arXiv research

It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same…

New findings on boosting sample complexity and implications for hardcore theorem.

Let $S=Γ\backslash \mathbb{H}$ be a hyperbolic surface of finite topological type, such that the Fuchsian group $Γ\le \operatorname{PSL}_2(\mathbb{R})$ is non-elementary, and consider any generating set $\mathfrak S$ of $Γ$. When sampling by an $n$-step random walk in $π_1(S) \cong Γ$ with each step given by an element…

The paper studies how more data affects prediction risk in high-dimensional models.

DM improves self-supervised transfer learning by matching target distributions.

Relationships that exist between the classical, Shannon-type, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive method to determine the quantizing dimension in Zador's theorem is provided. A geom…

A theorem for debiasing machine learning with finite sample guarantees.

We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error pr…

Condorcet's Jury Theorem has been invoked for ensemble classifiers to indicate that the combination of many classifiers can have better predictive performance than a single classifier. Such a theoretical underpinning is unknown for consensus clustering. This article extends Condorcet's Jury Theorem to the mean partitio…

PARIS reduces imbalanced regression datasets by pruning uninformative samples.

We provide a new local class-purity theorem for Lipschitz continuous DNN classifiers. In addition, we discuss how to achieve classification margin for training samples. Finally, we describe how to compute margin p-values for test samples.

The study tightens bounds on binomial probabilities and minimums using KL-divergence.

Efficient inference method for adaptive experiments with tighter confidence sequences.

Proofs high-dimensional spectrum convergence of weighted sample covariance.

New model shows hierarchical proof structure helps theorem provers.

Develops a new inference method for split-sample estimators using multiple splits.

The paper identifies a 'small' set of functions containing Gaussian process samples.

This paper introduces sample-averaged Q-learning for better RL performance.

The Sampled Gaussian Mechanism's noise level decreases with larger subsampling rates, improving privacy-utility trade-offs.

UD-SGD analysis shows efficient sampling by a few agents can outperform others.

We introduce a method that uses the Cauchy-Crofton formula and a new curvature formula from integral geometry to reweight the sampling probabilities of Metropolis-within-Gibbs algorithms in order to increase their convergence speed. We consider algorithms that sample from a probability density conditioned on a manifold…

We show that stochastic interpolation flow maps are Lipschitz with a sharp constant.

Develops an online Gaussian process method that maintains convergence guarantees without sample complexity issues.

New theorem improves spectral gap for sampling from mixture distributions.

Unified view of LR and RP gradients explained via divergence theorem.

The paper establishes CLTs for Markov chains and improves sampling algorithms for heavy-tailed distributions.

This paper strengthens the central limit theorem for order statistics using relative entropy.

Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality reduction methods allow out-of-sample extensions, by which an embedding can be applied to observations not present in the training set. Appli…

Often noisy point clouds are given as an approximation of a particular compact set of interest. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets …

We propose a general yet simple theorem describing the convergence of SGD under the arbitrary sampling paradigm. Our theorem describes the convergence of an infinite array of variants of SGD, each of which is associated with a specific probability law governing the data selection rule used to form mini-batches. This is…

In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method. The connections between FS-RBSDEs and optimal stopping time problems are investig…

Study shows a central limit theorem for random coverings of manifolds with nilpotent groups.

A new approach models exploration in continuous-time RL using random measures.

We consider the problem of estimating $\mathbb{E} [f(U^1, \ldots, U^d)]$, where $(U^1, \ldots, U^d)$ denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving this kind of high-dimensional numerical integration problem. In the case of depende…

Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes network, then every unambiguous causal conclusion produced by a consistent method f…

We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of convergence of entropic OT for empirical measures. Our analysis improves exponentially o…

Conventional approaches of sampling signals follow the celebrated theorem of Nyquist and Shannon. Compressive sampling, introduced by Donoho, Romberg and Tao, is a new paradigm that goes against the conventional methods in data acquisition and provides a way of recovering signals using fewer samples than the traditiona…

Adaptive sampler improves recommendation for implicit feedback data.

The paper reviews advances in estimating and understanding optimal transport maps.

Estimates CDF over complex regions using normalizing flows.

Sharp concentration bounds for i.i.d. variables.

The paper strengthens the classical result of MLE convergence to a Gaussian distribution.

This paper studies binary classification problem associated with a family of loss functions called large-margin unified machines (LUM), which offers a natural bridge between distribution-based likelihood approaches and margin-based approaches. It also can overcome the so-called data piling issue of support vector machi…

Paper presents a new policy gradient theorem using weak derivatives for reinforcement learning.

New analysis improves sample complexity for vanilla policy gradient methods.

Paper introduces a neural network training algorithm for noisy data that achieves optimal parameters and replicates real-world behaviors.

The study tightens the sample complexity for learning nonparametric mixture components.

New insights into variational inference using Monte Carlo estimates.