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# Learning equivalence classes of directed acyclic latent variable models from multiple datasets with overlapping variables, incl. discussion by Ricardo Silva

Published on May 06, 20113910 Views

While there has been considerable research in learning probabilistic graphical models from data for predictive and causal inference, almost all existing algorithms assume a single dataset of i.i.d

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#### Chapter list

Learning equivalence classes of acyclic models with latent and selection variables from multiple datasets with overlapping variables00:00

Learning from single i.i.d. dataset00:13

Learning from multiple datasets with overlapping variables00:59

Examples: Learning neural cascades during cognitive tasks01:54

Formal Problem Statement (1)03:37

Formal Problem Statement (2)03:56

Formal Problem Statement (3)04:23

Formal Problem Statement (4)04:28

Formal Problem Statement (6)04:40

Errors due to latent variables (1)05:32

Errors due to latent variables (2)05:55

Errors due to latent variables (3)06:06

Errors due to latent variables (4)06:26

Maximal Ancestral Graphs (1)06:50

Maximal Ancestral Graphs (2)07:30

Maximal Ancestral Graphs (3)07:53

Maximal Ancestral Graphs (4)08:21

Maximal Ancestral Graphs (5)08:37

Markov Equivalence and PAGs (1)10:48

Markov Equivalence and PAGs (2)11:45

Restated Goal12:54

Related Approach: ION Algorithm (1)13:59

Related Approach: ION Algorithm (2)15:11

Related Approach: ION Algorithm (3)15:38

Related Approach: ION Algorithm (4)15:50

Related Approach: ION Algorithm (5)16:41

Related Approach: ION Algorithm (6)17:09

Related Approach: ION Algorithm (7)17:17

Conditional Independence Testing with Multiple Datasets (1)17:40

Conditional Independence Testing with Multiple Datasets (2)17:54

Conditional Independence Testing with Multiple Datasets (3)18:09

Conditional Independence Testing with Multiple Datasets (4)18:27

Conditional Independence Testing with Multiple Datasets (5)18:45

Conditional Independence Testing with Multiple Datasets (6)18:49

Conditional Independence Testing with Multiple Datasets (7)19:06

Conditional Independence Testing with Multiple Datasets (8)19:24

The Integration of Overlapping Datasets (IOD) Algorith (1)19:53

The Integration of Overlapping Datasets (IOD) Algorith (2)20:18

The Integration of Overlapping Datasets (IOD) Algorith (3)20:37

The Integration of Overlapping Datasets (IOD) Algorith (4)21:11

The Integration of Overlapping Datasets (IOD) Algorith (5)21:34

Removing edges and adding orientations (1)21:58

Removing edges and adding orientations (2)22:15

Removing edges and adding orientations (3)22:39

Removing edges and adding orientations (4)22:44

Removing edges and adding orientations (5)23:33

Removing edges and adding orientations (6)24:16

Removing edges and adding orientations (7)24:50

Removing edges and adding orientations (8)24:54

Example (1)25:14

Example (2)25:30

Example (3)25:38

Example (4)25:51

Example (5)26:20

Correctness and Completeness (1)26:34

Correctness and Completeness (2)26:49

Correctness and Completeness (3)26:59

Simulations27:11

Simulations - 2 Datasets, |V| = 1427:42

Simulations - 3 Datasets, |V| = 1428:06

Application: Learning neural cascades during cognitive tasks28:10

Conclusion (1)28:54

Conclusion (2)29:07

Conclusion (3)29:16

Conclusion (4)29:27

Conclusion (5)29:31

Conclusion (6)29:34

Conclusion (7)29:38

Conclusion (8)29:47

Discussion of “Learning Equivalence Classes of Acyclic Models with Latent and Selection Variables from Multiple Datasets with Overlapping Variables”29:59

On overlapping variables and partial information30:20

Built-in robustness31:10

On selection bias31:55

Beyond independence constraints (1)32:33

Beyond independence constraints (2)33:07

The Bayesian approach33:44

Related problems: finding substructure by generalizing penalized composite likelihood?34:13

Other approaches: generalizing penalized composite likelihood?34:44