Related papers: Barely Biased Learning for Gaussian Process Regres…

Knot-based, sparse Gaussian processes have enjoyed considerable success as scalable approximations to full Gaussian processes. Problems can occur, however, when knot selection is done by optimizing the marginal likelihood. For example, the…

Bayesian inference offers benefits over maximum likelihood, but it also comes with computational costs. Computing the posterior is typically intractable, as is marginalizing that posterior to form the posterior predictive distribution. In…

The pseudo-marginal algorithm is a popular variant of the Metropolis--Hastings scheme which allows us to sample asymptotically from a target probability density $\pi$, when we are only able to estimate an unnormalized version of $\pi$…

When signals are measured through physical sensors, they are perturbed by noise. To reduce noise, low-pass filters are commonly employed in order to attenuate high frequency components in the incoming signal, regardless if they come from…

The accuracy of Bayesian inference can be negatively affected by the use of inaccurate forward models. In the case of gravitational-wave inference, accurate but computationally expensive waveform models are sometimes substituted with faster…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

Tuning parameters in supervised learning problems are often estimated by cross-validation. The minimum value of the cross-validation error can be biased downward as an estimate of the test error at that same value of the tuning parameter.…

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…

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…

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we…

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…

Probabilistic models are often trained by maximum likelihood, which corresponds to minimizing a specific f-divergence between the model and data distribution. In light of recent successes in training Generative Adversarial Networks,…

Gaussian processes regression models are an appealing machine learning method as they learn expressive non-linear models from exemplar data with minimal parameter tuning and estimate both the mean and covariance of unseen points. However,…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

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…

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done…

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…

Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…

Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…

Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…