Rapid technological advances during the last two decades have led to a data-driven revolution in biology opening up a plethora of opportunities to infer informative patterns that could lead to deeper biological understanding. Large volumes of data provided by such technologies, however, are not analyzable using hypothesis-driven significance tests and other cornerstones of orthodox statistics. We present powerful tools in machine learning and statistical inference for extracting biologically informative patterns and clinically predictive models using this data. Motivated by an existing graph partitioning framework, we first derive relationships between optimizing the regularized min-cut cost function used in spectral clustering and the relevance information as defined in the Information Bottleneck method. For fast-mixing graphs, we show that the regularized min-cut cost functions introduced by Shi and Malik over a decade ago can be well approximated as the rate of loss of predictive information about the location of random walkers on the graph. For graphs drawn from a generative model designed to describe community structure, the optimal information-theoretic partition and the optimal min-cut partition are shown to be the same with high probability. Next, we formulate the problem of identifying emerging viral pathogens and characterizing their transmission in terms of learning linear models that can predict the host of a virus using its sequence information. Motivated by an existing framework for representing biological sequence information, we learn sparse, tree-structured models, built from decision rules based on subsequences, to predict viral hosts from protein sequence data using multi-class Adaboost, a powerful discriminative machine learning algorithm. Furthermore, the predictive motifs robustly selected by the learning algorithm are found to show strong host-specificity and occur in highly conserved regions of the viral proteome. We then extend this learning algorithm to the problem of predicting disease risk in humans using single nucleotide polymorphisms (SNP) -- single-base pair variations -- in their entire genome. While genome-wide association studies usually aim to infer individual SNPs that are strongly associated with disease, we use popular supervised learning algorithms to infer sufficiently complex tree-structured models, built from single-SNP decision rules, that are both highly predictive (for clinical goals) and facilitate biological interpretation (for basic science goals). In addition to high prediction accuracies, the models identify 'hotspots' in the genome that contain putative causal variants for the disease and also suggest combinatorial interactions that are relevant for the disease. Finally, motivated by the insufficiency of quantifying biological interpretability in terms of model sparsity, we propose a hierarchical Bayesian model that infers hidden structured relationships between features while simultaneously regularizing the classification model using the inferred group structure. The appropriate hidden structure maximizes the log-probability of the observed data, thus regularizing a classifier while increasing its predictive accuracy. We conclude by describing different extensions of this model that can be applied to various biological problems, specifically those described in this thesis, and enumerate promising directions for future research.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/D82N5863 |
| Date | January 2011 |
| Creators | Raj, Anil |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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