Related papers: The Power of an Example: Hidden Set Size Approxima…
This paper studies the sample complexity of searching over multiple populations. We consider a large number of populations, each corresponding to either distribution P0 or P1. The goal of the search problem studied here is to find one…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
This paper addresses the problem of estimating the containment and similarity between two sets using only random samples from each set, without relying on sketches of full sets. The study introduces a binomial model for predicting the…
A canonical desideratum for prediction problems is that performance guarantees should hold not just on average over the population, but also for meaningful subpopulations within the overall population. But what constitutes a meaningful…
Subsampling from a large data set is useful in many supervised learning contexts to provide a global view of the data based on only a fraction of the observations. Diverse (or space-filling) subsampling is an appealing subsampling approach…
In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
Plant-capture is a variant of classical capture-recapture methods used to estimate the size of a population. In this method, decoys referred to as "plants" are introduced into the population in order to estimate the capture probability. The…
One of the core applications of machine learning to knowledge discovery consists on building a function (a hypothesis) from a given amount of data (for instance a decision tree or a neural network) such that we can use it afterwards to…
We investigate distribution testing with access to non-adaptive conditional samples. In the conditional sampling model, the algorithm is given the following access to a distribution: it submits a query set $S$ to an oracle, which returns a…
In the stochastic set cover problem (Grandoni et al., FOCS '08), we are given a collection $\mathcal{S}$ of $m$ sets over a universe $\mathcal{U}$ of size $N$, and a distribution $D$ over elements of $\mathcal{U}$. The algorithm draws $n$…
We consider the basic problem of learning an unknown partition of $n$ elements into at most $k$ sets using simple queries that reveal information about a small subset of elements. Our starting point is the well-studied pairwise same-set…
Capture-recapture methods aim to estimate the size of a closed population on the basis of multiple incomplete enumerations of individuals. In many applications, the individual probability of being recorded is heterogeneous in the…
A high number of discrete optimization problems, including Vertex Cover, Set Cover or Feedback Vertex Set, can be unified into the class of covering problems. Several of them were shown to be inapproximable by deterministic algorithms. This…
Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…
Adapting the final sample size of a trial to the evidence accruing during the trial is a natural way to address planning uncertainty. Designs with adaptive sample size need to account for their optional stopping to guarantee strict type-I…
In this paper, we develop an exact method for the determination of the minimum sample size for estimating the proportion of a finite population with prescribed margin of error and confidence level. By characterizing the behavior of the…
We are given $n$ balls and an unknown coloring of them with two colors. Our goal is to find a ball that belongs to the larger color class, or show that the color classes have the same size. We can ask sets of $k$ balls as queries, and the…