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

Interpretable Probabilistic Password Strength Meters via Deep Learning

Probabilistic password strength meters have been proved to be the most accurate tools to measure password strength. Unfortunately, by construction, they are limited to solely produce an opaque security estimation that fails to fully support the user during the password composition. In the present work, we move the first steps towards cracking the intelligibility barrier of this compelling class of meters. We show that probabilistic password meters inherently own the capability of describing the latent relation occurring between password strength and password structure. In our approach, the security contribution of each character composing a password is disentangled and used to provide explicit fine-grained feedback for the user. Furthermore, unlike existing heuristic constructions, our method is free from any human bias, and, more importantly, its feedback has a clear probabilistic interpretation. In our contribution: (1) we formulate the theoretical foundations of interpretable probabilistic password strength meters; (2) we describe how they can be implemented via an efficient and lightweight deep learning framework suitable for client-side operability.Comment: An abridged version of this paper appears in the proceedings of the 25th European Symposium on Research in Computer Security (ESORICS) 202

Using node ordering to improve Structure MCMC for Bayesian Model Averaging

In this thesis, I address an important problem of estimating the structure of Bayesian network models using Bayesian model averaging approach. Bayesian networks are probabilistic graphical models which are widely used for probabilistic inference and causal modeling. Learning the structure of Bayesian networks can reveal insights into the causal structure of the underlying domain. Owing to the super exponential structure space, it is a challenging task to find the most suitable network model that explains the data. The problem is worsened when the amount of available data is modest, as there might be numerous models with non negligible posterior. Therefore, we are interested in the calculation of posterior of a feature like presence of an edge from one particular node to another or a particular set being a parent of a specific node. The contribution of this thesis includes a Markov Chain Monte Carlo simulation approach to sample network structures from a posterior and then using Bayesian model averaging approach to estimate the posterior of various features

Probabilistic Inference Using Partitioned Bayesian Networks:Introducing a Compositional Framework

Probability theory offers an intuitive and formally sound way to reason in situations that involve uncertainty. The automation of probabilistic reasoning has many applications such as predicting future events or prognostics, providing decision support, action planning under uncertainty, dealing with multiple uncertain measurements, making a diagnosis, and so forth. Bayesian networks in particular have been used to represent probability distributions that model the various applications of uncertainty reasoning. However, present-day automated reasoning approaches involving uncertainty struggle when models increase in size and complexity to fit real-world applications.In this thesis, we explore and extend a state-of-the-art automated reasoning method, called inference by Weighted Model Counting (WMC), when applied to increasingly complex Bayesian network models. WMC is comprised of two distinct phases: compilation and inference. The computational cost of compilation has limited the applicability of WMC. To overcome this limitation we have proposed theoretical and practical solutions that have been tested extensively in empirical studies using real-world Bayesian network models.We have proposed a weighted variant of OBDDs, called Weighted Positive Binary Decision Diagrams (WPBDD), which in turn is based on the new notion of positive Shannon decomposition. WPBDDs are particularly well suited to represent discrete probabilistic models. The conciseness of WPBDDs leads to a reduction in the cost of probabilistic inference.We have introduced Compositional Weighted Model Counting (CWMC), a language-agnostic framework for probabilistic inference that partitions a Bayesian network into subproblems. These subproblems are then compiled and subsequently composed in order to perform inference. This approach significantly reduces the cost of compilation, yet increases the cost of inference. The best results are obtained by seeking a partitioning that allows compilation to (barely) become feasible, but no more, as compilation cost can be amortized over multiple inference queries.Theoretical concepts have been implemented in a readily available open-source tool called ParaGnosis. Further implementational improvements have been found through parallelism, by exploiting independencies that are introduced by CWMC. The proposed methods combined push the boundaries of WMC, allowing this state-of-the-art method to be used on much larger models than before