Related papers: $k$-Cut: A Simple Approximately-Uniform Method for…
Randomness extraction is an essential post-processing step in practical quantum cryptography systems. When statistical fluctuations are taken into consideration, the requirement of large input data size could heavily penalise the speed and…
We show how to find a minimum weight loop cutset in a Bayesian network with high probability. Finding such a loop cutset is the first step in the method of conditioning for inference. Our randomized algorithm for finding a loop cutset…
We consider the problem of subset selection for $\ell_{p}$ subspace approximation, i.e., given $n$ points in $d$ dimensions, we need to pick a small, representative subset of the given points such that its span gives $(1+\epsilon)$…
Modern statistical analysis often encounters datasets with large sizes. For these datasets, conventional estimation methods can hardly be used immediately because practitioners often suffer from limited computational resources. In most…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
Random sampling of graph partitions under constraints has become a popular tool for evaluating legislative redistricting plans. Analysts detect partisan gerrymandering by comparing a proposed redistricting plan with an ensemble of sampled…
The $k$-of-$n$ testing problem involves performing $n$ independent tests sequentially, in order to determine whether/not at least $k$ tests pass. The objective is to minimize the expected cost of testing. This is a fundamental and…
We present the first feasible method for sampling a dynamic data stream with deletions, where the sample consists of pairs $(k,C_k)$ of a value $k$ and its exact total count $C_k$. Our algorithms are for both Strict Turnstile data streams…
This note describes an algorithm for enumerating all the elements in a finite set based on uniformly random sampling from the set. This algorithm can be used for enumeration by fair sampling with quantum annealing. Our algorithm is based on…
Stratified sampling is a fast and simple method to generate point sets with uniform distribution in hypercubes. However, for the most common paraxial stratfication it has the prominent drawback that the number of sampled points in n…
The single transferable vote (STV) is a system of preferential proportional voting employed in multi-seat elections. Each ballot cast by a voter is a (potentially partial) ranking over a set of candidates. The margin of victory, or simply…
We propose a new algorithm for k-means clustering in a distributed setting, where the data is distributed across many machines, and a coordinator communicates with these machines to calculate the output clustering. Our algorithm guarantees…
This paper considers elections in which voters choose one candidate each, independently according to known probability distributions. A candidate receiving a strict majority (absolute or relative, depending on the version) wins. After the…
This paper proposes a sampling based planning algorithm to control autonomous vehicles. We propose an improved Rapidly-exploring Random Tree which includes the definition of K- nearest points and propose a two-stage sampling strategy to…
We study the problem of evaluating the excess risk of large-scale empirical risk minimization under the square loss. Leveraging the idea of wild refitting and resampling, we assume only black-box access to the training algorithm and develop…
Quantile computation is a core primitive in large-scale data analytics. In Spark, practitioners typically rely on the Greenwald-Khanna (GK) Sketch, an approximate method. When exact quantiles are required, the default option is an expensive…
An electoral quick count is a statistical procedure whose main objective is to obtain a relatively small but representative sample of all the polling stations in a certain election, and to measure the uncertainty about the final result…
We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering,…
An easy-to-implement form of the Metropolis Algorithm is described which, unlike most standard techniques, is well suited to sampling from multi-modal distributions on spaces with moderate numbers of dimensions (order ten) in environments…
Determinantal Point Processes (DPPs) are elegant probabilistic models of repulsion and diversity over discrete sets of items. But their applicability to large sets is hindered by expensive cubic-complexity matrix operations for basic tasks…