Bayesian Rule Learning Research Articles

A novel approach to modeling multifactorial diseases using Ensemble Bayesian Rule classifiers.

Modeling factors influencing disease phenotypes, from biomarker profiling study datasets, is a critical task in biomedicine. Such datasets are typically generated from high-throughput 'omic' technologies, which help examine disease mechanisms at an unprecedented resolution. These datasets are challenging because they are high-dimensional. The disease mechanisms they study are also complex because many diseases are multifactorial, resulting from the collective activity of several factors, each with a small effect. Bayesian rule learning (BRL) is a rule model inferred from learning Bayesian networks from data, and has been shown to be effective in modeling high-dimensional datasets. However, BRL is not efficient at modeling multifactorial diseases since it suffers from data fragmentation during learning. In this paper, we overcome this limitation by implementing and evaluating three types of ensemble model combination strategies with BRL- uniform combination (UC; same as Bagging), Bayesian model averaging (BMA), and Bayesian model combination (BMC)- collectively called Ensemble Bayesian Rule Learning (EBRL). We also introduce a novel method to visualize EBRL models, called the Bayesian Rule Ensemble Visualizing tool (BREVity), which helps extract interpret the most important rule patterns guiding the predictions made by the ensemble model. Our results using twenty-five public, high-dimensional, gene expression datasets of multifactorial diseases, suggest that, both EBRL models using UC and BMC achieve better predictive performance than BMA and other classic machine learning methods. Furthermore, BMC is found to be more reliable than UC, when the ensemble includes sub-optimal models resulting from the stochasticity of the model search process. Together, EBRL and BREVity provides researchers a promising and novel tool for modeling multifactorial diseases from high-dimensional datasets that leverages strengths of ensemble methods for predictive performance, while also providing interpretable explanations for its predictions.

Tunable structure priors for Bayesian rule learning for knowledge integrated biomarker discovery.

AIMTo develop a framework to incorporate background domain knowledge into classification rule learning for knowledge discovery in biomedicine.METHODSBayesian rule learning (BRL) is a rule-based classifier that uses a greedy best-first search over a space of Bayesian belief-networks (BN) to find the optimal BN to explain the input dataset, and then infers classification rules from this BN. BRL uses a Bayesian score to evaluate the quality of BNs. In this paper, we extended the Bayesian score to include informative structure priors, which encodes our prior domain knowledge about the dataset. We call this extension of BRL as BRLp. The structure prior has a λ hyperparameter that allows the user to tune the degree of incorporation of the prior knowledge in the model learning process. We studied the effect of λ on model learning using a simulated dataset and a real-world lung cancer prognostic biomarker dataset, by measuring the degree of incorporation of our specified prior knowledge. We also monitored its effect on the model predictive performance. Finally, we compared BRLp to other state-of-the-art classifiers commonly used in biomedicine.RESULTSWe evaluated the degree of incorporation of prior knowledge into BRLp, with simulated data by measuring the Graph Edit Distance between the true data-generating model and the model learned by BRLp. We specified the true model using informative structure priors. We observed that by increasing the value of λ we were able to increase the influence of the specified structure priors on model learning. A large value of λ of BRLp caused it to return the true model. This also led to a gain in predictive performance measured by area under the receiver operator characteristic curve (AUC). We then obtained a publicly available real-world lung cancer prognostic biomarker dataset and specified a known biomarker from literature [the epidermal growth factor receptor (EGFR) gene]. We again observed that larger values of λ led to an increased incorporation of EGFR into the final BRLp model. This relevant background knowledge also led to a gain in AUC.CONCLUSIONBRLp enables tunable structure priors to be incorporated during Bayesian classification rule learning that integrates data and knowledge as demonstrated using lung cancer biomarker data.

An Overview and Evaluation of Recent Machine Learning Imputation Methods Using Cardiac Imaging Data.

Many clinical research datasets have a large percentage of missing values that directly impacts their usefulness in yielding high accuracy classifiers when used for training in supervised machine learning. While missing value imputation methods have been shown to work well with smaller percentages of missing values, their ability to impute sparse clinical research data can be problem specific. We previously attempted to learn quantitative guidelines for ordering cardiac magnetic resonance imaging during the evaluation for pediatric cardiomyopathy, but missing data significantly reduced our usable sample size. In this work, we sought to determine if increasing the usable sample size through imputation would allow us to learn better guidelines. We first review several machine learning methods for estimating missing data. Then, we apply four popular methods (mean imputation, decision tree, k-nearest neighbors, and self-organizing maps) to a clinical research dataset of pediatric patients undergoing evaluation for cardiomyopathy. Using Bayesian Rule Learning (BRL) to learn ruleset models, we compared the performance of imputation-augmented models versus unaugmented models. We found that all four imputation-augmented models performed similarly to unaugmented models. While imputation did not improve performance, it did provide evidence for the robustness of our learned models.

Learning Parsimonious Classification Rules from Gene Expression Data Using Bayesian Networks with Local Structure.

The comprehensibility of good predictive models learned from high-dimensional gene expression data is attractive because it can lead to biomarker discovery. Several good classifiers provide comparable predictive performance but differ in their abilities to summarize the observed data. We extend a Bayesian Rule Learning (BRL-GSS) algorithm, previously shown to be a significantly better predictor than other classical approaches in this domain. It searches a space of Bayesian networks using a decision tree representation of its parameters with global constraints, and infers a set of IF-THEN rules. The number of parameters and therefore the number of rules are combinatorial to the number of predictor variables in the model. We relax these global constraints to a more generalizable local structure (BRL-LSS). BRL-LSS entails more parsimonious set of rules because it does not have to generate all combinatorial rules. The search space of local structures is much richer than the space of global structures. We design the BRL-LSS with the same worst-case time-complexity as BRL-GSS while exploring a richer and more complex model space. We measure predictive performance using Area Under the ROC curve (AUC) and Accuracy. We measure model parsimony performance by noting the average number of rules and variables needed to describe the observed data. We evaluate the predictive and parsimony performance of BRL-GSS, BRL-LSS and the state-of-the-art C4.5 decision tree algorithm, across 10-fold cross-validation using ten microarray gene-expression diagnostic datasets. In these experiments, we observe that BRL-LSS is similar to BRL-GSS in terms of predictive performance, while generating a much more parsimonious set of rules to explain the same observed data. BRL-LSS also needs fewer variables than C4.5 to explain the data with similar predictive performance. We also conduct a feasibility study to demonstrate the general applicability of our BRL methods on the newer RNA sequencing gene-expression data.

Learning multiple rules simultaneously: Affixes are more salient than reduplications

Language learners encounter numerous opportunities to learn regularities, but need to decide which of these regularities to learn, because some are not productive in their native language. Here, we present an account of rule learning based on perceptual and memory primitives (Endress, Dehaene-Lambertz, & Mehler, Cognition, 105(3), 577–614, 2007; Endress, Nespor, & Mehler, Trends in Cognitive Sciences, 13(8), 348–353, 2009), suggesting that learners preferentially learn regularities that are more salient to them, and that the pattern of salience reflects the frequency of language features across languages. We contrast this view with previous artificial grammar learning research, which suggests that infants “choose” the regularities they learn based on rational, Bayesian criteria (Frank & Tenenbaum, Cognition, 120(3), 360–371, 2013; Gerken, Cognition, 98(3)B67–B74, 2006, Cognition, 115(2), 362–366, 2010). In our experiments, adult participants listened to syllable strings starting with a syllable reduplication and always ending with the same “affix” syllable, or to syllable strings starting with this “affix” syllable and ending with the “reduplication”. Both affixation and reduplication are frequently used for morphological marking across languages. We find three crucial results. First, participants learned both regularities simultaneously. Second, affixation regularities seemed easier to learn than reduplication regularities. Third, regularities in sequence offsets were easier to learn than regularities at sequence onsets. We show that these results are inconsistent with previous Bayesian rule learning models, but mesh well with the perceptual or memory primitives view. Further, we show that the pattern of salience revealed in our experiments reflects the distribution of regularities across languages. Ease of acquisition might thus be one determinant of the frequency of regularities across languages.

CMRI-BED: A novel informatics framework for cardiac MRI biomarker extraction and discovery applied to pediatric cardiomyopathy classification.

BackgroundPediatric cardiomyopathies are a rare, yet heterogeneous group of pathologies of the myocardium that are routinely examined clinically using Cardiovascular Magnetic Resonance Imaging (cMRI). This gold standard powerful non-invasive tool yields high resolution temporal images that characterize myocardial tissue. The complexities associated with the annotation of images and extraction of markers, necessitate the development of efficient workflows to acquire, manage and transform this data into actionable knowledge for patient care to reduce mortality and morbidity.MethodsWe develop and test a novel informatics framework called cMRI-BED for biomarker extraction and discovery from such complex pediatric cMRI data that includes the use of a suite of tools for image processing, marker extraction and predictive modeling. We applied our workflow to obtain and analyze a dataset of 83 de-identified cases and controls containing cMRI-derived biomarkers for classifying positive versus negative findings of cardiomyopathy in children. Bayesian rule learning (BRL) methods were applied to derive understandable models in the form of propositional rules with posterior probabilities pertaining to their validity. Popular machine learning methods in the WEKA data mining toolkit were applied using default parameters to assess cross-validation performance of this dataset using accuracy and percentage area under ROC curve (AUC) measures.ResultsThe best 10-fold cross validation predictive performance obtained on this cMRI-derived biomarker dataset was 80.72% accuracy and 79.6% AUC by a BRL decision tree model, which is promising from this type of rare data. Moreover, we were able to verify that mycocardial delayed enhancement (MDE) status, which is known to be an important qualitative factor in the classification of cardiomyopathies, is picked up by our rule models as an important variable for prediction.ConclusionsPreliminary results show the feasibility of our framework for processing such data while also yielding actionable predictive classification rules that can augment knowledge conveyed in cardiac radiology outcome reports. Interactions between MDE status and other cMRI parameters that are depicted in our rules warrant further investigation and validation. Predictive rules learned from cMRI data to classify positive and negative findings of cardiomyopathy can enhance scientific understanding of the underlying interactions among imaging-derived parameters.

Novel MRI-derived quantitative biomarker for cardiac function applied to classifying ischemic cardiomyopathy within a Bayesian rule learning framework.

Characterization of regional left ventricular (LV) function may have application in prognosticating timely response and informing choice therapy in patients with ischemic cardiomyopathy. The purpose of this study is to characterize LV function through a systematic analysis of 4D (3D + time) endocardial motion over the cardiac cycle in an effort to define objective, clinically useful metrics of pathological remodeling and declining cardiac performance, using standard cardiac MRI data for two distinct patient cohorts accessed from CardiacAtlas.org: a) MESA - a cohort of asymptomatic patients; and b) DETERMINE - a cohort of symptomatic patients with a history of ischemic heart disease (IHD) or myocardial infarction. The LV endocardium was segmented and a signed phase-to-phase Hausdorff distance (HD) was computed at 3D uniformly spaced points tracked on segmented endocardial surface contours, over the cardiac cycle. An LV-averaged index of phase-to-phase endocardial displacement (P2PD) time-histories was computed at each tracked point, using the HD computed between consecutive cardiac phases. Average and standard deviation in P2PD over the cardiac cycle was used to prepare characteristic curves for the asymptomatic and IHD cohort. A novel biomarker of RMS error between mean patient-specific characteristic P2PD over the cardiac cycle for each individual patient and the cumulative P2PD characteristic of a cohort of asymptomatic patients was established as the RMS-P2PD marker. The novel RMS-P2PD marker was tested as a cardiac function based feature for automatic patient classification using a Bayesian Rule Learning (BRL) framework. The RMS-P2PD biomarker indices were significantly different for the symptomatic patient and asymptomatic control cohorts (p<0.001). BRL accurately classified 83.8% of patients correctly from the patient and control populations, with leave-one-out cross validation, using standard indices of LV ejection fraction (LV-EF) and LV end-systolic volume index (LV-ESVI). This improved to 91.9% with inclusion of the RMS-P2PD biomarker and was congruent with improvements in both sensitivity for classifying patients and specificity for identifying asymptomatic controls from 82.6% up to 95.7%. RMS-P2PD, when contrasted against a collective normal reference, is a promising biomarker to investigate further in its utility for identifying quantitative signs of pathological endocardial function which may boost standard image makers as precursors of declining cardiac performance.

Bayesian rule learning for biomedical data mining

Disease state prediction from biomarker profiling studies is an important problem because more accurate classification models will potentially lead to the discovery of better, more discriminative markers. Data mining methods are routinely applied to such analyses of biomedical datasets generated from high-throughput 'omic' technologies applied to clinical samples from tissues or bodily fluids. Past work has demonstrated that rule models can be successfully applied to this problem, since they can produce understandable models that facilitate review of discriminative biomarkers by biomedical scientists. While many rule-based methods produce rules that make predictions under uncertainty, they typically do not quantify the uncertainty in the validity of the rule itself. This article describes an approach that uses a Bayesian score to evaluate rule models. We have combined the expressiveness of rules with the mathematical rigor of Bayesian networks (BNs) to develop and evaluate a Bayesian rule learning (BRL) system. This system utilizes a novel variant of the K2 algorithm for building BNs from the training data to provide probabilistic scores for IF-antecedent-THEN-consequent rules using heuristic best-first search. We then apply rule-based inference to evaluate the learned models during 10-fold cross-validation performed two times. The BRL system is evaluated on 24 published 'omic' datasets, and on average it performs on par or better than other readily available rule learning methods. Moreover, BRL produces models that contain on average 70% fewer variables, which means that the biomarker panels for disease prediction contain fewer markers for further verification and validation by bench scientists.

Lazy Learning of Bayesian Rules

The naive Bayesian classifier provides a simple and effective approach to classifier learning, but its attribute independence assumption is often violated in the real world. A number of approaches have sought to alleviate this problem. A Bayesian tree learning algorithm builds a decision tree, and generates a local naive Bayesian classifier at each leaf. The tests leading to a leaf can alleviate attribute inter-dependencies for the local naive Bayesian classifier. However, Bayesian tree learning still suffers from the small disjunct problem of tree learning. While inferred Bayesian trees demonstrate low average prediction error rates, there is reason to believe that error rates will be higher for those leaves with few training examples. This paper proposes the application of lazy learning techniques to Bayesian tree induction and presents the resulting lazy Bayesian rule learning algorithm, called LBR. This algorithm can be justified by a variant of Bayes theorem which supports a weaker conditional attribute independence assumption than is required by naive Bayes. For each test example, it builds a most appropriate rule with a local naive Bayesian classifier as its consequent. It is demonstrated that the computational requirements of LBR are reasonable in a wide cross-section of natural domains. Experiments with these domains show that, on average, this new algorithm obtains lower error rates significantly more often than the reverse in comparison to a naive Bayesian classifier, C4.5, a Bayesian tree learning algorithm, a constructive Bayesian classifier that eliminates attributes and constructs new attributes using Cartesian products of existing nominal attributes, and a lazy decision tree learning algorithm. It also outperforms, although the result is not statistically significant, a selective naive Bayesian classifier.