Probabilistic Arithmetic Automata and Their Applications

We present a comprehensive review on probabilistic arithmetic automata (PAAs), a general model to describe chains of operations whose operands depend on chance, along with two algorithms to numerically compute the distribution of the results of such probabilistic calculations. PAAs provide a unifyin...

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Veröffentlicht in:IEEE/ACM transactions on computational biology and bioinformatics Jg. 9; H. 6; S. 1737 - 1750
Hauptverfasser: Marschall, T., Herms, I., Kaltenbach, H., Rahmann, S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.11.2012
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Algorithms
alignment seed
analysis of algorithms
Application programming interface
Arithmetic
Automata
Automation
Bioinformatics
clump
Computation
Computational Biology - methods
Computational modeling
Construction
DNA sequencing
dynamic programming
hidden Markov model
Hidden Markov models
Markov Chains
Markov processes
Mathematical models
Models, Biological
Models, Statistical
pattern matching
Pattern Recognition, Automated - methods
Peptide Mapping
peptide mass fingerprinting
Probabilistic automaton
Probabilistic logic
Probabilistic methods
Probability theory
Sensitivity and Specificity
Sequence Analysis, DNA
Statistics
string algorithm
Studies
text model
ISSN:1545-5963, 1557-9964, 1557-9964
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Zusammenfassung:We present a comprehensive review on probabilistic arithmetic automata (PAAs), a general model to describe chains of operations whose operands depend on chance, along with two algorithms to numerically compute the distribution of the results of such probabilistic calculations. PAAs provide a unifying framework to approach many problems arising in computational biology and elsewhere. We present five different applications, namely 1) pattern matching statistics on random texts, including the computation of the distribution of occurrence counts, waiting times, and clump sizes under hidden Markov background models; 2) exact analysis of window-based pattern matching algorithms; 3) sensitivity of filtration seeds used to detect candidate sequence alignments; 4) length and mass statistics of peptide fragments resulting from enzymatic cleavage reactions; and 5) read length statistics of 454 and IonTorrent sequencing reads. The diversity of these applications indicates the flexibility and unifying character of the presented framework. While the construction of a PAA depends on the particular application, we single out a frequently applicable construction method: We introduce deterministic arithmetic automata (DAAs) to model deterministic calculations on sequences, and demonstrate how to construct a PAA from a given DAA and a finite-memory random text model. This procedure is used for all five discussed applications and greatly simplifies the construction of PAAs. Implementations are available as part of the MoSDi package. Its application programming interface facilitates the rapid development of new applications based on the PAA framework.
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ISSN:1545-5963
1557-9964
1557-9964
DOI:10.1109/TCBB.2012.109