Related papers: Faster Gaussian Summation: Theory and Experiment
A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Generation expansion planning (GEP) is a prominent example of capacity expansion problems in operations research. Being generally NP-hard, GEP optimization models can become intractable when nonconvex dynamics, time-coupling constraints,…
We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
We show that common choices of kernel functions for a highly accurate and massively scalable nearest-neighbour based GP regression model (GPnn: \cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as dataset-size $n$ increases.…
To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
Learning the kernel parameters for Gaussian processes is often the computational bottleneck in applications such as online learning, Bayesian optimization, or active learning. Amortizing parameter inference over different datasets is a…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
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…
A classical method for risk-sensitive nonlinear control is the iterative linear exponential quadratic Gaussian algorithm. We present its convergence analysis from a first-order optimization viewpoint. We identify the objective that the…
Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…
Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…
This paper introduces a general method to approximate the convolution of an arbitrary program with a Gaussian kernel. This process has the effect of smoothing out a program. Our compiler framework models intermediate values in the program…
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new…