Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the optimal solution of this problem. It is well known that the ML estimator exists when the data is … Read more
Water supply of high-rise buildings requires pump systems to ensure pressure requirements. The design goal of these systems are energy and cost efficiency, both in terms of fixed cost as well as during operation. In this paper, cost optimal decentralized and tree-shaped water distribution networks are computed, where placements of pumps at different locations in … Read more
We consider the problem of estimating the parameters of a multivariate Gaussian mixture model (GMM) given access to $n$ samples $\x_1,\x_2,\ldots ,\x_n \in\mathbb{R}^d$ that are believed to have come from a mixture of multiple subpopulations. State-of-the-art algorithms used to recover these parameters use heuristics to either maximize the log-likelihood of the sample or try to … Read more
Hydropower is one of the world’s primary renewable energy sources whose usage has profound economic, environmental, and social impacts. We focus on the dispatch of generating units and the storage policy of hydro resources. In this context, an accurate assessment of the water opportunity-cost is cru- cial for driving the sustainable use of this scarce … Read more
One form of characterizing the expressiveness of a piecewise linear neural network is by the number of linear regions, or pieces, of the function modeled. We have observed substantial progress in this topic through lower and upper bounds on the maximum number of linear regions and a counting procedure. However, these bounds only account for … Read more
In this paper, we propose a new approach to solve low-rank tensor completion and robust tensor PCA. Our approach is based on some novel notion of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly symmetric M-rank. We discuss the connections between these new tensor ranks and the CP-rank and … Read more
In this work we analyze the structural properties of the set of feasible bookings in the European entry-exit gas market system. We present formal definitions of feasible bookings and then analyze properties that are important if one wants to optimize over them. Thus, we study whether the sets of feasible nominations and bookings are bounded, … Read more
We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the estimation problem is equivalent to a tractable convex … Read more
Modeling time-varying operations in complex energy systems optimization problems is often computationally intractable, and time-series input data are thus often aggregated to representative periods. In this work, we introduce a framework for using clustering methods for this purpose, and we compare both conventionally-used methods (k-means, k-medoids, and hierarchical clustering), and shape-based clustering methods (dynamic time … Read more
We consider the best subset selection problem in linear regression, i.e., finding a parsimonious subset of the regression variables that provides the best fit to the data according to some predefined criterion. We show that, for a broad range of criteria used in the statistics literature, the best subset selection problem can be modeled as … Read more