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We prove that for every $D \in \N$, and large enough constant $d \in \N$, with high probability over the choice of $G \sim G(n,d/n)$, the \Erdos-\Renyi random graph distribution, the canonical degree $2D$ Sum-of-Squares relaxation fails to…

Data Structures and Algorithms · Computer Science 2024-06-27 Pravesh Kothari , Aaron Potechin , Jeff Xu

We revisit the classic problem of estimating the degree distribution moments of an undirected graph. Consider an undirected graph $G=(V,E)$ with $n$ vertices, and define (for $s > 0$) $\mu_s = \frac{1}{n}\cdot\sum_{v \in V} d^s_v$. Our aim…

Data Structures and Algorithms · Computer Science 2017-02-17 Talya Eden , Dana Ron , C. Seshadhri

Current out-of-distribution detection approaches usually present special requirements (e.g., collecting outlier data and hyperparameter validation) and produce side effects (e.g., classification accuracy drop and slow/inefficient…

Machine Learning · Computer Science 2022-04-06 David Macêdo , Teresa Ludermir

Designing the sensing architecture for large-scale spatio-temporal systems is hard when accuracy requirements are specified but sensor models are uncertain or unavailable. Classical design treats sensor placement and estimation…

Information Theory · Computer Science 2026-05-13 Raktim Bhattacharya

The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…

Quantum Physics · Physics 2026-04-29 Bartosz Regula , Ludovico Lami , Nilanjana Datta

We consider the problem of testing whether a graph's degree distribution belongs to a particular family, such as poisson or scale-free, given that we only observe a sampled subgraph. In particular, we focus on induced subgraph sampling, a…

Methodology · Statistics 2017-10-16 Robert Garrard

We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…

Machine Learning · Statistics 2023-06-02 Elan Rosenfeld , Saurabh Garg

We introduce an S.o.S hierarchy of lower bounds for a polynomial optimization problem whose constraint is expressed as a matrix polynomial semidefinite inequality. Our approach involves utilizing a penalty function framework to directly…

Optimization and Control · Mathematics 2025-10-20 Hoang Anh Tran , Kim-Chuan Toh

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

Score-based Generative Models (SGMs) aim to sample from a target distribution by learning score functions using samples perturbed by Gaussian noise. Existing convergence bounds for SGMs in the W2-distance rely on stringent assumptions about…

Machine Learning · Statistics 2025-12-12 Marta Gentiloni-Silveri , Antonio Ocello

As deep learning methods form a critical part in commercially important applications such as autonomous driving and medical diagnostics, it is important to reliably detect out-of-distribution (OOD) inputs while employing these algorithms.…

Machine Learning · Computer Science 2018-09-12 Apoorv Vyas , Nataraj Jammalamadaka , Xia Zhu , Dipankar Das , Bharat Kaul , Theodore L. Willke

Out-of-distribution (OOD) detection approaches usually present special requirements (e.g., hyperparameter validation, collection of outlier data) and produce side effects (e.g., classification accuracy drop, slower energy-inefficient…

Machine Learning · Computer Science 2021-09-28 David Macêdo , Tsang Ing Ren , Cleber Zanchettin , Adriano L. I. Oliveira , Teresa Ludermir

We conjecture that every $n$-vertex graph of minimum degree at least $\frac k2$ and maximum degree at least $2k$ contains all trees with $k$ edges as subgraphs. We prove an approximate version of this conjecture for trees of bounded degree…

Combinatorics · Mathematics 2018-08-29 Guido Besomi , Matías Pavez-Signé , Maya Stein

In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common…

Optimization and Control · Mathematics 2017-02-09 N. H. Chieu , J. W. Feng , W. Gao , G. Li , D. Wu

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

Statistics Theory · Mathematics 2022-02-17 Bhaswar B. Bhattacharya , Rajarshi Mukherjee

We show that the outside equation of a bounded elliptically symmetric lens (ESL) exhibits a pseudo-caustic that arises from a branch cut. A pseudo-caustic is a curve in the source plane across which the number of images changes by one. The…

Earth and Planetary Astrophysics · Physics 2010-06-11 Sun Hong Rhie

This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis}…

Machine Learning · Computer Science 2015-10-20 Tengyu Ma , Avi Wigderson

Pseudo-labels are widely employed in weakly supervised 3D segmentation tasks where only sparse ground-truth labels are available for learning. Existing methods often rely on empirical label selection strategies, such as confidence…

Computer Vision and Pattern Recognition · Computer Science 2023-10-23 Liyao Tang , Zhe Chen , Shanshan Zhao , Chaoyue Wang , Dacheng Tao

Say that we are given samples from a distribution $\psi$ over an $n$-dimensional space. We expect or desire $\psi$ to behave like a product distribution (or a $k$-wise independent distribution over its marginals for small $k$). We propose…

Data Structures and Algorithms · Computer Science 2020-11-16 Parikshit Gopalan , Roie Levin , Udi Wieder

This paper studies the variance dichotomy in continuous simulation optimization (CSO). Existing literature shows a sharp contrast between deterministic CSO and stochastic CSO, with convergence rates in stochastic settings appearing…

Optimization and Control · Mathematics 2026-04-16 Jianzhong Du , L. Jeff Hong