Related papers: Gaussian Variational Inference with Non-Gaussian F…

We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…

We present a systematic study of likelihood functions used for Stochastic Gravitational Wave Background (SGWB) searches. By dividing the data into many short segments, one customarily takes advantage of the Central Limit Theorem to justify…

Precise positioning and navigation information has been increasingly important with the development of the consumer electronics market. Due to some deficits of Global Navigation Satellite System (GNSS), such as susceptible to interferences,…

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…

Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates…

The stochastic gravitational wave background (SGWB) can be observed in the nanohertz band using a pulsar timing array (PTA). Here a computationally efficient state-space framework is developed for analysing SGWB data, in which the…

Separating a stochastic gravitational wave background (SGWB) from noise is a challenging statistical task. One approach to establishing a detection criterion for the SGWB is using Bayesian evidence. If the evidence ratio (Bayes factor)…

The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian L\'evy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian…

Deep Gaussian processes (DGPs) provide a robust paradigm for Bayesian deep learning. In DGPs, a set of sparse integration locations called inducing points are selected to approximate the posterior distribution of the model. This is done to…

Variational inference (VI) is a method to approximate the computationally intractable posterior distributions that arise in Bayesian statistics. Typically, VI fits a simple parametric distribution to the target posterior by minimizing an…

Deep Gaussian processes (DGPs) can model complex marginal densities as well as complex mappings. Non-Gaussian marginals are essential for modelling real-world data, and can be generated from the DGP by incorporating uncorrelated variables…

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…

Reliable state estimation depends on accurately modeled noise covariances, which are difficult to determine in practice. This paper formulates the noise covariance estimation as a bilevel optimization problem that factorizes the joint…

Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational…

It is essential that a robot has the ability to determine its position and orientation to execute tasks autonomously. Heading estimation is especially challenging in indoor environments where magnetic distortions make magnetometer-based…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…

Variational inference (VI) seeks to approximate a target distribution $\pi$ by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates $\pi$ by minimizing the…

Ensemble transform Kalman filtering (ETKF) data assimilation is often used to combine available observations with numerical simulations to obtain statistically accurate and reliable state representations in dynamical systems. However, it is…

We consider the problem of learning a sparse graph underlying an undirected Gaussian graphical model, a key problem in statistical machine learning. Given $n$ samples from a multivariate Gaussian distribution with $p$ variables, the goal is…