Forward and Inverse Causal Inference with Multilinear (Tensor) Factor Analysis

M. Alex O. Vasilescu
University of California, Los Angeles (UCLA)

Developing causal explanations for correct results or for failures from mathematical equations and data is important in developing a trustworthy artificial intelligence, and retaining public trust. Causal explanations are germane to the "right to an explanation" statute, i.e, to data-driven decisions, such as those that rely on images. Tensor algebraic framework has been successfully employed for representing the causal structure of data formation in econometrics, psychometrics, and chemometrics. More recently, the tensor factor data analysis has been successfully employed to represent cause-and-effect in computer graphics, computer vision and machine learning. Computer graphics and computer vision problems, also known as forward and inverse imaging problems, have been cast as causal inference questions consistent with Donald Rubin's quantitative definition of causality, where "A causes B" means “the effect of A is B”, a measurable and experimentally repeatable quantity. Computer graphics may be viewed as addressing analogous questions to forward causal inference that addresses the “what if” question, and estimates a change in effects given a delta change in a causal factor. Computer vision may be viewed as addressing analogous questions to inverse causal inference that addresses the “why” question which we define as the estimation of causes given an estimated forward causal model, and a set of observations that constrain the solution set.

In the first part of the tutorial, we will address the "what if" causal question in a tensor framework, and model the mechanism of data formation with Multilinear PCA (MPCA), Multilinear ICA (MICA), Kernel MPCA and Kernel MICA. In the second part of the tutorial, we will discuss the "why" causal question and infer the causal factors of data formation from one or more unlabeled images given an estimated forward causal model. Addressing these questions within a tensor algebraic framework has yielded powerful statistical models that facilitate the analysis, recognition, synthesis, and interpretability of data.

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