Bayesian Extreme Learning
Abstract: This paper introduces a Bayesian extreme learning (BEL) model for analyzing high di- mensional datasets characterized by extreme values. The model synthesizes elements from information theory, Bayesian inference, machine learning, and extreme value theory. Conver- gence properties of the BEL model are established by declining Kullback-Leibler divergence between consecutive posterior distributions as the sample size grows. The model’s capa- bility to isolate extreme values is demonstrated by increasing entropy. Additionally, the paper validates the regularization optimality, where the optimal parameter configuration effectively minimizes the divergence from a specified reference distribution. The paper also shows the model’s proficiency in achieving near-optimal information extraction and its uni- versal approximation ability for continuous extreme value distributions across a range of tolerance levels. The model’s robustness and versatility are illustrated through examples, simulations, and applications, underscoring its potential utility in statistical learning within high-dimensional datasets.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Valentin_De_Bortoli1
Submission Number: 2155
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