Learning Treewidth-Bounded Bayesian Networks with Thousands of Variables

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian network greatly reduces the complexity of inferences. Yet, being a global property of the graph, it considerably increases the difficulty of the learning process. Our novel algorithm accomplishes this task, scaling both to large domains and to large treewidths. Our novel approach consistently outperforms the state of the art on experiments with up to thousands of variables.

Computational learning of the conditional phase-type (C-Ph) distribution: Learning C-Ph distributions

This paper presents a new algorithm for learning the structure of a special type of Bayesian network. The conditional phase-type (C-Ph) distribution is a Bayesian network that models the probabilistic causal relationships between a skewed continuous variable, modelled by the Coxian phase-type distribution, a special type of Markov model, and a set of interacting discrete variables. The algorithm takes a dataset as input and produces the structure, parameters and graphical representations of the fit of the C-Ph distribution as output.The algorithm, which uses a greedy-search technique and has been implemented in MATLAB, is evaluated using a simulated data set consisting of 20,000 cases. The results show that the original C-Ph distribution is recaptured and the fit of the network to the data is discussed.

Assessing length of stay and associated characteristics of geriatric patients in Northern Ireland

The effective provision of care for the elderly is becoming increasingly more difficult. This is due to the rising proportion of elderly in the population, increasing demands placed on the health services and the financial strain placed on an already stretched economy. The research presented in this paper uses three different models to represent the length of stay distribution of geriatric patients admitted to one of the six key acute hospitals in Northern Ireland and various patient characteristics associated with their respective length of stay. The accurate modelling of bed usage within wards would enable hospital managers to prepare patient discharge packages and rehabilitation services in advance. The models presented within the paper include a Cox proportional hazards model, a Bayesian network with a discrete variable to represent length of stay and a special conditional phase-type model (C-Ph) with a connecting outcome node. This research demonstrates the new efficient fitting algorithm employed for Coxian phase-type distributions while updating C-Ph models for recent elderly patient data.

The Conditional Phase-type distribution: Graphical Models for Continuous Non-Normal Data:The Conditional Phase-type (C-Ph) distribution:

Conditional Gaussian (CG) distributions allow the inclusion of both discrete and continuous variables in a model assuming that the continuous variable is normally distributed. However, the CG distributions have proved to be unsuitable for survival data which tends to be highly skewed. A new method of analysis is required to take into account continuous variables which are not normally distributed. The aim of this paper is to introduce the more appropriate conditional phase-type (C-Ph) distribution for representing a continuous non-normal variable while also incorporating the causal information in the form of a Bayesian network.

PROSTATIC INTRAEPITHELIAL NEOPLASIA (PIN) - PERFORMANCE OF BAYESIAN BELIEF NETWORK FOR DIAGNOSIS AND GRADING

Prostatic intraepithelial neoplasia (PIN) diagnosis and grading are affected by uncertainties which arise from the fact that almost all knowledge of PIN histopathology is expressed in concepts, descriptive linguistic terms, and words. A Bayesian belief network (BBN) was therefore used to reduce the problem of uncertainty in diagnostic clue assessment, while still considering the dependences between elements in the reasoning sequence. A shallow network was used with an open-tree topology, with eight first-level descendant nodes for the diagnostic clues (evidence nodes), each independently linked by a conditional probability matrix to a root node containing the diagnostic alternatives (decision node). One of the evidence nodes was based on the tissue architecture and the others were based on cell features. The system was designed to be interactive, in that the histopathologist entered evidence into the network in the form of likelihood ratios for outcomes at each evidence node. The efficiency of the network was tested on a series of 110 prostate specimens, subdivided as follows: 22 cases of non-neoplastic prostate or benign prostatic tissue (NP), 22 PINs of low grade (PINlow), 22 PINs of high grade (PINhigh), 22 prostatic adenocarcinomas with cribriform pattern (PACcri), and 22 prostatic adenocarcinomas with large acinar pattern (PAClgac). The results obtained in the benign and malignant categories showed that the belief for the diagnostic alternatives is very high, the values being in general more than 0.8 and often close to 1.0. When considering the PIN lesions, the network classified and graded most of the cases with high certainty. However, there were some cases which showed values less than 0.8 (13 cases out of 44), thus indicating that there are situations in which the feature changes are intermediate between contiguous categories or grades. Discrepancy between morphological grading and the BBN results was observed in four out of 44 PIN cases: one PINlow was classified as PINhigh and three PINhigh were classified as PINlow. In conclusion, the network can grade PlN lesions and differentiate them from other prostate lesions with certainty. In particular, it offers a descriptive classifier which is readily implemented and which allows the use of linguistic, fuzzy variables.

Locally regularised two-stage learning algorithm for RBF network centre selection

Nonlinear models constructed from radial basis function (RBF) networks can easily be over-fitted due to the noise on the data. While information criteria, such as the final prediction error (FPE), can provide a trade-off between training error and network complexity, the tunable parameters that penalise a large size of network model are hard to determine and are usually network dependent. This article introduces a new locally regularised, two-stage stepwise construction algorithm for RBF networks. The main objective is to produce a parsomous network that generalises well over unseen data. This is achieved by utilising Bayesian learning within a two-stage stepwise construction procedure to penalise centres that are mainly interpreted by the noise.

Bagging statistical network inference from large-scale gene expression data.

Modern biology and medicine aim at hunting molecular and cellular causes of biological functions and diseases. Gene regulatory networks (GRN) inferred from gene expression data are considered an important aid for this research by providing a map of molecular interactions. Hence, GRNs have the potential enabling and enhancing basic as well as applied research in the life sciences. In this paper, we introduce a new method called BC3NET for inferring causal gene regulatory networks from large-scale gene expression data. BC3NET is an ensemble method that is based on bagging the C3NET algorithm, which means it corresponds to a Bayesian approach with noninformative priors. In this study we demonstrate for a variety of simulated and biological gene expression data from S. cerevisiae that BC3NET is an important enhancement over other inference methods that is capable of capturing biochemical interactions from transcription regulation and protein-protein interaction sensibly. An implementation of BC3NET is freely available as an R package from the CRAN repository. © 2012 de Matos Simoes, Emmert-Streib.

A Bayesian analysis of the chromosome architecture of human disorders by integrating reductionist data

In this paper, we present a Bayesian approach to estimate a chromosome and a disorder network from the Online Mendelian Inheritance in Man (OMIM) database. In contrast to other approaches, we obtain statistic rather than deterministic networks enabling a parametric control in the uncertainty of the underlying disorder-disease gene associations contained in the OMIM, on which the networks are based. From a structural investigation of the chromosome network, we identify three chromosome subgroups that reflect architectural differences in chromosome-disorder associations that are predictively exploitable for a functional analysis of diseases.

EXPERT-SYSTEM SUPPORT USING BAYESIAN BELIEF NETWORKS IN THE DIAGNOSIS OF FINE-NEEDLE ASPIRATION BIOPSY SPECIMENS OF THE BREAST

Aim-To develop an expert system model for the diagnosis of fine needle aspiration cytology (FNAC) of the breast.

Methods-Knowledge and uncertainty were represented in the form of a Bayesian belief network which permitted the combination of diagnostic evidence in a cumulative manner and provided a final probability for the possible diagnostic outcomes. The network comprised 10 cytological features (evidence nodes), each independently linked to the diagnosis (decision node) by a conditional probability matrix. The system was designed to be interactive in that the cytopathologist entered evidence into the network in the form of likelihood ratios for the outcomes at each evidence node.

Results-The efficiency of the network was tested on a series of 40 breast FNAC specimens. The highest diagnostic probability provided by the network agreed with the cytopathologists' diagnosis in 100% of cases for the assessment of discrete, benign, and malignant aspirates. A typical probably benign cases were given probabilities in favour of a benign diagnosis. Suspicious cases tended to have similar probabilities for both diagnostic outcomes and so, correctly, could not be assigned as benign or malignant. A closer examination of cumulative belief graphs for the diagnostic sequence of each case provided insight into the diagnostic process, and quantitative data which improved the identification of suspicious cases.

Conclusion-The further development of such a system will have three important roles in breast cytodiagnosis: (1) to aid the cytologist in making a more consistent and objective diagnosis; (2) to provide a teaching tool on breast cytological diagnosis for the non-expert; and (3) it is the first stage in the development of a system capable of automated diagnosis through the use of expert system machine vision.

Drug treatment of macular oedema secondary to central retinal vein occlusion: a network meta-analysis

Objective
To indirectly compare aflibercept, bevacizumab, dexamethasone, ranibizumab and triamcinolone for treatment of macular oedema secondary to central retinal vein occlusion using a network meta-analysis (NMA).

Design
NMA.

Data sources
The following databases were searched from January 2005 to March 2013: MEDLINE, MEDLINE In-process, EMBASE; CDSR, DARE, HTA, NHSEED, CENTRAL; Science Citation Index and Conference Proceedings Citation Index-Science.

Eligibility criteria for selecting studies
Only randomised controlled trials assessing patients with macular oedema secondary to central retinal vein occlusion were included. Studies had to report either proportions of patients gaining ≥3 lines, losing ≥3 lines, or the mean change in best corrected visual acuity. Two authors screened titles and abstracts, extracted data and undertook risk of bias assessment. Bayesian NMA was used to compare the different interventions.

Results
Seven studies, assessing five drugs, were judged to be sufficiently comparable for inclusion in the NMA. For the proportions of patients gaining ≥3 lines, triamcinolone 4 mg, ranibizumab 0.5 mg, bevacizumab 1.25 mg and aflibercept 2 mg had a higher probability of being more effective than sham and dexamethasone. A smaller proportion of patients treated with triamcinolone 4 mg, ranibizumab 0.5 mg or aflibercept 2 mg lost ≥3 lines of vision compared to those treated with sham. Patients treated with triamcinolone 4 mg, ranibizumab 0.5 mg, bevacizumab 1.25 mg and aflibercept 2 mg had a higher probability of improvement in the mean best corrected visual acuity compared to those treated with sham injections.

Conclusions
We found no evidence of differences between ranibizumab, aflibercept, bevacizumab and triamcinolone for improving vision. The antivascular endothelial growth factors (VEGFs) are likely to be favoured because they are not associated with steroid-induced cataract formation. Aflibercept may be preferred by clinicians because it might require fewer injections.

Approximate credal network updating by linear programming with applications to decision making

Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to accurate inferences. A transformation is also derived to reduce decision making in credal networks based on the maximality criterion to updating. The decision task is proved to have the same complexity of standard inference, being NPPP-complete for general credal nets and NP-complete for polytrees. Similar results are derived for the E-admissibility criterion. Numerical experiments confirm a good performance of the method.

New Complexity Results for MAP in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. It is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure), which extends previous complexity results. Furthermore, a Fully Polynomial Time Approximation Scheme for MAP in networks with bounded treewidth and bounded number of states per variable is developed. Approximation schemes were thought to be impossible, but here it is shown otherwise under the assumptions just mentioned, which are adopted in most applications.

New Results for the MAP Problem in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. First, it is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure). Such proofs extend previous complexity results for the problem. Inapproximability results are also derived in the case of trees if the number of states per variable is not bounded. Although the problem is shown to be hard and inapproximable even in very simple scenarios, a new exact algorithm is described that is empirically fast in networks of bounded treewidth and bounded number of states per variable. The same algorithm is used as basis of a Fully Polynomial Time Approximation Scheme for MAP under such assumptions. Approximation schemes were generally thought to be impossible for this problem, but we show otherwise for classes of networks that are important in practice. The algorithms are extensively tested using some well-known networks as well as random generated cases to show their effectiveness.

NP-hardness of MAP in Ternary Tree Bayesian Networks

This paper strengthens the NP-hardness result for the (partial) maximum a posteriori (MAP) problem in Bayesian networks with topology of trees (every variable has at most one parent) and variable cardinality at most three. MAP is the problem of querying the most probable state configuration of some (not necessarily all) of the network variables given evidence. It is demonstrated that the problem remains hard even in such simplistic networks.