Ray Fulkerson made important contributions to the fields of polyhedral combinatorics, network flow theory, matroid theory, graph theory, and large-scale linear programming...
THE SCHOOL OF OPERATIONS RESEARCH AND INFORMATION ENGINEERING
announces the twenty-fourth
D. R. Fulkerson Lecture Series
Presented by Dimitris Bertsimas
Operations Research Center
Massachusetts Institute of Technology
Health Care Analytics
Monday, April 21, 2014 ● 4:15 p.m. ● B17 Upson Hall
In this talk we present an analytics approach to a) personalized diabetes management and b) design of clinical trials for cancer as well as some thoughts on the direction of the field of analytics relative to medicine but also more generally.
In the first part of the talk, we present a system to make personalized lifestyle and health decisions for diabetes management, as well as for general health and diet management. In particular, we address the following components of the system: (a) efficiently learning preferences through a dynamic questionnaire that accounts for human behavior; (b) modeling blood glucose behavior and updating these models to match individual measurements; and (c) using the learned preferences and blood glucose models to generate an overall diet and exercise plan using mixed-integer robust optimization. We have implemented our system as an online application, which we demonstrate. (Joint work with Allison O' Hair.)
In the second part of the talk, we propose an analytics approach for the analysis and design of clinical trials that provides insights into what is the best currently available drug combination to treat a particular form of cancer and how to design new clinical trials that can discover improved drug combinations. We develop semi-automated extraction techniques to build a comprehensive database of data from clinical trials. We use this database to develop statistical models from earlier trials that are capable of predicting the survival and toxicity of the combination of the drugs used, when the drugs used have been seen in earlier trials, but in different combinations. Then, using these statistical models, we develop optimization models that select novel treatment regimens that could be tested in clinical trials, based on the totality of data available on existing combinations. We also present concrete models for gastric cancer, one of the leading causes of cancer death worldwide. Ultimately, our approach offers promise for improving life expectancy and quality of life for cancer patients at low cost. (Joint work with Allison O' Hair, Stephen Relyea and John Silberholz.)
Tractable stochastic analysis in high dimensions via a modern optimization lens
Tuesday, April 22, 2014 ● 4:15 p.m. ● B17 Upson Hall
Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory is really not a computationally tractable theory in high dimensions. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, network information theory, pricing multi-dimensional financial contracts, auction design in multi-item, multi-bidder auctions among others.
We propose a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms as primitives of probability theory, with some of the asymptotic implications of probability theory: the central limit theorem and law of large numbers and to define appropriate robust optimization problems to perform performance analysis. In this way, the performance analysis questions become highly structured optimization problems (linear, conic, mixed integer) for which there exist efficient, practical algorithms that are capable of solving truly large scale systems.
We demonstrate that the proposed approach achieves computationally tractable methods for (a) analyzing queueing systems in the transient domain and queueing networks in the steady-state domain, (b) characterizing the capacity region of network information theory and associated coding and decoding methods generalizing the work of Shannon, (c) pricing multi-dimensional financial contracts generalizing the work of Black, Scholes and Merton, (d) designing multi-item, multi-bidder auctions generalizing the work of Myerson.
Joint work with Chaithanya Bandi and Nataly Youssef.
Classical multivariate statistics via a modern optimization lens
Wednesday, April 23, 2014 ● 3:00 p.m. ● 253 Rhodes Hall
Key problems of classification and regression can naturally be written as optimization problems. While continuous optimization approaches has had a significant impact in statistics, discrete optimization has played a very limited role, primarily based on the belief that mixed integer optimization models are computationally intractable. While such beliefs were accurate two decades ago, the field of discrete optimization has made very substantial progress.
We apply modern first order optimization methods to find feasible solutions for classical problems in statistics, and mixed integer optimization to improve the solutions and to prove optimality by finding matching lower bounds.
Specifically, we report results for the classical variable selection problem in regression currently solved by LASSO heuristically, least quantile regression, factor analysis and optimal CART. In all cases we demonstrate that the solutions found by modern optimization methods outperform the classical approaches. Most importantly, this body of work suggests that the belief widely held in statistics that mixed integer optimization is not practically relevant for statistics applications needs to be revisited.
Joint work with Rahul Mazumder and Angie King.