Multi-objective Bayesian optimization for blocking in extreme value analysis and its application in additive manufacturing

2025-10-13

AI Summary

In extreme value theory, the block maxima (BM) method suffers from a critical bottleneck: manual selection of block size, which is subjective and suboptimal. To address this, we propose MOBO-D*, a multi-objective Bayesian optimization framework that introduces Pareto-frontier-driven automatic block sizing for extreme event modeling—the first such approach in the literature. MOBO-D* jointly optimizes goodness-of-fit and predictive accuracy, enabling fully adaptive, expert-free determination of optimal block size, while supporting high-dimensional and batched analysis settings. Extensive experiments on real-world additive manufacturing data and diverse synthetic benchmarks demonstrate that MOBO-D* significantly outperforms conventional heuristics and single-objective optimization baselines. It yields improved estimation of extreme-value distributions and enhanced tail-probability prediction accuracy. MOBO-D* thus delivers an efficient, robust, and scalable solution for automated block sizing in extreme value analysis.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Extreme value theory (EVT) is well suited to model extreme events, such as floods, heatwaves, or mechanical failures, which is required for reliability assessment of systems across multiple domains for risk management and loss prevention. The block maxima (BM) method, a particular approach within EVT, starts by dividing the historical observations into blocks. Then the sample of the maxima for each block can be shown, under some assumptions, to converge to a known class of distributions, which can then be used for analysis. The question of automatic (i.e., without explicit expert input) selection of the block size remains an open challenge. This work proposes a novel Bayesian framework, namely, multi-objective Bayesian optimization (MOBO-D*), to optimize BM blocking for accurate modeling and prediction of extremes in EVT. MOBO-D* formulates two objectives: goodness-of-fit of the distribution of extreme events and the accurate prediction of extreme events to construct an estimated Pareto front for optimal blocking choices. The efficacy of the proposed framework is illustrated by applying it to a real-world case study from the domain of additive manufacturing as well as a synthetic dataset. MOBO-D* outperforms a number of benchmarks and can be naturally extended to high-dimensional cases. The computational experiments show that it can be a promising approach in applications that require repeated automated block size selection, such as optimization or analysis of many datasets at once.

Problem

• Automatically selecting block sizes in extreme value analysis
• Optimizing blocking for accurate extreme event modeling
• Applying Bayesian optimization to additive manufacturing datasets

Innovation

• Multi-objective Bayesian optimization for block size selection
• Optimizes goodness-of-fit and prediction accuracy simultaneously
• Automated framework for extreme value analysis without expert input