Stable Blanket with Hidden Variables and Cycles

Specialeforsvar: Hanqing Xiang

Titel: Stable Blanket with Hidden Variables and Cycles

Abstract: Stabilized regression is a framework that attempts to learn a regression function that remains stable across different environments. This thesis considers the causal interpretation of stabilized regression when there are potential hidden predictors, or the graphical model has cycles. Hidden variables and graphical models with cycles are common in real-world systems, so we believe that inscribing the relationship between the response and predictors in more generalized settings can benefit causal inference and decision making. The subject of brain science research is such a complex system that it may require graphical models with both cycles and hidden variables, which motivates us to read the distribution relationship of variables from complex graphs. In terms of hidden variables, we graphically characterize the sets of predictors which have a fixed dependence on the response among changing environments, and in turn, we find the most miniature set that is most predictive and can generalize to unseen interventions. When the graph has cycles, we extend the notion of the Markov blanket to ensure the regression relationship based on it can still minimize the prediction error and reduce the computation cost from amounts of predictors. We also define a unique stable blanket in these cases. Moreover, we illustrate the graphical features of the Markov blanket and the stable blanket in models with cycles and hidden variables. We discuss the relationship between these sets in different settings.

Vejleder: Niklas Phister

Censor:  Sören Möller, SDU