Related papers: Parameterizations for Gradient-based Markov Chain …
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
The efficiency of Markov Chain Monte Carlo (MCMC) depends on how the underlying geometry of the problem is taken into account. For distributions with strongly varying curvature, Riemannian metrics help in efficient exploration of the target…
Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
Finding effective ways to exploit parallel computing to accelerate Markov chain Monte Carlo methods is an important problem in Bayesian computation and related disciplines. In this paper, we consider the zeroth-order setting where the…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
Multi-task learning, which optimizes performance across multiple tasks, is inherently a multi-objective optimization problem. Various algorithms are developed to provide discrete trade-off solutions on the Pareto front. Recently, continuous…
Convergence diagnosis for Markov chain Monte Carlo is a matter of fundamental importance in computational statistics: it determines the resources allocated to a particular sampling problem and influences the practitioner's view of the…
A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel…
Manifold-valued parameters routinely arise in modern statistical applications such as in medical imaging, robotics, and computer vision, to name a few. While traditional Bayesian approaches are applicable to such settings by considering an…
Independent sampling of orthogonal polynomial bases via Monte Carlo is of interest for uncertainty quantification of models, using Polynomial Chaos (PC) expansions. It is known that bounding the spectral radius of a random matrix consisting…
Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…
Parametric Markov chains occur quite naturally in various applications: they can be used for a conservative analysis of probabilistic systems (no matter how the parameter is chosen, the system works to specification); they can be used to…
Stochastic gradient Markov chain Monte Carlo (MCMC) algorithms have received much attention in Bayesian computing for big data problems, but they are only applicable to a small class of problems for which the parameter space has a fixed…
We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…
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…
Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…