Related papers: Maxisets for Model Selection
This article describes posterior maximization for topic models, identifying computational and conceptual gains from inference under a non-standard parametrization. We then show that fitted parameters can be used as the basis for a novel…
This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
We consider a facility location problem, where the objective is to ``disperse'' a number of facilities, i.e., select a given number k of locations from a discrete set of n candidates, such that the average distance between selected…
Robust parameter estimation in computer vision is frequently accomplished by solving the maximum consensus (MaxCon) problem. Widely used randomized methods for MaxCon, however, can only produce {random} approximate solutions, while global…
By the nature of their construction, many statistical models for extremes result in likelihood functions that are computationally prohibitive to evaluate. This is consequently problematic for the purposes of likelihood-based inference. With…
We consider the problem of designing models to leverage a recently introduced approximate model averaging technique called dropout. We define a simple new model called maxout (so named because its output is the max of a set of inputs, and…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
In this paper, we consider two sequential decision making problems with a convexity structure, namely an energy storage optimization task and a multi-product assembly example. We formulate these problems in the stochastic programming…
We introduce the concepts of max-closedness and numeraires of convex subsets in the nonnegative orthant of the topological vector space of all random variables built over a probability space, equipped with a topology consistent with…
We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer…
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We…
We consider a simulation optimization problem for a context-dependent decision-making, which aims to determine the top-m designs for all contexts. Under a Bayesian framework, we formulate the optimal dynamic sampling decision as a…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
The graph theoretic concept of maximal independent set arises in several practical problems in computer science as well as in game theory. A maximal independent set is defined by the set of occupied nodes that satisfy some packing and…
In this paper, we describe a new way to get convergence rates for optimal methods in smooth (strongly) convex optimization tasks. Our approach is based on results for tasks where gradients have nonrandom small noises. Unlike previous…
If the assumed model does not accurately capture the underlying structure of the data, a statistical method is likely to yield sub-optimal results, and so model selection is crucial in order to conduct any statistical analysis. However, in…