A Trade-Off between Sample Complexity and Computational Complexity in Learning Boolean Networks from Time-Series Data

A key problem in molecular biology is to infer regulatory relationships between genes from expression data. This paper studies a simplified model of such inference problems in which one or more Boolean variables, modeling, for example, the expression levels of genes, each depend deterministically on...

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Bibliographic Details
Published in:IEEE/ACM transactions on computational biology and bioinformatics Vol. 7; no. 1; pp. 118 - 125
Main Authors: Perkins, T.J., Hallett, M.T.
Format: Journal Article
Language:English
Published: United States IEEE 01.01.2010
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Artificial Intelligence
association rules
Biological system modeling
Boolean functions
classification
clustering
Computational biology
Computational complexity
Computer Simulation
feature extraction or construction
Gene expression
Gene Expression Profiling - methods
Genetics
Inference algorithms
Input variables
Logistic Models
Machine learning
Models, Biological
Organisms
parameter learning
Proteome - metabolism
Signal Processing, Computer-Assisted
Signal Transduction - physiology
Studies
Time Factors
Time series analysis
Parameter learning
Clustering
classification
and association rules
Machine learning
Feature extraction or construction
ISSN:1545-5963, 1557-9964, 1557-9964
Online Access:Get full text
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Summary:A key problem in molecular biology is to infer regulatory relationships between genes from expression data. This paper studies a simplified model of such inference problems in which one or more Boolean variables, modeling, for example, the expression levels of genes, each depend deterministically on a small but unknown subset of a large number of Boolean input variables. Our model assumes that the expression data comprises a time series, in which successive samples may be correlated. We provide bounds on the expected amount of data needed to infer the correct relationships between output and input variables. These bounds improve and generalize previous results for Boolean network inference and continuous-time switching network inference. Although the computational problem is intractable in general, we describe a fixed-parameter tractable algorithm that is guaranteed to provide at least a partial solution to the problem. Most interestingly, both the sample complexity and computational complexity of the problem depend on the strength of correlations between successive samples in the time series but in opposing ways. Uncorrelated samples minimize the total number of samples needed while maximizing computational complexity; a strong correlation between successive samples has the opposite effect. This observation has implications for the design of experiments for measuring gene expression.
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ISSN:1545-5963
1557-9964
1557-9964
DOI:10.1109/TCBB.2008.38