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Analysis of pattern overlaps and exact computation of P-values of pattern occurrences numbers: case of Hidden Markov Models.

Régnier M, Furletova E, Yakovlev V, Roytberg M - Algorithms Mol Biol (2014)

Bottom Line: The nodes of the graph are associated with the overlaps of words from .The edges are associated to the prefix and suffix relations between overlaps.The gain in size of SufPref data structure leads to significant improvements in space and time complexity compared to existent algorithms.

View Article: PubMed Central - PubMed

Affiliation: INRIA, d'Estienne d'Orves 1, Palaiseau, 91120 France ; CNRS, d'Estienne d'Orves 1, Palaiseau, 91120 France ; LIX, Ecole Polytechnique, Batiment A. Turing, Palaiseau, 91128 France.

ABSTRACT

Background: Finding new functional fragments in biological sequences is a challenging problem. Methods addressing this problem commonly search for clusters of pattern occurrences that are statistically significant. A measure of statistical significance is the P-value of a number of pattern occurrences, i.e. the probability to find at least S occurrences of words from a pattern in a random text of length N generated according to a given probability model. All words of the pattern are supposed to be of same length.

Results: We present a novel algorithm SufPref that computes an exact P-value for Hidden Markov models (HMM). The algorithm is based on recursive equations on text sets related to pattern occurrences; the equations can be used for any probability model. The algorithm inductively traverses a specific data structure, an overlap graph. The nodes of the graph are associated with the overlaps of words from . The edges are associated to the prefix and suffix relations between overlaps. An originality of our data structure is that pattern need not be explicitly represented in nodes or leaves. The algorithm relies on the Cartesian product of the overlap graph and the graph of HMM states; this approach is analogous to the automaton approach from JBCB 4: 553-569. The gain in size of SufPref data structure leads to significant improvements in space and time complexity compared to existent algorithms. The algorithm SufPref was implemented as a C++ program; the program can be used both as Web-server and a stand alone program for Linux and Windows. The program interface admits special formats to describe probability models of various types (HMM, Bernoulli, Markov); a pattern can be described with a list of words, a PSSM, a degenerate pattern or a word and a number of mismatches. It is available at http://server2.lpm.org.ru/bio/online/sf/. The program was applied to compare sensitivity and specificity of methods for TFBS prediction based on P-values computed for Bernoulli models, Markov models of orders one and two and HMMs. The experiments show that the methods have approximately the same qualities.

No MeSH data available.


Related in: MedlinePlus

ROC-curves for recognition methods. The methods are described in the text and Table 3. Blue squares correspond to the method based on the number of occurrences. The ROC-curves for P-value based methods are almost coincide.
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Fig4: ROC-curves for recognition methods. The methods are described in the text and Table 3. Blue squares correspond to the method based on the number of occurrences. The ROC-curves for P-value based methods are almost coincide.

Mentions: The main results are given in Table 3 and Figure 4; the details of the experiments are given in [Additional file 8]. The Table shows sensitivity and specificity of recognition for various thresholds and probability models. The thresholds for P-value based methods were chosen to obtain approximately the same sensitivity as the method based on number of occurrences with corresponding minimal number of occurrences. One can see (see also Figure 4) that all P-value methods have approximately the same quality and outperform the method based on number of occurrences.Figure 4


Analysis of pattern overlaps and exact computation of P-values of pattern occurrences numbers: case of Hidden Markov Models.

Régnier M, Furletova E, Yakovlev V, Roytberg M - Algorithms Mol Biol (2014)

ROC-curves for recognition methods. The methods are described in the text and Table 3. Blue squares correspond to the method based on the number of occurrences. The ROC-curves for P-value based methods are almost coincide.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4307674&req=5

Fig4: ROC-curves for recognition methods. The methods are described in the text and Table 3. Blue squares correspond to the method based on the number of occurrences. The ROC-curves for P-value based methods are almost coincide.
Mentions: The main results are given in Table 3 and Figure 4; the details of the experiments are given in [Additional file 8]. The Table shows sensitivity and specificity of recognition for various thresholds and probability models. The thresholds for P-value based methods were chosen to obtain approximately the same sensitivity as the method based on number of occurrences with corresponding minimal number of occurrences. One can see (see also Figure 4) that all P-value methods have approximately the same quality and outperform the method based on number of occurrences.Figure 4

Bottom Line: The nodes of the graph are associated with the overlaps of words from .The edges are associated to the prefix and suffix relations between overlaps.The gain in size of SufPref data structure leads to significant improvements in space and time complexity compared to existent algorithms.

View Article: PubMed Central - PubMed

Affiliation: INRIA, d'Estienne d'Orves 1, Palaiseau, 91120 France ; CNRS, d'Estienne d'Orves 1, Palaiseau, 91120 France ; LIX, Ecole Polytechnique, Batiment A. Turing, Palaiseau, 91128 France.

ABSTRACT

Background: Finding new functional fragments in biological sequences is a challenging problem. Methods addressing this problem commonly search for clusters of pattern occurrences that are statistically significant. A measure of statistical significance is the P-value of a number of pattern occurrences, i.e. the probability to find at least S occurrences of words from a pattern in a random text of length N generated according to a given probability model. All words of the pattern are supposed to be of same length.

Results: We present a novel algorithm SufPref that computes an exact P-value for Hidden Markov models (HMM). The algorithm is based on recursive equations on text sets related to pattern occurrences; the equations can be used for any probability model. The algorithm inductively traverses a specific data structure, an overlap graph. The nodes of the graph are associated with the overlaps of words from . The edges are associated to the prefix and suffix relations between overlaps. An originality of our data structure is that pattern need not be explicitly represented in nodes or leaves. The algorithm relies on the Cartesian product of the overlap graph and the graph of HMM states; this approach is analogous to the automaton approach from JBCB 4: 553-569. The gain in size of SufPref data structure leads to significant improvements in space and time complexity compared to existent algorithms. The algorithm SufPref was implemented as a C++ program; the program can be used both as Web-server and a stand alone program for Linux and Windows. The program interface admits special formats to describe probability models of various types (HMM, Bernoulli, Markov); a pattern can be described with a list of words, a PSSM, a degenerate pattern or a word and a number of mismatches. It is available at http://server2.lpm.org.ru/bio/online/sf/. The program was applied to compare sensitivity and specificity of methods for TFBS prediction based on P-values computed for Bernoulli models, Markov models of orders one and two and HMMs. The experiments show that the methods have approximately the same qualities.

No MeSH data available.


Related in: MedlinePlus