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We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
Motivated by the application to German interest rates, we propose a timevarying autoregressive model for short and long term prediction of time series that exhibit a temporary non-stationary behavior but are assumed to mean revert in the…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
We propose a nonparametric procedure to achieve fast inference in generative graphical models when the number of latent states is very large. The approach is based on iterative latent variable preselection, where we alternate between…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
Gaussian processes (GPs) are powerful non-parametric function estimators. However, their applications are largely limited by the expensive computational cost of the inference procedures. Existing stochastic or distributed synchronous…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
In the analysis of observational data in social sciences and businesses, it is difficult to obtain a "(quasi) single-source dataset" in which the variables of interest are simultaneously observed. Instead, multiple-source datasets are…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a…
Advances in sensing technology have made it possible to collect large volumes of high-dimensional time-series data. In fields like genetics and neuroscience, key questions concern whether directed relationships between variables can be…
We reconcile the two worlds of dense and sparse modeling by exploiting the positive aspects of both. We employ a factor model and assume {the dynamic of the factors is non-pervasive while} the idiosyncratic term follows a sparse vector…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
The focus of this work is on spatial variable selection for scalar-on-image regression. We propose a new class of Bayesian nonparametric models, soft-thresholded Gaussian processes and develop the efficient posterior computation algorithms.…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
This paper introduces sparse dynamic chain graph models for network inference in high dimensional non-Gaussian time series data. The proposed method parametrized by a precision matrix that encodes the intra time-slice conditional…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…