Related papers: The Minimum Expectation Selection Problem

The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two $n\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone…

We give a constant factor polynomial time pseudo-approximation algorithm for min-sum clustering with or without outliers. The algorithm is allowed to exclude an arbitrarily small constant fraction of the points. For instance, we show how to…

We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…

Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in…

We consider the distinct elements problem, where the goal is to estimate the number of distinct colors in an urn containing $ k $ balls based on $n$ samples drawn with replacements. Based on discrete polynomial approximation and…

This paper considers the maximization of the expected maximum value of a portfolio of random variables subject to a budget constraint. We refer to this as the optimal college application problem. When each variable's cost, or each college's…

Motivated by crowd-sourcing applications, we consider a model where we have partial observations from a bivariate isotonic n x d matrix with an unknown permutation $\pi$ * acting on its rows. Focusing on the twin problems of recovering the…

In the best choice problem with random arrivals, an unknown number $n$ of rankable items arrive at times sampled from the uniform distribution. As is well known, a real-time player can ensure stopping at the overall best item with…

We consider election scenarios with incomplete information, a situation that arises often in practice. There are several models of incomplete information and accordingly, different notions of outcomes of such elections. In one well-studied…

Define Minimum Soapy Union (MinSU) as the following optimization problem: given a $k$-tuple $(X_1, X_2,..., X_k)$ of finite integer sets, find a $k$-tuple $(t_1, t_2,..., t_k)$ of integers that minimizes the cardinality of $(X_1 + t_1) \cup…

Sequential multi-class diagnosis, also known as multi-hypothesis testing, is a classical sequential decision problem with broad applications. However, the optimal solution remains, in general, unknown as the dynamic program suffers from the…

Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as…

We consider the problem: is the optimal expected total reward to reach a goal state in a partially observable Markov decision process (POMDP) below a given threshold? We tackle this -- generally undecidable -- problem by computing…

The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…

In this paper new complexity and approximation results on the robust versions of the representatives selection problem, under the scenario uncertainty representation, are provided, which extend the results obtained in the recent papers by…

We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…

Let $M$ be a real $r\times c$ matrix and let $k$ be a positive integer. In the column subset selection problem (CSSP), we need to minimize the quantity $\|M-SA\|$, where $A$ can be an arbitrary $k\times c$ matrix, and $S$ runs over all…

In this paper, we consider the optimal design of networked estimators to minimize the communication/measurement cost under the networked observability constraint. This problem is known as the minimum-cost networked estimation problem, which…

Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…