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NML computation algorithms for tree-structured multinomial Bayesian networks.

Petri Kontkanen¹, Hannes Wettig, Petri Myllymäki

¹Complex Systems Computation Group, Department of Computer Science, Helsinki Institute for Information Technology, University of Helsinki, Finland.

EURASIP Journal on Bioinformatics & Systems Biology

|April 3, 2008

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This study introduces efficient algorithms for computing the normalized maximum likelihood (NML) distribution, crucial for statistical inference in bioinformatics with large discrete datasets. These methods extend existing techniques to complex Bayesian networks, improving computational efficiency.

Area of Science:

Bioinformatics
Statistical Inference
Computational Biology

Background:

Bioinformatics frequently encounters large discrete datasets, necessitating efficient statistical methods.
The minimum description length (MDL) principle offers a robust framework for statistical inference.
Normalized maximum likelihood (NML) distribution is key to MDL but computationally intensive for discrete data.

Purpose of the Study:

To develop and extend efficient algorithms for computing the NML distribution for discrete data.
To address the computational bottleneck of NML calculations in complex models.

Main Methods:

Review of existing algorithms for NML computation in multinomial and naive Bayes models.
Extension of these algorithms to tree-structured Bayesian networks.

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Main Results:

Demonstrated efficient computation of NML distributions for complex Bayesian networks.
Provided a practical approach to applying MDL principles to large discrete bioinformatics datasets.

Conclusions:

The developed algorithms significantly improve the efficiency of NML computation for discrete data.
This work facilitates the application of MDL-based statistical inference in complex bioinformatics models.