Related papers: Low-rank tensor reconstruction of concentrated den…
Recently, there has been a growing interest in efficient numerical algorithms based on tensor networks and low-rank techniques to approximate high-dimensional functions and solutions to high-dimensional PDEs. In this paper, we propose a new…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
We consider the problem of estimating the uncertainty in statistical inverse problems using Bayesian inference. When the probability density of the noise and the prior are Gaussian, the solution of such a statistical inverse problem is also…
The reconstruction of the structure of biological tissue using electromyographic data is a non-invasive imaging method with diverse medical applications. Mathematically, this process is an inverse problem. Furthermore, electromyographic…
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…
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 paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing…
We present an optimal transport framework for performing regression when both the covariate and the response are probability distributions on a compact Euclidean subset $\Omega\subset\mathbb{R}^d$, where $d>1$. Extending beyond compactly…
This paper presents a light-weight, high-quality texture synthesis algorithm that easily generalizes to other applications such as style transfer and texture mixing. We represent texture features through the deep neural activation vectors…
We develop a methodology for the construction of a Hessian representation of Monte Carlo sets of parton distributions, based on the use of a subset of the Monte Carlo PDF replicas as an unbiased linear basis, and of a genetic algorithm for…
This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank…
We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…
Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, we propose a solution to this problem by using a family of Rotation-based Iterative…
Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond. Monotone triangular transport…
Bayesian inference for doubly intractable distributions is challenging because they include intractable terms, which are functions of parameters of interest. Although several alternatives have been developed for such models, they are…
This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color images…