# Data-driven decision making with applications to healthcare systems

Reconstructing a high-dimensional sparse vector from a small number of observationsis a well-studied problem in many scientific, economic and engineering disciplines, anda number of tools have been designed to address this problem. It is currently experiencinga 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. Thistalk describes contributions in both directions.In the first portion of this talk, I will describe the application of such tools for minimizingrehospitalizations--the admission of a patient to a hospital soon after discharge. Nearlyone in every five patients is readmitted within 30 days of their discharge, and the estimatedcost of such rehospitalizations to Medicare in 2004 was $17.4 billion. Hospitals aim to avoidrehospitalizations in a number of ways; for example, through patient education programs,follow-up home visits by pharmacists, and by supplying extensive discharge packages. Itis important to properly allocate these costly and limited resources. Using electronic healthrecords from a major hospital in the U.S., we have designed a predictive model whichidentifies patients with the highest risk of being rehospitalized, making it possible tosignificantly reduce rehospitalization costs.In the second portion, I will focus on the rigorous analysis of a recent family of iterativealgorithms for solving the above learning problems that are inspired by graphical modelsand ideas from statistical physics. These algorithms are exceptionally fast in yieldingaccurate predictions. Our analysis of these algorithms yields sharp formulas for theirasymptotic performance. In particular, we derive rigorous formulas for the mean squareerror 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