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Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian…
The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…
This paper develops a slice sampler for Bayesian linear regression models with arbitrary priors. The new sampler has two advantages over current approaches. One, it is faster than many custom implementations that rely on auxiliary latent…
Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…
In this paper, a quantum algorithm based on gaussian process regression model is proposed. The proposed quantum algorithm consists of three sub-algorithms. One is the first quantum subalgorithm to efficiently generate mean predictor. The…
In this paper, we investigate a class of approximate Gaussian processes (GP) obtained by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a dependent Gaussian prior distribution.…
Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…
Recently, a so-called E-MS algorithm was developed for model selection in the presence of missing data. Specifically, it performs the Expectation step (E step) and Model Selection step (MS step) alternately to find the minimum point of the…
In this paper we propose a generalization of a class of Gaussian Semiparametric Estimators (GSE) of the fractional differencing parameter for long-range dependent multivariate time series. We generalize a known GSE-type estimator by…
Gaussian processes provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…
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…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be…
Gaussian Boson Sampling (GBS) is a promising candidate for demonstrating quantum computational advantage and can be applied to solving graph-related problems. In this work, we propose Markov chain Monte Carlo-based algorithms to sample from…
We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…
Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources. Key to applying Gaussian process models is the availability of well-developed…
Gaussian Boson Sampling (GBS) is a recently developed paradigm of quantum computing consisting of sending a Gaussian state through a linear interferometer and then counting the number of photons in each output mode. When the system encodes…
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…