Related papers: High-dimensional density estimation with tensorizi…

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…

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…

In this paper, we propose new learning algorithms for approximating high-dimensional functions using tree tensor networks in a least-squares setting. Given a dimension tree or architecture of the tensor network, we provide an algorithm that…

A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that…

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…

In this paper, we describe a method for estimating the joint probability density from data samples by assuming that the underlying distribution can be decomposed as a mixture of product densities with few mixture components. Prior works…

In this paper we introduce a method for nonparametric density estimation on geometric networks. We define fused density estimators as solutions to a total variation regularized maximum-likelihood density estimation problem. We provide…

The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant calculations. This work addresses this challenge by performing…

Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…

Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicability and well-known success, transport maps suffer from…

Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. However, it has been noted that maximizing the log-likelihood within an energy-based…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors…

For intelligent transportation systems and autonomous vehicles to operate safely and efficiently, they must reliably predict the future motion and trajectory of surrounding agents within complex traffic environments. At the same time, the…

In this paper, we present two multidimensional power flow formulations based on a fixed-point iteration (FPI) algorithm to efficiently solve hundreds of thousands of power flows in distribution systems. The presented algorithms are the base…

We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors…

Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…

In recent years, promising statistical modeling approaches to tensor data analysis have been rapidly developed. Traditional multivariate analysis tools, such as multivariate regression and discriminant analysis, are generalized from…

Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the…

We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical…