A Correction of Pseudo Log-Likelihood Method

Shi Feng; Nuoya Xiong; Zhijie Zhang; Wei Chen

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arXiv · 2403.18127

A Correction of Pseudo Log-Likelihood Method

Shi Feng·Nuoya Xiong·Zhijie Zhang·Wei Chen

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Abstract

Pseudo log-likelihood is a type of maximum likelihood estimation (MLE) method used in various fields including contextual bandits, influence maximization of social networks, and causal bandits. However, in previous literature \citep{li2017provably, zhang2022online, xiong2022combinatorial, feng2023combinatorial1, feng2023combinatorial2}, the log-likelihood function may not be bounded, which may result in the algorithm they proposed not well-defined. In this paper, we give a counterexample that the maximum pseudo log-likelihood estimation fails and then provide a solution to correct the algorithms in \citep{li2017provably, zhang2022online, xiong2022combinatorial, feng2023combinatorial1, feng2023combinatorial2}.

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Shi Feng, Nuoya Xiong, Zhijie Zhang, Wei Chen. 2024-03-26. A Correction of Pseudo Log-Likelihood Method. https://arxiv.org/abs/2403.18127

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