Related papers: Expectation Consistent Approximate Inference: Gene…

Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…

In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…

We give convergence guarantees for estimating the coefficients of a symmetric mixture of two linear regressions by expectation maximization (EM). In particular, we show that the empirical EM iterates converge to the target parameter vector…

Grammatical Error Correction (GEC) faces a critical challenge concerning explainability, notably when GEC systems are designed for language learners. Existing research predominantly focuses on explaining grammatical errors extracted in…

We describe expectation propagation for approximate inference in dynamic Bayesian networks as a natural extension of Pearl s exact belief propagation.Expectation propagation IS a greedy algorithm, converges IN many practical cases, but NOT…

The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…

This paper considers the fundamental limit of compressed sensing for i.i.d. signal distributions and i.i.d. Gaussian measurement matrices. Its main contribution is a rigorous characterization of the asymptotic mutual information (MI) and…

Grammar error correction (GEC) is an important application aspect of natural language processing techniques. The past decade has witnessed significant progress achieved in GEC for the sake of increasing popularity of machine learning and…

Long range forecasts are the starting point of many decision support systems that need to draw inference from high-level aggregate patterns on forecasted values. State of the art time-series forecasting methods are either subject to concept…

Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in…

The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…

Belief propagation is known to perform extremely well in many practical statistical inference and learning problems using graphical models, even in the presence of multiple loops. The iterative use of belief propagation algorithm on loopy…

Random-effects meta-analyses have been widely applied in evidence synthesis for various types of medical studies. However, standard inference methods (e.g. restricted maximum likelihood estimation) usually underestimate statistical errors…

In this work, we investigate the question of how knowledge about expectations $\mathbb{E}(f_i(X))$ of a random vector $X$ translate into inequalities for $\mathbb{E}(g(X))$ for given functions $f_i$, $g$ and a random vector $X$ whose…

Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…

In this work, we adopt a general framework based on the Gibbs posterior to update belief distributions for inverse problems governed by partial differential equations (PDEs). The Gibbs posterior formulation is a generalization of standard…

Compressed sensing (CS) demonstrates that sparse signals can be recovered from underdetermined linear measurements. We focus on the joint sparse recovery problem where multiple signals share the same common sparse support sets, and they are…

We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant…

In this paper, we propose an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets. Instead of assuming the exact convex projection proposed in the literature, we allow each node to…

Generalized Vector Approximate Message Passing (GVAMP) is an efficient iterative algorithm for approximately minimum-mean-squared-error estimation of a random vector $\mathbf{x}\sim p_{\mathbf{x}}(\mathbf{x})$ from generalized linear…