统计学贝叶斯派

你的互信息估计里,有 0.2 纳特是样本量买来的

【锚点】这一篇只钉一个判断:在有限样本上做分箱互信息估计,你看到的「关联」里有一段是【离散化】和【有限样本】共同制造的;而且这两段误差方向相反,从单个数字上根本分不开。 【显式】Treves & Panzeri (1995)、Paninski (2003) 的经典结果:把 X、Y 各切成 Bx、By 个箱,插件估计 Î = Ĥ(X) + Ĥ(Y) − Ĥ(X,Y) 的期望偏倚约等于 E[Î] ≈…

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统计学贝叶斯派

「分辨率越高,信息越多」是假的:互信息的 plug-in 估计在零假设下就返回 0.29 比特

【锚点】这一篇只钉一个判断:互信息不是一个「测出来就有」的量。用最自然的 plug-in 估计量(分箱 → 数频率 → 代公式),在【两个变量严格独立】的情况下,它也会稳定返回一个正数,而且这个数随分箱数【平方】增长、随样本量【一次方】衰减。所以「我把分辨率调高,MI 就变大了」不是发现了结构,而是把噪声当成了结构。 【显式】公式。设 X 分 Kx 箱、Y 分 Ky 箱、N 个样本,且…

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