Related papers: Exact Solutions in Log-Concave Maximum Likelihood …

We study the dimensional Brunn-Minkowski inequality for even log-concave probability measures $\mu$ on $\mathbb{R}^n$ via an analytic approach based on diffusion operators and gradient estimates. Our main result asserts that for every pair…

We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/\delta)$, where $\delta$ is the desired target accuracy -- are achievable using stochastic…

An upper bound on the ergodic capacity of {\bf MIMO} channels was introduced recently in arXiv:0903.1952. This upper bound amounts to the maximization on the simplex of some multilinear polynomial $p(\lambda_1,...,\lambda_n)$ with…

With an eye towards human-centered automation, we contribute to the development of a systematic means to infer features of human decision-making from behavioral data. Motivated by the common use of softmax selection in models of human…

The capacity of 1-D constraints is given by the entropy of a corresponding stationary maxentropic Markov chain. Namely, the entropy is maximized over a set of probability distributions, which is defined by some linear requirements. In this…

AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…

In this paper, we consider the maximization of a probability $\mathbb{P}\{ \zeta \mid \zeta \in \mathbf{K}(\mathbf x)\}$ over a closed and convex set $\mathcal X$, a special case of the chance-constrained optimization problem. We define…

Constraining the maximum likelihood density estimator to satisfy a sufficiently strong constraint, $\log-$concavity being a common example, has the effect of restoring consistency without requiring additional parameters. Since many results…

Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the integers. A functional analogue of this geometric inequality…

The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

We study integration and $L^2$-approximation of functions of infinitely many variables in the following setting: The underlying function space is the countably infinite tensor product of univariate Hermite spaces and the probability measure…

In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of…

Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…

This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…

We propose a novel molecular computing scheme for statistical inference. We focus on the much-studied statistical inference problem of computing maximum likelihood estimators for log-linear models. Our scheme takes log-linear models to…