Related papers: Ensemble-Conditional Gaussian Processes (Ens-CGP):…
We tackle the problem of collaborative filtering (CF) with side information, through the lens of Gaussian Process (GP) regression. Driven by the idea of using the kernel to explicitly model user-item similarities, we formulate the GP in a…
Gaussian Processes (GPs) provide powerful probabilistic frameworks for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we investigate data sampled on one dimension (e.g., a scalar or…
Nonlinear/non-Gaussian filtering has broad applications in many areas of life sciences where either the dynamic is nonlinear and/or the probability density function of uncertain state is non-Gaussian. In such problems, the accuracy of the…
Gaussian-process state-space models (GP-SSMs) provide a flexible nonparametric alternative for modeling time-series dynamics that are nonlinear or difficult to specify parametrically. While the Kalman filter is effective for linear-Gaussian…
Conditional Gaussian graphical models (cGGM) are a recent reparametrization of the multivariate linear regression model which explicitly exhibits $i)$ the partial covariances between the predictors and the responses, and $ii)$ the partial…
The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…
We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
Convolved Gaussian Process (CGP) is able to capture the correlations not only between inputs and outputs but also among the outputs. This allows a superior performance of using CGP than standard Gaussian Process (GP) in the modelling of…
Multivariate Gaussian distributions enjoy Gaussian conditional distributions that makes conditioning easy: conditioning boils down to implementing analytical formulae for conditional means and covariances. For more general distributions,…
The ensemble Kalman filter (EnKF) is a Monte Carlo approximation of the Kalman filter for high dimensional linear Gaussian state space models. EnKF methods have also been developed for parameter inference of static Bayesian models with a…
Studying conditional independence among many variables with few observations is a challenging task. Gaussian Graphical Models (GGMs) tackle this problem by encouraging sparsity in the precision matrix through $l_q$ regularization with…
Creating low dimensional representations of a high dimensional data set is an important component in many machine learning applications. How to cluster data using their low dimensional embedded space is still a challenging problem in…
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian…
The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While these assumptions facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Non-parametric,…
We present Causal Posterior Estimation (CPE), a novel method for Bayesian inference in simulator models, i.e., models where the evaluation of the likelihood function is intractable or too computationally expensive, but where one can…
Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer…
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…
We introduce a cluster-based generative image segmentation framework to encode higher-level representations of visual concepts based on one-shot learning inspired by the Omniglot Challenge. The inferred parameters of each component of a…
Working with systems of partial differential equations (PDEs) is a fundamental task in computational science. Well-posed systems are addressed by numerical solvers or neural operators, whereas systems described by data are often addressed…