模式识别的可行速率
Achievable Rates for Pattern Recognition
摘要：
生物和机器模式识别系统面临着一个共同的挑战：给定关于未知物体的感知数据，通过将感知数据与存储在内存中的内部表示库进行比较来对物体进行分类。在许多感兴趣的情况下，要区分的模式的数量和原始数据的丰富性迫使识别系统在内部以压缩格式表示记忆和感官信息。然而，这些表示必须保留足够的信息，以适应环境的变化性和复杂性，否则识别将是不可靠的。因此，在专用于数据表示的资源量与识别系统可以可靠地操作的环境的复杂性之间存在固有的权衡。在本文中，我们描述了一个一般的数学模型，模式识别系统的资源限制，并显示如何上述资源复杂性的权衡可以表征在三个速率相关的位数可用于表示内存和传感器数据，和模式的数量填充一个给定的统计环境。我们证明了单字母信息的理论界可实现的速率，并说明了理论分析的基本情况下，模式数据是二进制或高斯。
英文摘要：
Biological and machine pattern recognition systems face a common challenge: Given sensory data about an unknown object, classify the object by comparing the sensory data with a library of internal representations stored in memory. In many cases of interest, the number of patterns to be discriminated and the richness of the raw data force recognition systems to internally represent memory and sensory information in a compressed format. However, these representations must preserve enough information to accommodate the variability and complexity of the environment, or else recognition will be unreliable. Thus, there is an intrinsic tradeoff between the amount of resources devoted to data representation and the complexity of the environment in which a recognition system may reliably operate. In this paper we describe a general mathematical model for pattern recognition systems subject to resource constraints, and show how the aforementioned resource-complexity tradeoff can be characterized in terms of three rates related to number of bits available for representing memory and sensory data, and the number of patterns populating a given statistical environment. We prove single-letter information theoretic bounds governing the achievable rates, and illustrate the theory by analyzing the elementary cases where the pattern data is either binary or Gaussian.
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