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This paper studies the problem of finding the exact ranking from noisy comparisons. A comparison over a set of $m$ items produces a noisy outcome about the most preferred item, and reveals some information about the ranking. By repeatedly…

Machine Learning · Computer Science 2021-07-30 Wenbo Ren , Jia Liu , Ness B. Shroff

In this paper we study functions with low influences on product probability spaces. The analysis of boolean functions with low influences has become a central problem in discrete Fourier analysis. It is motivated by fundamental questions…

Probability · Mathematics 2007-05-23 Elchanan Mossel , Ryan O'Donnell , Krzysztof Oleszkiewicz

Motivated by data-rich experiments in transcriptional regulation and sensory neuroscience, we consider the following general problem in statistical inference. When exposed to a high-dimensional signal S, a system of interest computes a…

Quantitative Methods · Quantitative Biology 2013-12-16 Justin B. Kinney , Gurinder S. Atwal

Noisy labels are commonly found in real-world data, which cause performance degradation of deep neural networks. Cleaning data manually is labour-intensive and time-consuming. Previous research mostly focuses on enhancing classification…

Machine Learning · Computer Science 2021-12-20 Chang Liu , Han Yu , Boyang Li , Zhiqi Shen , Zhanning Gao , Peiran Ren , Xuansong Xie , Lizhen Cui , Chunyan Miao

We provide a differentially private algorithm for hypothesis selection. Given samples from an unknown probability distribution $P$ and a set of $m$ probability distributions $\mathcal{H}$, the goal is to output, in a…

Data Structures and Algorithms · Computer Science 2021-01-05 Mark Bun , Gautam Kamath , Thomas Steinke , Zhiwei Steven Wu

Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…

Statistics Theory · Mathematics 2025-02-26 Atsutomo Yara , Yoshikazu Terada

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…

Machine Learning · Computer Science 2026-05-14 Yatin Dandi , Matteo Vilucchio , Luca Arnaboldi , Hugo Tabanelli , Florent Krzakala

We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability distribution $\nu = e^{-f}$ on $\mathbb{R}^n$. We prove a convergence guarantee in Kullback-Leibler (KL) divergence assuming $\nu$ satisfies a log-Sobolev…

Data Structures and Algorithms · Computer Science 2022-03-04 Santosh S. Vempala , Andre Wibisono

Knowledge distillation has emerged as a powerful technique for compressing large language models (LLMs) into efficient, deployable architectures while preserving their advanced capabilities. Recent advances in low-rank knowledge…

Machine Learning · Statistics 2026-03-25 Alberlucia Rafael Soarez , Daniel Kim , Mariana Costa , Alejandro Torre

We define tests of boolean functions which distinguish between linear (or quadratic) polynomials, and functions which are very far, in an appropriate sense, from these polynomials. The tests have optimal or nearly optimal trade-offs between…

Combinatorics · Mathematics 2007-05-23 Alex Samorodnitsky

We give a deterministic algorithm for approximately counting satisfying assignments of a degree-$d$ polynomial threshold function (PTF). Given a degree-$d$ input polynomial $p(x_1,\dots,x_n)$ over $R^n$ and a parameter $\epsilon> 0$, our…

Computational Complexity · Computer Science 2013-12-02 Anindya De , Rocco Servedio

We consider a multi-stage distributed detection scenario, where $n$ sensors and a fusion center (FC) are deployed to accomplish a binary hypothesis test. At each time stage, local sensors generate binary messages, assumed to be spatially…

Signal Processing · Electrical Eng. & Systems 2023-01-04 Guangyang Zeng , Xiaoqiang Ren , Junfeng Wu

Over the last decades, two distinct approaches have been instrumental to our understanding of the computational complexity of statistical estimation. The statistical physics literature predicts algorithmic hardness through local stability…

Statistics Theory · Mathematics 2026-03-23 Konstantinos Tsirkas , Leda Wang , Ilias Zadik

Provided an arbitrary nonintrusive load monitoring (NILM) algorithm, we seek bounds on the probability of distinguishing between scenarios, given an aggregate power consumption signal. We introduce a framework for studying a general NILM…

Applications · Statistics 2013-10-30 Roy Dong , Lillian Ratliff , Henrik Ohlsson , S. Shankar Sastry

Empirical causal claims depend on many analyst decisions, from selecting covariates to choosing estimators. Existing robustness tools summarize how results vary across these choices, but, to the best of our knowledge, do not answer:…

Methodology · Statistics 2026-05-05 Hoang Dang , Luan Pham , Minh Nguyen

In this paper, we introduce a new approach to proving the convergence of the Stochastic Approximation (SA) and the Stochastic Gradient Descent (SGD) algorithms. The new approach is based on a concept called GSLLN (Generalized Strong Law of…

Optimization and Control · Mathematics 2025-11-11 Rajeeva Laxman Karandikar , Bhamidi Visweswara Rao , Mathukumalli Vidyasagar

We initiate an investigation of node differential privacy for graphs in the local model of private data analysis. In our model, dubbed LNDP*, each node sees its own edge list and releases the output of a local randomizer on this input.…

Data Structures and Algorithms · Computer Science 2026-04-03 Sofya Raskhodnikova , Adam Smith , Connor Wagaman , Anatoly Zavyalov

Interpreting the inner workings of neural models is a key step in ensuring the robustness and trustworthiness of the models, but work on neural network interpretability typically faces a trade-off: either the models are too constrained to…

Computation and Language · Computer Science 2020-11-11 Phong Le , Willem Zuidema

Deep Metric Learning (DML) plays a critical role in various machine learning tasks. However, most existing deep metric learning methods with binary similarity are sensitive to noisy labels, which are widely present in real-world data. Since…

Computer Vision and Pattern Recognition · Computer Science 2021-11-02 Jiexi Yan , Lei Luo , Cheng Deng , Heng Huang

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Statistics Theory · Mathematics 2022-01-12 Antoine Godichon-Baggioni