Informs Annual Meeting Phoenix 2018

INFORMS Phoenix – 2018

WC01

Wednesday, 1:30PM - 3:00PM

well as outcome response, our framework for robust policy improvement optimizes the minimax regret of a candidate policy against the standard of care, generalizing inverse-propensity weighted estimators. We demonstrate our methods can achieve beneficial out-of-sample performance on synthetic data and construct an evaluation study from a large clinical trial. 2 - Statistics with Set-valued Functions: Applications to Inverse Approximation Optimization Anil Aswani, UC Berkeley, San Francisco, CA, 94103, United States Much statistical theory does not directly translate to sets because they do not form a vector space. Building on probability theory for random sets, this paper uses variational analysis to develop operational tools for statistics with set-valued functions. These tools are first applied to kernel regression of set-valued functions. The second application is to the problem of inverse approximate optimization, in which approximate solutions (corrupted by noise) to an optimization problem are observed and then used to estimate the amount of suboptimality of the solutions and the parameters of the optimization problem that generated the solutions. 3 - Detecting Communities in Relational Event Data with Non- negative Tensor Decomposition Xiaoyue Li, University of California-Davis, Davis, CA, United States A point-to-point process models timestamped interactions between two entities in their state spaces. This study looked into the NYC Taxi dataset, where there were interactions of taxi trips between locations with their timestamps being the pick- up times. Assuming the temporal pattern of taxi trip intensities can be determined by community labels of pick-up and drop-offs, like neighborhoods, airports and tourist locations, the intensity estimation naturally requires detecting this community structure. To this end, we applied point-to-point models and developed a multiplicative update algorithm to estimate the intensity with a non- negative low-rank tensor reconstruction of the dynamic network. 4 - A Semidefinite Programming-based Kernel Clustering Algorithm for Gaussian Mixture Models in the Presence of Outliers Prateek Raj Srivastava, University of Texas at Austin, Austin, TX, 78712, United States, Purnamrita Sarkar, Grani Adiwena Hanasusanto We consider the problem of clustering data points generated from a mixture of Gaussians in the presence of outliers. We propose a semidefinite programming- based algorithm that takes as input a kernel distance matrix to first denoise the original data, followed by spectral clustering to recover the true cluster labels of data points. Using Grothendieck’s inequality, we obtain theoretical guarantees on the error rates. Further, we compare the performance of our algorithm with other existing algorithms like k-means++ and vanilla spectral clustering. n WC03 North Bldg 121C Practice- Modeling and Optimization for Decision Making II Contributed Session Chair: Michele J. Fisher, Northwestern University, Regina, SK, S4S 2H7, Canada 1 - MCDA with Little or No Data Unique decisions involving multiple criteria are often characterised by conflicting or sparse data, or even no data, so we rely on expert judgment. In this talk I explain and illustrate seven best-practice principles, with evidence they lead to reliable and valid results. The principles include impartially facilitating decision conferences of diverse experts, engaging experts’ mental models, gaining clarity about the decision context, developing good definitions of criteria, applying proper scoring and weighting techniques, checking consistency, and conducting extensive sensitivity analyses. 2 - Optimization and Scheduling Methodologies to Enable Low Earth Orbit Nano-satellite Communication Michelle L. Song, University of Washington, Seattle, WA, 98105, United States, Cherry Yu Wakayama, Zelda B. Zabinsky Communications with low earth orbit nano-satellites (nanosats) are challenging due to short contact time intervals and uncertainty in successful delivery of messages. We present optimization models (with and without energy constraints) to enable timely delivery of messages between gateways and remote users via nanosats. Connections between nanosats and remote users may not be well established; the uncertainty is modeled using a chance constraint. A network flow program is formulated to optimize the scheduling/routing of messages. Decisions are chosen to minimize the delivery time. Although the decisions are binary variables, the models are shown to satisfy the integrality property. Lawrence D. Phillips, Emeritus Professor, London School of Economics & Political Science, London, NW3 1AH, United Kingdom

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Interpretable Machine Learning via Optimization Sponsored: Optimization/Optimization under Uncertainty Sponsored Session Chair: Dimitris Bertsimas, Massachusetts Institute of Technology, Cambridge, MA, 02139, United States 1 - Optimal Prescriptive Trees Jack Dunn, Massachusetts Institute of Technology, Cambridge, MA, United States, Dimitris Bertsimas, Nishanth Mundru Most machine learning approaches focus on predictive tasks, but in reality the final goal is actually to make optimal decisions. We present Optimal Prescriptive Trees (OPT), an interpretable approach for making personalized treatment prescriptions that learns from observational data. While constructing the tree, our method simultaneously infers the unknown counterfactuals in the data and learns to make optimal prescriptions, resulting in a decision tree that optimizes both the predictive and prescriptive error. OPT is interpretable, highly scalable, handles multiple treatments, and performs competitively with several state of the art methods. 2 - Optimal Online Impute Daisy Ying Zhuo, Massachusetts Institute of Technology, Cambridge, MA, United States, Dimitris Bertsimas, Colin F. Pawlowski Missing data is a common problem in real-world settings and has attracted significant attention in the statistical literature. We have proposed a flexible framework based on formal optimization to impute missing data that readily incorporate various predictive models including K-nearest neighbors, support vector machines, and decision tree based methods. More recently, building on this framework, we have developed a fast and accurate method to impute data in an online fashion, where observations with potential missing data are provided one at a time. In large-scale experiments with real-world data and a range of learning tasks, we demonstrate improved accuracy using this approach. 3 - Optimal Nonlinear Trees Yuchen Wang, Massachusetts Institute of Technology, Dimitris Bertsimas, Jack W. Dunn MARS is a greedy method for constructing a decision tree with nonlinear prediction functions in the leaves. We show that we can formulate the process of building such trees as a global optimization problem, which gives rise to our new method, Optimal Nonlinear Trees. We show in a collection of synthetic and real- world datasets that our Optimal Nonlinear Trees improve substantially over MARS, and also perform better than tree-based boosting methods like xgboost on most small to medium size datasets. 4 - Nonparametric Prescriptive Analytics with Continuous, Constrained Decisions Nishanth Mundru, Massachusetts Institute of Technology, Dimitris Bertsimas Most real world business analytics problems involve solving optimization problems that depend on uncertain parameters Y. Given historical data on uncertainties Y and observed covariates X, we consider the problem of prescribing optimal data driven decisions. Our work adapts nonparametric methods such as k-nearest neighbors, local kernel regression, trees, and random forests to learn from data in a single step and produce high quality decisions. We demonstrate the effectiveness of our methods by applying them on various problems. n WC02 North Bldg 121B Joint Session OPT-Uncert/APS: Optimization in Statistics I Sponsored: Optimization/Optimization under Uncertainty Sponsored Session Chair: Robert Bassett, Naval Postgraduate School, Monterey, CA, United States 1 - Robust Policy Improvement under Residual Confounding Angela Zhou, Cornell University ORIE, 206 Rhodes Hall, Ithaca, NY, 14853, United States, Nathan Kallus We study the problem of learning personalized decision policies from observational data which are robust in view of possible confounding. Unlike previous approaches for policy learning which assume unconfoundedness, that there are no unobserved confounders jointly affecting treatment assignment as

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