Related papers: Exact Likelihood Inference and Robust Filtering fo…

In object tracking and state estimation problems, ambiguous evidence such as imprecise measurements and the absence of detections can contain valuable information and thus be leveraged to further refine the probabilistic belief state. In…

Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…

Variable clustering is important for explanatory analysis. However, only few dedicated methods for variable clustering with the Gaussian graphical model have been proposed. Even more severe, small insignificant partial correlations due to…

We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…

We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…

Advancements in the sensitivity of gravitational wave detectors have increased the detection rate of transient astrophysical signals. We improve the existing BayesWave initialization algorithm and present a rapid, low latency approximate…

We study the reknown deconvolution problem of recovering a distribution function from independent replicates (signal) additively contaminated with random errors (noise), whose distribution is known. We investigate whether a Bayesian…

The Extreme Deconvolution method fits a probability density to a dataset where each observation has Gaussian noise added with a known sample-specific covariance, originally intended for use with astronomical datasets. The existing fitting…

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…

The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…

Considerable efforts have been devoted to statistical modeling and the characterization of channels in a range of statistical models for fading channels. In this paper, we consider a unified approach to model wireless channels by the…

Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…

In this paper, we characterize the noise of stochastic gradients and analyze the noise-induced dynamics during training deep neural networks by gradient-based optimizers. Specifically, we firstly show that the stochastic gradient noise…

When a gravitational wave encounters a massive object along the line of sight, repeated copies of the original signal may be produced due to gravitational lensing. In this paper, we develop a series of new machine-learning based statistical…

Using a semi-parametric approach based on the fourth-order Edgeworth expansion for the unknown signal distribution, we derive an explicit expression for the likelihood detection statistic in the presence of non-normally distributed…

It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…

Bayesian learning provides a unified skeleton to solve the electrophysiological source imaging task. From this perspective, existing source imaging algorithms utilize the Gaussian assumption for the observation noise to build the likelihood…

Inference-time scaling (ITS) in latent reasoning models typically relies on heuristic perturbations, such as dropout or fixed Gaussian noise, to generate diverse candidate trajectories. However, we show that stronger perturbations do not…

This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on…