Related papers: Convex Quantization Preserves Logconcavity
In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap…
It is proven that the logarithmic negativity does not increase on average under positive partial transpose preserving (PPT) operation including subselection (a set of operations that incorporate local operations and classical communication…
We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. We introduce conditions under which the result still holds for dependent variables. We argue that these…
We study a likelihood ratio test for the location of the mode of a log-concave density. Our test is based on comparison of the log-likelihoods corresponding to the unconstrained maximum likelihood estimator of a log-concave density and the…
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $\mu$ and $\nu$ such that $\nu$ is log-concave with respect to $\mu$.…
Penalized likelihood methods are fundamental to ultra-high dimensional variable selection. How high dimensionality such methods can handle remains largely unknown. In this paper, we show that in the context of generalized linear models,…
We show that a mixture of Beta distributions has log-concave density whenever the mixing weights are themselves log-concave. Some economic and statistical applications are provided in the last section.
We prove sharp anti-concentration results for log-concave random variables on the real line in both the discrete and continuous setting. Our approach is elementary and uses majorization techniques to recover and extend some recent and not…
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
We consider the nonparametric maximum likelihood estimation for the underlying event time based on mixed-case interval-censored data, under a log-concavity assumption on its distribution function. This generalized framework relaxes the…
Variable selection in linear regression has been a central topic in statistical research for decades. Bayesian variable selection methods, which account for uncertainty in both the regression coefficients and the noise variance, have…
Quantum entanglement is a useful resource for implementing communication tasks. However, for the resource to be useful in practice, it needs to be accessible by parties with bounded computational resources. Computational entanglement…
We consider the problem of causal inference based on observational data (or the related missing data problem) with a binary or discrete treatment variable. In that context, we study inference for the counterfactual density functions and…
The push-forward operation enables one to redistribute a probability measure through a deterministic map. It plays a key role in statistics and optimization: many learning problems (notably from optimal transport, generative modeling, and…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
Pairwise likelihood is a useful approximation to the full likelihood function for covariance estimation in high-dimensional context. It simplifies high-dimensional dependencies by combining marginal bivariate likelihood objects, thus making…
This paper compares convex and non-convex penalized likelihood methods in high-dimensional statistical modeling, focusing on their strengths and limitations. Convex penalties, like LASSO, offer computational efficiency and strong…
The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be non-negative and the integral of them over an entire hypersurface should be equal to one. To satisfy these…
A number of results related to statistical classification on convex sets are presented. In particular, the focus is on the case where some of the covariates in the data and observation being classified can be missing. The form of the…