Related papers: Expectation Consistent Approximate Inference: Gene…
Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits…
Conformal prediction, a post-hoc, distribution-free, finite-sample method of uncertainty quantification that offers formal coverage guarantees under the assumption of data exchangeability. Unfortunately, the resulting uncertainty regions…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
We propose a new sparse estimation method, termed MIC (Minimum approximated Information Criterion), for generalized linear models (GLM) in fixed dimensions. What is essentially involved in MIC is the approximation of the $\ell_0$-norm with…
Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate…
We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint…
We introduce an alternative closed form lower bound on the Gaussian process ($\mathcal{GP}$) likelihood based on the R\'enyi $\alpha$-divergence. This new lower bound can be viewed as a convex combination of the Nystr\"om approximation and…
While significant progress has been made in specifying neural networks capable of representing uncertainty, deep networks still often suffer from overconfidence and misaligned predictive distributions. Existing approaches for measuring this…
The convergence of expectation-maximization (EM)-based algorithms typically requires continuity of the likelihood function with respect to all the unknown parameters (optimization variables). The requirement is not met when parameters…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
In Generalized Linear Estimation (GLE) problems, we seek to estimate a signal that is observed through a linear transform followed by a component-wise, possibly nonlinear and noisy, channel. In the Bayesian optimal setting, Generalized…
This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean…
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…
Generative models provide a powerful framework for probabilistic reasoning. However, in many domains their use has been hampered by the practical difficulties of inference. This is particularly the case in computer vision, where models of…
Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between…
This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…
We propose a method to improve the efficiency and accuracy of amortized Bayesian inference by leveraging universal symmetries in the joint probabilistic model of parameters and data. In a nutshell, we invert Bayes' theorem and estimate the…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector $\mathbf{x}$ observed through a linear transform $\mathbf{A}$. In the case of large…