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Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along…
The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
In this paper we provide general conditions to check on the model and the prior to derive posterior concentration rates for data-dependent priors (or empirical Bayes approaches). We aim at providing conditions that are close to the…
We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…
An important task in the statistical analysis of inhomogeneous point processes is to investigate the influence of a set of covariates on the point-generating mechanism. In this article, we consider the nonparametric Bayesian approach to…
In his 1986 book, Aitchison explains that compositional data is regularly mishandled in statistical analyses, a pattern that continues to this day. The Dirichlet Type I distribution is a multivariate distribution commonly used to model a…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
We consider the problem of drawing samples from posterior distributions formed under a Dirichlet prior and a truncated multinomial likelihood, by which we mean a Multinomial likelihood function where we condition on one or more counts being…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…
In this paper, we consider objective Bayesian inference of the generalized exponential distribution using the independence Jeffreys prior and validate the propriety of the posterior distribution under a family of structured priors. We…
Bayesian neural networks (BNNs) combine the expressive power of deep learning with the advantages of Bayesian formalism. In recent years, the analysis of wide, deep BNNs has provided theoretical insight into their priors and posteriors.…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
We consider a sparse linear regression model with unknown symmetric error under the high-dimensional setting. The true error distribution is assumed to belong to the locally $\beta$-H\"{o}lder class with an exponentially decreasing tail,…
Quantile regression is often used when a comprehensive relationship between a response variable and one or more explanatory variables is desired. The traditional frequentists' approach to quantile regression has been well developed around…
The classical mixture of Gaussians model is related to K-means via small-variance asymptotics: as the covariances of the Gaussians tend to zero, the negative log-likelihood of the mixture of Gaussians model approaches the K-means objective,…
I propose a semiparametric Bayesian inference framework for conditional moment equalities. The core idea is that these models deterministically map a conditional distribution of data to a structural parameter via the restriction that a…
The bivariate normal density with unit variance and correlation $\rho$ is well-known. We show that by integrating out $\rho$, the result is a function of the maximum norm. The Bayesian interpretation of this result is that if we put a…
We present a nonparametric Bayesian joint model for multivariate continuous and categorical variables, with the intention of developing a flexible engine for multiple imputation of missing values. The model fuses Dirichlet process mixtures…