Related papers: Learning Partitions with Optimal Query and Round C…
We study the problem of clustering a set of items from binary user feedback. Such a problem arises in crowdsourcing platforms solving large-scale labeling tasks with minimal effort put on the users. For example, in some of the recent…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
We analyze the clustering problem through a flexible probabilistic model that aims to identify an optimal partition on the sample X 1 , ..., X n. We perform exact clustering with high probability using a convex semidefinite estimator that…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
Rounding has proven to be a fundamental tool in theoretical computer science. By observing that rounding and partitioning of $\mathbb{R}^d$ are equivalent, we introduce the following natural partition problem which we call the {\em secluded…
In the oracle identification problem, we are given oracle access to an unknown N-bit string x promised to belong to a known set C of size M and our task is to identify x. We present a quantum algorithm for the problem that is optimal in its…
In this paper, we consider the problem of noiseless non-adaptive group testing under the for-each recovery guarantee, also known as probabilistic group testing. In the case of $n$ items and $k$ defectives, we provide an algorithm attaining…
Motivated by applications in crowdsourced entity resolution in database, signed edge prediction in social networks and correlation clustering, Mazumdar and Saha [NIPS 2017] proposed an elegant theoretical model for studying clustering with…
The element distinctness problem is the problem of determining whether the elements of a list are distinct, that is, if $x=(x_1,...,x_N)$ is a list with $N$ elements, we ask whether the elements of $x$ are distinct or not. The solution in a…
We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the $[\Theta(\log n), \Theta(n)]$ region, in two settings. We present one…
Over the past decade, a long line of research has investigated the distributed complexity landscape of locally checkable labeling (LCL) problems on bounded-degree graphs, culminating in an almost-complete classification on general graphs…
Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time within $\Theta(n\log{n})$ in the…
We consider the problem of quantitative group testing (QGT), where the goal is to recover a sparse binary vector from aggregate subset-sum queries: each query selects a subset of indices and returns the sum of those entries.…
We study $k$-means clustering in a semi-supervised setting. Given an oracle that returns whether two given points belong to the same cluster in a fixed optimal clustering, we investigate the following question: how many oracle queries are…
An algorithm for structured database searching is presented and used to solve the set partition problem. O(n) oracle calls are required in order to obtain a solution, but the probability that this solution is optimal decreases exponentially…
We introduce an algorithm that, given n objects, learns a similarity matrix over all n^2 pairs, from crowdsourced data alone. The algorithm samples responses to adaptively chosen triplet-based relative-similarity queries. Each query has the…
We first consider the problem of learning $k$-parities in the on-line mistake-bound model: given a hidden vector $x \in \{0,1\}^n$ with $|x|=k$ and a sequence of "questions" $a_1, a_2, ...\in \{0,1\}^n$, where the algorithm must reply to…
We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-vector product (matvec) queries of the form $x \rightarrow Ax$ and $x \rightarrow A^Tx$. This…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…