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PubMed2005

Bayesian neural networks for bivariate binary data: an application to prostate cancer study.

Prostate cancer is one of the most common cancers in American men. The cancer could either be locally confined, or it could spread outside the organ. When locally confined, there are several options for treating and curing this disease. Otherwise, surgery is the only option, and in extreme cases of outside spread, it could very easily recur within a short time even after surgery and subsequent radiation therapy. Hence, it is important to know, based on pre-surgery biopsy results how likely the cancer is organ-confined or not. The paper considers a hierarchical Bayesian neural network approach for posterior prediction probabilities of certain features indicative of non-organ confined prostate cancer. In particular, we find such probabilities for margin positivity (MP) and seminal vesicle (SV) positivity jointly. The available training set consists of bivariate binary outcomes indicating the presence or absence of the two. In addition, we have certain covariates such as prostate specific antigen (PSA), gleason score and the indicator for the cancer to be unilateral or bilateral (i.e. spread on one or both sides) in one data set and gene expression microarrays in another data set. We take a hierarchical Bayesian neural network approach to find the posterior prediction probabilities for a test and validation set, and compare these with the actual outcomes for the first data set. In case of the microarray data we use leave one out cross-validation to access the accuracy of our method. We also demonstrate the superiority of our method to the other competing methods through a simulation study. The Bayesian procedure is implemented by an application of the Markov chain Monte Carlo numerical integration technique. For the problem at hand, our Bayesian bivariate neural network procedure is shown to be superior to the classical neural network, Radford Neal's Bayesian neural network as well as bivariate logistic models to predict jointly the MP and SV in a patient in both the data sets as well as in the simulation study.

Bayes Theorem↗
PubMed1999

Bayesian neural networks for classification: how useful is the evidence framework?

This paper presents an empirical assessment of the Bayesian evidence framework for neural networks using four synthetic and four real-world classification problems. We focus on three issues; model selection, automatic relevance determination (ARD) and the use of committees. Model selection using the evidence criterion is only tenable if the number of training examples exceeds the number of network weights by a factor of five or ten. With this number of available examples, however, cross-validation is a viable alternative. The ARD feature selection scheme is only useful in networks with many hidden units and for data sets containing many irrelevant variables. ARD is also useful as a hard feature selection method. Results on applying the evidence framework to the real-world data sets showed that committees of Bayesian networks achieved classification accuracies similar to the best alternative methods. Importantly, this was achievable with a minimum of human intervention.

Journal Article↗
PubMed2003

A hybrid Bayesian-neural network approach for probabilistic modeling of bacterial growth/no-growth interface.

A hybrid probabilistic modeling approach that integrates artificial neural networks (ANNs) with statistical Bayesian conditional probability estimation is proposed. The suggested approach benefits from the power of ANNs as highly flexible nonlinear mapping paradigms, and the Bayes' theorem for computing probabilities of bacterial growth with the aid of Parzen's probability distribution function estimators derived for growth and no-growth (G/NG) states. The proposed modeling approach produces models that can predict the probability of growth of targeted microorganism as affected by a set of parameters pertaining to extrinsic factors and operating conditions. The models also can be used to define the probabilistic boundary (interface) between growth and no-growth, and as such can define and predict the values of critical parameters required to keep a desired pre-specified bacterial growth risk in check. A modular system incorporating the various computational modules was constructed to illustrate the application of the hybrid approach to the probabilistic modeling of growth of pathogenic Escherichia coli strain as affected by temperature and water activity. The proposed approach was compared to other techniques including the traditional linear and nonlinear logistic regression. Results indicated that the hybrid approach outperforms the other approaches in its accuracy as well as flexibility to extract the implicit interrelationships between the various parameters. Advantages and limitations of the approach were also discussed and compared to those of other techniques.

Bayes Theorem↗
PubMed1994

Artificial intelligence in radiology: decision support systems.

Computer-based systems that incorporate artificial intelligence techniques can help physicians make decisions about their patients' care. In radiology, systems have been developed to help physicians choose appropriate radiologic procedures and to formulate accurate diagnoses. These decision support systems use techniques such as rule-based reasoning, artificial neural networks, hypertext, Bayesian networks, and case-based reasoning. This article reviews these artificial intelligence techniques, describes their application in radiology, and discusses the role that decision support systems may play in radiology's future.

Artificial Intelligence↗
PubMed2006

ARACNE: an algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context.

BACKGROUND: Elucidating gene regulatory networks is crucial for understanding normal cell physiology and complex pathologic phenotypes. Existing computational methods for the genome-wide "reverse engineering" of such networks have been successful only for lower eukaryotes with simple genomes. Here we present ARACNE, a novel algorithm, using microarray expression profiles, specifically designed to scale up to the complexity of regulatory networks in mammalian cells, yet general enough to address a wider range of network deconvolution problems. This method uses an information theoretic approach to eliminate the majority of indirect interactions inferred by co-expression methods. RESULTS: We prove that ARACNE reconstructs the network exactly (asymptotically) if the effect of loops in the network topology is negligible, and we show that the algorithm works well in practice, even in the presence of numerous loops and complex topologies. We assess ARACNE's ability to reconstruct transcriptional regulatory networks using both a realistic synthetic dataset and a microarray dataset from human B cells. On synthetic datasets ARACNE achieves very low error rates and outperforms established methods, such as Relevance Networks and Bayesian Networks. Application to the deconvolution of genetic networks in human B cells demonstrates ARACNE's ability to infer validated transcriptional targets of the cMYC proto-oncogene. We also study the effects of misestimation of mutual information on network reconstruction, and show that algorithms based on mutual information ranking are more resilient to estimation errors. CONCLUSION: ARACNE shows promise in identifying direct transcriptional interactions in mammalian cellular networks, a problem that has challenged existing reverse engineering algorithms. This approach should enhance our ability to use microarray data to elucidate functional mechanisms that underlie cellular processes and to identify molecular targets of pharmacological compounds in mammalian cellular networks.

Algorithms↗
PubMed2004

Genomic approaches in dissecting complex biological pathways.

Advances in genomic research have provided many types of large-scale data that contain rich information on various biological pathways. Intensive efforts have been made to qualitatively or quantitatively model biological pathways using these genomic data. Some general network properties, such as the scale-free property and network motifs, have been discussed and various network models have been applied to reconstruct pathways. However, there is a lack of systematic integration of prior knowledge and different genomic data in these analyses. In this review, we discuss pathway reconstruction under the consideration of the complexity embedded in the biological system, and the global and local properties of biological pathways. We review major methodologies, including clustering methods, scale-free networks models, Bayesian networks models, Boolean networks models, systems of differential equations, and data integration methods. We focus on the difficulty of each methodology in modeling biological pathways, and emphasize that different models capture different aspects of biological pathways or genomic data. The 'noisy' large-scale genomic data require the mathematical models and computational methods to be both robust and identifiable. In addition, we believe that ideal models should have the capability of incorporating various data types and these models need to be assessed through rigorous comparisons with empirical data.

Bayes Theorem↗
PubMed1997

Inducing practice guidelines from a hospital database.

Improving health care quality requires the elimination of unnecessary variation in the care process. Decision support applications already exist that can foster adherence to standards. The challenge resides in developing standards consistent with good medical practice. In this paper we present our efforts in determining where sufficient clinical data are captured electronically to automatically define a care process, and what analyses can be done to identify additional data that would allow a care process to be defined. Data routinely collected by a hospital information system have been examined. The analysis tools utilized include logistic regression, a neural network, a Bayesian network, and a rule induction program.

Bayes Theorem↗
PubMed2001

A comparison of classification algorithms to automatically identify chest X-ray reports that support pneumonia.

We compared the performance of expert-crafted rules, a Bayesian network, and a decision tree at automatically identifying chest X-ray reports that support acute bacterial pneumonia. We randomly selected 292 chest X-ray reports, 75 (25%) of which were from patients with a hospital discharge diagnosis of bacterial pneumonia. The reports were encoded by our natural language processor and then manually corrected for mistakes. The encoded observations were analyzed by three expert systems to determine whether the reports supported pneumonia. The reference standard for radiologic support of pneumonia was the majority vote of three physicians. We compared (a) the performance of the expert systems against each other and (b) the performance of the expert systems against that of four physicians who were not part of the gold standard. Output from the expert systems and the physicians was transformed so that comparisons could be made with both binary and probabilistic output. Metrics of comparison for binary output were sensitivity (sens), precision (prec), and specificity (spec). The metric of comparison for probabilistic output was the area under the receiver operator characteristic (ROC) curve. We used McNemar's test to determine statistical significance for binary output and univariate z-tests for probabilistic output. Measures of performance of the expert systems for binary (probabilistic) output were as follows: Rules--sens, 0.92; prec, 0.80; spec, 0.86 (Az, 0.960); Bayesian network--sens, 0.90; prec, 0.72; spec, 0.78 (Az, 0.945); decision tree--sens, 0.86; prec, 0.85; spec, 0.91 (Az, 0.940). Comparisons of the expert systems against each other using binary output showed a significant difference between the rules and the Bayesian network and between the decision tree and the Bayesian network. Comparisons of expert systems using probabilistic output showed no significant differences. Comparisons of binary output against physicians showed differences between the Bayesian network and two physicians. Comparisons of probabilistic output against physicians showed a difference between the decision tree and one physician. The expert systems performed similarly for the probabilistic output but differed in measures of sensitivity, precision, and specificity produced by the binary output. All three expert systems performed similarly to physicians.

Acute Disease↗
PubMedDate not supplied

Combining geometric and probabilistic reasoning for computer-based penetrating-trauma assessment.

OBJECTIVE: To ascertain whether three-dimensional geometric and probabilistic reasoning methods can be successfully combined for computer-based assessment of conditions arising from ballistic penetrating trauma to the chest and abdomen. DESIGN: The authors created a computer system (TraumaSCAN) that integrates three-dimensional geometric reasoning about anatomic likelihood of injury with probabilistic reasoning about injury consequences using Bayesian networks. Preliminary evaluation of TraumaSCAN was performed via a retrospective study testing performance of the system on data from 26 cases of actual gunshot wounds. MEASUREMENTS: Areas under the receiver operating characteristics (ROC) curve were calculated for each condition modeled in TraumaSCAN that was present in the 26 cases. The comprehensiveness and relevance of the TraumaSCAN diagnosis for the 26 cases were used to assess the overall performance of the system. To test the ability of TraumaSCAN to handle limited findings, these measurements were calculated both with and without input of observed findings into the Bayesian network. RESULTS: For the 11 conditions assessed, the worst area under the ROC curve with no observed findings input into the Bayesian network was 0.542 (95% CI, 0.146-0.937), the median was 0.883 (95% CI, 0.713-1.000), and the best was 1.00 (95% CI, 1.000-1.000). The worst area under the ROC curve with all observed findings input into the Bayesian network was 0.835 (95% CI, 0.602-1.000), the median was 0.941 (95% CI, 0.827-1.000), and the best was 0.992 (95% CI, 0.965-1.000). A comparison of the areas under the curve obtained with and without input of observed findings into the Bayesian network showed that there were significant differences for 2 of the 11 conditions assessed. CONCLUSION: A computer-based method that combines geometric and probabilistic reasoning shows promise as a tool for assessing ballistic penetrating trauma to the chest and abdomen.

Bayes Theorem↗
PubMed1997

Subtle changes in benign tissue adjacent to prostate neoplasia detected with a Bayesian belief network.

The aim of this paper was to test the usefulness of a Bayesian belief network (BBN) as a decision support system in the uncertainty assessment of benign prostatic tissue, either associated or not with inflammation or adjacent to prostatic adenocarcinoma (PAC) or prostatic intraepithelial neoplasia (PIN). A shallow network was used with eight first-level descendant nodes for the diagnostic clues, each independently linked by a conditional probability matrix to a root node containing the diagnostic alternatives. One diagnostic evidence node was based on the tissue architecture and the others were based on cell features. The efficacy of the network was tested on a series of 45 simple prostatectomy specimens, subdivided as follows; benign prostatic tissue not associated with other diseases (15 cases), associated with acute and/or chronic inflammation (15 cases), and adjacent to accidentally discovered PAC or PIN (15 cases). The highest belief values for the diagnostic alternative normal prostate (NP) were obtained in the 15 cases not associated with other diseases, the mean value being 0.996. The 15 cases evaluated in areas with inflammation showed the lowest belief values for NP (mean 0.774). For the 15 cases evaluated in specimens with PAC or PIN, the belief values for NP were intermediate between those from normal prostatic tissue associated with inflammation and those not associated (mean 0.925). Moreover, it was found that subtle changes were also present at a certain distance from the tumour. In conclusion, the network can be used as a decision support system to differentiate with high certainty benign prostate adjacent to PAC or PIN from benign prostatic tissue either associated or not with inflammation. The subtle morphological alteration detected with the BBN may be considered malignancy-associated changes.

Adenocarcinoma↗
PubMed2004

Hierarchical Bayesian neural network for gene expression temporal patterns.

There are several important issues to be addressed for gene expression temporal patterns' analysis: first, the correlation structure of multidimensional temporal data; second, the numerous sources of variations with existing high level noise; and last, gene expression mostly involves heterogeneous multiple dynamic patterns. We propose a Hierarchical Bayesian Neural Network model to account for the input correlations of time course gene array data. The variations in absolute gene expression levels and the noise can be estimated with the hierarchical Bayesian setting. The network parameters and the hyperparameters were simultaneously optimized with Monte Carlo Markov Chain simulation. Results show that the proposed model and algorithm can well capture the dynamic feature of gene expression temporal patterns despite the high noise levels, the highly correlated inputs, the overwhelming interactions, and other complex features typically present in microarray data. We test and demonstrate the proposed models with yeast cell cycle temporal data sets. The model performance of Hierarchical Bayesian Neural Network was compared to other popular machine learning methods such as Nearest Neighbor, Support Vector Machine, and Self Organized Map.

Journal Article↗
PubMed1999

Model-independent mean-field theory as a local method for approximate propagation of information.

We present a systematic approach to mean-field theory (MFT) in a general probabilistic setting without assuming a particular model. The mean-field equations derived here may serve as a local, and thus very simple, method for approximate inference in probabilistic models such as Boltzmann machines or Bayesian networks. Our approach is 'model-independent' in the sense that we do not assume a particular type of dependences; in a Bayesian network, for example, we allow arbitrary tables to specify conditional dependences. In general, there are multiple solutions to the mean-field equations. We show that improved estimates can be obtained by forming a weighted mixture of the multiple mean-field solutions. Simple approximate expressions for the mixture weights are given. The general formalism derived so far is evaluated for the special case of Bayesian networks. The benefits of taking into account multiple solutions are demonstrated by using MFT for inference in a small and in a very large Bayesian network. The results are compared with the exact results.

Child↗
PubMed2005

Predictive Bayesian neural network models of MHC class II peptide binding.

We used Bayesian regularized neural networks to model data on the MHC class II-binding affinity of peptides. Training data consisted of sequences and binding data for nonamer (nine amino acid) peptides. Independent test data consisted of sequences and binding data for peptides of length </=25. We assumed that MHC class II-binding activity of peptides depends only on the highest ranked embedded nonamer and that reverse sequences of active nonamers are inactive. We also internally validated the models by using 30% of the training data in an internal test set. We obtained robust models, with near identical statistics for multiple training runs. We determined how predictive our models were using statistical tests and area under the Receiver Operating Characteristic (ROC) graphs (A(ROC)). Most models gave training A(ROC) values close to 1.0 and test set A(ROC) values >0.8. We also used both amino acid indicator variables (bin20) and property-based descriptors to generate models for MHC class II-binding of peptides. The property-based descriptors were more parsimonious than the indicator variable descriptors, making them applicable to larger peptides, and their design makes them able to generalize to unknown peptides outside of the training space. None of the external test data sets contained any of the nonamer sequences in the training sets. Consequently, the models attempted to predict the activity of truly unknown peptides not encountered in the training sets. Our models were well able to tackle the difficult problem of correctly predicting the MHC class II-binding activities of a majority of the test set peptides. Exceptions to the assumption that nonamer motif activities were invariant to the peptide in which they were embedded, together with the limited coverage of the test data, and the fuzziness of the classification procedure, are likely explanations for some misclassifications.

Amino Acid Sequence↗
PubMed2001

Comparing Bayesian neural network algorithms for classifying segmented outdoor images.

In this paper we investigate the Bayesian training of neural networks for region labelling of segmented outdoor scenes; the data are drawn from the Sowerby Image Database of British Aerospace. Neural networks are trained with two Bayesian methods, (i) the evidence framework of MacKay (1992a,b) and (ii) a Markov Chain Monte Carlo method due to Neal (1996). The performance of the two methods is compared to evaluating the empirical learning curves of neural networks trained with the two methods. We also investigate the use of the Automatic Relevance Determination method for input feature selection.

Algorithms↗
PubMed2004

Site-specific updating and aggregation of Bayesian belief network models for multiple experts.

A method for combining multiple expert opinions that are encoded in a Bayesian Belief Network (BBN) model is presented and applied to a problem involving the cleanup of hazardous chemicals at a site with contaminated groundwater. The method uses Bayes Rule to update each expert model with the observed evidence, then uses it again to compute posterior probability weights for each model. The weights reflect the consistency of each model with the observed evidence, allowing the aggregate model to be tailored to the particular conditions observed in the site-specific application of the risk model. The Bayesian update is easy to implement, since the likelihood for the set of evidence (observations for selected nodes of the BBN model) is readily computed by sequential execution of the BBN model. The method is demonstrated using a simple pedagogical example and subsequently applied to a groundwater contamination problem using an expert-knowledge BBN model. The BBN model in this application predicts the probability that reductive dechlorination of the contaminant trichlorethene (TCE) is occurring at a site--a critical step in the demonstration of the feasibility of monitored natural attenuation for site cleanup--given information on 14 measurable antecedent and descendant conditions. The predictions for the BBN models for 21 experts are weighted and aggregated using examples of hypothetical and actual site data. The method allows more weight for those expert models that are more reflective of the site conditions, and is shown to yield an aggregate prediction that differs from that of simple model averaging in a potentially significant manner.

Algorithms↗
PubMed2000

Using a Bayesian belief network to aid differential diagnosis of tropical bovine diseases.

The examination of presenting signs has always played an important role in the diagnosis of diseases in animal populations. In the case of diseases of tropical cattle, such expertise is often scarce and confined to those experts with many years of experience. To capture, conserve and disseminate such valuable expert knowledge remains a key challenge to the application of knowledge-based systems in veterinary medicine. In this communication, we explore the use of a Bayesian belief network to quantify expert opinion with a view to estimating the likelihood of various diseases in the presence and absence of certain signs. Information was elicited from a panel of 44 experienced veterinarians to provide the response matrix of 27 signs associated with 20 commonly occurring diseases in sub-Saharan cattle. Using this prior information, estimates of the probability of certain signs occurring with each disease were calculated from which the Bayesian belief network was able to propagate the posterior probability of each of the diseases based on the observed signs. The method as an aid in making diagnosis is discussed. It is recognised that such an approach is but one strand in the process of arriving at a diagnosis. For ease of use and accessibility, the approach has been converted into the software program CaDDiS (Cattle Disease Diagnosis System) which is available for consultation on the World Wide Web.

Animals↗
PubMed1998

Diagnosis of early acute renal allograft rejection by evaluation of multiple histological features using a Bayesian belief network.

BACKGROUND AND AIMS: The development of the Banff classification of renal transplant pathology has allowed the standardisation of approaches to transplant biopsy histology and reduced interobserver and interdepartmental variation. The usefulness of the Banff classification in the diagnosis of acute rejection has previously been tested by sending sections from 21 "difficult" biopsies to almost all of the renal transplant pathologists in the UK. Although the Banff classification improved reproducibility, the accuracy of diagnosis of early acute rejection was unchanged from the "conventional" approach. Perhaps this is because in making a diagnosis of acute rejection, the Banff classification uses only two features: tubulitis and intimal arteritis. To include more features on a systematic basis would be laborious for a human observer. Therefore, a Bayesian belief network was developed for this task. METHODS: The network was initialised with observations from 110 transplant biopsies. Its performance was then tested on 21 biopsies that had been seen by 37 different renal transplant pathologists in an earlier study. These biopsies had been selected to represent histologically difficult problems but, in retrospect, they all had clear diagnoses of rejection or non-rejection on clinical grounds. RESULTS: Using the Bayesian belief network, a relatively inexperienced pathologist made 19 of 21 correct diagnoses, better than had been achieved by any of the pathologists who had seen the same sections previously (17 of 21), and considerably better than the average proportion of correct diagnoses provided by all 37 renal transplant pathologists (65%). Application of the system by a second pathologist produced a tendency to overdiagnosis of acute rejection, illustrating the consequences of interobserver variation. CONCLUSIONS: In the diagnosis of acute rejection, further useful information can be extracted from features that are currently not considered in the Banff classification. Integration of data by a computer can give a more reliable diagnosis of early acute rejection, but routine application will require the development of a more sophisticated system that can also accommodate clinical data, perhaps one that can continue to "learn" as more data are entered.

Acute Disease↗
PubMed2000

Predicting ICU mortality: a comparison of stationary and nonstationary temporal models.

OBJECTIVE: This study evaluates the effectiveness of the stationarity assumption in predicting the mortality of intensive care unit (ICU) patients at the ICU discharge. DESIGN: This is a comparative study. A stationary temporal Bayesian network learned from data was compared to a set of (33) nonstationary temporal Bayesian networks learned from data. A process observed as a sequence of events is stationary if its stochastic properties stay the same when the sequence is shifted in a positive or negative direction by a constant time parameter. The temporal Bayesian networks forecast mortalities of patients, where each patient has one record per day. The predictive performance of the stationary model is compared with nonstationary models using the area under the receiver operating characteristics (ROC) curves. RESULTS: The stationary model usually performed best. However, one nonstationary model using large data sets performed significantly better than the stationary model. CONCLUSION: Results suggest that using a combination of stationary and nonstationary models may predict better than using either alone.

Artificial Intelligence↗