In this paper, we propose a new kernel-based co-occurrence measure that can
be applied to sparse linguistic expressions (e.g., sentences) with a very short
learning time, as an alternative to pointwise mutual information (PMI). As well
as deriving PMI from mutual information, we derive this new measure from the
Hilbert--Schmidt independence criterion (HSIC); thus, we call the new measure
the pointwise HSIC (PHSIC). PHSIC can be interpreted as a smoothed variant of
PMI that allows various similarity metrics (e.g., sentence embeddings) to be
plugged in as kernels. Moreover, PHSIC can be estimated by simple and fast
(linear in the size of the data) matrix calculations regardless of whether we
use linear or nonlinear kernels. Empirically, in a dialogue response selection
task, PHSIC is learned thousands of times faster than an RNN-based PMI while
outperforming PMI in accuracy. In addition, we also demonstrate that PHSIC is
beneficial as a criterion of a data selection task for machine translation
owing to its ability to give high (low) scores to a consistent (inconsistent)
pair with other pairs.

本文提出了一种基于 Hilbert-Schmidt 独立准则（HSIC）的新内核共现测量方式，称为 pointwise HSIC（PHSIC），可用于稀疏语言表达（例如句子），并且学习时间非常短，是点间互信息（PMI）的替代方法，并且在对话响应选择任务中，PHSIC 比基于 RNN 的 PMI 快几千倍的学习速度，同时准确性也更好。