Related papers: The Bayesian update: variational formulations and …

We introduce a novel one-parameter variational objective that lower bounds the data evidence and enables the estimation of approximate fractional posteriors. We extend this framework to hierarchical construction and Bayes posteriors,…

In many modern applications, discretely-observed data may be naturally understood as a set of functions. Functional data often exhibit two confounded sources of variability: amplitude (y-axis) and phase (x-axis). The extraction of amplitude…

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…

Classical worst-case optimization theory neither explains the success of optimization in machine learning, nor does it help with step size selection. In this paper we demonstrate the viability and advantages of replacing the classical…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

The main object of Bayesian statistical inference is the determination of posterior distributions. Sometimes these laws are given for quantities devoid of empirical value. This serious drawback vanishes when one confines oneself to…

A common problem in Machine Learning and statistics consists in detecting whether the current sample in a stream of data belongs to the same distribution as previous ones, is an isolated outlier or inaugurates a new distribution of data. We…

Proximal Markov Chain Monte Carlo is a novel construct that lies at the intersection of Bayesian computation and convex optimization, which helped popularize the use of nondifferentiable priors in Bayesian statistics. Existing formulations…

We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint…

We study the posterior contraction rates of a Bayesian method with Gaussian process priors in nonparametric regression and its plug-in property for differential operators. For a general class of kernels, we establish convergence rates of…

We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…

This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…

Normalizing flows can generate complex target distributions and thus show promise in many applications in Bayesian statistics as an alternative or complement to MCMC for sampling posteriors. Since no data set from the target posterior…

A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to…

Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

In this paper, we consider the inverse problem of determining the permeability of the subsurface from hydraulic head measurements, within the framework of a steady Darcy model of groundwater flow. We study geometrically defined prior…

This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of…

Bayesian inference typically relies on specifying a parametric model that approximates the data-generating process. However, misspecified models can yield poor convergence rates and unreliable posterior calibration. Bayesian empirical…