Instance-Specific Causal Bayesian Network Structure Learning

Much of science consists of discovering and modeling causal relationships in nature. Causal knowledge provides insight into the mechanisms acting currently (e.g., the side-effects caused by a new medication) and the prediction of outcomes that will follow when actions are taken (e.g., the chance that a disease will be cured if a particular medication is taken). In the past 30 years, there has been tremendous progress in developing computational methods for discovering causal knowledge from observational data. Some of the most significant progress in causal discovery research has occurred using causal Bayesian networks (CBNs). A CBN is a probabilistic graphical model that includes nodes and edges. Each node corresponds to a domain variable and each edge (or arc) is interpreted as a causal relationship between a parent node (a cause) and a child node (an effect), relative to the other nodes in the network. In this dissertation, I focus on two problems: (1) developing efficient CBN structure learning methods that learn CBNs in the presence of latent variables (i.e., unmeasured or hidden variables). Handling latent variables is important in causal discovery since it can induce dependencies that need to be distinguished from direct causation. (2) developing instance-specific CBN structure learning algorithms to learn a CBN that is specific to an instance (e.g., patient), both with and without latent variables. Learning instance-specific CBNs is important in many areas of science, especially the biomedical domain; however, it is an under-studied research problem. In this dissertation, I develop various novel instance-specific CBN structure learning methods and evaluate them using simulated and real-world data

Reasoning about Independence in Probabilistic Models of Relational Data

We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data inaccurately infers conditional independence. We introduce relational d-separation, a theory for deriving conditional independence facts from relational models. We provide a new representation, the abstract ground graph, that enables a sound, complete, and computationally efficient method for answering d-separation queries about relational models, and we present empirical results that demonstrate effectiveness.Comment: 61 pages, substantial revisions to formalisms, theory, and related wor

Efficient computational strategies to learn the structure of probabilistic graphical models of cumulative phenomena

Structural learning of Bayesian Networks (BNs) is a NP-hard problem, which is further complicated by many theoretical issues, such as the I-equivalence among different structures. In this work, we focus on a specific subclass of BNs, named Suppes-Bayes Causal Networks (SBCNs), which include specific structural constraints based on Suppes' probabilistic causation to efficiently model cumulative phenomena. Here we compare the performance, via extensive simulations, of various state-of-the-art search strategies, such as local search techniques and Genetic Algorithms, as well as of distinct regularization methods. The assessment is performed on a large number of simulated datasets from topologies with distinct levels of complexity, various sample size and different rates of errors in the data. Among the main results, we show that the introduction of Suppes' constraints dramatically improve the inference accuracy, by reducing the solution space and providing a temporal ordering on the variables. We also report on trade-offs among different search techniques that can be efficiently employed in distinct experimental settings. This manuscript is an extended version of the paper "Structural Learning of Probabilistic Graphical Models of Cumulative Phenomena" presented at the 2018 International Conference on Computational Science