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Inference in Hybrid Bayesian Networks with Mixtures of Truncated Exponentials
, 2003
"... Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for solving hybrid Bayesian networks. Any probability density function can be approximated with an MTE potential, which can always by marginalized in closed form. This allows propagation to be done exactly us ..."
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Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for solving hybrid Bayesian networks. Any probability density function can be approximated with an MTE potential, which can always by marginalized in closed form. This allows propagation to be done exactly using the ShenoyShafer architecture for computing marginals, with no restrictions on the construction of a join tree.
Conditional Density Estimation with Class Probability Estimators
"... Abstract. Many regression schemes deliver a point estimate only, but often it is useful or even essential to quantify the uncertainty inherent in a prediction. If a conditional density estimate is available, then prediction intervals can be derived from it. In this paper we compare three techniques ..."
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Abstract. Many regression schemes deliver a point estimate only, but often it is useful or even essential to quantify the uncertainty inherent in a prediction. If a conditional density estimate is available, then prediction intervals can be derived from it. In this paper we compare three techniques for computing conditional density estimates using a class probability estimator, where this estimator is applied to the discretized target variable and used to derive instance weights for an underlying univariate density estimator; this yields a conditional density estimate. The three density estimators we compare are: a histogram estimator that has been used previously in this context, a normal density estimator, and a kernel estimator. In our experiments, the latter two deliver better performance, both in terms of crossvalidated loglikelihood and in terms of quality of the resulting prediction intervals. The empirical coverage of the intervals is close to the desired confidence level in most cases. We also include results for point estimation, as well as a comparison to Gaussian process regression and nonparametric quantile estimation. 1
A Comparison of Bayesian Network Learning Algorithms from Continuous Data
 in AMIA
, 2005
"... Abstract. Learning a Bayesian network from data is an important problem in biomedicine for the automatic construction of decision support systems and inference of plausible causal relations. Most Bayesian network learning algorithms require discrete data; however discretization may impact the qualit ..."
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Abstract. Learning a Bayesian network from data is an important problem in biomedicine for the automatic construction of decision support systems and inference of plausible causal relations. Most Bayesian network learning algorithms require discrete data; however discretization may impact the quality of the learned structure. In this project, we present a comparison of different approaches for learning from continuous data to identify the most promising one and to quantify the impact of discretization in Bayesian network learning. Problem Description. Despite the wide applicability of Bayesian networks in biomedicine, the fact that most Bayesian network structure learning algorithms require discrete data is a limitation since biomedical and biological data are routinely continuous. Studies usually employ simple discretization techniques such as frequencybased partitions. By neglecting to adequately address the ramifications of discretization, researchers unknowingly may lose information such as interactions and dependencies between variables and impact the learned structure. Unfortunately, there is no consensus on a standard procedure for discretization. Consequently, it is still an unresolved research question as how to best handle continuous data. There are three typical approaches to learning network structure with continuous data. First, data can be discretized prior to and independent from the application of the learning algorithm. Second, the discretization can be integrated into the learning phase in an effort to exploit the synergies. Algorithms following this approach output a discretization of the input variables and the network structure. Third, learning can be done directly with continuous data without committing to a specific discretization for the variables. Purpose. This project has two major components. First, it comprehensively compares the three different approaches in order to ascertain the relative strengths and weaknesses of each and to quantify the impact of discretization in network learning. Secondly, it presents a toolkit of discretization and learning techniques for use by biomedical researchers. The specific algorithms that are compared are:
Online Estimation of Discrete Densities
"... Abstract—We address the problem of estimating a discrete joint density online, that is, the algorithm is only provided the current example and its current estimate. The proposed online estimator of discrete densities, EDDO (Estimation of Discrete Densities Online), uses classifier chains to model de ..."
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Abstract—We address the problem of estimating a discrete joint density online, that is, the algorithm is only provided the current example and its current estimate. The proposed online estimator of discrete densities, EDDO (Estimation of Discrete Densities Online), uses classifier chains to model dependencies among features. Each classifier in the chain estimates the probability of one particular feature. Because a single chain may not provide a reliable estimate, we also consider ensembles of classifier chains and ensembles of weighted classifier chains. For all density estimators, we provide consistency proofs and propose algorithms to perform certain inference tasks. The empirical evaluation of the estimators is conducted in several experiments and on data sets of up to several million instances: We compare them to density estimates computed from Bayesian structure learners, evaluate them under the influence of noise, measure their ability to deal with concept drift, and measure the runtime performance. Our experiments demonstrate that, even though designed to work online, EDDO delivers estimators of competitive accuracy compared to batch Bayesian structure learners and batch variants of EDDO. I.
Online Estimation of Discrete Densities using Classifier Chains
"... Abstract. We propose an approach to estimate a discrete joint density online, that is, the algorithm is only provided the current example, its current estimate, and a limited amount of memory. To design an online estimator for discrete densities, we use classifier chains to model dependencies among ..."
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Abstract. We propose an approach to estimate a discrete joint density online, that is, the algorithm is only provided the current example, its current estimate, and a limited amount of memory. To design an online estimator for discrete densities, we use classifier chains to model dependencies among features. Each classifier in the chain estimates the probability of one particular feature. Because a single chain may not provide a reliable estimate, we also consider ensembles of classifier chains. Our experiments on synthetic data show that the approach is feasible and the estimated densities approach the true, known distribution with increasing amounts of data. 1