统计序列匹配的指数一致低复杂度检验
Exponentially Consistent Low Complexity Tests for Statistical Sequence Matching
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中文总结 AI 辅助
针对统计序列匹配，提出指数一致低复杂度检验，其定长检验性能优于现有穷举法，序贯检验性能更优，并推广至匹配数未知场景。
中文摘要 AI 辅助
为实现统计序列匹配的实际应用，我们提出了指数一致的低复杂度检验，并界定了所提检验误差概率的指数衰减率。在统计序列匹配中，给定两个包含多条序列的数据库，每个数据库中的每条序列均独立同分布地来自某一不同分布；若一对序列分别来自两个数据库且由同一分布生成，则称这对序列匹配，匹配序列对的数量（即匹配数）可为0或正数。我们考虑匹配数已知和未知两种情况：当匹配数已知且为正时，任务是识别所有匹配序列对。为构造定长检验，我们计算两个数据库中所有序列对的评分函数值，将评分函数值足够小的序列对判定为匹配对。我们证明所提检验具有指数一致性，在复杂度与性能的权衡上优于现有采用穷举搜索的定长检验。为构造序贯检验，我们需额外设置一个正阈值以确定停止时间，且证明所提序贯检验的性能严格优于定长检验。随后，我们将结果推广至匹配数未知的情况。
英文摘要
Towards practical applications of statistical sequence matching, we propose low complexity tests that are exponentially consistent and bound the exponential decay rates for error probabilities of our proposed tests. In statistical sequence matching, one is given two databases of multiple sequences, where in each database, each sequence is generated i.i.d. from a distinct distribution. A pair of sequences, one from each database, is said matched if they are generated from the same distribution. The number of matched pairs of sequences, a.k.a, the number of matches, can be either zero or positive. We consider both cases of known and unknown number of matches. When the number of matches is known and positive, the task is to identify all matched pairs of sequences. To construct fixed-length tests, we calculate the scoring function values for all pairs of sequences across the two databases and identify the matched pairs as those having small enough pairwise scoring function values. We show that our proposed test is exponentially consistent, which strikes a better tradeoff between complexity and performance than existing fixed-length tests that use exhaustive search. To construct sequential tests, we need an additional positive threshold to determine the stopping time, and we show that our sequential test achieves strictly better performance than our fixed-length test. Subsequently, we generalize our results to the case with unknown number of matches.
