
SecondOrder Asymptotically Optimal Statistical Classification
Motivated by realworld machine learning applications, we analyze approx...
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Nonparametric Detection of Anomalous Data Streams
A nonparametric anomalous hypothesis testing problem is investigated, in...
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Sequential Classification with Empirically Observed Statistics
Motivated by realworld machine learning applications, we consider a sta...
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Improper vs finitely additive distributions as limits of countably additive probabilities
In Bayesian statistics, improper distributions and finitely additive pro...
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LinearComplexity ExponentiallyConsistent Tests for Universal Outlying Sequence Detection
The problem of universal outlying sequence detection is studied, where t...
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A KernelBased Nonparametric Test for Anomaly Detection over Line Networks
The nonparametric problem of detecting existence of an anomalous interva...
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Nonparametric Detection of Geometric Structures over Networks
Nonparametric detection of existence of an anomalous structure over a ne...
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SecondOrder Asymptotically Optimal Universal Outlying Sequence Detection with Reject Option
Motivated by practical machine learning applications, we revisit the outlying sequence detection problem (Li et al., TIT 2014) and derive fundamental limits of optimal detection when the reject option is allowed for outlying sequences. In outlying sequence detection (OSD) one is given multiple observed sequences, where most sequences are generated i.i.d. from a nominal distribution. The task is to discern the set of outlying sequences that are generated according to anomalous distributions. In OSD, the nominal and anomalous distributions are unknown. In this paper, we consider the case where there is a reject option for the OSD, i.e., reject the samples as insufficient for reliable outlying sequence detection (cf. Bartlett et al., JMLR 2008). We study the tradeoff among the probabilities of misclassification error, false alarm and false reject for tests that satisfy weak conditions on the rate of decrease of these error probabilities as a function of sequence length. We propose a secondorder asymptotically optimal test which provides a finite sample approximation. We first consider the case of at most one outlying sequence and then generalize our results to multiple outlying sequences where each outlying sequence can follow a different anomalous distribution.
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