On learning the structure of Bayesian Networks and submodular function maximization

Learning the structure of dependencies among multiple random variables is a problem of considerable theoretical and practical interest. In practice, score optimisation with multiple restarts provides a practical and surprisingly successful solution, yet the conditions under which this may be a well founded strategy are poorly understood. In this paper, we prove that the problem of identifying the structure of a Bayesian Network via regularised score optimisation can be recast, in expectation, as a submodular optimisation problem, thus guaranteeing optimality with high probability. This result both explains the practical success of optimisation heuristics, and suggests a way to improve on such algorithms by artificially simulating multiple data sets via a bootstrap procedure. We show on several synthetic data sets that the resulting algorithm yields better recovery performance than the state of the art, and illustrate in a real cancer genomic study how such an approach can lead to valuable practical insights.

Combining Bayesian Approaches and Evolutionary Techniques for the Inference of Breast Cancer Networks

Gene and protein networks are very important to model complex large-scale systems in molecular biology. Inferring or reverseengineering such networks can be defined as the process of identifying gene/protein interactions from experimental data through computational analysis. However, this task is typically complicated by the enormously large scale of the unknowns in a rather small sample size. Furthermore, when the goal is to study causal relationships within the network, tools capable of overcoming the limitations of correlation networks are required. In this work, we make use of Bayesian Graphical Models to attach this problem and, specifically, we perform a comparative study of different state-of-the-art heuristics, analyzing their performance in inferring the structure of the Bayesian Network from breast cancer data.

Parallel Implementation of Efficient Search Schemes for the Inference of Cancer Progression Models

The emergence and development of cancer is a consequence of the accumulation over time of genomic mutations involving a specific set of genes, which provides the cancer clones with a functional selective advantage. In this work, we model the order of accumulation of such mutations during the progression, which eventually leads to the disease, by means of probabilistic graphic models, i.e., Bayesian Networks (BNs). We investigate how to perform the task of learning the structure of such BNs, according to experimental evidence, adopting a global optimization meta-heuristics. In particular, in this work we rely on Genetic Algorithms, and to strongly reduce the execution time of the inference -- which can also involve multiple repetitions to collect statistically significant assessments of the data -- we distribute the calculations using both multi-threading and a multi-node architecture. The results show that our approach is characterized by good accuracy and specificity; we also demonstrate its feasibility, thanks to a 84x reduction of the overall execution time with respect to a traditional sequential implementation.

Exposing the Probabilistic Causal Structure of Discrimination

Discrimination discovery from data is an important task aiming at identifying patterns of illegal and unethical discriminatory activities against protected-by-law groups, e.g., ethnic minorities. While any legally-valid proof of discrimination requires evidence of causality, the state-of-the-art methods are essentially correlation-based, albeit, as it is well known, correlation does not imply causation. In this paper we take a principled causal approach to the data mining problem of discrimination detection in databases. Following Suppes' probabilistic causation theory, we define a method to extract, from a dataset of historical decision records, the causal structures existing among the attributes in the data. The result is a type of constrained Bayesian network, which we dub Suppes-Bayes Causal Network (SBCN). Next, we develop a toolkit of methods based on random walks on top of the SBCN, addressing different anti-discrimination legal concepts, such as direct and indirect discrimination, group and individual discrimination, genuine requirement, and favoritism. Our experiments on real-world datasets confirm the inferential power of our approach in all these different tasks.

A Model of Selective Advantage for the Efficient Inference of Cancer Clonal Evolution

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.

Inference of Cancer Progression Models with Biological Noise

Many applications in translational medicine require the understanding of how diseases progress through the accumulation of persistent events. Specialized Bayesian networks called monotonic progression networks offer a statistical framework for modeling this sort of phenomenon. Current machine learning tools to reconstruct Bayesian networks from data are powerful but not suited to progression models. We combine the technological advances in machine learning with a rigorous philosophical theory of causation to produce Polaris, a scalable algorithm for learning progression networks that accounts for causal or biological noise as well as logical relations among genetic events, making the resulting models easy to interpret qualitatively. We tested Polaris on synthetically generated data and showed that it outperforms a widely used machine learning algorithm and approaches the performance of the competing special-purpose, albeit clairvoyant algorithm that is given a priori information about the model parameters. We also prove that under certain rather mild conditions, Polaris is guaranteed to converge for sufficiently large sample sizes. Finally, we applied Polaris to point mutation and copy number variation data in Prostate cancer from The Cancer Genome Atlas (TCGA) and found that there are likely three distinct progressions, one major androgen driven progression, one major non-androgen driven progression, and one novel minor androgen driven progression.