Related papers: Gaussian Process Regression for Maximum Entropy Di…
When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…
We consider the problem of Gaussian multiplier bootstrap procedures for the $k$th largest statistics and functions of the top $k$ order statistics, which are commonly encountered in high-dimensional statistical inference. Such a problem has…
Differential entropy and log determinant of the covariance matrix of a multivariate Gaussian distribution have many applications in coding, communications, signal processing and statistical inference. In this paper we consider in the high…
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the…
We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior distribution, and the increase of the…
Traditionally, the Method of (Shannon-Kullback's) Relative Entropy Maximization (REM) is considered with linear moment constraints. In this work, the method is studied under frequency moment constraints which are non-linear in…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X in R^n in a polyhedron P in R^n, by solving a certain entropy maximization…
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on the Hellinger distance between the true posterior…
Gaussian process emulators of computationally expensive computer codes provide fast statistical approximations to model physical processes. The training of these surrogates depends on the set of design points chosen to run the simulator.…
We study a distributionally robust optimization formulation (i.e., a min-max game) for two representative problems in Bayesian nonparametric estimation: Gaussian process regression and, more generally, linear inverse problems. Our…
Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…
This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…
In this work an approximated path integral model describing the dynamics of a inextensible chain is presented. To this purpose, the nonlinear constraints which enforce the property of inextensibility of the chain are relaxed and are just…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
The entropy computation of Gaussian mixture distributions with a large number of components has a prohibitive computational complexity. In this paper, we propose a novel approach exploiting the sphere decoding concept to bound and…
The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…