, 2007]
45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E   J j j tnJ 1 , 11  Advances in automating analysis of neural time series [Bishop, 2007]
45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E   J j j tnJ 1 , 11  Advances in automating analysis of neural time series [Bishop, 2007]
45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E   J j j tnJ 1 , 11  Sampled from the posterior distribution Advances in automating analysis of neural time series [Bishop, 2007]
45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E   J j j tnJ 1 , 11  Sampled from the posterior distribution Markov Chain Monte Carlo (MCMC) Advances in automating analysis of neural time series [Bishop, 2007]
46 Let’s recap Advances in automating analysis of neural time series
46 Let’s recap Data likelihood term Advances in automating analysis of neural time series
46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Advances in automating analysis of neural time series
46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Latent variable Advances in automating analysis of neural time series
46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Latent variable EM algorithm Advances in automating analysis of neural time series
46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Latent variable EM algorithm E step: MCMC to learn weights       tn, 1  E Advances in automating analysis of neural time series
46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Latent variable EM algorithm E step: MCMC to learn weights M step: Weighted CSC       tn, 1  E Advances in automating analysis of neural time series
47 -CSC on simulated data Advances in automating analysis of neural time series [Jost et al., 2006]
48 -CSC with  = 2 (reduces to Gaussian) Advances in automating analysis of neural time series
48 -CSC with  = 2 (reduces to Gaussian) Advances in automating analysis of neural time series
49 -CSC with ≠2 Advances in automating analysis of neural time series
49 -CSC with ≠2 Advances in automating analysis of neural time series
Advances in automating analysis of neural time series 50 Conclusion
Advances in automating analysis of neural time series 50 Conclusion Data sharing And data standards
Advances in automating analysis of neural time series 50 Conclusion Data sharing And data standards Autoreject to remove artifacts
Advances in automating analysis of neural time series 50 Conclusion Data sharing And data standards Autoreject to remove artifacts αCSC to learn recurring waveforms
Alexandre Gramfort Denis Engemann Yousra Bekhti Eric LarsonUmut Şimşekli Tom Dupré la Tour Credits 51Advances in automating analysis of neural time series
52 Thank you Advances in automating analysis of neural time series

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Advances in automating analysis of neural time series

  • 1. Advances in automating analysis of neural time series Mainak Jas Advisor: Alexandre Gramfort Ph.D. defense April 12, 2018
  • 2. Advances in automating analysis of neural time series 2 Where does the data come from?
  • 3. Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG)
  • 4. Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG)
  • 5. Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG) Spontaneous brain activity
  • 6. Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG) Earth’s magnetic field Spontaneous brain activity
  • 7. Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG) Earth’s magnetic field Traffic, Electrical disturbance Spontaneous brain activity
  • 8. Advances in automating analysis of neural time series 2 Where does the data come from? Electroencephalography (EEG) Magnetoencephalography (MEG) Earth’s magnetic field Traffic, Electrical disturbance Spontaneous brain activity Sensor noise
  • 9. Advances in automating analysis of neural time series 3 We will analyze multivariate time series
  • 10. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
  • 11. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
  • 12. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
  • 13. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
  • 14. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time
  • 15. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trigger channel
  • 16. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trials Trigger channel
  • 17. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trials Trigger channel
  • 18. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trials Trigger channel Evoked response
  • 19. Advances in automating analysis of neural time series 3 We will analyze multivariate time series Time Trials Trigger channel Evoked response N170: faces P300: surprise N400: words etc.
  • 20. 4 Manual analysis cannot be scaled and is not reproducible
  • 21. 4 Manual analysis cannot be scaled and is not reproducible 1http://biorxiv.org/content/biorxiv/early/2016/02/12/039354.full.pdf (A practical guide for improving transparency and reproducibility in neuroimaging research) “Quite often in the course of a project parameters are modified, list of subjects are changed, and processing steps need to be rerun … automating instead of manual interventions can really pay off” —Russel Poldrack1
  • 22. 4 Manual analysis cannot be scaled and is not reproducible 1http://biorxiv.org/content/biorxiv/early/2016/02/12/039354.full.pdf (A practical guide for improving transparency and reproducibility in neuroimaging research) “Quite often in the course of a project parameters are modified, list of subjects are changed, and processing steps need to be rerun … automating instead of manual interventions can really pay off” —Russel Poldrack1 Advances in automating analysis of neural time series
  • 23. Advances in automating analysis of neural time series 5 Contributions
  • 24. Advances in automating analysis of neural time series 5 Contributions Reproducibility • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Brain Imaging Methods) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data)
  • 25. Advances in automating analysis of neural time series 5 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Brain Imaging Methods) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
  • 26. Advances in automating analysis of neural time series 5 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Brain Imaging Methods) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
  • 27. Advances in automating analysis of neural time series 6 Contribution I: Brain Imaging Data Structure (BIDS) validator
  • 28. Advances in automating analysis of neural time series 6 Contribution I: Brain Imaging Data Structure (BIDS) validator - Automatic converter MNE-BIDS - BIDS compatible dataset ds000248
  • 29. Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
  • 30. Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis code [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
  • 31. Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis code ? [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
  • 32. Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis code ? http://mne-tools.github.io/mne-biomag-group-demo/ [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
  • 33. Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis •Diagnostic plots code ? http://mne-tools.github.io/mne-biomag-group-demo/ [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
  • 34. Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis •Diagnostic plots •Alternatives code ? http://mne-tools.github.io/mne-biomag-group-demo/ [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
  • 35. Advances in automating analysis of neural time series 7 Contribution II: Tutorial paper on group analysis •Diagnostic plots •Alternatives •Statistics code ? http://mne-tools.github.io/mne-biomag-group-demo/ [Jas, Larson, Engemann, Taulu, Hamalainen, Gramfort. 2017]
  • 36. Advances in automating analysis of neural time series 8 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Neuroscience) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
  • 37. Advances in automating analysis of neural time series 9 Contribution III: Automatic rejection of artifactssensors Trials [Jas, Engemann, Raimondo, Bekhti, Gramfort. NeuroImage. 2017] Bad trial
  • 38. Related work Riemannian Potato [Barachant, 2013] PREP (RANSAC) [Bigdely-Shamlo, 2015] FASTER [Nolan, 2010] 10 Robust regression [Diedrichsen, 2005] Sensor Noise Suppression [Cheveigné, 2008] Advances in automating analysis of neural time series
  • 39. Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes
  • 40. Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A
  • 41. Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A
  • 42. Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A
  • 43. Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A A < threshold τ
  • 44. Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A A < threshold τ Good data Yes?
  • 45. Advances in automating analysis of neural time series 11 Rejecting based on peak-to-peak amplitudes Peak-to-peak amplitude A A < threshold τ Good data Bad data Yes? No?
  • 46. Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12Advances in automating analysis of neural time series
  • 47. Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12 Too few trials! Advances in automating analysis of neural time series
  • 48. Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12 Too few trials! Advances in automating analysis of neural time series
  • 49. Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12 Too few trials! Outliers not removed Advances in automating analysis of neural time series
  • 50. Observation: The optimal threshold retains sufficient trials while rejecting outliers. 12 Too few trials! Outliers not removedOptimal Advances in automating analysis of neural time series Evoked response
  • 51. 13 How do we measure data quality? Many trials for a single sensor
  • 52. 13 Artifact How do we measure data quality? Many trials for a single sensor
  • 53. 13 Artifact How do we measure data quality? Many trials for a single sensor
  • 54. 13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set
  • 55. 13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set XvalXtrain(τ)
  • 56. 13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set XvalXtrain(τ)
  • 57. 13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set Xval Fro RMSE = Xtrain(τ)
  • 58. (lower error = cleaner training set) 13 Artifact How do we measure data quality? Many trials for a single sensor Training set Validation set Xval Fro RMSE = Xtrain(τ)
  • 59. 14 But what if my validation data also has artifacts? Advances in automating analysis of neural time series
  • 60. 14 But what if my validation data also has artifacts? Validation set Advances in automating analysis of neural time series
  • 61. 14 But what if my validation data also has artifacts? Xval Validation set Advances in automating analysis of neural time series
  • 62. 14 But what if my validation data also has artifacts? Xval Xval ~ Validation set Advances in automating analysis of neural time series
  • 63. 14 But what if my validation data also has artifacts? Xval Xval ~ Answer: use the median instead of the mean RMSE= Xtrain(τ) Xval ~ Fro Validation set Advances in automating analysis of neural time series
  • 64. Autoreject (global) vs. human threshold 15Advances in automating analysis of neural time series
  • 65. Autoreject (global) vs. human threshold 15Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
  • 66. Autoreject (global) vs. human threshold 1.85 1.95 2.05 2.15 2.25 2.35 40 57 73 90 106 123 139 156 172 189 RMSE(μV) Threshold (μV) RMSE Autoreject (global) Manual 15Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
  • 67. Autoreject (global) vs. human threshold 1.85 1.95 2.05 2.15 2.25 2.35 40 57 73 90 106 123 139 156 172 189 RMSE(μV) Threshold (μV) RMSE Autoreject (global) Manual 15 Average with 5-fold cross-validation Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
  • 68. Autoreject (global) vs. human threshold 1.85 1.95 2.05 2.15 2.25 2.35 40 57 73 90 106 123 139 156 172 189 RMSE(μV) Threshold (μV) RMSE Autoreject (global) Manual 15 Average with 5-fold cross-validation Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
  • 69. Autoreject (global) vs. human threshold 1.85 1.95 2.05 2.15 2.25 2.35 40 57 73 90 106 123 139 156 172 189 RMSE(μV) Threshold (μV) RMSE Autoreject (global) Manual 15 Average with 5-fold cross-validation Advances in automating analysis of neural time series Remove trial if data in any sensor > τ
  • 70. How to sample the thresholds? 16
  • 71. How to sample the thresholds? 16 error Thresholds
  • 72. How to sample the thresholds? 16 error Thresholds
  • 73. How to sample the thresholds? 16 Grid search error Thresholds
  • 74. How to sample the thresholds? 16 Grid search Grid resolution error Thresholds
  • 75. How to sample the thresholds? 16 Random search error Thresholds
  • 76. 17 Bayesian optimization: a more efficient approach Thresholds error
  • 77. 17 Bayesian optimization: a more efficient approach Thresholds error
  • 78. 17 Bayesian optimization: a more efficient approach Thresholds error Gaussian process
  • 79. 17 Bayesian optimization: a more efficient approach Thresholds error Exploration vs exploitation dilemma Gaussian process
  • 80. 17 Bayesian optimization: a more efficient approach Thresholds error Exploration vs exploitation dilemma Gaussian process Acquisition function
  • 81. 17 Bayesian optimization: a more efficient approach Thresholds error Exploration vs exploitation dilemma Gaussian process Acquisition function
  • 82. 18 Each sensor has a different threshold
  • 83. 18 0 5 10 15 20 25 123 225 327 430 532 634 736 839 Numberofsensors Threshold (fT/cm) Each sensor has a different threshold
  • 84. 18 0 5 10 15 20 25 123 225 327 430 532 634 736 839 Numberofsensors Threshold (fT/cm) Each sensor has a different threshold Sensors Trials
  • 85. 18 0 5 10 15 20 25 123 225 327 430 532 634 736 839 Numberofsensors Threshold (fT/cm) Each sensor has a different threshold Sensors Trials
  • 86. 18 0 5 10 15 20 25 123 225 327 430 532 634 736 839 Numberofsensors Threshold (fT/cm) Each sensor has a different threshold Sensors Trials
  • 87. 19 Schematic of the complexity of the problem Trials Sensors
  • 88. 19 Schematic of the complexity of the problem Trials Sensors Bad trial
  • 89. 19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor
  • 90. 19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor
  • 91. 19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
  • 92. 19 Schematic of the complexity of the problem Naïve solution: Drop bad trials and sensors Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
  • 93. 19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts Naïve solution: Drop bad trials and sensors
  • 94. 19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts Naïve solution: Drop bad trials and sensors
  • 95. 19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
  • 96. 19 Schematic of the complexity of the problem Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial
  • 97. 19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial Interpolation Bad sensor Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
  • 98. 19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial Interpolation • EEG: Spherical splines • MEG: MNE Bad sensor [Hamalainen et al., 1994] [Perrin et al., 1989] Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
  • 99. 19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial Interpolation • EEG: Spherical splines • MEG: MNE Bad sensor [Hamalainen et al., 1994] [Perrin et al., 1989] Else: interpolate ρ (=2) worst bad sensors per trial Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
  • 100. 19 Schematic of the complexity of the problem Proposed solution: Naïve solution: Drop bad trials and sensors if #bad-sensors > κ (=4) drop trial Else: interpolate ρ (=2) worst bad sensors per trial Interpolation • EEG: Spherical splines • MEG: MNE Bad sensor [Hamalainen et al., 1994] [Perrin et al., 1989] Trials Sensors Bad trial Globally bad sensor Locally bad sensor Local artifacts
  • 101. Autoreject in action: MNE sample data (MEG) 20http://autoreject.github.io/auto_examples/plot_auto_repair.html
  • 102. 21 Autoreject in action (EEG data) Advances in automating analysis of neural time series Before autoreject After autoreject 19 subject Faces dataset [Wakeman and Henson, 2015]
  • 103. 22 Quantitative evaluation Advances in automating analysis of neural time series [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
  • 104. 22 Quantitative evaluation Advances in automating analysis of neural time series   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
  • 105. 22 Quantitative evaluation Advances in automating analysis of neural time series one subject   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
  • 106. 22 Quantitative evaluation Advances in automating analysis of neural time series Competing method better one subject   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
  • 107. 22 Quantitative evaluation Advances in automating analysis of neural time series Autoreject better Competing method better one subject   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
  • 108. 22 Quantitative evaluation Advances in automating analysis of neural time series Autoreject better Competing method better one subject   humanmethod XX [Nolan, 2010] [Bigdely-Shamlo, 2015] [Cheveigné, 2008]
  • 109. Transparency: an example diagnostic plot 23http://autoreject.github.io/auto_examples/plot_visualize_bad_epochs.html
  • 110. Transparency: an example diagnostic plot 23 Sensor to be interpolated http://autoreject.github.io/auto_examples/plot_visualize_bad_epochs.html
  • 111. Transparency: an example diagnostic plot 23 Sensor to be interpolated Bad sensor but not going to be interpolated http://autoreject.github.io/auto_examples/plot_visualize_bad_epochs.html
  • 112. Transparency: an example diagnostic plot 23 Sensor to be interpolated Bad sensor but not going to be interpolated Bad trials http://autoreject.github.io/auto_examples/plot_visualize_bad_epochs.html
  • 113. Advances in automating analysis of neural time series 24 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Neuroscience) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
  • 114. Advances in automating analysis of neural time series 24 Contributions Reproducibility Automation • A tutorial paper for group analysis of M/EEG data (submitted to Frontiers in Neuroscience) • Brain Imaging Data Structure for MEG (submitted to Nature, Scientific Data) • Autoreject to remove artifacts (NeuroImage, 2017) • AlphaCSC to learn brain waveforms (NIPS, 2017)
  • 115. Contribution IV: Learn representations from neural data #1 Shape of brain rhythms matter 25Advances in automating analysis of neural time series [Cole and Voytek, 2017] μ rhythm [Jas, Dupré la Tour, Şimşekli, Gramfort. NIPS. 2017]
  • 116. Contribution IV: Learn representations from neural data #1 Shape of brain rhythms matter 25Advances in automating analysis of neural time series [Cole and Voytek, 2017] μ rhythm [Jas, Dupré la Tour, Şimşekli, Gramfort. NIPS. 2017]
  • 117. Contribution IV: Learn representations from neural data #2 Filtering #1 Shape of brain rhythms matter 25Advances in automating analysis of neural time series [Cole and Voytek, 2017] μ rhythm [Jas, Dupré la Tour, Şimşekli, Gramfort. NIPS. 2017]
  • 118. Contribution IV: Learn representations from neural data #2 Filtering #1 Shape of brain rhythms matter 25Advances in automating analysis of neural time series [Cole and Voytek, 2017] μ rhythm asymmetry [Jas, Dupré la Tour, Şimşekli, Gramfort. NIPS. 2017]
  • 119. Some attempts in the neuroscience community 26Advances in automating analysis of neural time series
  • 120. Some attempts in the neuroscience community 26 Adaptive Waveform Learning [Hitziger, 2017] Template waveform Coefficient updates waveform updates Different durations Advances in automating analysis of neural time series
  • 121. Some attempts in the neuroscience community Sliding Window Method [Gips et al., 2017] 26 Adaptive Waveform Learning [Hitziger, 2017] Template waveform Coefficient updates waveform updates Different durations Advances in automating analysis of neural time series
  • 122. Some attempts in the neuroscience community Sliding Window Method [Gips et al., 2017] MoTIF [Jost et al., 2006] 26 Adaptive Waveform Learning [Hitziger, 2017] Template waveform Coefficient updates waveform updates Different durations Learning recurrent waveforms in EEG [Brockmeier & Principe, 2016] Multivariate temporal dictionary learning [Barthélemy et al., 2013] Advances in automating analysis of neural time series
  • 123. The problem setup (simulation) 27Advances in automating analysis of neural time series
  • 124. The problem setup (simulation) 27Advances in automating analysis of neural time series
  • 125. The problem setup (simulation) 27Advances in automating analysis of neural time series
  • 126. The problem setup (simulation) Two different atoms (can have more) 27Advances in automating analysis of neural time series
  • 127. The problem setup (simulation) Different amplitudes Two different atoms (can have more) 27Advances in automating analysis of neural time series
  • 128. The problem setup (simulation) Different locations Different amplitudes Two different atoms (can have more) 27Advances in automating analysis of neural time series
  • 129. The problem setup (simulation) Different locations Different amplitudes Two different atoms (can have more) Atoms can even overlap 27Advances in automating analysis of neural time series
  • 130. The problem setup (simulation) Different locations Different amplitudes Two different atoms (can have more) Small gaussian noise Atoms can even overlap 27Advances in automating analysis of neural time series
  • 131. 28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015]
  • 132. 28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] =nx
  • 133. 28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] *=nx k d k nz
  • 134. 28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] *=nx k d k nz 
  • 135. 28 Convolutional Sparse Coding (CSC) formulation Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
  • 136. 28 Convolutional Sparse Coding (CSC) formulation             n kn k n k k n k n zd zzdx , 2 2 , *min  Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
  • 137. 28 Convolutional Sparse Coding (CSC) formulation Penalty to enforce sparsity             n kn k n k k n k n zd zzdx , 2 2 , *min  Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
  • 138. 28 Convolutional Sparse Coding (CSC) formulation Penalty to enforce sparsity             n kn k n k k n k n zd zzdx , 2 2 , *min  s.t. 0k nz Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
  • 139. 28 Convolutional Sparse Coding (CSC) formulation d k 2 2 ≤ 1 Penalty to enforce sparsity             n kn k n k k n k n zd zzdx , 2 2 , *min  s.t. 0k nz Advances in automating analysis of neural time series [Kavukcuoglu et al., 2010] [Zeiler et al. 2010][Gross et al., 2012][Heidi et al., 2015] * * = = nx k d k nz  
  • 140. Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  29Advances in automating analysis of neural time series
  • 141. Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  29Advances in automating analysis of neural time series • Not jointly convex in both d and z
  • 142. Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed
  • 143. Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
  • 144. Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  d-step 29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
  • 145. Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  z-step 29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
  • 146. Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  d-step 29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
  • 147. Basic strategy: alternate minimization             n kn k n k k n k n zd zzdx , 2 2 , * 2 1 min  z-step 29Advances in automating analysis of neural time series • Not jointly convex in both d and z • Convex when d or z is fixed • Alternate minimization guarantees cost function goes down at every step
  • 148. z-step: The Toeplitz matrix trick 30Advances in automating analysis of neural time series
  • 149. z-step: The Toeplitz matrix trick k n kk n k zDzd * 30Advances in automating analysis of neural time series
  • 150. z-step: The Toeplitz matrix trick k n kk n k zDzd * k D 30Advances in automating analysis of neural time series
  • 151. z-step: The Toeplitz matrix trick k n kk n k zDzd * k D k nz 30Advances in automating analysis of neural time series
  • 152. z-step: The Toeplitz matrix trick k n kk n k zDzd * k D k nz    kn k n n k k n k n z zzDx , 2 2 min  30Advances in automating analysis of neural time series
  • 153. z-step: The Toeplitz matrix trick 31Advances in automating analysis of neural time series
  • 154. z-step: The Toeplitz matrix trick k k n k zD 31Advances in automating analysis of neural time series
  • 155. z-step: The Toeplitz matrix trick 1 D k k n k zD 1 nz 31Advances in automating analysis of neural time series
  • 156. z-step: The Toeplitz matrix trick 1 D k D k k n k zD 1 nz k nz 31Advances in automating analysis of neural time series
  • 157. [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz 31Advances in automating analysis of neural time series
  • 158. [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 31Advances in automating analysis of neural time series
  • 159.         n nnn z zDzx  2 2 2 1 min [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 31Advances in automating analysis of neural time series
  • 160.           n nnn n zDzx z  2 2 2 1 [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 31Advances in automating analysis of neural time series
  • 161.           n nnn n zDzx z  2 2 2 1 [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 1 )( nn T DzxD 31Advances in automating analysis of neural time series
  • 162.           n nnn n zDzx z  2 2 2 1 [ ] z-step: The Toeplitz matrix trick … … 1 D k D k k n k zD 1 nz k nz nDz 1 )( nn T DzxD Now, we can feed the gradient to L-BFGS-B optimization algorithm 31Advances in automating analysis of neural time series
  • 163.              n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 k nZ 32Advances in automating analysis of neural time series
  • 164.              n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 k nZ 32Advances in automating analysis of neural time series
  • 165.              n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 k nZ 32Advances in automating analysis of neural time series
  • 166.              n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 k nZ 32Advances in automating analysis of neural time series
  • 167.              n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 k nZ 32Advances in automating analysis of neural time series
  • 168.              n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 0 .5 0 k nZ 32Advances in automating analysis of neural time series
  • 169.              n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 0 .5 0 0 2 4 k nZ k d 32Advances in automating analysis of neural time series
  • 170.              n kn k n k k n k n d zzdx , 2 2 1 * 2 1 min2 2  k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 0 .5 0 0 2 4 k nZ k d kk n k n k dZzd * 32Advances in automating analysis of neural time series
  • 171.             n k kk nn d dZx 2 2 1 2 1 min2 2 k nz d-step: Strided matrices 00 0 1 0 .5 0 0 0 1 00 1 01 0 0 0 .5 0 .5 0 0 2 4 k nZ k d kk n k n k dZzd * We remove the regularization term as it doesn’t depend on d 32Advances in automating analysis of neural time series Least square problem under unit norm constraint
  • 172. 33 d-step: The atoms are updated using LBFGS-B Advances in automating analysis of neural time series
  • 173. 33 d-step: The atoms are updated using LBFGS-B              n k kk nnk dZx d 2 2 2 1 Advances in automating analysis of neural time series
  • 174. 33 d-step: The atoms are updated using LBFGS-B              n k kk nnk dZx d 2 2 2 1          k kk nn Tk n dZxZ Advances in automating analysis of neural time series
  • 175. 33 d-step: The atoms are updated using LBFGS-B              n k kk nnk dZx d 2 2 2 1          2 ˆ 1 ,1minˆˆ k kk d dd 1. Gradient step 2. Projection step          k kk nn Tk n dZxZ Advances in automating analysis of neural time series Projected gradient descent
  • 176. 33 d-step: The atoms are updated using LBFGS-B              n k kk nnk dZx d 2 2 2 1          2 ˆ 1 ,1minˆˆ k kk d dd 1. Gradient step 2. Projection step          k kk nn Tk n dZxZ Advances in automating analysis of neural time series In practice, it is more complicated … LBFGS-B in the dual Projected gradient descent
  • 177. Putting it all together 34Advances in automating analysis of neural time series
  • 178. Putting it all together z update 34Advances in automating analysis of neural time series
  • 179. Putting it all together z update Toeplitz D 34Advances in automating analysis of neural time series
  • 180. Putting it all together z update d update Toeplitz D 34Advances in automating analysis of neural time series
  • 181. Putting it all together z update d update Toeplitz D Strided Z 34Advances in automating analysis of neural time series
  • 182. Putting it all together z update d update Toeplitz D Strided Z (L-BFGS-B) (L-BFGS-B) 34Advances in automating analysis of neural time series
  • 183. Putting it all together z update d update Toeplitz D Strided Z (L-BFGS-B) (L-BFGS-B) Alternate minimization 34Advances in automating analysis of neural time series
  • 184. 35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom Advances in automating analysis of neural time series
  • 185. 35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom Advances in automating analysis of neural time series
  • 186. 35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes Advances in automating analysis of neural time series
  • 187. 35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes 1 hour Advances in automating analysis of neural time series
  • 188. 35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes 1 hour Advances in automating analysis of neural time series
  • 189. 35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes 1 hour 45 minutes Advances in automating analysis of neural time series
  • 190. 35 The quasi-Newton solvers outperform ADMM solvers K = 10 atoms L = 32 samples per atom 30 minutes 1 hour 45 minutes 2 hours Advances in automating analysis of neural time series
  • 191. 36 The quasi-Newton solver outperform ADMM solvers Advances in automating analysis of neural time series
  • 192. 36 The quasi-Newton solver outperform ADMM solvers ADMM solvers Advances in automating analysis of neural time series
  • 193. 36 The quasi-Newton solver outperform ADMM solvers Different random seeds ADMM solvers Advances in automating analysis of neural time series
  • 194. Cross frequency coupling uncovered via CSC ~80 Hz 37Advances in automating analysis of neural time series [Canolty, 2006] [Dupré la Tour, 2017]
  • 195. Challenge Neural data often contains transient artifacts 38Advances in automating analysis of neural time series
  • 196. 39 CSC in the presence of transient artifacts Advances in automating analysis of neural time series
  • 197. 39 CSC in the presence of transient artifacts Advances in automating analysis of neural time series
  • 198. 39 Neural signals CSC in the presence of transient artifacts Advances in automating analysis of neural time series
  • 199. 39 Transient artifacts Neural signals CSC in the presence of transient artifacts Advances in automating analysis of neural time series
  • 200. A probabilistic interpretation 40Advances in automating analysis of neural time series
  • 201. A probabilistic interpretation 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
  • 202. A probabilistic interpretation          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
  • 203. A probabilistic interpretation        1,*~,| 1 , K k k n k tn zdNdzx          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate Data likelihood 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
  • 204. A probabilistic interpretation )(~, k tnz       1,*~,| 1 , K k k n k tn zdNdzx          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate PriorData likelihood 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
  • 205. A probabilistic interpretation )(~, k tnz       1,*~,| 1 , K k k n k tn zdNdzx          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate PriorData likelihood 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min 
  • 206. A probabilistic interpretation )(~, k tnz       1,*~,| 1 , K k k n k tn zdNdzx          tn k k tntn zd zpzdxpzd , ,, , )(log),|(logmaxarg*)*,( Maximum a posteriori estimate PriorData likelihood 40Advances in automating analysis of neural time series             n kn k n k k n k n zd zzdx , 2 2 , *min  Sparser activations
  • 207. Alpha-stable distributions ),,,(~ SX 41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996]
  • 208. Alpha-stable distributions ),,,(~ SX 41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
  • 209. Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent 41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
  • 210. Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
  • 211. Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),(  41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
  • 212. Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),0( Scale parameter ),(  41Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
  • 213. Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),0( Scale parameter ),(  41 Special cases Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
  • 214. Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),0( Scale parameter ),(  41 Special cases Normal distribution ),,0,2(~  SX Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
  • 215. Alpha-stable distributions ),,,(~ SX ]2,0(Characteristic exponent Skewness parameter ]1,1[  Location parameter ),0( Scale parameter ),(  41 Special cases Normal distribution ),,0,2(~  SX ),,0,1(~  SX Cauchy distribution Advances in automating analysis of neural time series [Samorodnitsky et al., 1996] Heavy tail
  • 216. 42        1,*~,| 1 , K k k n k tn zdNdzx From light tails to heavy tails         K k k n k tn zdSdzx 1 , *,2/1,0,~,|  2 Symmetric alpha-stable distributions Advances in automating analysis of neural time series
  • 217. Symmetric α-stable distribution is conditionally Gaussian 43Advances in automating analysis of neural time series [Samorodnitsky et al., 1996]
  • 218. Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|  Advances in automating analysis of neural time series [Samorodnitsky et al., 1996]
  • 219.        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|  Advances in automating analysis of neural time series [Samorodnitsky et al., 1996]
  • 220.        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|  Advances in automating analysis of neural time series from a positive stable distribution tn, [Samorodnitsky et al., 1996]
  • 221.        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|             n kn k n k k n k n n zd zzdx , 2 2 , * 1 min   Weighted CSC! Advances in automating analysis of neural time series from a positive stable distribution tn, [Samorodnitsky et al., 1996]
  • 222.        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Symmetric α-stable distribution is conditionally Gaussian 43         K k k n k tn zdSdzx 1 , *,2/1,0,~,|             n kn k n k k n k n n zd zzdx , 2 2 , * 1 min   Weighted CSC! Advances in automating analysis of neural time series But is not known …tn, from a positive stable distribution tn, [Samorodnitsky et al., 1996]
  • 223. EM algorithm is used to estimate MAP when some variables are missing 44Advances in automating analysis of neural time series [Dempster et. al., 1977]
  • 224. EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E Advances in automating analysis of neural time series [Dempster et. al., 1977]
  • 225. EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E                  n kn k n k k n k n n i zzdxEzdB , 2 2 )( * 1 ),(   Advances in automating analysis of neural time series [Dempster et. al., 1977]
  • 226. EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E                  n kn k n k k n k n n i zzdxEzdB , 2 2 )( * 1 ),(   Advances in automating analysis of neural time series [Dempster et. al., 1977] weights
  • 227. EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step Maximization step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E ),(maxarg),( )( , )1()1( zdBzd i zd ii                   n kn k n k k n k n n i zzdxEzdB , 2 2 )( * 1 ),(   Advances in automating analysis of neural time series [Dempster et. al., 1977] weights
  • 228. EM algorithm is used to estimate MAP when some variables are missing 44 Expectation step Maximization step )(log)],|,([log),( ),,|( )( zpzdxpzdB zdxp i  E ),(maxarg),( )( , )1()1( zdBzd i zd ii                   n kn k n k k n k n n i zzdxEzdB , 2 2 )( * 1 ),(   Iterate until convergence Advances in automating analysis of neural time series [Dempster et. al., 1977] weights
  • 229. 45 For the E-step, we compute the expectation using sampling Advances in automating analysis of neural time series [Bishop, 2007]
  • 230. 45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E Advances in automating analysis of neural time series [Bishop, 2007]
  • 231. 45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E   J j j tnJ 1 , 11  Advances in automating analysis of neural time series [Bishop, 2007]
  • 232. 45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E   J j j tnJ 1 , 11  Advances in automating analysis of neural time series [Bishop, 2007]
  • 233. 45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E   J j j tnJ 1 , 11  Sampled from the posterior distribution Advances in automating analysis of neural time series [Bishop, 2007]
  • 234. 45 For the E-step, we compute the expectation using sampling       tntn tntn dzdxp ,, ,, ),,|( 11   E   J j j tnJ 1 , 11  Sampled from the posterior distribution Markov Chain Monte Carlo (MCMC) Advances in automating analysis of neural time series [Bishop, 2007]
  • 235. 46 Let’s recap Advances in automating analysis of neural time series
  • 236. 46 Let’s recap Data likelihood term Advances in automating analysis of neural time series
  • 237. 46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Advances in automating analysis of neural time series
  • 238. 46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Latent variable Advances in automating analysis of neural time series
  • 239. 46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Latent variable EM algorithm Advances in automating analysis of neural time series
  • 240. 46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Latent variable EM algorithm E step: MCMC to learn weights       tn, 1  E Advances in automating analysis of neural time series
  • 241. 46 Let’s recap Data likelihood term        tn K k k n k tntn zdNdzx , 1 ,, 2 1 ,*~,,|  Conditionally Gaussian Latent variable EM algorithm E step: MCMC to learn weights M step: Weighted CSC       tn, 1  E Advances in automating analysis of neural time series
  • 242. 47 -CSC on simulated data Advances in automating analysis of neural time series [Jost et al., 2006]
  • 243. 48 -CSC with  = 2 (reduces to Gaussian) Advances in automating analysis of neural time series
  • 244. 48 -CSC with  = 2 (reduces to Gaussian) Advances in automating analysis of neural time series
  • 245. 49 -CSC with ≠2 Advances in automating analysis of neural time series
  • 246. 49 -CSC with ≠2 Advances in automating analysis of neural time series
  • 247. Advances in automating analysis of neural time series 50 Conclusion
  • 248. Advances in automating analysis of neural time series 50 Conclusion Data sharing And data standards
  • 249. Advances in automating analysis of neural time series 50 Conclusion Data sharing And data standards Autoreject to remove artifacts
  • 250. Advances in automating analysis of neural time series 50 Conclusion Data sharing And data standards Autoreject to remove artifacts αCSC to learn recurring waveforms
  • 251. Alexandre Gramfort Denis Engemann Yousra Bekhti Eric LarsonUmut Şimşekli Tom Dupré la Tour Credits 51Advances in automating analysis of neural time series
  • 252. 52 Thank you Advances in automating analysis of neural time series