Related papers: Inference and Modeling with Log-concave Distributi…

Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…

In this article, we revisit the problem of estimating the unknown zero-symmetric distribution in a two-component location mixture model, considered in previous works, now under the assumption that the zero-symmetric distribution has a…

We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and…

Large Language Models (LLMs) have recently been successfully applied to regression tasks -- such as time series forecasting and tabular prediction -- by leveraging their in-context learning abilities. However, their autoregressive decoding…

The analysis of datasets taking the form of simple, undirected graphs continues to gain in importance across a variety of disciplines. Two choices of null model, the logistic-linear model and the implicit log-linear model, have come into…

The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of…

A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions,…

Robust inferential methods based on divergences measures have shown an appealing trade-off between efficiency and robustness in many different statistical models. In this paper, minimum density power divergence estimators (MDPDEs) for the…

In this note, we show that the convolution of a discrete symmetric log-concave distribution and a discrete symmetric bimodal distribution can have any strictly positive number of modes. A similar result is proved for smooth distributions.

Langevin Monte Carlo (LMC) is an iterative algorithm used to generate samples from a distribution that is known only up to a normalizing constant. The nonasymptotic dependence of its mixing time on the dimension and target accuracy is…

We extend the Langevin Monte Carlo (LMC) algorithm to compactly supported measures via a projection step, akin to projected Stochastic Gradient Descent (SGD). We show that (projected) LMC allows to sample in polynomial time from a…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…

A logconcave likelihood is as important to proper statistical inference as a convex cost function is important to variational optimization. Quantization is often disregarded when writing likelihood models, ignoring the limitations of the…

We provide results demonstrating the smoothness of some marginal log-linear parameterizations for distributions on multi-way contingency tables. First we give an analytical relationship between log-linear parameters defined within different…

Normalizing flows are a widely used class of latent-variable generative models with a tractable likelihood. Affine-coupling (Dinh et al, 2014-16) models are a particularly common type of normalizing flows, for which the Jacobian of the…

Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…

Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…

In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…

By the Pr\'ekopa-Leindler inequality, the difference $X-X'$ has a log-concave density provided that $X$ has a log-concave density and $X, X'$ are independent and identically distributed. We prove that the opposite direction does not always…

Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…