Tenenbaum J B, Griffiths T L
Department of Psychology, Stanford University, Stanford, CA 94305-2130, USA.
Behav Brain Sci. 2001 Aug;24(4):629-40; discussion 652-791. doi: 10.1017/s0140525x01000061.
Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models.
谢泼德认为，一条通用法则应适用于感知和认知的不同领域的泛化，以及不同物种甚至不同星球的生物体之间的泛化。从关于自然类别的一些基本假设出发，他推导出一个指数衰减函数作为通用泛化梯度的形式，这与广泛的实证数据惊人地吻合。然而，他最初的公式仅适用于从单个遇到的刺激到单个新刺激的泛化的理想情况，以及适用于可以表示为连续度量心理空间中的点的刺激。在这里，我们将谢泼德的理论重塑为一个更通用的贝叶斯框架，并展示这如何自然地将他的方法扩展到从具有任意表征结构的多个相关刺激进行泛化的更现实情况。我们的框架还包含了特沃斯基的相似性集合论模型的一个版本，该模型传统上被认为是谢泼德的相似性和泛化连续度量空间模型的主要替代方案。这种统一不仅使我们能够在集合论方法和空间方法之间进行深入的类比，而且还能显著提高集合论模型的解释力。
