Efficient and accurate P-value computation for Position Weight Matrices.
Bottom Line:
For many examples of PWMs, they fail to give accurate results in a reasonable amount of time.The main idea is to use a series of discretized score distributions that improves the final result step by step until some convergence criterion is met.Experimental results show that it achieves better performance in terms of computational time and precision than existing tools.
Affiliation: LIFL, UMR CNRS 8022, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq, France. helene.touzet@lifl.fr
ABSTRACT
Background: Position Weight Matrices (PWMs) are probabilistic representations of signals in sequences. They are widely used to model approximate patterns in DNA or in protein sequences. The usage of PWMs needs as a prerequisite to knowing the statistical significance of a word according to its score. This is done by defining the P-value of a score, which is the probability that the background model can achieve a score larger than or equal to the observed value. This gives rise to the following problem: Given a P-value, find the corresponding score threshold. Existing methods rely on dynamic programming or probability generating functions. For many examples of PWMs, they fail to give accurate results in a reasonable amount of time. Results: The contribution of this paper is two fold. First, we study the theoretical complexity of the problem, and we prove that it is NP-hard. Then, we describe a novel algorithm that solves the P-value problem efficiently. The main idea is to use a series of discretized score distributions that improves the final result step by step until some convergence criterion is met. Moreover, the algorithm is capable of calculating the exact P-value without any error, even for matrices with non-integer coefficient values. The same approach is also used to devise an accurate algorithm for the reverse problem: finding the P-value for a given score. Both methods are implemented in a software called TFM-PVALUE, that is freely available. Conclusion: We have tested TFM-PVALUE on a large set of PWMs representing transcription factor binding sites. Experimental results show that it achieves better performance in terms of computational time and precision than existing tools. No MeSH data available. Related in: MedlinePlus |
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Mentions: Lemma 9 is used through a stepwise algorithm to compute the P-value of a score threshold. Let α be the score for which we want to determine the associated P-value. We estimate the score distribution Q iteratively. For that, we consider a series of round matrices Mε for decreasing values of ε, and calculate successive values P-value (Mε, α). The efficiency of the method is guaranteed by two properties. First, we introduce a stop condition that allows us to stop as soon as it is guaranteed that the exact value of the P-value is reached. Second, we carefully select relevant portions of the score distribution for which the computation should go on. This tends to restrain the score range to inspect at each step. The algorithm is displayed in Figure 5. |
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Affiliation: LIFL, UMR CNRS 8022, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq, France. helene.touzet@lifl.fr
Background: Position Weight Matrices (PWMs) are probabilistic representations of signals in sequences. They are widely used to model approximate patterns in DNA or in protein sequences. The usage of PWMs needs as a prerequisite to knowing the statistical significance of a word according to its score. This is done by defining the P-value of a score, which is the probability that the background model can achieve a score larger than or equal to the observed value. This gives rise to the following problem: Given a P-value, find the corresponding score threshold. Existing methods rely on dynamic programming or probability generating functions. For many examples of PWMs, they fail to give accurate results in a reasonable amount of time.
Results: The contribution of this paper is two fold. First, we study the theoretical complexity of the problem, and we prove that it is NP-hard. Then, we describe a novel algorithm that solves the P-value problem efficiently. The main idea is to use a series of discretized score distributions that improves the final result step by step until some convergence criterion is met. Moreover, the algorithm is capable of calculating the exact P-value without any error, even for matrices with non-integer coefficient values. The same approach is also used to devise an accurate algorithm for the reverse problem: finding the P-value for a given score. Both methods are implemented in a software called TFM-PVALUE, that is freely available.
Conclusion: We have tested TFM-PVALUE on a large set of PWMs representing transcription factor binding sites. Experimental results show that it achieves better performance in terms of computational time and precision than existing tools.
No MeSH data available.