arXiv research

Study uniform consistency in nonparametric mixture models and mixed regression.

Uniform consistency proven for spatial distribution and depth estimators in any dimension.

New algorithm achieves strong consistency in binary non-uniform hypergraph classification.

The paper explores why a specific type of predictor works well in noisy data.

No algorithm outperforms uniform sampling in A/B testing.

We derive high-probability finite-sample uniform rates of consistency for $k$-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that $k$-NN regression adapts to an unknown lower intrinsic dimension automatically. We then apply the $k$-NN regression rates to establish new …

Spectral algorithm recovers community structure in sparse hypergraphs.

New method detects communities in hypergraphs by embedding them into a vector space.

Implementing $k$-NN classification using Gromov--Wasserstein distances

Counterexamples show failure of uniform laws of large numbers for subdifferentials.

New uniformity tester ensures consistent results across different samples.

Uniform convergence of interpolators proven for Gaussian data.

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …

Study uniform learnability of binary classification networks with communication.

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most first-order methods only guarantee an ergodic convergence rate, that is, the uniform…

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions indexed by a vector of parameters. A key step in the method of proof is to show the…

We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known error-variance, we define and study versions of the estimators when the error-varian…

MAS scores cluster size consistency from points, robust to label changes.

In 1976, Dodziuk and Patodi employed Whitney forms to define a combinatorial codifferential operator on cochains, and they raised the question whether it is consistent in the sense that for a smooth enough differential form the combinatorial codifferential of the associated cochain converges to the exterior codifferent…

The paper provides consistency results for KDE on manifolds with irregular kernels.

In this note, we mainly focus on the existence of pseudo-Einstein contact forms, an upper bound eigenvalue estimate for the CR Paneitz operator and its applications to the uniformization theorem for Sasakian space form in an embeddable closed strictly pseudoconvex CR 3-manifold. Firstly, the existence of pseudo-Einstei…

In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on partitioning weighted uniform hypergraphs---a problem often encountered in computer …

The paper proposes a uniformity regularization scheme to improve deep neural network transferability.

We propose a general framework for solving the group synchronization problem, where we focus on the setting of adversarial or uniform corruption and sufficiently small noise. Specifically, we apply a novel message passing procedure that uses cycle consistency information in order to estimate the corruption levels of gr…

Learning ReLU networks to high uniform accuracy requires exponentially many samples.

We introduce a new discrete system that arises from ellipsoidal billiards and is closely related to the double reflection nets. The system is defined on the lattice of a uniform honeycomb consisting of rectified hypercubes and cross polytopes. In the $2$-dimensional case, the lattice is regular and it incorporates dyna…

The paper provides bounds on the CDF of a variable under nonstationary conditions.

We consider a parabolic-like systems of differential equations involving geometrical quantities to examine uniformization theorems for two- and three-dimensional closed orientable manifolds. We find that in the two-dimensional case there is a simple gauge theoretic flow for a connection built from a Riemannian structur…

A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate scalings of graph parameters that provably lead to a well-defined limiting post…

This thesis relaxes assumptions for causal discovery, making methods applicable to more complex systems.

We give a condition which ensures that the Paneitz operator of an embedded three-dimensional CR manifold is nonnegative and has kernel consisting only of the CR pluriharmonic functions. Our condition requires uniform positivity of the Webster scalar curvature and the stability of the CR pluriharmonic functions for a re…

Selecting more uniformly distributed data improves training efficiency and performance.

The paper constructs noncompact hyperbolic surfaces with uniform spectral gaps using random graph models.

The paper defines Benoist-Hulin groups and explores their properties.

Community detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging sys…

Associated to each material body $\mathcal{B}$ there exists a groupoid $Ω\left( \mathcal{B} \right)$ consisting of all the material isomorphisms connecting the points of $\mathcal{B}$. The uniformity character of $\mathcal{B}$ is reflected in the properties of $Ω\left( \mathcal{B} \right)$: $\mathcal{B}$ is uniform if,…

Unified framework for robust clustering under various dissimilarity measures.

Develops Aleksandrov reflection for hyperbolic flows, proving convergence to umbilic surfaces.

We study collapsed manifolds with Ricci bounded covering geometry i.e., Ricci curvature is bounded below and the Riemannian universal cover is non-collapsed or consists of uniform Reifenberg points. Via Ricci flows' techniques, we partially extend the nilpotent structural results of Cheeger-Fukaya-Gromov, on collapsed …

We study the problem of nonparametric dependence detection. Many existing methods may suffer severe power loss due to non-uniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test of independence through the new framework of binary expansion statistics (BEStat…

Continuous representations have been widely adopted in recommender systems where a large number of entities are represented using embedding vectors. As the cardinality of the entities increases, the embedding components can easily contain millions of parameters and become the bottleneck in both storage and inference du…

We construct families of functions in involution for transverse Poisson structures at nilpotent elements of Lie-Poisson structures on simple Lie algebras by using the argument shift method. Examples show that these families contain completely integrable systems that consist of polynomial functions. We provide a uniform…

GADD accelerates uniform-rate discrete diffusion models by 2 orders of magnitude.

We generalize the setting of online clustering of bandits by allowing non-uniform distribution over user frequencies. A more efficient algorithm is proposed with simple set structures to represent clusters. We prove a regret bound for the new algorithm which is free of the minimal frequency over users. The experiments …

New method combines strengths of two PCL approaches without density ratio estimation.

We determine the asymptotic growth rate of the diameter of the random hyperbolic surfaces constructed by Brooks and Makover. This model consists of a uniform gluing of $2n$ hyperbolic ideal triangles along their sides followed by a compactification to get a random hyperbolic surface of genus roughly $n/2$. We show that…

UDM reparameterization improves language model generation.

Geometric interpretation improves VAE performance and robustness.