Comparative Study of Granger Causality Algorithm for Gene Regulatory Network
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This document summarizes a study that compares three algorithms for inferring gene regulatory networks from time series data: MVGC, Lasso, and Copula. The algorithms were implemented and their performance evaluated on both synthetic 3-variable and 5-variable time series datasets using seven different metrics. For 3-variable data, MVGC generally performed best, while for 5-variable data its performance was most consistent. Lasso worked best for high numbers of time points. Copula showed optimized performance for intermediate time points. Overall, MVGC provided the best average performance across conditions, but the best algorithm depended on factors like the number of variables and time points. Future work could explore non-linear models and applications to real biological datasets.
Comparative Study of Granger Causality Algorithm for Gene Regulatory Network
- 1. INVESTIGATION OF IMAGE PROCESSING ALGORITHMS FOR MEDICAL APPLICATION Zhafir AglnaTijani U1120208F A final year project presentation in partial fullfilment of the requirement for the degree of Bachelor of Engineering 1
- 3. Background and Theory •Problems and Objectives •Gene Regulatory Network •Granger Causality •3 Methods of Granger Causality •Project Focus Implementation Result and Discussion Conclusion Outline 3
- 4. “It is more pragmatic to cure the cause of disease at its sources than to handle the actual diseases” Gene 4
- 5. • The Interaction between genes is called Gene Regulatory Network • The discovery of this network still have a lot of challenge because of complexity of the network • Efficient Computational Tools are required To find an effective and efficient means to discover unknown Gene Regulatory Network Objective 5
- 6. Modelling of GRN • Nodes and Edges • Depicting the relation between genes • Obtained from DNA Microarray • Prominent Method : Granger Causality http://img.medicalxpress.com/newman/gfx/news/hires/2013/1-novelnoninva.jpg 6
- 7. Granger Causality • Method for Time Series Analysis • Utilized Vector Auto-regression (VAR) Model to calculate causality based on Time Series data. Granger (1969) A B Time Series Time Series Ut = 𝑘=1 𝑝 AkUt−k + εt 𝐹𝑌→𝑋 ≡ ln |Σ 𝑥𝑥 ′ | |Σ 𝑥𝑥| 7
- 8. Granger Causality “If past values of A and B can predict future value of B better than past values of B alone, Then, time series A granger cause time series B” Granger (1969) A B Time Series Time Series 8
- 9. MVGC Lasso CopulaBarnett et al. (2013) Arnold et al. (2007) Liu and Bahadori (2012) 3 Methods of Implementing Granger Causality “These 3 Methods has been implemented independently, but never been compared using the same condition.” 9
- 10. Main Focus of the Project • Comparative Study of Algorithms • Focus on the Performance of 3 Algorithms • Finding Strength and Weaknesses • Utilizing Control Variables and Metrics Performance 10
- 11. Background and Theory Implementation Result and Discussion Conclusion •Control Variables •Causality Graph and Matrix •Edge Analysis) •Performance Metrics •Data for Analysis Outline 11
- 12. Implementation Time Series input GC Algorithm Causality Matrix and Graph Edge Analysis Data for Discussion • Implementation using MATLAB 2010b • Based on Existing Toolboxes : • MVGC Toolbox ( Barnett, 2013 ) • Lasso Granger • Copula Granger ( Liu and Bahadori, 2012 ) • GLMnet Program Flow 12
- 13. Implementation Control Variables • Based on Set of Equations • Linear Time Series Dataset • Generated by specifying The Number of Time Points • Advantages : • Provide Ground Truth Network : Actual Causality of the Time Series • Ground Truth can be compared with the Algorithm Output to measure the performance of Algorithms • 2 Types of Dataset : 3-VAR and 5-VAR Time Series • 8 different Number of Time Points : 200, 400, 800, 1200, 1600, 2400, 3200, 4000 Synthetic Time Series Dataset 13
- 14. 3 Granger Causality Algorithms 14
- 15. Causality Matrix • 1 represent : Link Exist between Variables • 0 represent : Link Does not Exist 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 • Output of GC Algorithm is the Causality Matrix • Depict granger causality between time series 15
- 16. Edge Analysis • The result of Algorithm are masked with Binary Masking with the threshold of 0.0001 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 • Edge Analysis is a method to measure the performance of an Algorithm by comparing it with the Benchmark • Benchmark = Ground Truth 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 Ground Truth Lasso Method 16
- 17. Edge Analysis For above example • TP : 4 • TN : 6 • FP : 13 • FN : 2 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 0 • Using Parameters from Confusion Matrix : • True Positives, True Negatives, False Positives, and False Negatives 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 Ground Truth Lasso Method 17
- 18. 7 Performance Metrics 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 = 𝑇𝑃 𝑇𝑃 + 𝐹𝑁 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 = 𝑇𝑁 𝑇𝑁 + 𝐹𝑃 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = 𝑇𝑃 𝑇𝑃 + 𝐹𝑃 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒 = 𝐹𝑃 𝑇𝑁 + 𝐹𝑃 𝐹𝑎𝑙𝑠𝑒 𝐷𝑖𝑠𝑐𝑜𝑣𝑒𝑟𝑦 𝑅𝑎𝑡𝑒 = 𝐹𝑃 𝑇𝑃 + 𝐹𝑃 𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = 𝑇𝑃 + 𝑇𝑁 𝑇𝑃 + 𝑇𝑁 + 𝐹𝑃 + 𝐹𝑁 𝐹1 𝑆𝑐𝑜𝑟𝑒 = 2𝑇𝑃 2𝑇𝑃 + 𝐹𝑃 + 𝐹𝑁 • Calculated based on the value of TP, TN, FP, and FN • Used in Past Research in Similar Topic 18
- 19. Data for Analysis • The Result of Granger Causality depends on the generated time series • Few sample was not sufficient, Since time series generated was different each time • The experiment was iterated by 2000 times • Mean Value of each performance metrics will be the basis for comparative study 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 Lasso : 1st Iteration Lasso : 2nd Iteration 19
- 20. Background and Theory Implementation Result and Discussion Conclusion Outline •Performance Metrics Scores •Specific Result •5-VAR Accuracy •3-VAR and 5-VAR F1 Score •Overall Score Result 20
- 21. Scores of Metrics • Bar chart to represent the score of each performance metrics on 3 methods • X axis : Number of Time Points • Y axis : Score of Metrics • 7 Metrics Performance • 2 Scenario : 3-VAR and 5-VAR 0 0.1 0.2 0.3 0.4 0.5 0.6 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 F1 Score MVGC LASSO COPULA 21
- 22. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 Specificity MVGC LASSO COPULA 0 0.2 0.4 0.6 0.8 1 1.2 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 Sensitivity MVGC LASSO COPULA 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 Precision MVGC LASSO COPULA 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 False Positive Rate MVGC LASSO COPULA 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 False Discovery Rate MVGC LASSO COPULA 0 0.1 0.2 0.3 0.4 0.5 0.6 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 Accuracy MVGC LASSO COPULA 22
- 23. 0 0.1 0.2 0.3 0.4 0.5 0.6 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 Accuracy MVGC LASSO COPULA 5-VAR Accuracy • Accuracy • Proportion of true result among total links available • MVGC • Increasing as Number of time Points Increase • Score range was small ( around 0,1 ) • Lasso • Increasing as Number of Time Points Increase • Two extreme scores, Wide score Range • Copula • Optimized during number of time points around 400 • Bad performance at higher number of time points 23
- 24. 3-VAR and 5-VAR F1 Score • F1 Score • Statistical Significance based on Harmonic mean of Precision and Recall • MVGC • Consistent Pattern, Increases as time point increases • Lasso • Contrast Pattern • Heavily affected by number of variables • Copula • Unique Pattern • Has a certain point / range where performance is optimized 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR3 F1 Score MVGC LASSO COPULA 0 0.1 0.2 0.3 0.4 0.5 0.6 200 400 800 1200 1600 2400 3200 4000 Score Number of Time Points VAR5 F1 Score MVGC LASSO COPULA 24
- 25. Overall Performance Metrics type Best Performance Average Performance Worst Performance Sensitivity Lasso Copula MVGC Specificity MVGC Lasso Copula Precision MVGC Lasso Copula False Positive Rate MVGC Lasso Copula False Discovery Rate MVGC Lasso Copula Accuracy MVGC Lasso Copula F1 – Score MVGC Lasso Copula 3 – Variable Time Series • Overall performance based on average score of all time points • MVGC Outperforms other two methods in 3-VAR Scenario • Lasso scores was good during high number of time points • Copula has certain range which their score was high ( around 200 – 800 time points ), but outside of that the score were lower than other method 25
- 26. Metrics type Best Performance Average Performance Worst Performance Sensitivity MVGC Copula Lasso Specificity Lasso Copula MVGC Precision MVGC Copula Lasso False Positive Rate Lasso Copula MVGC False Discovery Rate MVGC Copula Lasso Accuracy Copula MVGC Lasso F1 – Score MVGC Copula Lasso 5 – Variable Time Series • MVGC shows Consistency in both 5-VAR and 3-VAR • Copula provides best accuracy compared to other method, especially during 200 – 800 time points • Lasso score is the highest during high number of time points, but the score during low number of time points were low. 26
- 27. Background and Theory Implementation Result and Discussion Conclusion Outline •Conclusion •Future Works 27
- 28. Conclusion • 3 Methods of GC : MVGC, Lasso, and Copula can be compared using 7 Performance Metrics • MVGC provides consistency in most of condition • Lasso has advantages in handling high number of time points • Copula has certain range which their performance was optimized • Even though overall score favours MVGC compared to other methods, the results are still conditional 28
- 29. Suggestions for Future Work • Granger Causality Algorithms for non-linear Data • Non-linear data provides better representation for Gene Regulatory Network • Application to Real Dataset • Granger Causality Analysis may be applied to real dataset • Other Algorithm for GRN ( Dynamic Bayesian Network ) • DBN is another prominent method in this topic 29
- 30. Thank You 30
- 31. Q & A 31