Informs Annual Meeting 2017

SB64

INFORMS Houston – 2017

SB63

leveraging tools from distributionally robust optimization. For example, we derive an optimal generalization error bound for linear prediction with Lipschitz loss. (iii) It suggests a novel and systematic way to regularize problems in deep learning. As an example, we demonstrate superior performance on training generative adversarial networks (GANs) using our new regularization scheme. 2 - A Cluster Fusion Penalty for Grouping Response Variables in Multivariate Regression Models Brad Price, West Virginia University, College of Business and Economics, P.O. Box 6025, Morgantown, WV, 26506, United States, brad.price@mail.wvu.edu We propose a method for estimating coefficients in multivariate regression when there is a clustering structure to the response variables. The proposed method includes a fusion penalty, to shrink the difference in fitted values from responses in the same cluster, and an L1 penalty for simultaneous variable selection and estimation. The method can be used when the grouping structure of the response variables is known or unknown. When the clustering structure is unknown the method will simultaneously estimate the clusters of the response and the regression coe cients. Theoretical results are presented for the penalized least squares case, including asymptotic results allowing for p n. We extend our method to the setting where the responses are binomial variables. A coordinate descent algorithm is proposed for both the normal and binomial likelihood, which can easily be extended to other glm settings. Simulations and data examples from business operations and genomics are presented to show the merits of both the least squares and binomial methods. 3 - Statistical Degradation Modeling and Prognostics of Multiple Sensor Signals via Data Fusion: A Composite Health Index Approach Changyue Song, University of Wisconsin-Madison, Rm 3221, Nowadays multiple sensors have been widely used to monitor the degradation status of a unit simultaneously. As those sensor signals are often correlated and measure different characteristics of the same unit, effective fusion of such diverse “gene pool” is important to better understand the degradation process and produce more accurate prediction of the remaining useful life (RUL). This is a challenging task as the true degradation status cannot be directly observed, and the degradation process has to comply with the engineering principles governing the underlying failure mechanism. To address this issue, this article proposes a novel data fusion method that constructs a composite health index (HI) via the combination of multiple sensor signals for better characterizing the degradation process. In particular, we formulate this problem as an indirect supervised learning problem and leverage the quantile regression to derive the optimal fusion coefficient. In this way, the prognostic performance of the proposed method is theoretically guaranteed. To the best of our knowledge, this is the first paper that provides the theoretical analysis of the data fusion method for degradation modeling and prognostics. Simulation studies are conducted to evaluate the proposed method in different scenarios. A case study on the degradation of aircraft engines is also performed, which shows the superior performance of our method over the existing HI-based methods. 4 - Frequentist Consistency of Variational Bayes Yixin Wang, Columbia University, New York, NY, United States, yixin.wang.sh@gmail.com A key challenge for modern Bayesian statistics is how to perform scalable inference of posterior distributions. To address this challenge, variational Bayes (VB) methods have emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) methods. VB methods tend to be faster while achieving comparable predictive performance. However, there are few theoretical results around!”. In this paper, we establish frequentist consistency and asymptotic normality of VB methods. Specifically, we connect VB methods to point estimates based on variational approximations, called frequentist variational approximations, and we use the connection to prove a variational Bernstein-von- Mises theorem. The theorem leverages the theoretical characterizations of frequentist variational approximations to understand asymptotic properties of VB. In summary, we prove that (1) the VB posterior converges to the Kullback-Leibler (%&) minimizer of a normal distribution, centered at the truth and (2) the corresponding variational expectation of the parameter is consistent and asymptotically normal. As applications of the theorem, we derive asymptotic properties of VB posteriors in Bayesian mixture models, Bayesian generalized linear mixed models, and Bayesian stochastic block models. We conduct a simulation study to illustrate these theoretical results. Mechanical Engineering Building, 1513 University Ave, Madison, WI, 53715, United States, csong39@wisc.edu

370D Redesigning Electricity Markets and Pricing to Account for Uncertainty Invited: Energy and Climate Invited Session Chair: Ramteen Sioshansi, The Ohio State University, 240 Baker Systems Engineering Building, 1971 Neil Avenue, Columbus, OH, 43210-1271, United States, sioshansi.1@osu.edu Co-Chair: Antonio J. Conejo, The Ohio State University, 286 Baker Systems Engineering Building, 1971 Neil Avenue, Columbus, OH, 43210-1271, United States, conejonavarro.1@osu.edu 1 - Price Formation with an Evolving Resource Mix Congcong Wang, MISO, 720 City Center Dr, Carmel, IN, 46032, United States, cwang@misoenergy.org With an evolving resource mix including increasing renewable penetration and demand-side participation, pricing needs have changed and will continue to change as resources are operated to balance variations and uncertainties in net demands throughout the day. This talk tries to provide a holistic view of the price formation challenges and how MISO is preparing for the low-carbon future. Numerical examples will be presented to illustrate the pricing challenges and potential solutions, including but not limited to sustainability of traditional resources facing prices driven down by low-marginal costs renewables and Richard O’Neill, Chief Economist, Federal Energy Regulatory Commission, 12601 Meadowood Drive, Silver Spring, MD, 20904, United States, richard.oneill@ferc.gov We examine four pricing methods for non-convex auctions markets comparing the properties of each including transparency, make-whole payments, entry price signals, price signals for price-responsive demand. 3 - A Market Design Integrating the View of Stochastic Producers Antonio J. Conejo, The Ohio State University, Department of Integrated Systems Engineering, 210 Baker Systems Building, Columbus, OH, 43210, United States, conejonavarro.1@osu.edu, Ramteen Sioshansi The goal of this presentation is to reexamine the design of electricity markets in light of the fundamental changes that electric power systems are undergoing, while account for the two decades of experience we have with restructured electricity markets. This includes increasing use of non-dispatchable, uncertain, and variable weather-dependent renewable energy, the use of distributed energy resources, and novel uses of electricity by end consumers. 370E Data Mining Best Paper Award II Sponsored: Data Mining Sponsored Session Chair: Tong Wang, University of Iowa, Pappajohn Business Build, 21 East Market Street, Iowa City, IA, 52245, United States, tong-wang@uiowa.edu 1 - Wasserstein Distributional Robustness and Regularization in Statistical Learning Rui Gao, Georgia Institute of Technology, 755 Ferst Drive NW, ISyE Main Building, Atlanta, GA, 30332-0205, United States, rgao32@gmail.com A central problem in statistical learning is to design algorithms that not only perform well on training data, but also generalize to new and unseen data. In this paper, we tackle this problem by formulating a distributionally robust stochastic optimization problem, which minimizes the worst-case expected loss over a family of distributions that are close to the empirical distribution in Wasserstein distances. We establish a relation between such Wasserstein distributionally robust stochastic optimization and the gradient-norm regularization. In particular, we identify a broad class of loss functions, for which the worst-case expected loss is upper and lower bounded by some gradient-norm regularization problems. Moreover, we show that the gap between the upper and lower bounds is asymptotically zero with probability one. The relation between Wasserstein distributional robustness and regularization has the following important implications: (i) It provides new interpretations for problems involving regularization, including a great number of statistical learning problems, and several discrete choice models such as the multinomial logit. (ii) It enables a new method to derive generalization error bounds for statistical learning problems, by SB64 flexibility of resources that must be maintained for reliability needs. 2 - Pricing Methods in ISO Day-ahead and Real-time Auction Markets

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