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We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

We propose a practical Bayesian optimization method using Gaussian process regression, of which the marginal likelihood is maximized where the number of model selection steps is guided by a pre-defined threshold. Since Bayesian optimization…

In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for $L_{2,1}$ norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

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…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…

We introduce a new interpretation of sparse variational approximations for Gaussian processes using inducing points, which can lead to more scalable algorithms than previous methods. It is based on decomposing a Gaussian process as a sum of…

We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the…

Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…

Hard optimization problems are often approached by finding approximate solutions. Here, we highlight the concept of proportional sampling and discuss how it can be used to improve the performance of stochastic algorithms for optimization.…

We propose a Gaussian variational inference framework for the motion planning problem. In this framework, motion planning is formulated as an optimization over the distribution of the trajectories to approximate the desired trajectory…

Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…

The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable.…

This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…

This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…

Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

Distributed inference/estimation in Bayesian framework in the context of sensor networks has recently received much attention due to its broad applicability. The variational Bayesian (VB) algorithm is a technique for approximating…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…