Related papers: Learning from Summarized Data: Gaussian Process Re…
Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…
Quantile regression is a powerful tool for inferring how covariates affect specific percentiles of the response distribution. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the…
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.…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
We propose a new framework for 2-D interpreting (features and samples) black-box machine learning models via a metamodeling technique, by which we study the output and input relationships of the underlying machine learning model. The…
Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…
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…
Recent work in scalable approximate Gaussian process regression has discussed a bias-variance-computation trade-off when estimating the log marginal likelihood. We suggest a method that adaptively selects the amount of computation to use…
Manifold learning methods are useful for high dimensional data analysis. Many of the existing methods produce a low dimensional representation that attempts to describe the intrinsic geometric structure of the original data. Typically, this…
We introduce constrained Gaussian process (CGP), a Gaussian process model for random functions that allows easy placement of mathematical constrains (e.g., non-negativity, monotonicity, etc) on its sample functions. CGP comes with…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
Understanding sub-cellular protein localisation is an essential component to analyse context specific protein function. Recent advances in quantitative mass-spectrometry (MS) have led to high resolution mapping of thousands of proteins to…
Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…
There are so many models in the literature that it is difficult for practitioners to decide which combinations are likely to be effective for a new task. This paper attempts to address this question by capturing relationships among…
Quasi-periodicity refers to a pattern in a function where it appears periodic but has evolving amplitudes over time. This is often the case in practical settings such as the modeling of case counts of infectious disease or the carbon…
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…
As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…