模式识别的分层测试设计
Hierarchical testing designs for pattern recognition
摘要：
我们探索的理论基础的“20个问题”的方法来模式识别。分析的对象是计算过程本身，而不是概率分布（贝叶斯推断）或决策边界（统计学习）。我们的配方是出于应用场景的解释，其中有很多可能的解释的数据，一个（“背景”）是统计上占主导地位的，它是必要的，以限制密集的计算真正的模糊区域。这里的重点是模式过滤：给定一个可能的模式或解释的大集合Y，将真实的一个Y缩小到"检测到的“模式的一个小（随机）子集\hat Y \subsetY，以进行进一步的，更密集的处理。为此，我们考虑Y \in A与非特异性替代物Y \in A^c的假设检验族。每个测试具有空的I型错误，并且候选集合A \subsetY被布置在嵌套分区的层级中。这些测试的特点是范围（|A|），功率（或II型错误）和算法成本。我们考虑顺序测试策略，其中的决策是迭代的，根据过去的结果，关于下一步执行哪个测试以及何时停止测试。然后，将集合\hat Y视为未被所执行的测试排除的模式的集合。策略的总成本是“测试成本”和“后处理成本”的总和（与|\hat Y|），并分析了相应的最优化问题。
英文摘要：
We explore the theoretical foundations of a ``twenty questions'' approach to pattern recognition. The object of the analysis is the computational process itself rather than probability distributions (Bayesian inference) or decision boundaries (statistical learning). Our formulation is motivated by applications to scene interpretation in which there are a great many possible explanations for the data, one (``background'') is statistically dominant, and it is imperative to restrict intensive computation to genuinely ambiguous regions. The focus here is then on pattern filtering: Given a large set Y of possible patterns or explanations, narrow down the true one Y to a small (random) subset \hat Y\subsetY of ``detected'' patterns to be subjected to further, more intense, processing. To this end, we consider a family of hypothesis tests for Y\in A versus the nonspecific alternatives Y\in A^c. Each test has null type I error and the candidate sets A\subsetY are arranged in a hierarchy of nested partitions. These tests are then characterized by scope (|A|), power (or type II error) and algorithmic cost. We consider sequential testing strategies in which decisions are made iteratively, based on past outcomes, about which test to perform next and when to stop testing. The set \hat Y is then taken to be the set of patterns that have not been ruled out by the tests performed. The total cost of a strategy is the sum of the ``testing cost'' and the ``postprocessing cost'' (proportional to |\hat Y|) and the corresponding optimization problem is analyzed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
