**Forward and Inverse Causal Inference in a Tensor Framework**

**M. Alex O. Vasilescu**

Institute of Pure and Applied Mathematics, UCLA

Institute of Pure and Applied Mathematics, UCLA

**1-2:00 pm Monday, March 29, 2021**

via WebEx

via WebEx

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. 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 a forward causal model, and a set of observations that constrain the solution set. Tensor algebra is a suitable and transparent framework for modeling the mechanism that generates observed data. Tensor-based data analysis, also known in the literature as structural equation modeling with multimode latent variables, has been employed in representing the causal factor structure of data formation in econometrics, psychometric, and chemometrics since the 1960s. More recently, tensor factor analysis has been successfully employed to represent cause-and-effect in computer vision, and computer graphics, or for prediction and dimensionality reduction in machine learning tasks.

M. Alex O. Vasilescu received her education at the Massachusetts Institute of Technology and the University of Toronto. She is currently a senior fellow at UCLA’s Institute of Pure and Applied mathematics (IPAM) that has held research scientist positions at the MIT Media Lab from 2005-07 and at New York University’s Courant Institute of Mathematical Sciences from 2001-05. Vasilescu introduced the tensor paradigm for computer vision, computer graphics, and machine learning. She addressed causal inferencing questions by framing computer graphics and computer vision as multilinear problems. Causal inferencing in a tensor framework facilitates the analysis, recognition, synthesis, and interpretability of data. The development of the tensor framework has been spearheaded with premier papers, such as Human Motion Signatures (2001), TensorFaces (2002), Multilinear Independent Component Analysis (2005), TensorTextures (2004), and Multilinear Projection for Recognition (2007, 2011). Vasilescu’s face recognition research, known as TensorFaces, has been funded by the TSWG, the Department of Defenses Combating Terrorism Support Program, Intelligence Advanced Research Projects Activity (IARPA), and NSF. Her work was featured on the cover of Computer World and in articles in the New York Times, Washington Times, etc. MIT’s Technology Review Magazine named her to their TR100 list of honorees, and the National Academy of Science co-awarded the Keck Futures Initiative Grant.

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