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The contextual bandit framework is widely used to solve sequential optimization problems where the reward of each decision depends on auxiliary context variables. In settings such as medicine, business, and engineering, the decision maker…

Gaussian processes are a fundamental statistical tool used in a wide range of applications. In the spatio-temporal setting, several families of covariance functions exist to accommodate a wide variety of dependence structures arising in…

We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the…

Gaussian process is one of the most popular non-parametric Bayesian methodologies for modeling the regression problem. It is completely determined by its mean and covariance functions. And its linear property makes it relatively…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…

Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same…

Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…

Optimizing wheat variety selection for high performance in different environmental conditions is critical for reliable food production and stable incomes for growers. We employ a statistical machine learning framework utilizing Gaussian…

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where…

Gaussian processes (GP) are powerful tools for probabilistic modeling purposes. They can be used to define prior distributions over latent functions in hierarchical Bayesian models. The prior over functions is defined implicitly by the mean…

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…

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance…

A simple and widely adopted approach to extend Gaussian processes (GPs) to multiple outputs is to model each output as a linear combination of a collection of shared, unobserved latent GPs. An issue with this approach is choosing the number…

We introduce a novel way to combine boosting with Gaussian process and mixed effects models. This allows for relaxing, first, the zero or linearity assumption for the prior mean function in Gaussian process and grouped random effects models…

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…

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…