Linear-Complexity Exponentially-Consistent Tests for Universal Outlying Sequence Detection

Bu, Yuheng; Zou, Shaofeng; Veeravalli, Venugopal V.

doi:10.1109/tsp.2019.2901364

Cited by 14 publications

(23 citation statements)

References 21 publications

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“…Our problem is also related but different from a class of outlying sequence detection problems studied in [21]- [24]. Our model has training sequences associated with hypotheses, whereas the previous results did not consider such information.…”

Section: B Related Workmentioning

confidence: 96%

Data-Driven Nonparametric Existence and Association Problems

Liu

Liang

Cui

2018

IEEE Trans. Signal Process.

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We investigate two closely related nonparametric hypothesis testing problems. In the first problem (i.e., the existence problem), we test whether a testing data stream is generated by one of a set of composite distributions. In the second problem (i.e., the association problem), we test which one of the multiple distributions generates a testing data stream. We assume that some distributions in the set are unknown with only training sequences generated by the corresponding distributions are available. For both problems, we construct the generalized likelihood (GL) tests, and characterize the error exponents of the maximum error probabilities. For the existence problem, we show that the error exponent is mainly captured by the Chernoff information between the set of composite distributions and alternative distributions. For the association problem, we show that the error exponent is captured by the minimum Chernoff information between each pair of distributions as well as the KL divergences between the approximated distributions (via training sequences) and the true distributions. We also show that the ratio between the lengths of training and testing sequences plays an important role in determining the error decay rate.

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Section: B Related Workmentioning

confidence: 96%

Data-Driven Nonparametric Existence and Association Problems

Liu

Liang

Cui

2018

IEEE Trans. Signal Process.

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“…This implies that the distance between any two points originating from the same cluster is less than the distance between any two points in different clusters, which is a common assumption used to guarantee clustering performance [38], [39] (see Fig. 4).…”

Section: B Non-negative Matrix Factorizationmentioning

confidence: 99%

Optimal Recovery of Missing Values for Non-Negative Matrix Factorization

Chen

Varshney

2021

IEEE Open J. Signal Process.

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Missing values imputation is often evaluated on some similarity measure between actual and imputed data. However, it may be more meaningful to evaluate downstream algorithm performance after imputation than the imputation itself. We describe a straightforward unsupervised imputation algorithm, a minimax approach based on optimal recovery, and derive probabilistic error bounds on downstream non-negative matrix factorization (NMF). Under certain geometric conditions, we prove upper bounds on NMF relative error, which is the first bound of this type for missing values. We also give probabilistic bounds for the same geometric assumptions. Experiments on image data and biological data show that this theoretically-grounded technique performs as well as or better than other imputation techniques that account for local structure. We also comment on imputation fairness.

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“…Information measures play important roles in not only traditional information theory but also numerous applications of big data, such as detection, classification and clustering [73], [74]. In fact, by facilitating the small probability elements, some information measures focusing on rare events are proposed to settle the big data problems such as anomaly detection, feature selection and pattern recognition [75]- [77].…”

Section: Information Theories and Technologies For Measuring Rarementioning

confidence: 99%

“…• Information Preprocessing: Considering the information preprocessing, information divergences play vital roles in discriminating different distributions (namely information identification). That is, the information divergence can be used as a test tool for outlier detection [73], [74], [100]. In particular, an information divergence between two distributions, denoted by F(•), can classify the pending sample sequences X (i) into the normal sequence set M t or the outlier sequence set M f .…”

Section: Applications In Message Processingmentioning

confidence: 99%

Importance of Small Probability Events in Big Data: Information Measures, Applications, and Challenges

et al. 2019

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In many applications (e.g., anomaly detection and security systems) of smart cities, rare events dominate the importance of the total information on big data collected by the Internet of Things (IoT). That is, it is pretty crucial to explore the valuable information associated with the rare events involved in minority subsets of the voluminous amounts of data. To do so, how to effectively measure the information with the importance of the small probability events from the perspective of information theory is a fundamental question. This paper first makes a survey of some theories and models with respect to importance measures and investigates the relationship between subjective or semantic importance and rare events in big data. Moreover, some applications for message processing and data analysis are discussed in the viewpoint of information measures. In addition, based on rare events detection, some open challenges related to information measures, such as smart cities, autonomous driving, and anomaly detection in the IoT, are introduced which can be considered as future research directions.

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Linear-Complexity Exponentially-Consistent Tests for Universal Outlying Sequence Detection

Cited by 14 publications

References 21 publications

Data-Driven Nonparametric Existence and Association Problems

Data-Driven Nonparametric Existence and Association Problems

Optimal Recovery of Missing Values for Non-Negative Matrix Factorization

Importance of Small Probability Events in Big Data: Information Measures, Applications, and Challenges

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