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Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick…
A nonparametric method to predict non-Markovian time series of partially observed dynamics is developed. The prediction problem we consider is a supervised learning task of finding a regression function that takes a delay embedded…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
We forecast a single time series using a high-dimensional set of predictors. When these predictors share common underlying dynamics, an approximate latent factor model provides a powerful characterization of their co-movements Bai(2003).…
The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…
Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to…
Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…
Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity…
A Kernel Adaptive Metropolis-Hastings algorithm is introduced, for the purpose of sampling from a target distribution with strongly nonlinear support. The algorithm embeds the trajectory of the Markov chain into a reproducing kernel Hilbert…
Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of…
Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian…
This paper presents an adaptive online learning framework for systems with uncertain parameters to ensure safety-critical control in non-stationary environments. Our approach consists of two phases. The initial phase is centered on a novel…
This paper introduces a novel statistical regression framework that allows the incorporation of consistency constraints. A linear and nonlinear (kernel-based) formulation are introduced, and both imply closed-form analytical solutions. The…
We study location-scale mixture priors for nonparametric statistical problems, including multivariate regression, density estimation and classification. We show that a rate-adaptive procedure can be obtained if the prior is properly…
The lack of sufficient flexibility is the key bottleneck of kernel-based learning that relies on manually designed, pre-given, and non-trainable kernels. To enhance kernel flexibility, this paper introduces the concept of…
In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…
We revisit Rahimi and Recht (2007)'s kernel random Fourier features (RFF) method through the lens of the PAC-Bayesian theory. While the primary goal of RFF is to approximate a kernel, we look at the Fourier transform as a prior distribution…
Conditional kernel mean embeddings are nonparametric models that encode conditional expectations in a reproducing kernel Hilbert space. While they provide a flexible and powerful framework for probabilistic inference, their performance is…