Oral Session 7

Date

January 10, 2014

Speaker

Jennifer Chayes, Nils E Napp, and Yuchen Zhang

Affiliation

MSR New England, Harvard University, UC Berkeley

Overview

Belief Propagation Algorithms: From Matching Problems to Network Discovery in Cancer Genomics – We review belief propagation algorithms inspired by the study of phase transitions in combinatorial optimization problems. In particular, we present rigorous results on convergence of such algorithms for matching and associated bargaining problems on networks. We also present a belief propagation algorithm for the prize- collecting Steiner tree problem, for which rigorous convergence results are not yet known. Finally, we show how this algorithm can be used to discover pathways in cancer genomics, and to suggest possible drug targets for cancer therapy. These methods give us the ability to share information across multiple patients to help reconstruct highly patient-specific networks.

Message Passing Inference with Chemical Reaction Networks – Recent work on molecular programming has explored new possibilities for computational abstractions with biomolecules, including logic gates, neural networks, and linear systems. In the future such abstractions might enable nanoscale devices that can sense and control the world at a molecular scale. Just as in macroscale robotics, it is critical that such devices can learn about their environment and reason under uncertainty. At this small scale, systems are typically modeled as chemical reaction networks. In this work, we develop a procedure that can take arbitrary probabilistic graphical models, represented as factor graphs over discrete random variables, and compile them into chemical reaction networks that implement inference. In particular, we show that marginalization based on sum-product message passing can be implemented in terms of reactions between chemical species whose concentrations represent probabilities. We show algebraically that the steady state concentration of these species correspond to the marginal distributions of the random variables in the graph and validate the results in simulations. As with standard sum-product inference, this procedure yields exact results for tree-structured graphs, and approximate solutions for loopy graphs.

Information-theoretic lower bounds for distributed statistical estimation with communication constraints – We establish minimax risk lower bounds for distributed statistical estimation given a budget B of the total number of bits that may be communicated. Such lower bounds in turn reveal the minimum amount of communication required by any procedure to achieve the classical optimal rate for statistical estimation. We study two classes of protocols in which machines send messages either independently or interactively. The lower bounds are established for a variety of problems, from estimating the mean of a population to estimating parameters in linear regression or binary classification.

Speakers

Jennifer Chayes, Nils E Napp, and Yuchen Zhang

Jennifer Tour Chayes is Distinguished Scientist and Managing Director of Microsoft Research New England in Cambridge, Massachusetts, which she co-founded in 2008, and Microsoft Research New York City, which she co-founded in 2012. Chayes was Research Area Manager for Mathematics, Theoretical Computer Science and Cryptography at Microsoft Research Redmond until 2008. Chayes joined Microsoft Research in 1997, when she co-founded the Theory Group. Before that, she was for many years Professor of Mathematics at UCLA. Chayes is the author of about 125 academic papers and the inventor of over 25 patents. Her research areas include phase transitions in discrete mathematics and computer science, structural and dynamical properties of self-engineered networks, graph algorithms, and algorithmic game theory. Chayes received her B.A. in biology and physics at Wesleyan University, where she graduated first in her class, and her Ph.D. in mathematical physics at Princeton. She did her postdoctoral work in the Mathematics and Physics Departments at Harvard and Cornell. She is the recipient of the National Science Foundation Postdoctoral Fellowship, the Sloan Fellowship, and the UCLA Distinguished Teaching Award. Chayes has recently been the recipient of many leadership awards including the Leadership Award of Women Entrepreneurs in Science and Technology, the Women Who Lead Award, the Women to Watch Award of the Boston Business Journal, and the Women of Leadership Vision Award of the Anita Borg Institute. She has twice been a member of the Institute for Advanced Study in Princeton. Chayes is a Fellow of the American Association for the Advancement of Science, the Fields Institute, the Association for Computing Machinery, and the American Mathematical Society.

People

  • Portrait of Jennifer Chayes

    Jennifer Chayes

    Technical Fellow & Managing Director, Microsoft Research New England, New York City and Montreal