Related papers: Gaussian Process Regression for Maximum Entropy Di…

When constructing a Bayesian Machine Learning model, we might be faced with multiple different prior distributions and thus are required to properly consider them in a sensible manner in our model. While this situation is reasonably well…

In this paper, we propose a data based transformation for infinite-dimensional Gaussian processes and derive its limit theorem. For a classification problem, this transformation induces complete separation among the associated Gaussian…

Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local…

Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…

In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…

The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region…

Reconstructing 4D or 6D phase space distributions from 1D or 2D measurements is a challenging inverse problem encountered in particle accelerators. Entropy maximization is an established method to incorporate prior information in the…

We present a novel kernel over the space of probability measures based on the dual formulation of optimal regularized transport. We propose an Hilbertian embedding of the space of probabilities using their Sinkhorn potentials, which are…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…

Gaussian processes are a versatile probabilistic machine learning model whose effectiveness often depends on good hyperparameters, which are typically learned by maximising the marginal likelihood. In this work, we consider iterative…

Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing…

Model Predictive Control evolved as the state of the art paradigm for safety critical control tasks. Control-as-Inference approaches thereof model the constrained optimization problem as a probabilistic inference problem. The constraints…

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…

The pervasive presence spatial and size structure in biological populations challenges fundamental assumptions at the heart of continuum models of population dynamics based on mean densities (local or global) only. Individual-based models…

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…

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…

It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper…

We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…