CSE Colloquium: Cause and Effect in a Tensor Framework

Abstract: Determining the causal factors of observable sensory data allows intelligent agents to better understand and navigate the world – an important goal of artificial intelligence, and an important goal of data science. There are two types of causal reasoning: forward causal inferencing, in which effects are inferred from causes, and backward causal inferencing in which causes are inferred from effects. These are analogous to computer graphics and computer vision questions, respectively. Natural images are the composite consequence of multiple constituent factors related to scene structure, illumination conditions (i.e. the location and types of light sources), and imaging conditions (i.e. viewpoint, viewing direction, lens type and other camera characteristics). Scene structure is composed of a set of objects that appear to be formed from a recursive hierarchy of perceptual wholes and parts whose properties, such as shape, reflectance, and color, constitute a hierarchy of intrinsic causal factors of object appearance. Object appearance is the compositional consequence of both an object’s intrinsic causal factors, and extrinsic causal factors with the latter related to illumination and imaging. Intrinsic and extrinsic causal factors confound each other’s contribution, hindering recognition and animation. Multilinear algebra, the algebra of higher-order tensors, offers a potent mathematical framework for analyzing the multifactor structure of image ensembles and for addressing the difficult problem of disentangling the constituent factors or modes. 

This talk will address the basics of tensor algebra, the best practice for representing and disentangling the hierarchical variance of each causal factor, plus common tensor misconceptions. All demonstrated with applications that will include face recognition and facial animation. 

Biography: M. Alex O. Vasilescu (http://www.cs.ucla.edu/~maov) received her education at the Massachusetts Institute of Technology and the University of Toronto. She introduced the tensor paradigm for computer vision, computer graphics, machine learning, and extended the tensor algebraic framework by generalizing concepts from linear algebra. Starting in the early 2000s, she re-framed the analysis, recognition, synthesis, and interpretability of sensory data as multilinear tensor factorization problems that represent and demonstratively disentangle the causal factors of data formation. The tensor framework is a powerful paradigm whose utility has been further underscored by recent theoretical evidence that deep learning is a neural network approximation of multilinear tensor factorization, and shallow networks are linear tensor factorizations (CP decomposition). Vasilescu’s face recognition research, known as TensorFaces, has been funded by the TSWG, the Department of Defenses Combating Terrorism Support Program, and by IARPA, Intelligence Advanced Research Projects Activity. Her work was featured on the cover of Computer World Canada (currently, IT World Canada), and in articles in the New York Times, Washington Times, etc. MIT's Technology Review named her as TR100 honoree, and the National Academy of Science co-awarded the Keck Futures Initiative Grant.