arXiv research

New algorithm identifies good arms with fewer samples when thresholds are close.

Study on discrete Okounkov bodies and their applications.

Study on detecting and recovering hidden dense cycles in random graphs.

Prediction markets and crypto options show persistent pricing gaps.

Detection of dense cycles in graphs reveals a gap between easy detection and hard recovery.

The paper analyzes RLVR's training dynamics, proving convergence depends on aligning update direction with Gradient Gap.

Statistical-computational gap found in aligning multiple Gaussian graphs.

New insights into binary perceptron reveal phase transitions and algorithmic thresholds.

New local-search methods close the gap in sparse tensor PCA.

Characterizes optimal reconstruction error in high-dimensional Gaussian mixtures.

This paper connects ultrametric overlap gap properties to parametric RDT for symmetric binary perceptrons.

Random projections improve classifier generalization without needing to choose the best threshold.

Study potential computational gaps in symmetric binary perceptrons using fl-RDT.

Noisy Max and Sparse Vector are selection algorithms for differential privacy and serve as building blocks for more complex algorithms. In this paper we show that both algorithms can release additional information for free (i.e., at no additional privacy cost). Noisy Max is used to return the approximate maximizer amon…

This paper develops several average-case reduction techniques to show new hardness results for three central high-dimensional statistics problems, implying a statistical-computational gap induced by robustness, a detection-recovery gap and a universality principle for these gaps. A main feature of our approach is to ma…

The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple non-overlapping) signal submatrix…

The use of M-estimators in generalized linear regression models in high dimensional settings requires risk minimization with hard $L_0$ constraints. Of the known methods, the class of projected gradient descent (also known as iterative hard thresholding (IHT)) methods is known to offer the fastest and most scalable sol…

We study the spectral gap of the Erdős--Rényi random graph through the connectivity threshold. In particular, we show that for any fixed $δ> 0$ if $p \ge \frac{(1/2 + δ) \log n}{n},$ then the normalized graph Laplacian of an Erdős--Rényi graph has all of its nonzero eigenvalues tightly concentrated around $1$. We est…

The stochastic block model is one of the oldest and most ubiquitous models for studying clustering and community detection. In an exciting sequence of developments, motivated by deep but non-rigorous ideas from statistical physics, Decelle et al. conjectured a sharp threshold for when community detection is possible in…

Class imbalance presents a major hurdle in the application of data mining methods. A common practice to deal with it is to create ensembles of classifiers that learn from resampled balanced data. For example, bagged decision trees combined with random undersampling (RUS) or the synthetic minority oversampling technique…

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m \rightarrow \infty$ and $α= m/n$ stays finite. Using exact but non-rigorous methods from statistical physics, we determine the critical value of $α$ and the distance between…

Graphical Lasso (GL) is a popular method for learning the structure of an undirected graphical model, which is based on an $l_1$ regularization technique. The objective of this paper is to compare the computationally-heavy GL technique with a numerically-cheap heuristic method that is based on simply thresholding the s…

The paper studies how arm selection in a bandit problem changes with shape constraints.

SoftAD improves classification accuracy with less fine-tuning and fewer computational costs.

Adversarial training leads to large generalization gap, decomposed into bias and variance.

Study quantifies performance gap between tensor and matrix-based approaches in nested matrix-tensor model.

Paper proves first non-trivial PTF testing lower bounds for NGCA.

We relax demographic parity in regression by enforcing parity at quantile levels and score thresholds.

This paper studies the problem of adaptively sampling from K distributions (arms) in order to identify the largest gap between any two adjacent means. We call this the MaxGap-bandit problem. This problem arises naturally in approximate ranking, noisy sorting, outlier detection, and top-arm identification in bandits. Th…

The availability of large microarray data has led to a growing interest in biclustering methods in the past decade. Several algorithms have been proposed to identify subsets of genes and conditions according to different similarity measures and under varying constraints. In this paper we focus on the exclusive row bicl…

New algorithm detects communities near KS threshold with optimal rate, even in noisy conditions.

The study proves a gap theorem for CAT(0) spaces with a constant below 1/(6√π).

The stochastic block model (SBM) is a random graph model with different group of vertices connecting differently. It is widely employed as a canonical model to study clustering and community detection, and provides a fertile ground to study the information-theoretic and computational tradeoffs that arise in combinatori…

CSA fills a gap in RLVR-trained LLM deployment by providing anytime-valid selective risk control.

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, in which a prominent eigenvector is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughout the sciences. Baik, Ben Arous and Pé…

Study optimal policies under budget and coverage constraints.

We carry out a large-scale empirical data analysis to examine the efficiency of the so-called pairs trading. On the basis of relevant three thresholds, namely, starting, profit-taking, and stop-loss for the `first-passage process' of the spread (gap) between two highly-correlated stocks, we construct an effective strat…

QAOA matches classical tensor power iteration in spiked tensor model recovery.

We analyse the learning performance of Distributed Gradient Descent in the context of multi-agent decentralised non-parametric regression with the square loss function when i.i.d. samples are assigned to agents. We show that if agents hold sufficiently many samples with respect to the network size, then Distributed Gra…

Learning β for k-SAT with one sample is hard, especially for low degrees.

Estimating the leading principal components of data, assuming they are sparse, is a central task in modern high-dimensional statistics. Many algorithms were developed for this sparse PCA problem, from simple diagonal thresholding to sophisticated semidefinite programming (SDP) methods. A key theoretical question is und…

New insights into balancing reward and fairness in stochastic MAB.

In cellular systems, the user equipment (UE) can request a change in the frequency band when its rate drops below a threshold on the current band. The UE is then instructed by the base station (BS) to measure the quality of candidate bands, which requires a measurement gap in the data transmission, thus lowering the da…

One of the most challenging problems in kernel online learning is to bound the model size and to promote the model sparsity. Sparse models not only improve computation and memory usage, but also enhance the generalization capacity, a principle that concurs with the law of parsimony. However, inappropriate sparsity mode…

The paper studies inference in hypergraph β-models with multiple layers.

Constant Proportion Portfolio Insurance (CPPI) is a strategy designed to give participation in a risky asset while protecting the invested capital. Some gap risk due to extreme events is often kept by the issuer of the product: a put option on the CPPI strategy is included in the product. In this paper we present a new…

DNF-Net tackles tabular data challenges with neural architecture.

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