In this article, we strengthen the proof methods of some previously weakly
consistent variants of random forests into strongly consistent proof methods,
and improve the data utilization of these variants, in order to obtain better
theoretical properties and experimental performance. In addition, based on the
multinomial random forest (MRF) and Bernoulli random forest (BRF), we propose a
data-driven multinomial random forest (DMRF) algorithm, which has lower
complexity than MRF and higher complexity than BRF while satisfying strong
consistency. It has better performance in classification and regression
problems than previous RF variants that only satisfy weak consistency, and in
most cases even surpasses standard random forest. To the best of our knowledge,
DMRF is currently the most excellent strongly consistent RF variant with low
algorithm complexity

该研究改善了以往弱一致的随机森林变体的证明方法，提高了数据利用率，实现了更好的理论性能和实验表现。同时，基于多项式随机森林和伯努利随机森林，提出了一个数据驱动的多项式随机森林算法，具有低算法复杂度和强一致性。在分类和回归问题上表现优异，是目前为止最优秀的强一致性的随机森林变体之一。

基于数据的多项式随机森林

Data-driven multinomial random forest

In this paper, we introduce a divide-and-conquer algorithm to improve
sentence alignment speed. We utilize external bilingual sentence embeddings to
find accurate hard delimiters for the parallel texts to be aligned. We use
Monte Carlo simulation to show experimentally that using this
divide-and-conquer algorithm, we can turn any quadratic time complexity
sentence alignment algorithm into an algorithm with average time complexity of
O(NlogN). On a standard OCR-generated dataset, our method improves the
Bleualign baseline by 3 F1 points. Besides, when computational resources are
restricted, our algorithm is faster than Vecalign in practice.

本研究介绍了一种分治算法，利用外部双语句子嵌入来找到精确的边界，将任何二次时间复杂度的句子对齐算法转化为平均时间复杂度为 O (NlogN) 的算法，并在标准 OCR 生成的数据集上将 Bleualign 基线提高了 3 个 F1 点。

分治法提高句子对齐精度

Improve Sentence Alignment by Divide-and-conquer

Let {\alpha} be the maximal value such that the product of an n x n^{\alpha}
matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic
operations. In this paper we show that \alpha>0.30298, which improves the
previous record \alpha>0.29462 by Coppersmith (Journal of Complexity, 1997).
More generally, we construct a new algorithm for multiplying an n x n^k matrix
by an n^k x n matrix, for any value k\neq 1. The complexity of this algorithm
is better than all known algorithms for rectangular matrix multiplication. In
the case of square matrix multiplication (i.e., for k=1), we recover exactly
the complexity of the algorithm by Coppersmith and Winograd (Journal of
Symbolic Computation, 1990).
These new upper bounds can be used to improve the time complexity of several
known algorithms that rely on rectangular matrix multiplication. For example,
we directly obtain a O(n^{2.5302})-time algorithm for the all-pairs shortest
paths problem over directed graphs with small integer weights, improving over
the O(n^{2.575})-time algorithm by Zwick (JACM 2002), and also improve the time
complexity of sparse square matrix multiplication.

本文主要研究矩阵乘法相关问题，提出了一种新算法，相比于之前的算法能够更快地计算带有权值的有向图中的所有点对最短路径问题和稀疏矩阵的乘法问题。