Representing Cause-and-Effect in a Tensor Framework
Speaker: M. Alex O. Vasilescu, UCLA Computer Graphics and Vision Lab
Location: 60 Fifth Avenue 150
Date: December 3, 2019, 12:30 p.m.
Host: Ken Perlin
Statistical data analysis that disentangles the causal factors of data formation and computes a representation that facilitates the analysis, visualization, compression, approximation, and/or interpretation of the data is challenging and of paramount importance.
“Natural images are the composite consequence of multiple constituent factors related to scene structure, illumination conditions, and imaging conditions. 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.” (Vasilescu and Terzopoulos, 2002 )
Scene structure is composed from 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 (i.e. the location and types of light sources), imaging (i.e. viewpoint, viewing direction, lens type and other camera characteristics). Intrinsic and extrinsic causal factors confound each other’s contribution, hindering recognition and animation such as expression retargeting.
This talk will address the basics of tensor algebra, the meaning of "intrinsic vs extrinsic" causality, 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.
M. Alex O. Vasilescu received her education at the Massachusetts Institute of Technology and the University of Toronto. Vasilescu 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 suitable for mathematically representing cause-and-effect and demonstratively disentangling the causal factors of observable data. The tensor framework is a powerful paradigm whose utility and value has been further underscored by recently provided theoretical evidence showing that deep learning is a neural network approximation of multilinear tensor factorization. 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, and in articles in the New York Times, Washington Times, etc. MITs Technology Review Magazine named her as a TR100 honoree, and the National Academy of Science co-awarded the KeckFutures Initiative Grant.
Refreshments will be offered starting 15 minutes prior to the scheduled start of the talk.