A survey on independence-based Markov networks learning

This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine learning. Markov networks, together with Bayesian networks, are probabilistic graphical models, a widely used formalism for handling probability distributions in intelligent systems. Learning graphical models from data have been extensively applied for the case of Bayesian networks, but for Markov networks learning it is not tractable in practice. However, this situation is changing with time, given the exponential growth of computers capacity, the plethora of available digital data, and the researching on new learning technologies. This work stresses on a technology called independence-based learning, which allows the learning of the independence structure of those networks from data in an efficient and sound manner, whenever the dataset is sufficiently large, and data is a representative sampling of the target distribution. In the analysis of such technology, this work surveys the current state-of-the-art algorithms for learning Markov networks structure, discussing its current limitations, and proposing a series of open problems where future works may produce some advances in the area in terms of quality and efficiency. The paper concludes by opening a discussion about how to develop a general formalism for improving the quality of the structures learned, when data is scarce.Comment: 35 pages, 1 figur

Markov network structure discovery using independence tests

We investigate efficient algorithms for learning the structure of a Markov network from data using the independence-based approach. Such algorithms conduct a series of conditional independence tests on data, successively restricting the set of possible structures until there is only a single structure consistent with the outcomes of the conditional independence tests executed (if possible). As Pearl has shown, the instances of the conditional independence relation in any domain are theoretically interdependent, made explicit in his well-known conditional independence axioms. The first couple of algorithms we discuss, GSMN and GSIMN, exploit Pearl\u27s independence axioms to reduce the number of tests required to learn a Markov network. This is useful in domains where independence tests are expensive, such as cases of very large data sets or distributed data. Subsequently, we explore how these axioms can be exploited to correct the outcome of unreliable statistical independence tests, such as in applications where little data is available. We show how the problem of incorrect tests can be mapped to inference in inconsistent knowledge bases, a problem studied extensively in the field of non-monotonic logic. We present an algorithm for inferring independence values based on a sub-class of non-monotonic logics: the argumentation framework. Our results show the advantage of using our approach in the learning of structures, with improvements in the accuracy of learned networks of up to 20%. As an alternative to logic-based interdependence among independence tests, we also explore probabilistic interdependence. Our algorithm, called PFMN, takes a Bayesian particle filtering approach, using a population of Markov network structures to maintain the posterior probability distribution over them given the outcomes of the tests performed. The result is an approximate algorithm (due to the use of particle filtering) that is useful in domains where independence tests are expensive

Equilibrium in the Computing Continuum through Active Inference

Computing Continuum (CC) systems are challenged to ensure the intricate requirements of each computational tier. Given the system's scale, the Service Level Objectives (SLOs) which are expressed as these requirements, must be broken down into smaller parts that can be decentralized. We present our framework for collaborative edge intelligence enabling individual edge devices to (1) develop a causal understanding of how to enforce their SLOs, and (2) transfer knowledge to speed up the onboarding of heterogeneous devices. Through collaboration, they (3) increase the scope of SLO fulfillment. We implemented the framework and evaluated a use case in which a CC system is responsible for ensuring Quality of Service (QoS) and Quality of Experience (QoE) during video streaming. Our results showed that edge devices required only ten training rounds to ensure four SLOs; furthermore, the underlying causal structures were also rationally explainable. The addition of new types of devices can be done a posteriori, the framework allowed them to reuse existing models, even though the device type had been unknown. Finally, rebalancing the load within a device cluster allowed individual edge devices to recover their SLO compliance after a network failure from 22% to 89%

Development and benchmarking a novel scatter search algorithm for learning probabilistic graphical models in healthcare

Healthcare data of small sizes are widespread, and the challenge of building accurate inference models is difficult. Many machine learning algorithms exist, but many are black boxes. Explainable models in healthcare are essential, so healthcare practitioners can understand the developed model and incorporate domain knowledge into the model. Probabilistic graphical models offer a visual way to represent relationships between data. Here we develop a new scatter search algorithm to learn Bayesian networks. This machine learning approach is applied to three case studies to understand the effectiveness in comparison with traditional machine learning techniques. First, a new scatter search approach is presented to construct the structure of a Bayesian network. Statistical tests are used to build small Directed acyclic graphs combined in an iterative process to build up multiple larger graphs. Probability distributions are fitted as the graphs are built up. These graphs are then scored based on classification performance. Once no new solutions can be found, the algorithm finishes. The first study looks at the effectiveness of the scatter search constructed Bayesian network against other machine learning algorithms in the same class. These algorithms are benchmarked against standard datasets from the UCI Machine Learning Repository, which has many published studies. The second study assesses the effectiveness of the scatter search Bayesian network for classifying ovarian cancer patients. Multiple other machine learning algorithms were applied alongside the Bayesian network. All data from this study were collected by clinicians from the Aneurin Bevan University Health Board. The study concluded that machine-learning techniques could be applied to classify patients based on early indicators. The third and final study looked into applying machine learning techniques to no-show breast cancer follow-up patients. Once again, the scatter search Bayesian network was used alongside other machine learning approaches. Socio-demographic and socio-economic factors involving low to middle-income families were used in this study with feature selection techniques to improve machine learning performance. It was found machine learning, when used with feature selection, could classify no-show patients with reasonable accuracy

Mining multi-dimensional concept-drifting data streams using Bayesian network classifiers

In recent years, a plethora of approaches have been proposed to deal with the increasingly challenging task of mining concept-drifting data streams. However, most of these approaches can only be applied to uni-dimensional classification problems where each input instance has to be assigned to a single output class variable. The problem of mining multi-dimensional data streams, which includes multiple output class variables, is largely unexplored and only few streaming multi-dimensional approaches have been recently introduced. In this paper, we propose a novel adaptive method, named Locally Adaptive-MB-MBC (LA-MB-MBC), for mining streaming multi-dimensional data. To this end, we make use of multi-dimensional Bayesian network classifiers (MBCs) as models. Basically, LA-MB-MBC monitors the concept drift over time using the average log-likelihood score and the Page-Hinkley test. Then, if a concept drift is detected, LA-MB-MBC adapts the current MBC network locally around each changed node. An experimental study carried out using synthetic multi-dimensional data streams shows the merits of the proposed method in terms of concept drift detection as well as classification performance

Extending Bayesian network models for mining and classification of glaucoma

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Glaucoma is a degenerative disease that damages the nerve fiber layer in the retina of the eye. Its mechanisms are not fully known and there is no fully-effective strategy to prevent visual impairment and blindness. However, if treatment is carried out at an early stage, it is possible to slow glaucomatous progression and improve the quality of life of sufferers. Despite the great amount of heterogeneous data that has become available for monitoring glaucoma, the performance of tests for early diagnosis are still insufficient, due to the complexity of disease progression and the diffculties in obtaining sufficient measurements. This research aims to assess and extend Bayesian Network (BN) models to investigate the nature of the disease and its progression, as well as improve early diagnosis performance. The exibility of BNs and their ability to integrate with clinician expertise make them a suitable tool to effectively exploit the available data. After presenting the problem, a series of BN models for cross-sectional data classification and integration are assessed; novel techniques are then proposed for classification and modelling of glaucoma progression. The results are validated against literature, direct expert knowledge and other Artificial Intelligence techniques, indicating that BNs and their proposed extensions improve glaucoma diagnosis performance and enable new insights into the disease process