Bayesian Extreme Learning
Abstract: This paper presents a Bayesian extreme learning framework for analyzing high-dimensional datasets impacted by extreme events. By employing information-theoretic measures, the framework refines posterior distributions and incorporates a regularization term that opti- mizes the balance between model complexity and data fit. This approach reduces the risk of overfitting. Contributions include deriving convergence properties and establishing uni- versal approximation capabilities for continuous extreme value distributions. The empirical study utilizes diverse economic and financial sectors to examine extremities posed by the COVID-19 pandemic. The findings highlight the framework’s predictive accuracy compared to conventional statistical and machine learning techniques.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: Here's a summary of the major changes made to the manuscript based on reviewers feedback:
1) The entire manuscript has been rewritten to eliminate repetitions and unsupported claims. It now systematically aligns with themes of estimation and inference. The paper's structure has been reorganized to logically transition from theoretical foundations to practical applications, covering the principles, methods, challenges, and empirical analyses associated with the Bayesian extreme learning framework.
2) The abstract has been rewritten to simplify technical terms without compromising precision and highlight the contributions, including information-theoretic measures for refining posterior distributions and the inclusion of a regularization term to balance model complexity and data fit.
3) The distinction between the BEL model as both a statistical model and a computational method has been clarified. Definition and algorithm descriptions have been refined for clarity and precision.
4) Propositions and their proofs have been revised for mathematical rigor. This includes clearer explanations, properly formatted expressions, and a thorough illustration of assumptions used in proofs.
5) Each subsection now concludes with paragraphs that enhance the motivation behind theoretical findings, link the contributions to existing literature, and provide context to the integration of advanced statistical techniques such as sparsity-inducing priors and the handling of multimodality with Dirichlet Processes.
6) The empirical section has been divided to address the implementation and its application to real-world datasets separately. A comparative analysis with conventional statistical and machine learning methods is included to demonstrate the BEL model's efficacy, especially in handling extreme value distributions in economic and financial sectors.
Assigned Action Editor: ~Valentin_De_Bortoli1
Submission Number: 2155
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