Related papers: Statistical Mechanical Analysis of Gaussian Proces…

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori…

Sensor-based sorting systems enable the physical separation of a material stream into two fractions. The sorting decision is based on the image data evaluation of the sensors used and is carried out using actuators. Various process…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…

Parameter estimation is a major challenge in computational modeling of biological processes. This is especially the case in image-based modeling where the inherently quantitative output of the model is measured against image data, which is…

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…

In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…

Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…

We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Sequential algorithms are popular for experimental design, enabling emulation, optimisation and inference to be efficiently performed. For most of these applications bespoke software has been developed, but the approach is general and many…

Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…

A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables…

Gaussian graphical regressions have emerged as a powerful approach for regressing the precision matrix of a Gaussian graphical model on covariates, which, unlike traditional Gaussian graphical models, can help determine how graphs are…

The modeling and simulation of dynamical systems is a necessary step for many control approaches. Using classical, parameter-based techniques for modeling of modern systems, e.g., soft robotics or human-robot interaction, is often…