用矩阵运算加速大二值数据集的互信息计算，提速最高达5万倍。
Fast Mutual Information Computation for Large Binary Datasets
- 将传统逐对计算转为向量化矩阵操作，实现批量处理
- 在最大数据集上计算速度提升最高50,000倍
- 适合高维数据中的基因组、自然语言等场景研究者
互信息（Mutual Information, MI）是一种强大的统计度量，用于量化随机变量之间的共享信息，在基因组学、自然语言处理和网络科学等高维数据分析中尤为关键。然而，对于大规模数据集，传统的两两计算方式导致计算成本过高。本文提出一种基于矩阵的算法，通过向量化操作和优化的矩阵计算，将传统的逐对计算转变为批量矩阵运算，实现了所有变量对之间的高效互信息计算。实验结果表明，在最优实现下，最大数据集上的计算时间最多可缩短50,000倍，尤其在使用硬件优化框架时效果显著。该方法有望突破互信息在数据驱动研究中的计算瓶颈，拓展其应用范围。
原文摘要 · Abstract (English)
Mutual Information (MI) is a powerful statistical measure that quantifies shared information between random variables, particularly valuable in high-dimensional data analysis across fields like genomics, natural language processing, and network science. However, computing MI becomes computationally prohibitive for large datasets where it is typically required a pairwise computational approach where each column is compared to others. This work introduces a matrix-based algorithm that accelerates MI computation by leveraging vectorized operations and optimized matrix calculations. By transforming traditional pairwise computational approaches into bulk matrix operations, the proposed method enables efficient MI calculation across all variable pairs. Experimental results demonstrate significant performance improvements, with computation times reduced up to 50,000 times in the largest dataset using optimized implementations, particularly when utilizing hardware optimized frameworks. The approach promises to expand MI's applicability in data-driven research by overcoming previous computational limitations.
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