Related papers: Sampling through iterated approximation: Gradient-…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…
Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…
When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…
Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…
In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…
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…
We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
Sample-based Bayesian inference provides a route to uncertainty quantification in the geosciences, and inverse problems in general, though is very computationally demanding in the naive form that requires simulating an accurate computer…
Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…
We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU…
Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…
We propose an adaptive importance sampling scheme for Gaussian approximations of intractable posteriors. Optimization-based approximations like variational inference can be too inaccurate while existing Monte Carlo methods can be too slow.…
We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…