TY - JOUR

T1 - Efficient optimal Kolmogorov approximation of random variables

AU - Cohen, Liat

AU - Grinshpoun, Tal

AU - Weiss, Gera

N1 - Publisher Copyright:
© 2024 Elsevier B.V.

PY - 2024/4

Y1 - 2024/4

N2 - Discrete random variables are essential ingredients in various artificial intelligence problems. These include the estimation of the probability of missing the deadline in a series-parallel schedule and the assignment of suppliers to tasks in a project in a manner that maximizes the probability of meeting the overall project deadline. The solving of such problems involves repetitive operations, such as summation, over random variables. However, these computations are NP-hard. Therefore, we explore techniques and methods for approximating random variables with a given support size and minimal Kolmogorov distance. We examine both the general problem of approximating a random variable and a one-sided version in which over-approximation is allowed but not under-approximation. We propose several algorithms and evaluate their performance through computational complexity analysis and empirical evaluation. All the presented algorithms are optimal in the sense that given an input random variable and a requested support size, they return a new approximated random variable with the requested support size and minimal Kolmogorov distance from the input random variable. Our approximation algorithms offer useful estimations of probabilities in situations where exact computations are not feasible due to NP-hardness complexity.

AB - Discrete random variables are essential ingredients in various artificial intelligence problems. These include the estimation of the probability of missing the deadline in a series-parallel schedule and the assignment of suppliers to tasks in a project in a manner that maximizes the probability of meeting the overall project deadline. The solving of such problems involves repetitive operations, such as summation, over random variables. However, these computations are NP-hard. Therefore, we explore techniques and methods for approximating random variables with a given support size and minimal Kolmogorov distance. We examine both the general problem of approximating a random variable and a one-sided version in which over-approximation is allowed but not under-approximation. We propose several algorithms and evaluate their performance through computational complexity analysis and empirical evaluation. All the presented algorithms are optimal in the sense that given an input random variable and a requested support size, they return a new approximated random variable with the requested support size and minimal Kolmogorov distance from the input random variable. Our approximation algorithms offer useful estimations of probabilities in situations where exact computations are not feasible due to NP-hardness complexity.

KW - Data compression

KW - Deadline constraints

KW - Discrete random variables

KW - Kolmogorov approximation

KW - One-sided approximation

KW - Statistical distance measures

KW - Support size reduction

KW - Task scheduling

UR - http://www.scopus.com/inward/record.url?scp=85183942089&partnerID=8YFLogxK

U2 - 10.1016/j.artint.2024.104086

DO - 10.1016/j.artint.2024.104086

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AN - SCOPUS:85183942089

SN - 0004-3702

VL - 329

JO - Artificial Intelligence

JF - Artificial Intelligence

M1 - 104086

ER -