New Upper Bound Method Advances Solutions for Maximum-Entropy Remote Sampling Problem
Researchers have developed a novel "hyper-scaled NLP bound" (hNLP) method to improve solutions for the maximum-entropy remote sampling problem (MERSP), which selects informative subsets of variables from larger datasets. The work builds on two upper-bounding methods from 25 years ago and establishes theoretical dominance results between them. This advancement could improve branch-and-bound algorithms used to solve moderate-sized instances of this optimization problem in machine learning and information theory.
The maximum-entropy remote sampling problem involves selecting a subset of random variables that maximizes information about unobservable target variables, assuming a joint Gaussian distribution with known covariance. The researchers propose the hyper-scaled NLP bound based on convex relaxation, which generalizes the previous complementary NLP bound and provides theoretical guarantees for when it strictly dominates earlier methods. A key innovation is the ability to handle rank-deficient covariance matrices under certain conditions, extending beyond the previous NLP bound's requirement for positive definite matrices. The work includes variable-fixing methodology for branch-and-bound algorithms and procedures for calculating hyper-scaling parameters. Numerical experiments on benchmark instances demonstrate the effectiveness of these approaches in advancing the algorithmic state-of-the-art for MERSP.
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- arXiv cs.LGCenter
The hyper-scaled NLP bound for maximum-entropy remote sampling
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