Related papers: Optimal Bounds for Noisy Sorting
Preference alignment is pivotal for empowering large language models (LLMs) to generate helpful and harmless responses. However, the performance of preference alignment is highly sensitive to the prevalent noise in the preference data.…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…
The distinct elements problem is one of the fundamental problems in streaming algorithms --- given a stream of integers in the range $\{1,\ldots,n\}$, we wish to provide a $(1+\varepsilon)$ approximation to the number of distinct elements…
Sorting is a foundational problem in computer science that is typically employed on sequences or total orders. More recently, a more general form of sorting on partially ordered sets (or posets), where some pairs of elements are…
In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…
This paper considers the task of performing binary search under noisy decisions, focusing on the application of target area localization. In the presence of noise, the classical partitioning approach of binary search is prone to error…
We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…
We consider the problem of sequential decision making on random fields corrupted by noise. In this scenario, the decision maker observes a noisy version of the data, yet judged with respect to the clean data. In particular, we first…
Numerous studies have shown that label noise can lead to poor generalization performance, negatively affecting classification accuracy. Therefore, understanding the effectiveness of classifiers trained using deep neural networks in the…
We solve the dynamic Predecessor Problem with high probability (whp) in constant time, using only $n^{1+\delta}$ bits of memory, for any constant $\delta > 0$. The input keys are random wrt a wider class of the well studied and practically…
Consider the problem: we are given $n$ boxes, labeled $\{1,2,\ldots, n\}$ by an adversary, each containing a single number chosen from an unknown distribution; these $n$ distributions are not necessarily identical. We are also given an…
The 1-center clustering with outliers problem asks about identifying a prototypical robust statistic that approximates the location of a cluster of points. Given some constant $0 < \alpha < 1$ and $n$ points such that $\alpha n$ of them are…
We study maximum selection and sorting of $n$ numbers using pairwise comparators that output the larger of their two inputs if the inputs are more than a given threshold apart, and output an adversarially-chosen input otherwise. We consider…
Quantum multiparameter estimation involves estimating multiple parameters simultaneously and can be more precise than estimating them individually. Our interest here is to determine fundamental quantum limits to the achievable…
Binary search finds a given element in a sorted array with an optimal number of $\log n$ queries. However, binary search fails even when the array is only slightly disordered or access to its elements is subject to errors. We study the…
In this paper we study the classical problem of throughput maximization. In this problem we have a collection $J$ of $n$ jobs, each having a release time $r_j$, deadline $d_j$, and processing time $p_j$. They have to be scheduled…
In this paper, we consider the group testing problem with adaptive test designs and noisy outcomes. We propose a computationally efficient four-stage procedure with components including random binning, identification of bins containing…
In the online sorting problem, $n$ items are revealed one by one and have to be placed (immediately and irrevocably) into empty cells of a size-$n$ array. The goal is to minimize the sum of absolute differences between items in consecutive…