推广的普遍规律
The Generalized Universal Law of Generalization
摘要：
谢泼德认为，存在一个强有力的心理学定律，它将心理空间中一对物品之间的距离与它们相互混淆的概率联系起来。具体而言，混淆的概率是项目对之间的距离的负指数函数。在实验环境中，距离通常是根据多维欧几里得空间来定义的，但这种假设似乎不太可能适用于复杂的刺激。我们表明，尽管如此，普遍规律的推广可以在更复杂的设置任意刺激，使用更普遍的距离测量。这个通用距离被定义为将两个感兴趣的项目的表示相互转换的最短程序的长度：算法信息距离。它是普适的，因为它缩小了所有可计算距离：它是最小的可计算距离。我们证明了推广的普遍规律在概率为1的情况下成立，前提是混淆概率是可计算的。我们还给出了一个数学上更吸引人的形式
英文摘要：
It has been argued by Shepard that there is a robust psychological law that relates the distance between a pair of items in psychological space and the probability that they will be confused with each other. Specifically, the probability of confusion is a negative exponential function of the distance between the pair of items. In experimental contexts, distance is typically defined in terms of a multidimensional Euclidean space-but this assumption seems unlikely to hold for complex stimuli. We show that, nonetheless, the Universal Law of Generalization can be derived in the more complex setting of arbitrary stimuli, using a much more universal measure of distance. This universal distance is defined as the length of the shortest program that transforms the representations of the two items of interest into one another: the algorithmic information distance. It is universal in the sense that it minorizes every computable distance: it is the smallest computable distance. We show that the universal law of generalization holds with probability going to one-provided the confusion probabilities are computable. We also give a mathematically more appealing form
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