Learning Bayesian Network Classifiers Research Articles

Alleviating the attribute conditional independence and I.I.D. assumptions of averaged one-dependence estimator by double weighting

Learning Bayesian network classifiers (BNCs) from data is NP-hard. Of numerous BNCs, averaged one-dependence estimator (AODE) performs extremely well against more sophisticated newcomers, and its trade-off between bias and variance can be attributed to the independence assumption and i.i.d. assumption, which respectively address the issues of structure complexity and data complexity. To alleviate these assumptions and improve AODE, we propose to apply double weighting, including attribute weighting and model weighting, to finely tune the estimates of conditional probability based on generative learning and joint probability based on discriminative learning, respectively. Instance weighting is introduced to define the information-theoretic metrics for identifying the variation in probability distributions for different data points. This highly scalable learning approach can establish a decision boundary that is specifically tailored to each instance. Our extensive experimental evaluation on 34 datasets from the UCI machine learning repository shows that, attribute weighting and model weighting are complementary although they can work separately. The proposed AODE applying double weighting schema, called DWAODE, is a competitive alternative to other weighting approaches. The experimental results show that DWAODE demonstrates significant advantage in terms of zero–one loss, bias–variance decomposition, RMSE (root mean squared error), Friedman and Nemenyi tests.

Hierarchical Independence Thresholding for learning Bayesian network classifiers

Bayesian networks are powerful tools for knowledge representation and inference under conditions of uncertainty. However, learning an optimal Bayesian network classifier (BNC) is an NP-hard problem since its topology complexity increases exponentially with the number of attributes. Researchers proposed to apply information-theoretic criteria to measure conditional dependence, and independence assumptions are introduced implicitly or explicitly to simplify the network topology of BNC. In this paper, we clarify the mapping relationship between conditional mutual information and local topology, and then illustrate that informational independence does not correspond to probabilistic independence, the criterion of probabilistic independence does not necessarily hold for the independence topology. A novel framework of semi-naive Bayesian operation, called Hierarchical Independence Thresholding (HIT), is presented to efficiently identify informational conditional independence and probabilistic conditional independence by applying an adaptive thresholding method, redundant edges will be filtered out and the learned topology will fit the data better. Extensive experimental evaluation on 58 publicly available datasets reveals that when HIT is applied to BNCs (such as tree augmented Naive Bayes or k-dependence Bayesian classifier), the final BNCs achieve competitive classification performance compared to state-of-the-art learners such as Random Forest and Logistic regression.

Bnclassify: Learning Bayesian Network Classifiers

The bnclassify package provides state-of-the art algorithms for learning Bayesian network classifiers from data. For structure learning it provides variants of the greedy hill-climbing search, a well-known adaptation of the Chow-Liu algorithm and averaged one-dependence estimators. It provides Bayesian and maximum likelihood parameter estimation, as well as three naive-Bayes-specific methods based on discriminative score optimization and Bayesian model averaging. The implementation is efficient enough to allow for time-consuming discriminative scores on medium-sized data sets. bnclassify provides utilities for model evaluation, such as cross-validated accuracy and penalized log-likelihood scores, and analysis of the underlying networks, including network plotting via the Rgraphviz package. It is extensively tested, with over 200 automated tests that give a code coverage of 94%. Here we present the main functionalities, illustrate them with a number of data sets, and comment on related software.

Discretizing environmental data for learning Bayesian-network classifiers

For predicting the presence of different bird species in Andalusia from land-use data, we compare the performances of Bayesian-network classifiers and logistic-regression models. In our study, both well balanced and less balanced data sets are used, and models are learned from both the original continuous data and from the data after discretization. For the latter purpose, four different discretization methods, called Equal Frequency, Equal Width, Chi-Merge and MDLP, are compared. The experimental results from our species data sets suggest that the simple Naive Bayesian classifiers are preferable to logistic-regression models and that the relatively unknown Chi-Merge method is the preferred method for discretizing these environmental data.

Discriminative Learning of Bayesian Networks via Factorized Conditional Log-Likelihood

We propose an efficient and parameter-free scoring criterion, the factorized conditional log-likelihood (fCLL), for learning Bayesian network classifiers. The proposed score is an approximation of the conditional log-likelihood criterion. The approximation is devised in order to guarantee decomposability over the network structure, as well as efficient estimation of the optimal parameters, achieving the same time and space complexity as the traditional log-likelihood scoring criterion. The resulting criterion has an information-theoretic interpretation based on interaction information, which exhibits its discriminative nature. To evaluate the performance of the proposed criterion, we present an empirical comparison with state-of-the-art classifiers. Results on a large suite of benchmark data sets from the UCI repository show that fCLL-trained classifiers achieve at least as good accuracy as the best compared classifiers, using significantly less computational resources.

Learning Bayesian network classifiers from label proportions

This paper deals with a classification problem known as learning from label proportions. The provided dataset is composed of unlabeled instances and is divided into disjoint groups. General class information is given within the groups: the proportion of instances of the group that belong to each class.We have developed a method based on the Structural EM strategy that learns Bayesian network classifiers to deal with the exposed problem. Four versions of our proposal are evaluated on synthetic data, and compared with state-of-the-art approaches on real datasets from public repositories. The results obtained show a competitive behavior for the proposed algorithm.

Learning Bayesian network classifiers by risk minimization

Bayesian networks (BNs) provide a powerful graphical model for encoding the probabilistic relationships among a set of variables, and hence can naturally be used for classification. However, Bayesian network classifiers (BNCs) learned in the common way using likelihood scores usually tend to achieve only mediocre classification accuracy because these scores are less specific to classification, but rather suit a general inference problem. We propose risk minimization by cross validation (RMCV) using the 0/1 loss function, which is a classification-oriented score for unrestricted BNCs. RMCV is an extension of classification-oriented scores commonly used in learning restricted BNCs and non-BN classifiers. Using small real and synthetic problems, allowing for learning all possible graphs, we empirically demonstrate RMCV superiority to marginal and class-conditional likelihood-based scores with respect to classification accuracy. Experiments using twenty-two real-world datasets show that BNCs learned using an RMCV-based algorithm significantly outperform the naive Bayesian classifier (NBC), tree augmented NBC (TAN), and other BNCs learned using marginal or conditional likelihood scores and are on par with non-BN state of the art classifiers, such as support vector machine, neural network, and classification tree. These experiments also show that an optimized version of RMCV is faster than all unrestricted BNCs and comparable with the neural network with respect to run-time. The main conclusion from our experiments is that unrestricted BNCs, when learned properly, can be a good alternative to restricted BNCs and traditional machine-learning classifiers with respect to both accuracy and efficiency.

Conversion of categorical variables into numerical variables via Bayesian network classifiers for binary classifications

Many pattern classification algorithms such as Support Vector Machines (SVMs), Multi-Layer Perceptrons (MLPs), and K-Nearest Neighbors (KNNs) require data to consist of purely numerical variables. However many real world data consist of both categorical and numerical variables. In this paper we suggest an effective method of converting the mixed data of categorical and numerical variables into data of purely numerical variables for binary classifications. Since the suggested method is based on the theory of learning Bayesian Network Classifiers (BNCs), it is computationally efficient and robust to noises and data losses. Also the suggested method is expected to extract sufficient information for estimating a minimum-error-rate (MER) classifier. Simulations on artificial data sets and real world data sets are conducted to demonstrate the competitiveness of the suggested method when the number of values in each categorical variable is large and BNCs accurately model the data.

Learning Bayesian Network Classifiers: Searching in a Space of Partially Directed Acyclic Graphs

There is a commonly held opinion that the algorithms for learning unrestricted types of Bayesian networks, especially those based on the score+search paradigm, are not suitable for building competitive Bayesian network-based classifiers. Several specialized algorithms that carry out the search into different types of directed acyclic graph (DAG) topologies have since been developed, most of these being extensions (using augmenting arcs) or modifications of the Naive Bayes basic topology. In this paper, we present a new algorithm to induce classifiers based on Bayesian networks which obtains excellent results even when standard scoring functions are used. The method performs a simple local search in a space unlike unrestricted or augmented DAGs. Our search space consists of a type of partially directed acyclic graph (PDAG) which combines two concepts of DAG equivalence: classification equivalence and independence equivalence. The results of exhaustive experimentation indicate that the proposed method can compete with state-of-the-art algorithms for classification.