arXiv subjects

Jun Diao

Publications and source records attributed to Jun Diao.

3 recordsLinked to original sources

arXiv2025

Exponentially Consistent Low Complexity Tests for Outlier Hypothesis Testing

We revisit outlier hypothesis testing, propose exponentially consistent low complexity fixed-length and sequential tests and show that our tests achieve better tradeoff between detection performance and computational complexity than existing tests that use exhaustive search. Specifically, in outlier hypothesis testing, one is given a list of observed sequences, most of which are generated i.i.d. from a nominal distribution while the rest sequences named outliers are generated i.i.d. from another anomalous distribution. The task is to identify all outliers when both the nominal and anomalous distributions are unknown. There are two basic settings: fixed-length and sequential. In the fixed-length setting, the sample size of each observed sequence is fixed a priori while in the sequential setting, the sample size is a random number that can be determined by the test designer to ensure reliable decisions. For the fixed-length setting, we strengthen the results of Bu \emph{et. al} (TSP 2019) by i) allowing for scoring functions beyond KL divergence and further simplifying the test design when the number of outliers is known and ii) proposing a new test, explicitly bounding the detection performance of the test and characterizing the tradeoff among exponential decay rates of three error probabilities when the number of outliers is unknown. For the sequential setting, our tests for both cases are novel and enable us to reveal the benefit of sequentiality. Finally, for both fixed-length and sequential settings, we demonstrate the penalty of not knowing the number of outliers on the detection performance.

cs.IT↗

arXiv2024

Sequential Outlier Hypothesis Testing under Universality Constraints

We revisit sequential outlier hypothesis testing and derive bounds on achievable exponents when both the nominal and anomalous distributions are unknown. The task of outlier hypothesis testing is to identify the set of outliers that are generated from an anomalous distribution among all observed sequences where the rest majority are generated from a nominal distribution. In the sequential setting, one obtains a symbol from each sequence per unit time until a reliable decision could be made. For the case with exactly one outlier, our exponent bounds are tight, providing exact large deviations characterization of sequential tests and strengthening a previous result of Li, Nitinawarat and Veeravalli (2017). In particular, the average sample size of our sequential test is bounded universally under any pair of nominal and anomalous distributions and our sequential test achieves larger Bayesian exponent than the fixed-length test, which could not be guaranteed by the sequential test of Li, Nitinawarat and Veeravalli (2017). For the case with at most one outlier, we propose a threshold-based test that has bounded expected stopping time under mild conditions and we bound the exponential decay rate of error probabilities under each non-null hypothesis and the null hypothesis. Our sequential test resolves the tradeoff among the exponential decay rates of misclassification, false reject and false alarm probabilities for the fixed-length test of Zhou, Wei and Hero (TIT 2022). Finally, with a further step towards practical applications, we generalize our results to the cases of multiple outliers and show that there is a penalty in the error exponents when the number of outliers is unknown.

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arXiv2022

Achievable Error Exponents for Two-Phase Multiple Classification

We revisit $M$-ary classification of Gutman (TIT 1989), where one is tasked to determine whether a testing sequence is generated with the same distribution as one of the $M$ training sequences or not. Our main result is a two-phase test, its theoretical analysis and its optimality guarantee. Specifically, our two-phase test is a special case of a sequential test with only two decision time points: the first phase of our test is a fixed-length test with a reject option, the second-phase of our test proceeds only if a reject option is decided in the first phase and the second phase of our test does \emph{not} allow a reject option. To provide theoretical guarantee for our test, we derive achievable error exponents using the method of types and derive a converse result for the optimal sequential test using the techniques recently proposed by Hsu, Li and Wang (ITW, 2022) for binary classification. Analytically and numerically, we show that our two phase test achieves the performance of an optimal sequential test with proper choice of test parameters. In particular, similarly as the optimal sequential test, our test does not need a final reject option to achieve the optimal error exponent region while an optimal fixed-length test needs a reject option to achieve the same region. Finally, we specialize our results to binary classification when $M=2$ and to $M$-ary hypothesis testing when the ratio of the lengths of training sequences and testing sequences tends to infinity so that generating distributions can be estimated perfectly.

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