Related papers: Query complexity of heavy hitter estimation

We introduce a structured quantum search algorithm that leverages entanglement maps and a fixed-point method to minimize oracle query complexity in unsorted datasets. By partitioning qubits into rows based on their entanglement order, the…

Motivated by crowdsourced computation, peer-grading, and recommendation systems, Braverman, Mao and Weinberg [STOC'16] studied the \emph{query} and \emph{round} complexity of fundamental problems such as finding the maximum (\textsc{max}),…

We study the query complexity of computing a function f:{0,1}^n-->R_+ in expectation. This requires the algorithm on input x to output a nonnegative random variable whose expectation equals f(x), using as few queries to the input x as…

We define and study a new type of quantum oracle, the quantum conditional oracle, which provides oracle access to the conditional probabilities associated with an underlying distribution. Amongst other properties, we (a) obtain speed-ups…

We apply information-based complexity analysis to support vector machine (SVM) algorithms, with the goal of a comprehensive continuous algorithmic analysis of such algorithms. This involves complexity measures in which some higher order…

Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…

We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…

Semi-supervised active clustering (SSAC) utilizes the knowledge of a domain expert to cluster data points by interactively making pairwise "same-cluster" queries. However, it is impractical to ask human oracles to answer every pairwise…

This paper deals with recovering an unknown vector $\theta$ from the noisy data $Y=A\theta+\sigma\xi$, where $A$ is a known $(m\times n)$-matrix and $\xi$ is a white Gaussian noise. It is assumed that $n$ is large and $A$ may be severely…

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

Let $P$ be a set of $m$ points in ${\mathbb R}^2$, let $\Sigma$ be a set of $n$ semi-algebraic sets of constant complexity in ${\mathbb R}^2$, let $(S,+)$ be a semigroup, and let $w: P \rightarrow S$ be a weight function on the points of…

Given a vector of probability distributions, or arms, each of which can be sampled independently, we consider the problem of identifying the partition to which this vector belongs from a finitely partitioned universe of such vector of…

While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with…

Uncertain, or probabilistic, graphs have been increasingly used to represent noisy linked data in many emerging applications, and have recently attracted the attention of the database research community. A fundamental problem on uncertain…

We revisit one of the most basic and widely applicable techniques in the literature of differential privacy - the sparse vector technique [Dwork et al., STOC 2009]. This simple algorithm privately tests whether the value of a given query on…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…

Estimating the difficulty of a dataset typically involves comparing state-of-the-art models to humans; the bigger the performance gap, the harder the dataset is said to be. However, this comparison provides little understanding of how…

We consider the task of estimating a high-dimensional directed acyclic graph, given observations from a linear structural equation model with arbitrary noise distribution. By exploiting properties of common random graphs, we develop a new…