Incomplete graphical model inference via latent tree aggregation

Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical cases, not all variables involved in the network have been observed, and the samples are actually drawn from a distribution where some variables have been marginalized out. This challenges the sparsity assumption commonly made in graphical model inference, since marginalization yields locally dense structures, even when the original network is sparse. We present a procedure for inferring Gaussian graphical models when some variables are unobserved, that accounts both for the influence of missing variables and the low density of the original network. Our model is based on the aggregation of spanning trees, and the estimation procedure on the Expectation-Maximization algorithm. We treat the graph structure and the unobserved nodes as missing variables and compute posterior probabilities of edge appearance. To provide a complete methodology, we also propose several model selection criteria to estimate the number of missing nodes. A simulation study and an illustration flow cytometry data reveal that our method has favorable edge detection properties compared to existing graph inference techniques. The methods are implemented in an R package

A novel approach for pilot error detection using Dynamic Bayesian Networks

In the last decade Dynamic Bayesian Networks (DBNs) have become one type of the most attractive probabilistic modelling framework extensions of Bayesian Networks (BNs) for working under uncertainties from a temporal perspective. Despite this popularity not many researchers have attempted to study the use of these networks in anomaly detection or the implications of data anomalies on the outcome of such models. An abnormal change in the modelled environment's data at a given time, will cause a trailing chain effect on data of all related environment variables in current and consecutive time slices. Albeit this effect fades with time, it still can have an ill effect on the outcome of such models. In this paper we propose an algorithm for pilot error detection, using DBNs as the modelling framework for learning and detecting anomalous data. We base our experiments on the actions of an aircraft pilot, and a flight simulator is created for running the experiments. The proposed anomaly detection algorithm has achieved good results in detecting pilot errors and effects on the whole system. © Springer Science+Business Media 2014

Doctor of Philosophy

dissertationTemporal reasoning denotes the modeling of causal relationships between different variables across different instances of time, and the prediction of future events or the explanation of past events. Temporal reasoning helps in modeling and understanding interactions between human pathophysiological processes, and in predicting future outcomes such as response to treatment or complications. Dynamic Bayesian Networks (DBN) support modeling changes in patients' condition over time due to both diseases and treatments, using probabilistic relationships between different clinical variables, both within and across different points in time. We describe temporal reasoning and representation in general and DBN in particular, with special attention to DBN parameter learning and inference. We also describe temporal data preparation (aggregation, consolidation, and abstraction) techniques that are applicable to medical data that were used in our research. We describe and evaluate various data discretization methods that are applicable to medical data. Projeny, an opensource probabilistic temporal reasoning toolkit developed as part of this research, is also described. We apply these methods, techniques, and algorithms to two disease processes modeled as Dynamic Bayesian Networks. The first test case is hyperglycemia due to severe illness in patients treated in the Intensive Care Unit (ICU). We model the patients' serum glucose and insulin drip rates using Dynamic Bayesian Networks, and recommend insulin drip rates to maintain the patients' serum glucose within a normal range. The model's safety and efficacy are proven by comparing it to the current gold standard. The second test case is the early prediction of sepsis in the emergency department. Sepsis is an acute life threatening condition that requires timely diagnosis and treatment. We present various DBN models and data preparation techniques that detect sepsis with very high accuracy within two hours after the patients' admission to the emergency department. We also discuss factors affecting the computational tractability of the models and appropriate optimization techniques. In this dissertation, we present a guide to temporal reasoning, evaluation of various data preparation, discretization, learning and inference methods, proofs using two test cases using real clinical data, an open-source toolkit, and recommend methods and techniques for temporal reasoning in medicine