arXiv research

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

Sharp inequality between TV and Hellinger distances for Gaussian mixtures.

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

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

Parallel sampling for smooth distributions with fast convergence.

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

Stable GFlowNets prevent loss spikes and mode collapse in training.

Flow matching KL divergence bound derived for smooth distributions.

We analyze the performance of the Tukey median estimator under total variation (TV) distance corruptions. Previous results show that under Huber's additive corruption model, the breakdown point is 1/3 for high-dimensional halfspace-symmetric distributions. We show that under TV corruptions, the breakdown point reduces …

Robustly clusters mixtures of Gaussians even with outliers.

New algorithm reduces TV-denoising to adaptive online learning.

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

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

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…

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

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

Two new deterministic offspring selection methods reduce statistical distance in SMC and pMCMC.

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

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

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

New method for tensor completion using nonconvex dual total variation.

New algorithms help machines forget old data efficiently.

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

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

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…

Diffusion models adapt to low-dimensional data regardless of coefficient choices.

Estimates BV functions from noisy data using Voronoi diagrams.

New algorithm samples from log-concave distributions with high accuracy in polynomial time.

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 …

New model for shape graph registration with partial matching constraints.

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…

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

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

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

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…

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

Optimal locally private hypothesis selection with interactive rounds.

New geometric insights reveal properties of adversarial training problems.

Optimal pre-processing reduces disparate impact by minimizing total variation distance.

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…

We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the distances themselves. We use this ordinal information along with the low-dimensionality…

Diffusion models achieve high-quality samples from complex high-dimensional Gaussian mixtures without scaling with dimension.

Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multiplicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the…

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…