Title: Group Symmetry and Covariance Regularization
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the notion of a symmetric model via group invariance. We propose projection onto a group fixed point subspace as a fundamental way of regularizing covariance matrices in the high-dimensional regime. In terms of parameters associated to the group we derive precise rates of convergence of the regularized covariance matrix and demonstrate that significant statistical gains may be expected in terms of the sample complexity. We further explore the consequences of symmetry on related model-selection problems such as the learning of sparse covariance and inverse covariance matrices. We also illustrate our results with simulations.
Joint work with Venkat Chandrasekaran.
*** Eric’s talk:
Title: Incredible Machines: Body, Brain and Robot.
Understanding what enables human-level dexterity is a task which continually seems within reach, but escapes at the last minute. The subjective human experience is one in which controlling our bodies to manipulate objects in the environment often feels effortless, but we are beginning to understand that there are elegant biomechanical and neural resources being used outside of our awareness.
Given certain constraints, robots can be made to accomplish particular tasks; even thousands of years ago Hero of Alexandria described a machine which could pour wine into glasses. How is it that our robots remain almost as single-purpose while we humans can do this and then drink from those glasses without crushing them, perhaps while absentmindedly writing with a pen? This ability to maneuver arbitrary objects in arbitrary ways, somehow compensating for the uncertain surfaces, frictions, and weights of the hand and environment, is dexterity.
There is a neural component of this capability, in which brains read from sensors, performing some sorts of operations with them which yield signals sent to the physical component of dexterity: the tendon-driven body, and specifically for our interest, the hands.
I will describe some of the efforts being made in understanding biological and engineered systems for movement control, and present our efforts to adapt state-of-the-art control methods to achieve manipulation tasks using a unique robot which mimics the human hand. These efforts have the potential to improve robotics, but conversely allow us to answer concrete questions about what must be happening in brains and bodies.
Discovery Building, Orchard View Room
Eric Rombokas, Parikshit Shah