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Continuous latent time series models are prevalent in Bayesian modeling; examples include the Kalman filter, dynamic collaborative filtering, or dynamic topic models. These models often benefit from structured, non mean field variational…

We introduce Deep Linear Discriminant Analysis (DeepLDA) which learns linearly separable latent representations in an end-to-end fashion. Classic LDA extracts features which preserve class separability and is used for dimensionality…

Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…

The variational autoencoder (VAE) is a powerful generative model that can estimate the probability of a data point by using latent variables. In the VAE, the posterior of the latent variable given the data point is regularized by the prior…

The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…

This paper introduces Concurrent Valuation Algebras (CVAs), a novel extension of ordered valuation algebras (OVAs). CVAs include two combine operators representing parallel and sequential products, adhering to a weak exchange law. This…

Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and…

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

Models of discrete-valued outcomes are easily misspecified if the data exhibit zero-inflation, overdispersion or contamination. Without additional knowledge about the existence and nature of this misspecification, model inference and…

Variational autoencoders (VAEs) have been widely applied for text modeling. In practice, however, they are troubled by two challenges: information underrepresentation and posterior collapse. The former arises as only the last hidden state…

The finite invert Beta-Liouville mixture model (IBLMM) has recently gained some attention due to its positive data modeling capability. Under the conventional variational inference (VI) framework, the analytically tractable solution to the…

A framework to boost the efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. We call it the refined variational approximation. Its strength lies both…

Diffusion language models (DLMs) have recently emerged as competitive alternatives to autoregressive (AR) language models, yet differences in their activation dynamics remain poorly understood. We characterize these dynamics in LLaDA-8B and…

When trained effectively, the Variational Autoencoder (VAE) is both a powerful language model and an effective representation learning framework. In practice, however, VAEs are trained with the evidence lower bound (ELBO) as a surrogate…

Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…

Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to…

Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…

Despite the success in learning semantically meaningful, unsupervised disentangled representations, variational autoencoders (VAEs) and their variants face a fundamental theoretical challenge: substantial evidence indicates that…