  Recently, there has been a resurgence of interest in rigorous algorithms for
the inference of cancer progression from genomic data. The motivations are
manifold: (i) growing NGS and single cell data from cancer patients, (ii) need
for novel Data Science and Machine Learning algorithms to infer models of
cancer progression, and (iii) a desire to understand the temporal and
heterogeneous structure of tumor to tame its progression by efficacious
therapeutic intervention. This thesis presents a multi-disciplinary effort to
model tumor progression involving successive accumulation of genetic
alterations, each resulting populations manifesting themselves in a cancer
phenotype. The framework presented in this work along with algorithms derived
from it, represents a novel approach for inferring cancer progression, whose
accuracy and convergence rates surpass the existing techniques. The approach
derives its power from several fields including algorithms in machine learning,
theory of causality and cancer biology. Furthermore, a modular pipeline to
extract ensemble-level progression models from sequenced cancer genomes is
proposed. The pipeline combines state-of-the-art techniques for sample
stratification, driver selection, identification of fitness-equivalent
exclusive alterations and progression model inference. Furthermore, the results
are validated by synthetic data with realistic generative models, and
empirically interpreted in the context of real cancer datasets; in the later
case, biologically significant conclusions are also highlighted. Specifically,
it demonstrates the pipeline's ability to reproduce much of the knowledge on
colorectal cancer, as well as to suggest novel hypotheses. Lastly, it also
proves that the proposed framework can be applied to reconstruct the
evolutionary history of cancer clones in single patients, as illustrated by an
example from clear cell renal carcinomas.
