Comparison of Statistical Significance Criteria

Régnier, Mireille

doi:10.1142/s0219720006002028

Cited by 18 publications

(16 citation statements)

References 25 publications

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“…The Gaussian approximation however, presents relatively large RMSE (average of about 12%) and d T V values. These results support the experiments presented in [30], which has concluded that the Gaussian approximation is not suited to motifs.…”

Section: Measuring the Poisson And Gaussian Ap-supporting

confidence: 91%

“…The exact distribution is compared to the Gaussian and compound Poisson approximations in the extraction of exceptional words of the phage Lambda genome. In [30], the drawbacks of the Gaussian approximation are analyzed. Schbath [35] studies the statistical distributions of word counts in Markov chains.…”

Section: Related Workmentioning

confidence: 99%

“…Further, one should consider that the test must be executed for all extracted motifs. Approximate or asymptotic distributions are widely used in the literature [19,21,29,30,32,33], as they can reduce the computation time by one order or magnitude (see section 5). This difference stretches out along the size of the Binomial parameters.…”

Section: Approximating P-valuesmentioning

confidence: 99%

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Time Series Motifs Statistical Significance

Castro¹,

Azevedo²

2011

Proceedings of the 2011 SIAM International Conference on Data Mining

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Time series motif discovery is the task of extracting previously unknown recurrent patterns from time series data. It is an important problem within applications that range from finance to health. Many algorithms have been proposed for the task of efficiently finding motifs. Surprisingly, most of these proposals do not focus on how to evaluate the discovered motifs. They are typically evaluated by human experts. This is unfeasible even for moderately sized datasets, since the number of discovered motifs tends to be prohibitively large. Statistical significance tests are widely used in bioinformatics and association rules mining communities to evaluate the extracted patterns. In this work we present an approach to calculate time series motifs statistical significance. Our proposal leverages work from the bioinformatics community by using a symbolic definition of time series motifs to derive each motif's p-value. We estimate the expected frequency of a motif by using Markov Chain models. The p-value is then assessed by comparing the actual frequency to the estimated one using statistical hypothesis tests. Our contribution gives means to the application of a powerful technique -statistical tests -to a time series setting. This provides researchers and practitioners with an important tool to evaluate automatically the degree of relevance of each extracted motif.

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Section: Measuring the Poisson And Gaussian Ap-supporting

confidence: 91%

Section: Related Workmentioning

confidence: 99%

Section: Approximating P-valuesmentioning

confidence: 99%

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Time Series Motifs Statistical Significance

Castro¹,

Azevedo²

2011

Proceedings of the 2011 SIAM International Conference on Data Mining

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“…When all probabilities p i are equal, say p i = p, and M is large, φ(t) = µ(e t ) = (p(e t − 1) + 1) M converges to the probability generating function of the Gaussian law, and large deviation results are known [DZ98] or, in the context of computational biology [Wat95,RV06]. It is worth noticing that Large Power Theorem steadily applies.…”

Section: Short Sequencesmentioning

confidence: 99%

“…Simulations on biological data are presented in [MRSKL04]. This point is extensively discussed in [RV06].…”

Section: Introductionmentioning

confidence: 99%

Large deviation properties for patterns

Bourdon

Régnier

2014

Journal of Discrete Algorithms

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Deciding whether a given pattern is overrepresented or under-represented according to a given background model is a key question in computational biology. Such a decision is usually made by computing some p-values reflecting the "exceptionality" of a pattern in a given sequence or set of sequences. In the simplest cases (short and simple patterns, simple background model, small number of sequences), an exact p-value can be computed with a tractable complexity. The realistic cases are in general too complicated to get such an exact p-value. Approximations are thus proposed (Gaussian, Poisson, Large deviation approximations). These approximations are applicable under some conditions: Gaussian approximations are valid in the central domain while Poisson and Large deviations approximations are valid for rare events. In the present paper, we prove a large deviation approximation to the double strands counting problem that refers to a counting of a given pattern in a set of sequences that arise from both strands of the genome. Here dependencies between a sequence and its complement plays a fundamental role. General combinatorial properties of the pattern allow to deal with such a dependency. A large deviation result is also provided for a set of small sequences.

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Significant motifs in time series

Castro

Azevedo

2012

Statistical Analysis

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Time series motif discovery is the task of extracting previously unknown recurrent patterns from time series data. It is an important problem within applications that range from finance to health. Many algorithms have been proposed for the task of efficiently finding motifs. Surprisingly, most of these proposals do not focus on how to evaluate the discovered motifs. They are typically evaluated by human experts. This is unfeasible even for moderately sized datasets, since the number of discovered motifs tends to be prohibitively large. Statistical significance tests are widely used in the data mining communities to evaluate extracted patterns. In this work we present an approach to calculate time series motifs statistical significance. Our proposal leverages work from the bioinformatics community by using a symbolic definition of time series motifs to derive each motif's p-value. We estimate the expected frequency of a motif by using Markov Chain models. The p-value is then assessed by comparing the actual frequency to the estimated one using statistical hypothesis tests. Our contribution gives means to the application of a powerful technique-statistical tests-to a time series setting. This provides researchers and practitioners with an important tool to evaluate automatically the degree of relevance of each extracted motif.

show abstract

Comparison of Statistical Significance Criteria

Cited by 18 publications

References 25 publications

Time Series Motifs Statistical Significance

Time Series Motifs Statistical Significance

Large deviation properties for patterns

Significant motifs in time series

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