Minimal Variance Model Aggregation: A principled, non-intrusive, and versatile integration of black box models

2024-09-25

AI Summary

This work addresses the limitations of existing black-box model ensembling approaches—namely, their reliance on model architecture and poor generalization. We propose Minimal Empirical Variance Aggregation (MEVA), a model-agnostic linear ensemble method that performs end-to-end optimization solely on model predictions. Its core innovation lies in replacing conventional error minimization with empirical variance minimization as the aggregation objective; we theoretically establish that this strategy yields superior statistical robustness under finite-sample regimes and unifies ensemble learning with general error estimation. MEVA requires no access to internal model parameters or gradients, making it compatible with diverse predictors—including machine learning models and numerical PDE solvers. Extensive experiments across data science and partial differential equation solving tasks demonstrate consistent improvements in both predictive accuracy and stability, validating MEVA’s generality and practical efficacy.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Whether deterministic or stochastic, models can be viewed as functions designed to approximate a specific quantity of interest. We introduce Minimal Empirical Variance Aggregation (MEVA), a data-driven framework that integrates predictions from various models, enhancing overall accuracy by leveraging the individual strengths of each. This non-intrusive, model-agnostic approach treats the contributing models as black boxes and accommodates outputs from diverse methodologies, including machine learning algorithms and traditional numerical solvers. We advocate for a point-wise linear aggregation process and consider two methods for optimizing this aggregate: Minimal Error Aggregation (MEA), which minimizes the prediction error, and Minimal Variance Aggregation (MVA), which focuses on reducing variance. We prove a theorem showing that MVA can be more robustly estimated from data than MEA, making MEVA superior to Minimal Empirical Error Aggregation (MEEA). Unlike MEEA, which interpolates target values directly, MEVA formulates aggregation as an error estimation problem, which can be performed using any backbone learning paradigm. We demonstrate the versatility and effectiveness of our framework across various applications, including data science and partial differential equations, illustrating its ability to significantly enhance both robustness and accuracy.

Problem

• Integrates predictions from diverse models to enhance accuracy.
• Minimizes variance in model aggregation for robust predictions.
• Applies to various fields like data science and differential equations.

Innovation

• Minimal Empirical Variance Aggregation (MEVA) framework
• Non-intrusive, model-agnostic black box integration
• Point-wise linear aggregation optimizing variance reduction