相关论文: Predictive density estimation under the Wasserstei…

We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show…

The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for learning data-adaptive latent distributions using…

Shape restriction, like monotonicity or convexity, imposed on a function of interest, such as a regression or density function, allows for its estimation without smoothness assumptions. The concept of $k$-monotonicity encompasses a family…

Computer vision systems that are deployed in safety-critical applications need to quantify their output uncertainty. We study regression from images to parameter values and here it is common to detect uncertainty by predicting probability…

Flexibly modeling how an entire density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete…

The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…

We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a…

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…

Construction of ambiguity set in robust optimization relies on the choice of divergences between probability distributions. In distribution learning, choosing appropriate probability distributions based on observed data is critical for…

This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class…

This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire $d$-dimensional distribution is approximately preserved under random…

The Busemann function has recently found much interest in a variety of geometric machine learning problems, as it naturally defines projections onto geodesic rays of Riemannian manifolds and generalizes the notion of hyperplanes. As several…

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…

We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on…

In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a Kullback-Leibler type loss for a single model maximum likelihood estimate.…

Standard present day large-scale structure (LSS) analyses make a major assumption in their Bayesian parameter inference --- that the likelihood has a Gaussian form. For summary statistics currently used in LSS, this assumption, even if the…

Learning conditional densities and identifying factors that influence the entire distribution are vital tasks in data-driven applications. Conventional approaches work mostly with summary statistics, and are hence inadequate for a…

We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (possibly discontinuous) flux function are inferred from noisy…

We study prior distributions for Poisson parameter estimation under $L^1$ loss. Specifically, we construct a new family of prior distributions whose optimal Bayesian estimators (the conditional medians) can be any prescribed increasing…