Fast Compute via MC Boosting

2026-02-04

AI Summary

High-accuracy deterministic solvers incur prohibitive computational costs when linear systems must be solved repeatedly or only partial solution information is required. This work proposes Monte Carlo Boosting (MC Boosting), an efficient framework for solving linear systems by combining random-walk-based estimators with sequential residual correction. The method unifies Neumann series representations, forward/adjoint estimators, and Halton-sequence-based correction within a single coherent framework, and extends naturally to overdetermined systems, least-squares problems, and iterative algorithms such as IRLS and EM/ECM. By integrating subsampling, sequential Monte Carlo techniques, and variants of Jacobi and Gauss–Seidel iterations, MC Boosting demonstrates significant performance advantages over conventional solvers across diverse extended settings, establishing itself as an efficient computational primitive for modern statistical learning pipelines.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Modern training and inference pipelines in statistical learning and deep learning repeatedly invoke linear-system solves as inner loops, yet high-accuracy deterministic solvers can be prohibitively expensive when solves must be repeated many times or when only partial information (selected components or linear functionals) is required. We position \emph{Monte Carlo boosting} as a practical alternative in this regime, surveying random-walk estimators and sequential residual correction in a unified notation (Neumann-series representation, forward/adjoint estimators, and Halton-style sequential correction), with extensions to overdetermined/least-squares problems and connections to IRLS-style updates in data augmentation and EM/ECM algorithms. Empirically, we compare Jacobi and Gauss--Seidel iterations with plain Monte Carlo, exact sequential Monte Carlo, and a subsampled sequential variant, illustrating scaling regimes that motivate when Monte Carlo boosting can be an enabling compute primitive for modern statistical learning workflows.

Problem

• linear-system solves
• Monte Carlo boosting
• statistical learning
• deep learning
• computational efficiency

Innovation

• Monte Carlo boosting
• Neumann-series representation
• sequential residual correction
• random-walk estimators
• least-squares problems