Related papers: $k$-Cut: A Simple Approximately-Uniform Method for…
Consider the fundamental problem of drawing a simple random sample of size k without replacement from [n] := {1, . . . , n}. Although a number of classical algorithms exist for this problem, we construct algorithms that are even simpler,…
We give efficient algorithms for volume sampling, i.e., for picking $k$-subsets of the rows of any given matrix with probabilities proportional to the squared volumes of the simplices defined by them and the origin (or the squared volumes…
We propose a sampling scheme suitable for reducing a data set prior to selecting a hypothesis with minimum empirical risk. The sampling only considers a subset of the ultimate (unknown) hypothesis set, but can nonetheless guarantee that the…
Slice sampling is an efficient Markov Chain Monte Carlo algorithm to sample from an unnormalized density with acceptance ratio always $1$. However, when the variable to sample is unbounded, its "stepping-out" heuristic works only locally,…
The shrinking rank method is a variation of slice sampling that is efficient at sampling from multivariate distributions with highly correlated parameters. It requires that the gradient of the log-density be computable. At each individual…
Chain-of-thought (CoT) reasoning with self-consistency improves performance by aggregating multiple sampled reasoning paths. In this setting, correctness is no longer tied to a single reasoning trace but to the aggregation rule over a pool…
Finding outlying elements in probability distributions can be a hard problem. Taking a real example from Voting Rights Act enforcement, we consider the problem of maximizing the number of simultaneous majority-minority districts in a…
The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good subset. We formulate…
We consider elections where the voters come one at a time, in a streaming fashion, and devise space-efficient algorithms which identify an approximate winning committee with respect to common multiwinner proportional representation voting…
There are many sources of error in counting votes: the apparent winner might not be the rightful winner. Hand tallies of the votes in a random sample of precincts can be used to test the hypothesis that a full manual recount would find a…
We consider a multi-pivot QuickSort algorithm using $K\in\mathbb{N}$ pivot elements to partition a nonsorted list into $K+1$ sublists in order to proceed recursively on these sublists. For the partitioning stage, various strategies are in…
We provide approximation algorithms for two problems, known as NECKLACE SPLITTING and $\epsilon$-CONSENSUS SPLITTING. In the problem $\epsilon$-CONSENSUS SPLITTING, there are $n$ non-atomic probability measures on the interval $[0, 1]$ and…
We study the use of sampling for efficiently mining the top-K frequent itemsets of cardinality at most w. To this purpose, we define an approximation to the top-K frequent itemsets to be a family of itemsets which includes (resp., excludes)…
Drawing a random sample of ballots to conduct a risk-limiting audit generally requires knowing how the ballots cast in an election are organized into groups, for instance, how many containers of ballots there are in all and how many ballots…
The Count-Min sketch is an important and well-studied data summarization method. It allows one to estimate the count of any item in a stream using a small, fixed size data sketch. However, the accuracy of the sketch depends on…
We provide practical, efficient, and nonparametric methods for auditing the fairness of deployed classification and regression models. Whereas previous work relies on a fixed-sample size, our methods are sequential and allow for the…
The margin of victory of an election is a useful measure to capture the robustness of an election outcome. It also plays a crucial role in determining the sample size of various algorithms in post election audit, polling etc. In this work,…
In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…
Statistical inference is often simplified by sample-splitting. This simplification comes at the cost of the introduction of randomness not native to the data. We propose a simple procedure for sequentially aggregating statistics constructed…
In this paper we introduce a new sampling algorithm which has the potential to be adopted as a universal replacement to the Metropolis--Hastings algorithm. It is related to the slice sampler, and motivated by an algorithm which is…