arXiv research

New method relaxes TV distance for two-sample testing without distributional assumptions.

Sharp inequality between TV and Hellinger distances for Gaussian mixtures.

New algorithm reduces TV-denoising to adaptive online learning.

Study on kinetic Langevin diffusions and their couplings, showing subtle TV bounds and new non-Markovian couplings.

New method for tensor completion using nonconvex dual total variation.

RFM uses tangent vector fields to match data on manifolds, analyzing TV convergence for Euler discretization.

Paper proposes a method to estimate total variation distance for synthetic data fidelity.

New algorithms help machines forget old data efficiently.

Estimates BV functions from noisy data using Voronoi diagrams.

Stable GFlowNets prevent loss spikes and mode collapse in training.

The paper examines how to test if two learning algorithms produce similar outcomes.

Flow matching KL divergence bound derived for smooth distributions.

Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\ell_1$ minimization and nuclear norm minimization are…

Parallel sampling for smooth distributions with fast convergence.

Decision trees and shallow neural networks have different geometric complexities, impacting their interpretability and accuracy.

A generalized additive model (GAM, Hastie and Tibshirani (1987)) is a nonparametric model by the sum of univariate functions with respect to each explanatory variable, i.e., $f({\mathbf x}) = \sum f_j(x_j)$, where $x_j\in\mathbb{R}$ is $j$-th component of a sample ${\mathbf x}\in \mathbb{R}^p$. In this paper, we introd…

This paper accelerates TV regularization algorithms by unrolling proximal gradient descent.

Estimates TV distance between autoregressive models under different access models.

Improved sampling from high-dimensional Gaussians using smoothed scores.

Unified analysis of MPLE for Ising models with bounded operator norm or infinity norm.

Graphs with non-negative Ollivier-Ricci curvature cannot be expanders.

Tukey median performance analyzed under TV corruptions.

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an…

Paper studies statistical properties of DP data synthesis algorithms based on Bayesian networks.

This work improves the Euler method for masked diffusion models, providing tighter convergence guarantees.

This paper improves non-asymptotic bounds for denoising diffusions, focusing on the Ornstein-Uhlenbeck process.

The paper sets sample complexity bounds for learning high-dimensional simplices in noisy data.

Robustly clusters mixtures of Gaussians even with outliers.

We study \emph{TV regularization}, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for $\ell_p$-norm TV. The most important among these is $\ell_1$-norm TV, for whose prox-operator we present a new geometric analysis which unveils a …

Study sample complexity of robust binary hypothesis testing under different contamination models.

Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. A remarkable result due to Yatracos shows that this problem is tractable in the following sense: there exists an algorithm that use…

This paper deals with continuity preservation when minimizing generalized total variation with a $L^2$ fidelity term or a Dirichlet boundary condition. We extend several recent results in the two cases, mainly by showing comparison principles for the prescribed mean curvature problem satisfied by the level-sets of such…

New framework robustly handles outliers in Wasserstein DRO for better decision-making.

Optimal algorithm for LQR control with improved regret bound.

The total variation (TV) penalty, as many other analysis-sparsity problems, does not lead to separable factors or a proximal operatorwith a closed-form expression, such as soft thresholding for the $\ell\_1$ penalty. As a result, in a variational formulation of an inverse problem or statisticallearning estimation, it l…

The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited…

Paper tackles Byzantine attacks in distributed learning with a new ADMM method.

Estimating the level set of a signal from measurements is a task that arises in a variety of fields, including medical imaging, astronomy, and digital elevation mapping. Motivated by scenarios where accurate and complete measurements of the signal may not available, we examine here a simple procedure for estimating the…

Improves diffusion models by controlling total variance and signal-to-noise-ratio.

We propose and analyze a method for semi-supervised learning from partially-labeled network-structured data. Our approach is based on a graph signal recovery interpretation under a clustering hypothesis that labels of data points belonging to the same well-connected subset (cluster) are similar valued. This lends natur…

New algorithms minimize dynamic regret for strongly convex losses.

Polynomial-time algorithm learns high-dimensional halfspaces without labels.

This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using …

This paper analyzes discrete diffusion models, deriving convergence bounds for their generated samples.

Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, the interpretability of PCA remains limited. However, in neuroimaging, it is essential to uncove…

This work improves the convergence theory of diffusion models for generating samples from complex distributions.

Langevin dynamics fails to produce accurate samples even with small score function errors.

Optimal locally private hypothesis selection with interactive rounds.