Measuring the Likelihood of Numerical Constraints

Authors: Marco Console, Matthias Hofer, Leonid Libkin

IJCAI 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical Our goal is to measure the likelihood of the satisfaction of numerical constraints in the absence of prior information. We study expressive constraints... We show that for constraints on n variables, the proper way to define such a measure is as the limit... We prove that the existence of such a limit is closely related to the notion of o-minimality from model theory... We look at computing and approximating such likelihoods for order and linear constraints, and prove an impossibility result for approximating with multiplicative error. However, as the likelihood is a number between 0 and 1, an approximation scheme with additive error is acceptable, and we give it for arbitrary linear constraints.
Researcher Affiliation Academia Marco Console , Matthias Hofer and Leonid Libkin School of Informatics, University of Edinburgh {mconsole, mhofer, libkin}@inf.ed.ac.uk
Pseudocode Yes Algorithm 1 apx-mes
Open Source Code No The paper does not contain any statement about open-source code availability nor does it provide a link.
Open Datasets No The paper is theoretical, focused on mathematical definitions, proofs, and algorithm design. It does not involve any empirical training on datasets.
Dataset Splits No The paper is theoretical and does not involve empirical evaluation with data splits.
Hardware Specification No The paper is purely theoretical and does not report on any empirical experiments or the hardware used to conduct them.
Software Dependencies No The paper is theoretical and focuses on mathematical concepts and algorithm design. It does not list specific software dependencies with version numbers required for implementation or replication.
Experiment Setup No The paper is theoretical and does not describe any empirical experiments, thus no experimental setup details like hyperparameters are provided.