Bayesian Network Structure Learning with Permutation Tests

In literature there are several studies on the performance of Bayesian network structure learning algorithms. The focus of these studies is almost always the heuristics the learning algorithms are based on, i.e. the maximisation algorithms (in score-based algorithms) or the techniques for learning the dependencies of each variable (in constraint-based algorithms). In this paper we investigate how the use of permutation tests instead of parametric ones affects the performance of Bayesian network structure learning from discrete data. Shrinkage tests are also covered to provide a broad overview of the techniques developed in current literature.Comment: 13 pages, 4 figures. Presented at the Conference 'Statistics for Complex Problems', Padova, June 15, 201

Bayesian Networks Analysis of Malocclusion Data

In this paper we use Bayesian networks to determine and visualise the interactions among various Class III malocclusion maxillofacial features during growth and treatment. We start from a sample of 143 patients characterised through a series of a maximum of 21 different craniofacial features. We estimate a network model from these data and we test its consistency by verifying some commonly accepted hypotheses on the evolution of these disharmonies by means of Bayesian statistics. We show that untreated subjects develop different Class III craniofacial growth patterns as compared to patients submitted to orthodontic treatment with rapid maxillary expansion and facemask therapy. Among treated patients the CoA segment (the maxillary length) and the ANB angle (the antero-posterior relation of the maxilla to the mandible) seem to be the skeletal subspaces that receive the main effect of the treatment

Who learns better Bayesian network structures: Accuracy and speed of structure learning algorithms

Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based algorithms, which use goodness-of-fit scores as objective functions to maximise; and hybrid algorithms that combine both approaches. Constraint-based and score-based algorithms have been shown to learn the same structures when conditional independence and goodness of fit are both assessed using entropy and the topological ordering of the network is known [1]. In this paper, we investigate how these three classes of algorithms perform outside the assumptions above in terms of speed and accuracy of network reconstruction for both discrete and Gaussian Bayesian networks. We approach this question by recognising that structure learning is defined by the combination of a statistical criterion and an algorithm that determines how the criterion is applied to the data. Removing the confounding effect of different choices for the statistical criterion, we find using both simulated and real-world complex data that constraint-based algorithms are often less accurate than score-based algorithms, but are seldom faster (even at large sample sizes); and that hybrid algorithms are neither faster nor more accurate than constraint-based algorithms. This suggests that commonly held beliefs on structure learning in the literature are strongly influenced by the choice of particular statistical criteria rather than just by the properties of the algorithms themselves.CEG and JMG were supported by the project MULTI-SDM (CGL2015-66583-R, MINECO/FEDER)

Bayesian Networks Analysis of Malocclusion Data

In this paper we use Bayesian networks to determine and visualise the interactions among various Class III malocclusion maxillofacial features during growth and treatment. We start from a sample of 143 patients characterised through a series of a maximum of 21 different craniofacial features. We estimate a network model from these data and we test its consistency by verifying some commonly accepted hypotheses on the evolution of these disharmonies by means of Bayesian statistics. We show that untreated subjects develop different Class III craniofacial growth patterns as compared to patients submitted to orthodontic treatment with rapid maxillary expansion and facemask therapy. Among treated patients the CoA segment (the maxillary length) and the ANB angle (the antero-posterior relation of the maxilla to the mandible) seem to be the skeletal subspaces that receive the main effect of the treatment

Bayesian optimization of the PC algorithm for learning Gaussian Bayesian networks

The PC algorithm is a popular method for learning the structure of Gaussian Bayesian networks. It carries out statistical tests to determine absent edges in the network. It is hence governed by two parameters: (i) The type of test, and (ii) its significance level. These parameters are usually set to values recommended by an expert. Nevertheless, such an approach can suffer from human bias, leading to suboptimal reconstruction results. In this paper we consider a more principled approach for choosing these parameters in an automatic way. For this we optimize a reconstruction score evaluated on a set of different Gaussian Bayesian networks. This objective is expensive to evaluate and lacks a closed-form expression, which means that Bayesian optimization (BO) is a natural choice. BO methods use a model to guide the search and are hence able to exploit smoothness properties of the objective surface. We show that the parameters found by a BO method outperform those found by a random search strategy and the expert recommendation. Importantly, we have found that an often overlooked statistical test provides the best over-all reconstruction results

Decentralized Dictionary Learning Over Time-Varying Digraphs

This paper studies Dictionary Learning problems wherein the learning task is distributed over a multi-agent network, modeled as a time-varying directed graph. This formulation is relevant, for instance, in Big Data scenarios where massive amounts of data are collected/stored in different locations (e.g., sensors, clouds) and aggregating and/or processing all data in a fusion center might be inefficient or unfeasible, due to resource limitations, communication overheads or privacy issues. We develop a unified decentralized algorithmic framework for this class of nonconvex problems, which is proved to converge to stationary solutions at a sublinear rate. The new method hinges on Successive Convex Approximation techniques, coupled with a decentralized tracking mechanism aiming at locally estimating the gradient of the smooth part of the sum-utility. To the best of our knowledge, this is the first provably convergent decentralized algorithm for Dictionary Learning and, more generally, bi-convex problems over (time-varying) (di)graphs

Learning Bayesian Networks from Big Data with Greedy Search

Learning the structure of Bayesian networks from data is known to be a computationally challenging, NP-hard problem. The literature has long investigated how to perform structure learning from data containing large numbers of variables, following a general interest in high-dimensional applications (“small n, large p”) in systems biology and genetics. More recently, data sets with large numbers of observations (the so-called “big data”) have become increasingly common; and these data sets are not necessarily high-dimensional, sometimes having only a few tens of variables depending on the application. We revisit the computational complexity of Bayesian network structure learning in this setting, showing that the common choice of measuring it with the number of estimated local distributions leads to unrealistic time complexity estimates for the most common class of score based algorithms, greedy search. We then derive more accurate expressions under common distributional assumptions. These expressions suggest that the speed of Bayesian network learning can be improved by taking advantage of the availability of closed form estimators for local distributions with few parents. Furthermore, we find that using predictive instead of in sample goodness-of-fit scores improves speed; and we confirm that is improves the accuracy of network reconstruction as well, as previously observed by Chickering and Heckerman (2000). We demonstrate these results on large real-world environmental and epidemiological data; and on reference data sets available from public repositories

Learning Bayesian networks from big data with greedy search: computational complexity and efficient implementation

Learning the structure of Bayesian networks from data is known to be a computationally challenging, NP-hard problem. The literature has long investigated how to perform structure learning from data containing large numbers of variables, following a general interest in high-dimensional applications (“small n, large p”) in systems biology and genetics. More recently, data sets with large numbers of observations (the so-called “big data”) have become increasingly common; and these data sets are not necessarily high-dimensional, sometimes having only a few tens of variables depending on the application. We revisit the computational complexity of Bayesian network structure learning in this setting, showing that the common choice of measuring it with the number of estimated local distributions leads to unrealistic time complexity estimates for the most common class of score-based algorithms, greedy search. We then derive more accurate expressions under common distributional assumptions. These expressions suggest that the speed of Bayesian network learning can be improved by taking advantage of the availability of closed-form estimators for local distributions with few parents. Furthermore, we find that using predictive instead of in-sample goodness-of-fit scores improves speed; and we confirm that it improves the accuracy of network reconstruction as well, as previously observed by Chickering and Heckerman (Stat Comput 10: 55–62, 2000). We demonstrate these results on large real-world environmental and epidemiological data; and on reference data sets available from public repositories

Nodular Thyroid Disease in the Era of Precision Medicine

Management of thyroid nodules in the era of precision medicine is continuously changing. Neck ultrasound plays a pivotal role in the diagnosis and several ultrasound stratification systems have been proposed in order to predict malignancy and help clinicians in therapeutic and follow-up decision. Ultrasound elastosonography is another powerful diagnostic technique and can be an added value to stratify the risk of malignancy of thyroid nodules. Moreover, the development of new techniques in the era of "Deep Learning," has led to a creation of machine-learning algorithms based on ultrasound examinations that showed similar accuracy to that obtained by expert radiologists. Despite new technologies in thyroid imaging, diagnostic surgery in 50-70% of patients with indeterminate cytology is still performed. Molecular tests can increase accuracy in diagnosis when performed on "indeterminate" nodules. However, the more updated tools that can be used to this purpose in order to "rule out" (Afirma GSC) or "rule in" (Thyroseq v3) malignancy, have a main limitation: the high costs. In the last years various image-guided procedures have been proposed as alternative and less invasive approaches to surgery for symptomatic thyroid nodules. These minimally invasive techniques (laser and radio-frequency ablation, high intensity focused ultrasound and percutaneous microwave ablation) results in nodule shrinkage and improvement of local symptoms, with a lower risk of complications and minor costs compared to surgery. Finally, ultrasound-guided ablation therapy was introduced with promising results as a feasible treatment for low-risk papillary thyroid microcarcinoma or cervical lymph node metastases

Citizen Hariri and neoliberal politics in postwar Lebanon

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