Related papers: Generalized Minimum Error Entropy for Adaptive Fil…

Gaussian and Laplacian entropy models are proved effective in learned point cloud attribute compression, as they assist in arithmetic coding of latents. However, we demonstrate through experiments that there is still unutilized information…

Estimators of information theoretic measures such as entropy and mutual information are a basic workhorse for many downstream applications in modern data science. State of the art approaches have been either geometric (nearest neighbor (NN)…

The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a…

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training…

By formulating the inverse problem of partial differential equations (PDEs) as a statistical inference problem, the Bayesian approach provides a general framework for quantifying uncertainties. In the inverse problem of PDEs, parameters are…

We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise…

A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…

We introduce a balloon estimator in a generalized expectation-maximization method for estimating all parameters of a Gaussian mixture model given one data sample per mixture component. Instead of limiting explicitly the model size, this…

Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…

Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists. This is because the vast majority of…

Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian…

Kernel density estimation (KDE) is a popular statistical technique for estimating the underlying density distribution with minimal assumptions. Although they can be shown to achieve asymptotic estimation optimality for any input…

We approach multivariate mode estimation through Gibbs distributions and introduce GERVE (Gibbs-measure Entropy-Regularised Variational Estimation), a likelihood-free framework that approximates Gibbs measures directly from samples by…

A major effort in modern high-dimensional statistics has been devoted to the analysis of linear predictors trained on nonlinear feature embeddings via empirical risk minimization (ERM). Gaussian equivalence theory (GET) has emerged as a…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…