Reconstructing a high-dimensional sparse vector from a small number of observations is a well-studied problem in many scientific, economic and engineering disciplines, and a number of tools have been designed to address this problem. It is currently experiencing a resurgence due to new applications, such as data-driven medicine and online advertising, and due to the need for accurate predictions under time and complexity constraints. This talk describes contributions in both directions. In the first portion of this talk, I will describe the application of such tools for minimizing rehospitalizations--the admission of a patient to a hospital soon after discharge. Nearly one in every five patients is readmitted within 30 days of their discharge, and the estimated cost of such rehospitalizations to Medicare in 2004 was $17.4 billion. Hospitals aim to avoid rehospitalizations in a number of ways; for example, through patient education programs, follow-up home visits by pharmacists, and by supplying extensive discharge packages. It is important to properly allocate these costly and limited resources. Using electronic health records from a major hospital in the U.S., we have designed a predictive model which identifies patients with the highest risk of being rehospitalized, making it possible to significantly reduce rehospitalization costs. In the second portion, I will focus on the rigorous analysis of a recent family of iterative algorithms for solving the above learning problems that are inspired by graphical models and ideas from statistical physics. These algorithms are exceptionally fast in yielding accurate predictions. Our analysis of these algorithms yields sharp formulas for their asymptotic performance. In particular, we derive rigorous formulas for the mean square error of the LASSO estimator. The first portion is joint work with M. Braverman, M. Gillam, M. Smith, and E. Horvitz. The second portion is joint work with A. Montanari, and J. Bento.
Thursday, October 06, 2011
Free and open to the public