Algorithms for discovery of multiple Markov boundaries: application to the molecular signature multiplicity problem
Statnikov, Alexander Romanovich
Algorithms for discovery of a Markov boundary from data constitute one of the most important recent developments in machine learning, primarily because they offer a principled solution to the variable/feature selection problem and give insight about local causal structure. Even though there is always a single Markov boundary of the response variable in faithful distributions, distributions with violations of the intersection property may have multiple Markov boundaries. Such distributions are abundant in practical data-analytic applications, and there are several reasons why it is important to induce all Markov boundaries from such data. However, there are currently no practical algorithms that can provably accomplish this task. To this end, I propose a novel generative algorithm (termed TIE*) that can discover all Markov boundaries from data. The generative algorithm can be instantiated to discover Markov boundaries independent of data distribution. I prove correctness of the generative algorithm and provide several admissible instantiations. The new algorithm is then applied to identify the set of maximally predictive and non-redundant molecular signatures. TIE* identifies exactly the set of true signatures in simulated distributions and yields signatures with significantly better predictivity and reproducibility than prior algorithms in human microarray gene expression datasets. The results of this thesis also shed light on the causes of molecular signature multiplicity phenomenon.