Related papers: Adaptive Bayesian estimation in indirect Gaussian …
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…
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…
A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…
We consider the problem of Bayesian causal discovery for the standard model of linear structural equations with equivariant Gaussian noise. A uniform prior is placed on the space of directed acyclic graphs (DAGs) over a fixed set of…
Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…
We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
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…
We consider models of Bayesian inference of signals with vectorial components of finite dimensionality. We show that, under a proper perturbation, these models are replica symmetric in the sense that the overlap matrix concentrates. The…
Posterior sampling by Monte Carlo methods provides a more comprehensive solution approach to inverse problems than computing point estimates such as the maximum posterior using optimization methods, at the expense of usually requiring many…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these…
In this paper, we study a class of non-parametric density estimators under Bayesian settings. The estimators are piecewise constant functions on binary partitions. We analyze the concentration rate of the posterior distribution under a…
Preferential Bayesian optimization allows optimization of objectives that are either expensive or difficult to measure directly, by relying on a minimal number of comparative evaluations done by a human expert. Generating candidate…
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…
We review common situations in Bayesian latent variable models where the prior distribution that a researcher specifies differs from the prior distribution used during estimation. These situations can arise from the positive definite…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
We consider the utilization of a computational model to guide the optimal acquisition of experimental data to inform the stochastic description of model input parameters. Our formulation is based on the recently developed consistent…