An interactive approach for cleaning noisy observations in Bayesian networks with the help of an expert

An interactive approach for cleaning noisy
observations in Bayesian networks with the
help of an expert
Andrés R. Masegosa and Serafín Moral
Department of Computer Science and Artiﬁcial Intelligence
University of Granada
Granada, September 2012
PGM 2012 Granada (Spain) 1/31

Outline
1 Introduction
2 Modelling noisy observations and expert knowledge
3 Cleaning noisy observations with the help of expert
knowledge
Entropy-based approach
Cost-based approach
EM algorithm to estimate the noise rate
4 Experimental evaluation
5 Conclusions and future works

Introduction
Part I
Introduction

Introduction
Bayesian Networks in Intelligent Software Systems

Introduction
Evidence Gathering Process
Sensor failure (GPS, Vision, etc).
Noisy transmissions in a communication channel.
Outliers is a particular case of a noisy observation.
Human errors with the GUI of the system.
...

Introduction
Problem of Noisy Observations

Introduction
Automatic Data Cleaning Methods
Mandatory in most of the practical data mining problems: poor quality data.
Many different approaches are proposed to address this problem (Zhu and Wu, 2006).
They are automatic methods where humans/experts do not play an active role.

Introduction
New Cleaning Methods: misspelled words in smartphones
System detects a corrupted noisy observation.
System displays alternative words (i.e. ﬁxed observations).
The user ultimately decides which is the correct one.
The system interacts with the user.

Introduction
An Interactive Data Cleaning Method
Noisy observations: some values of the observations are noisy (i.e. different from its actual value).
Our data model is a Bayesian network over multinomial data.
The noisy process needs to be explicitly modelled.
We assume the existence of an expert able to provide knowledge about speciﬁc parts of the observation
vector.

Modelling Noisy Observations and Expert Knowledge
Part II
Modelling Noisy Observations and
Expert Knowledge

Notation
We assume that we have a set of observable variables: O = {O1, ..., Op}.
o is a particular observation vector.
P(O) is modelled by a given Bayesian network.
We assume there is noise when observing these variables.

Notation
O = {O1, ..., Op} noisy observable variables
o is a particular noisy observation vector.

Notation
O = {O1, ..., Op} noisy observable variables
o is a particular noisy observation vector.
Our goal
To detect the noisy observations: oi = oi .
To recover the true observations: o = {o1, ..., op}.
... with the help of an expert.

Modelling noisy observations
We artiﬁcially add two new variables to each observable variable:
Oi is the noisy observable variable associated to Oi .

Ni indicates if there is a noisy observation with probability ηi , which is
assumed to be a known value.

Ni indicates if there is a noisy observation with probability ηi , which is
The conditional P(Oi |Oi , Ni ) deﬁnes the noise model.

Modelling expert knowledge
We also add two new variables to each observable variable:
Oe
i is the variable which receives the expert knowledge associated to Oi .

Oe
Ei indicates if the knowledge is correct with probability τi , which is

Oe
Ei indicates if the knowledge is correct with probability τi , which is
The conditional P(Oe
i |Oi , Ei ) deﬁnes how the expert gives wrong answers.

A model for noisy observations and expert knowledge
Automatic cleaning method
Recover the most probable explanation of the observable variables given the
noisy observations:
oMPE
= arg max
O=o
P(O = o|O = o )

noisy observations:
oMPE
= arg max
O=o
P(O = o|O = o )
Not a good solution.
There exist alternative explanations, O = o, with
non-negligible probability.

noisy observations:
oMPE
= arg max
O=o
P(O = o|O = o )
Not a good solution.
There exist alternative explanations, O = o, with
non-negligible probability.
Use expert knowledge to discard those alternative
explanations.

Interactive Cleaning: Entropy Based Approach
Part III
Interactive Cleaning: Entropy
Based Approach

Cleaning noisy observations with the help of expert knowledge
Entropy Based Approach
Reduce the conditional entropy of the true observations:
H(O|O = o )
The lower this entropy, the stronger our conﬁdence in the oMPE .

H(O|O = o )
Our strategy is to request to the expert the knowledge which most reduces
the above entropy (the highest information gain):
IG(O, Oe
i |o )
Expert should submit his/her belief about the true value of Oi .

H(O|O = o )
Our strategy is to request to the expert the knowledge which most reduces
the above entropy (the highest information gain):
IG(O, Oe
i |o )
Expert should submit his/her belief about the true value of Oi .
The Oe
i with the highest information gain is the one with the highest entropy:
arg max
Oe
i
IG(O, Oe
i |o ) = arg max
Oe
i
(H(Oe
i |O = o ) − H(Ei ))

Algorithm
1: oe
= ∅.

Algorithm
1: oe
= ∅.
2: repeat
3: Compute the Oe
i variable with the highest information gain:
Oe
max = arg max
Oe
i
IG(O; Oe
i |o , oe
)
4: if IG(O; Oe
i |o , oe
) > λ then
5: Ask the expert about Oi .
6: oe
= oe
∪ oe
max .
7: end if
8: until end

Algorithm
1: oe
= ∅.
2: repeat
3: Compute the Oe
i variable with the highest information gain:
Oe
max = arg max
Oe
i
IG(O; Oe
i |o , oe
)
4: if IG(O; Oe
i |o , oe
) > λ then
6: oe
= oe
∪ oe
max .
7: end if
8: until end
9:
10: return oMPE
= arg maxO=o P(O = o|o , oe
);

Interactive Cleaning: Cost Based Approach
Part IV
Interactive Cleaning: Cost Based
Approach

Cost Based Approach
We model the problem using as a decision making problem:
Fixing Decisions, Fi , about observation Oi with overall cost, CF.
Asking Decisions, Ai , about observation Oi with cost, CAi .
Problem: ﬁnd the optimal set of ﬁxing decisions F and asking decisions A with
lowest expected cost.

Cost Based Approach
We model the problem using as a decision making problem:
Fixing Decisions, Fi , about observation Oi with overall cost, CF.
Asking Decisions, Ai , about observation Oi with cost, CAi .
Problem: find the optimal set of fixing decisions F and asking decisions A with
lowest expected cost.
Solving this decision problem
It is computationally unfeasible if the number variables is large:
Unconstrained Decision Problem: no sequential order in the decisions.
Each decision depends on the information of the variables in O ∪ Oe.
Approximate solution based on several simplifications.

Cost Based Approach
Simpliﬁcations
The decision problem is solved for a particular noisy observation vector o .
Cost of ﬁxing computed as a sum of independent costs: CF =
p
i=1 CFi .
We assume that we have p different decision problems:
Problem Di involves decisions Ai and {F1, ..., Fp}.
When solving Di we do not ask for the rest of the variables.

Cost Based Approach
Solving Problem Di
Expected cost gain: The difference in the expected cost between asking and
not asking about Oi :
CG(Ai |o , oe
) = c(Dn
i ) − c(Da
i )
c(Dn
i ): expected cost when no asking about Oi .
c(Da
i ): expected cost when asking about Oi .

Cost Based Approach
Solving Problem Di
Expected cost gain: The difference in the expected cost between asking and
not asking about Oi :
CG(Ai |o , oe
) = c(Dn
i ) − c(Da
i )
c(Dn
i ): expected cost when no asking about Oi .
c(Da
i ): expected cost when asking about Oi .
Fixing Decisions: we compute for each decision Fi the value fj such that
fj = arg min
fj oj
CFj (fj , oj )P(oj |o , oe
)
The minimization problem can be solved in constant time after the observations
have been propagated:
0/1 cost error: select the oj with the highest probability.

Cost Based Approach
Algorithm
1: oe
= ∅.
2: repeat
3: Compute the decision Ai the highest expected cost gain:
Amax = arg max
Ai
CG(Ai |o , oe
)
4: if CG(Amax |o , oe
) > 0 then
6: oe
= oe
∪ oe
max .
7: end if
8: until end
9:
10: return fj = arg minfj oj
CFj (fj , oj )P(oj |o , oe
);

Part V
EM algorithm to estimate the
noise rate

EM Algorithm to estimate the unknown noise rates τi
We are given a set of M noisy observations:D = {o(1)
, ..., o(M)
}.

, ..., o(M)
}.
The EM algorithm is applied to estimate the MAP estimate of the parameters
τ = (τ1, ..., τp).
O = {O1, ..., Op} and N = {N1, ..., Np} are the hidden variables.

, ..., o(M)
}.
The EM algorithm is applied to estimate the MAP estimate of the parameters
τ = (τ1, ..., τp).
O = {O1, ..., Op} and N = {N1, ..., Np} are the hidden variables.
Expectation step: Given a current estimate of τ<k>.
Compute P(Ni = noise|o (j), τ<k>) propagating in the extended BN for
j-th data sample.
Maximization step:
τ<k+1>
i =
j P(Ni = noise|o (j); τ<k>)
M

Experimental Evaluation
Part VI

Experimental Set-up

Experiments on Alarm with 5% noise rate
Noise Rate
With no expert knowledge only a minor proportion of the errors are identiﬁed
and we might introduce new errors.
The introduction of the expert knowledge boost the precision of the detected
errors.

Experiments on Alarm with 5% noise rate
Precision
With no expert knowledge only a minor proportion of the errors are identiﬁed
and we might introduce new errors.
The introduction of the expert knowledge boost the precision and the recall of
the detected errors.

Conclusions and Future Works
Part VII

Conclusions:
We have proposed an interactive method for cleaning noisy
observations in Bayesian networks.
One speciﬁc module in our intelligent software system.
The performance strongly depends of the particular model.

Conclusions:
We have proposed an interactive method for cleaning noisy
observations in Bayesian networks.
One speciﬁc module in our intelligent software system.
The performance strongly depends of the particular model.
Future Works:
Implement this approach in a real intelligent system.
Extend this method assuming that we do not know neither the
parameters of the network nor the structure.

Thanks for you attention!!!

An interactive approach for cleaning noisy observations in Bayesian networks with the help of an expert

More Related Content

Viewers also liked (6)

Similar to An interactive approach for cleaning noisy observations in Bayesian networks with the help of an expert (12)

More from NTNU (18)

Recently uploaded (20)

An interactive approach for cleaning noisy observations in Bayesian networks with the help of an expert