Related papers: Lower bounds for oblivious subspace embeddings

We prove multi-pass streaming lower bounds for uniformity testing over a domain of size $2m$. The tester receives a stream of $n$ i.i.d. samples and must distinguish (i) the uniform distribution on $[2m]$ from (ii) a Paninski-style planted…

We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length $n$ are observed after passing it through a random $m \times n$ measurement matrix. We…

Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…

We study the problem of agnostically learning halfspaces which is defined by a fixed but unknown distribution $\mathcal{D}$ on $\mathbb{Q}^n\times \{\pm 1\}$. We define $\mathrm{Err}_{\mathrm{HALF}}(\mathcal{D})$ as the least error of a…

In open-set semi-supervised learning (OSSL), we consider unlabeled datasets that may contain unknown classes. Existing OSSL methods often use the softmax confidence for classifying data as in-distribution (ID) or out-of-distribution (OOD).…

We prove a half-space theorem for an ideal Scherk graph $\Sigma\subset M\times\mathbb R$ over a polygonal domain $D\subset M,$ where $M$ is a Hadamard surface whose curvature is bounded above by a negative constant. More precisely, we show…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

In the last decades, the necessity to process massive amounts of textual data fueled the development of compressed text indexes: data structures efficiently answering queries on a given text while occupying space proportional to the…

We prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy [Spherical dispersion with an application to polygonal approximation of curves, Anz. \"Osterreich. Akad. Wiss.…

Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…

Learning from data in the presence of outliers is a fundamental problem in statistics. In this work, we study robust statistics in the presence of overwhelming outliers for the fundamental problem of subspace recovery. Given a dataset where…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter---the total length of all pieces of their boundaries visible from above. We prove that if the centers…

Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes. We show that there exists a constant $C$ such that for every positive integers $a,b$ and a graph…

In 2013, Koldobsky posed the problem to find a constant $d_n$, depending only on the dimension $n$, such that for any origin-symmetric convex body $K\subset\mathbb{R}^n$ there exists an $(n-1)$-dimensional linear subspace…

Given a lower envelope in the form of an arbitrary sequence $u$, let $LSP(u, d)$ denote the maximum length of any subsequence of $u$ that can be realized as the lower envelope of a set of polynomials of degree at most $d$. Let $sp(m, d)$…

Low-density spreading non-orthogonal multiple-access (LDS-NOMA) is considered where $K$ single-antenna user-equipments (UEs) communicate with a base-station (BS) over $F$ fading sub-carriers. Each UE $k$ spreads its data symbols over…

Under a set of assumptions on a family of submanifolds $\subset {\mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform…

We present a PTAS for agnostically learning halfspaces w.r.t. the uniform distribution on the $d$ dimensional sphere. Namely, we show that for every $\mu>0$ there is an algorithm that runs in time $\mathrm{poly}(d,\frac{1}{\epsilon})$, and…

Let G = (V,E) be an n-vertex graph and M_d a d-vertex graph, for some constant d. Is M_d a subgraph of G? We consider this problem in a model where all n processes are connected to all other processes, and each message contains up to O(log…