Related papers: Bayesian Lasso Posterior Sampling via Parallelized…

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 propose the first Bayesian encoder for metric learning. Rather than relying on neural amortization as done in prior works, we learn a distribution over the network weights with the Laplace Approximation. We actualize this by first…

In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double…

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,…

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the…

We consider Bayesian inference when only a limited number of noisy log-likelihood evaluations can be obtained. This occurs for example when complex simulator-based statistical models are fitted to data, and synthetic likelihood (SL) method…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…

Recent methods for deep metric learning have been focusing on designing different contrastive loss functions between positive and negative pairs of samples so that the learned feature embedding is able to pull positive samples of the same…

A natural way to quantify uncertainties in Gaussian mixture models (GMMs) is through Bayesian methods. That said, sampling from the joint posterior distribution of GMMs via standard Markov chain Monte Carlo (MCMC) imposes several…

We present Automatic Laplace Collapsed Sampling (ALCS), a general framework for marginalising latent parameters in Bayesian models using automatic differentiation, which we combine with nested sampling to explore the hyperparameter space in…

We present a simple method to obtain optimal posterior distributions and improve the quality of Bayesian inference with reduced human and computational effort. Bayes' Theorem is reformulated in the language of statistical mechanics, wherein…

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…

Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…

Diffusion models have shown strong performances in solving inverse problems through posterior sampling while they suffer from errors during earlier steps. To mitigate this issue, several Decoupled Posterior Sampling methods have been…

Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…

Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the…

For $\mathcal{O}$ a bounded domain in $\mathbb{R}^d$ and a given smooth function $g:\mathcal{O}\to\mathbb{R}$, we consider the statistical nonlinear inverse problem of recovering the conductivity $f>0$ in the divergence form equation $$…

Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…

We present a Bayesian scheme for the approximate diagonalisation of several square matrices which are not necessarily symmetric. A Gibbs sampler is derived to simulate samples of the common eigenvectors and the eigenvalues for these…