Related papers: Constructive Universal High-Dimensional Distributi…
We study how well generative adversarial networks (GAN) learn probability distributions from finite samples by analyzing the convergence rates of these models. Our analysis is based on a new oracle inequality that decomposes the estimation…
In this paper, we analyze the scalability of a recent Wasserstein-distance approach for training stochastic neural networks (SNNs) to reconstruct multidimensional random field models. We prove a generalization error bound for reconstructing…
We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels…
In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…
We present a fully constructive analysis of deep ReLU neural networks for classification and function approximation tasks. First, we prove that any dataset with $N$ distinct points in $\mathbb{R}^d$ and $M$ output classes can be exactly…
This paper investigates the ability of generative networks to convert their input noise distributions into other distributions. Firstly, we demonstrate a construction that allows ReLU networks to increase the dimensionality of their noise…
Object density reconstruction from projections containing scattered radiation and noise is of critical importance in many applications. Existing scatter correction and density reconstruction methods may not provide the high accuracy needed…
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…
This paper explores the problem of generative modeling, aiming to simulate diverse examples from an unknown distribution based on observed examples. While recent studies have focused on quantifying the statistical precision of popular…
We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local…
This work addresses two fundamental limitations in neural network approximation theory. We demonstrate that a three-dimensional network architecture enables a significantly more efficient representation of sawtooth functions, which serves…
Given any deep fully connected neural network, initialized with random Gaussian parameters, we bound from above the quadratic Wasserstein distance between its output distribution and a suitable Gaussian process. Our explicit inequalities…
Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…
The problem of estimating the probability distribution of labels has been widely studied as a label distribution learning (LDL) problem, whose applications include age estimation, emotion analysis, and semantic segmentation. We propose a…
Deep neural networks often generalize well despite heavy over-parameterization, challenging classical parameter-based analyses. We study generalization from a representation-centric perspective and analyze how the geometry of learned…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
The efficacy of deep neural networks is heavily reliant on the design of non-linear activation functions, yet existing approaches often struggle to balance optimization stability with computational efficiency. While piecewise linear…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…