Related papers: Query complexity of heavy hitter estimation

We consider the problem of selecting a subset of alternatives given noisy evaluations of the relative strength of different alternatives. We wish to select a k-subset (for a given k) that provides a maximum likelihood estimate for one of…

A conditional sampling oracle for a probability distribution D returns samples from the conditional distribution of D restricted to a specified subset of the domain. A recent line of work (Chakraborty et al. 2013 and Cannone et al. 2014)…

Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…

We consider the problem of finding the $k^{th}$ highest element in a totally ordered set of $n$ elements (select), and partitioning a totally ordered set into the top $k$ and bottom $n-k$ elements (partition) using pairwise comparisons.…

We study quantum algorithms that are given access to trusted and untrusted quantum witnesses. We establish strong limitations of such algorithms, via new techniques based on Laurent polynomials (i.e., polynomials with positive and negative…

This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…

Consider the Hitting Set problem where, for a given universe $\mathcal{X} = \left\{ 1, ... , n \right\}$ and a collection of subsets $\mathcal{S}_1, ... , \mathcal{S}_m$, one seeks to identify the smallest subset of $\mathcal{X}$ which has…

Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…

One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database.…

Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…

Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…

In many applications that involve processing high-dimensional data, it is important to identify a small set of entities that account for a significant fraction of detections. Rather than formalize this as a clustering problem, in which all…

We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…

We revisit the noisy binary search model of Karp and Kleinberg, in which we have $n$ coins with unknown probabilities $p_i$ that we can flip. The coins are sorted by increasing $p_i$, and we would like to find where the probability crosses…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

We consider PAC-learning a good item from $k$-subsetwise feedback information sampled from a Plackett-Luce probability model, with instance-dependent sample complexity performance. In the setting where subsets of a fixed size can be tested…

Consider a generalization of the classical binary search problem in linearly sorted data to the graph-theoretic setting. The goal is to design an adaptive query algorithm, called a strategy, that identifies an initially unknown target…

Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…

Span programs are a model of computation that have been used to design quantum algorithms, mainly in the query model. For any decision problem, there exists a span program that leads to an algorithm with optimal quantum query complexity,…

The weight decision problem, which requires to determine the Hamming weight of a given binary string, is a natural and important problem, with applications in cryptanalysis, coding theory, fault-tolerant circuit design and so on. In…