Related papers: Functional Integration on Constrained Function Spa…

Some well-known examples of constrained quantum systems commonly quantized via Feynman path integrals are re-examined using the notion of conditional integrators introduced in [1]. The examples yield some new perspectives on old results. As…

We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the…

In 1948 Feynman introduced functional integration. Long ago the problematic aspect of measures in the space of fields was overcome with the introduction of volume elements in Probability Space, leading to stochastic formulations. More…

The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…

We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…

This article revisits the problem of Bayesian shape-restricted inference in the light of a recently developed approximate Gaussian process that admits an equivalent formulation of the shape constraints in terms of the basis coefficients. We…

We are often interested in identifying the feasible subset of a decision space under multiple constraints to permit effective design exploration. If determining feasibility required computationally expensive simulations, the cost of…

Estimation of parameters that obey specific constraints is crucial in statistics and machine learning; for example, when parameters are required to satisfy boundedness, monotonicity, or linear inequalities. Traditional approaches impose…

We introduce a novel generative formulation of deep probabilistic models implementing "soft" constraints on their function dynamics. In particular, we develop a flexible methodological framework where the modeled functions and derivatives…

In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…

In this paper, we study integral functionals defined on spaces of functions with values on general (non-separable) Banach spaces. We introduce a new class of integrands and multifunctions for which we obtain measurable selection results.…

We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible, the general idea is first illustrated on the simplest case: a…

Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…

We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated,…

Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…

During the last decades, many methods for the analysis of functional data including classification methods have been developed. Nonetheless, there are issues that have not been adressed satisfactorily by currently available methods, as, for…