Related papers: Minimax Rate of Distribution Estimation on Unknown…

There has been a growing interest in statistical inference from data satisfying the so-called manifold hypothesis, assuming data points in the high-dimensional ambient space to lie in close vicinity of a submanifold of much lower dimension.…

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…

We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on Fefferman's solution to the geometric Whitney problem, our…

Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…

Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypothesis, which states that observed data lies on a…

We focus on the problem of manifold estimation: given a set of observations sampled close to some unknown submanifold $M$, one wants to recover information about the geometry of $M$. Minimax estimators which have been proposed so far all…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…

Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

We want to reconstruct a signal based on inhomogeneous data (the amount of data can vary strongly), using the model of regression with a random design. Our aim is to understand the consequences of inhomogeneity on the accuracy of estimation…

Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical…

A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

Generative networks have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that generative networks can generate high-dimensional complex data from a low-dimensional easy-to-sample…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

We study the approximate nearest neighbour method for cost-sensitive classification on low-dimensional manifolds embedded within a high-dimensional feature space. We determine the minimax learning rates for distributions on a smooth…

In recent years there has been increased interest in understanding the interplay between deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses on understanding the reasons why commonly-used DGMs succeed or…