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.

翻译：在统计学习与深度学习的现代训练与推理流程中，线性系统求解作为内层循环被反复调用。然而，当求解需要重复多次或仅需部分信息（如选定分量或线性泛函）时，高精度确定性求解器的计算成本可能过高。本文提出将**蒙特卡洛加速**作为该场景下的实用替代方案，通过统一的数学表述（诺依曼级数表示、前向/伴随估计器及Halton式序列校正）系统综述随机游走估计器与序列残差校正方法，并将其扩展至超定/最小二乘问题，同时建立其与数据增强中IRLS式更新及EM/ECM算法的联系。在实证研究中，我们对比了雅可比迭代、高斯-赛德尔迭代与朴素蒙特卡洛方法、精确序列蒙特卡洛方法及子采样序列变体，通过展示不同规模下的计算特性，阐明了蒙特卡洛加速在何种计算体系下能成为现代统计学习流程中具有赋能价值的计算原语。