Dependency patterns for latent variable discovery
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The document discusses dependency patterns for discovering latent variables in causal models, emphasizing the importance of recognizing these variables, which are often unmeasured or unknown. It covers methodologies for identifying triggers that represent sets of dependencies that cannot be modeled completely, and showcases experimental findings using these triggers in causal discovery. Future work aims to enhance existing algorithms and extend the application of trigger models in latent variable discovery.
Dependency patterns for latent variable discovery
- 1. Dependency Patterns For LatentVariable Discovery By Xuhui Zhang, Kevin Korb,Ann Nicholson and Steven Mascaro
- 2. Presentation Layout 1. Background 2. Dependency Patterns (Triggers) Discovery for latent variable 3. Applying Triggers in causal discovery 4. Analysis & Future Work
- 3. Background
- 4. Causal Model & Non-Causal Model Causal model Naive Bayes (anti-causal) model
- 6. Latent Variables Latent variables are those we cannot measure them or those do not known they exist. Newton explained motion via gravity (a latent variable). Darwin proposed evolutionary theory but could only guess about the role of genes (a latent variable). therealdegree.wordpress.com save-our-green.com
- 7. Why learning latent variables is important? Simplify the network: Help us to explain the true dependency structure:
- 8. Latent variables discovery algorithms ? Constraint-based algorithms 1) Involve statistical tests for conditional independence. 2) Return a statistically equivalent class that contains the true model. ? Metric-based algorithms ? 1) Use a scoring metric to evaluate potential models ? 2) Find a network structure with a good score
- 9. Dependency Patterns (Triggers) Discovery for latent variable
- 11. What isTrigger? ? Latent variables are typically considered only in scenarios where they are common causes (Friedman, 1997). ? The set of dependencies of a latent variables is a trigger if and only if these dependency sets cannot be matched by any fully models. ? Trigger models can better encode the actual dependencies and independencies.
- 12. A Systematic Search for FindingTriggers
- 13. Experiment Results (Triggers) Triggers: E.g., for four variables, the two triggers are:
- 14. Experiment Results (Triggers) For five variables, all the triggers are:
- 15. ApplyingTriggers in causal discovery
- 16. Triggers + Chi-square test ? Pre-compute all triggers. ? Get the full dependency matrices of a given data set by applying conditional chi-square test. ? Check whether the dependencies match any one of the triggers.
- 17. A Simulated Data
- 18. Results
- 19. Results CaMML GeNIe (PC) X Y Z W X Y Z W
- 20. Results Tetrad (PC) Tetrad (FCI) X Y Z W X Y Z W
- 21. Analysis & Future work
- 22. Analysis ? CaMML fails to detect latent variable because there is no latent variable discovery algorithms implemented in CaMML. ? Our simple learner have successfully matched the dependencies in the data with one of the triggers. ? Both PC and FCI use an arc with two arrowheads to imply the existence of a latent variable.
- 23. Future work ? Extent the program with more than one latent variables. ? Parameterize latent variable models. ? Try to implement our trigger program into CaMML.
- 24. References ? Korb, Kevin B, & Nicholson,Ann E. (2003). Bayesian artificial intelligence: CRC press. ? Pearl, Judea. (2000). Causality: models, reasoning and inference (Vol. 29): Cambridge Univ Press. ? Spirtes, Peter, Glymour, Clark, & Scheines, Richard. (1993). Causation, prediction, and search (Vol. 81): Springer NewYork. ? Friedman, Nir. (1997). Learning belief networks in the presence of missing values and hidden variables. ICML. ? Meek, Christopher. (1997). Graphical Models: Selecting causal and statistical models. PhD thesis, Carnegie Mellon University. ? O’Donnell, R, Korb, K, & Allison, Lloyd. (2007). Causal KL: Evaluating causal discovery: Citeseer.
- 25. Thanks for listening!!! Any questions? Xuhui Zhang Nov 25th, 2015 @ABNMS