Concha Bielza

Multi-dimensional classification with Bayesian networks

Multi-dimensional classification aims at finding a function that assigns a vector of class values to a given vector of features. In this paper, this problem is tackled by a general family of models, called multi-dimensional Bayesian network classifiers (MBCs). This probabilistic graphical model organizes class and feature variables as three different subgraphs: class subgraph, feature subgraph, and bridge (from class to features) subgraph. Under the standard 0-1 loss function, the most probable explanation (MPE) must be computed, for which we provide theoretical results in both general MBCs and in MBCs decomposable into maximal connected components. Moreover, when computing the MPE, the vector of class values is covered by following a special ordering (gray code). Under other loss functions defined in accordance with a decomposable structure, we derive theoretical results on how to minimize the expected loss. Besides these inference issues, the paper presents flexible algorithms for learning MBC structures from data based on filter, wrapper and hybrid approaches. The cardinality of the search space is also given. New performance evaluation metrics adapted from the single-class setting are introduced. Experimental results with three benchmark data sets are encouraging, and they outperform state-of-the-art algorithms for multi-label classification.

Comparison of Bayesian networks and artificial neural networks for quality detection in a machining process

Machine tool automation is an important aspect for manufacturing companies facing the growing demand of profitability and high quality products as a key for competitiveness. The purpose of supervising machining processes is to detect interferences that would have a negative effect on the process but mainly on the product quality and production time. In a manufacturing environment, the prediction of surface roughness is of significant importance to achieve this objective. This paper shows the efficacy of two different machine learning classification methods, Bayesian networks and artificial neural networks, for predicting surface roughness in high-speed machining. Experimental tests are conducted using the same data set collected in our own milling process for each classifier. Various measures of merit of the models and statistical tests demonstrate the superiority of Bayesian networks in this field. Bayesian networks are also easier to interpret that artificial neural networks.

A review on evolutionary algorithms in Bayesian network learning and inference tasks

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Bayesian networks are one of the most widely used class of these models. Some of the inference and learning tasks in Bayesian networks involve complex optimization problems that require the use of meta-heuristic algorithms. Evolutionary algorithms, as successful problem solvers, are promising candidates for this purpose. This paper reviews the application of evolutionary algorithms for solving some NP-hard optimization tasks in Bayesian network inference and learning.

Bayesian chain classifiers for multidimensional classification

In multidimensional classification the goal is to assign an instance to a set of different classes. This task is normally addressed either by defining a compound class variable with all the possible combinations of classes (label power-set methods, LPMs) or by building independent classifiers for each class (binary-relevance methods, BRMs). However, LPMs do not scale well and BRMs ignore the dependency relations between classes. We introduce a method for chaining binary Bayesian classifiers that combines the strengths of classifier chains and Bayesian networks for multidimensional classification. The method consists of two phases. In the first phase, a Bayesian network (BN) that represents the dependency relations between the class variables is learned from data. In the second phase, several chain classifiers are built, such that the order of the class variables in the chain is consistent with the class BN. At the end we combine the results of the different generated orders. Our method considers the dependencies between class variables and takes advantage of the conditional independence relations to build simplified models. We perform experiments with a chain of naive Bayes classifiers on different benchmark multidimensional datasets and show that our approach outperforms other state-of-the-art methods.

A review of estimation of distribution algorithms in bioinformatics.

Evolutionary search algorithms have become an essential asset in the algorithmic toolbox for solving high-dimensional optimization problems in across a broad range of bioinformatics problems. Genetic algorithms, the most well-known and representative evolutionary search technique, have been the subject of the major part of such applications. Estimation of distribution algorithms (EDAs) offer a novel evolutionary paradigm that constitutes a natural and attractive alternative to genetic algorithms. They make use of a probabilistic model, learnt from the promising solutions, to guide the search process. In this paper, we set out a basic taxonomy of EDA techniques, underlining the nature and complexity of the probabilistic model of each EDA variant. We review a set of innovative works that make use of EDA techniques to solve challenging bioinformatics problems, emphasizing the EDA paradigms potential for further research in this domain.

Discrete Bayesian Network Classifiers: A Survey

We have had to wait over 30 years since the naive Bayes model was first introduced in 1960 for the so-called Bayesian network classifiers to resurge. Based on Bayesian networks, these classifiers have many strengths, like model interpretability, accommodation to complex data and classification problem settings, existence of efficient algorithms for learning and classification tasks, and successful applicability in real-world problems. In this article, we survey the whole set of discrete Bayesian network classifiers devised to date, organized in increasing order of structure complexity: naive Bayes, selective naive Bayes, seminaive Bayes, one-dependence Bayesian classifiers, k-dependence Bayesian classifiers, Bayesian network-augmented naive Bayes, Markov blanket-based Bayesian classifier, unrestricted Bayesian classifiers, and Bayesian multinets. Issues of feature subset selection and generative and discriminative structure and parameter learning are also covered.

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms.

A survey on multi-output regression

In recent years, a plethora of approaches have been proposed to deal with the increasingly challenging task of multi‐output regression. This study provides a survey on state‐of‐the‐art multi‐output regression methods, that are categorized as problem transformation and algorithm adaptation methods. In addition, we present the mostly used performance evaluation measures, publicly available data sets for multi‐output regression real‐world problems, as well as open‐source software frameworks. WIREs Data Mining Knowl Discov 2015, 5:216–233. doi: 10.1002/widm.1157

Multi-objective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

This paper proposes a new multiobjective estimation of distribution algorithm (EDA) based on joint probabilistic modeling of objectives and variables. This EDA uses the multidimensional Bayesian network as its probabilistic model. In this way, it can capture the dependencies between objectives, variables and objectives, as well as the dependencies learned between variables in other Bayesian network-based EDAs. This model leads to a problem decomposition that helps the proposed algorithm find better tradeoff solutions to the multiobjective problem. In addition to Pareto set approximation, the algorithm is also able to estimate the structure of the multiobjective problem. To apply the algorithm to many-objective problems, the algorithm includes four different ranking methods proposed in the literature for this purpose. The algorithm is first applied to the set of walking fish group problems, and its optimization performance is compared with a standard multiobjective evolutionary algorithm and another competitive multiobjective EDA. The experimental results show that on several of these problems, and for different objective space dimensions, the proposed algorithm performs significantly better and on some others achieves comparable results when compared with the other two algorithms. The algorithm is then tested on the set of CEC09 problems, where the results show that multiobjective optimization based on joint model estimation is able to obtain considerably better fronts for some of the problems compared with the search based on conventional genetic operators in the state-of-the-art multiobjective evolutionary algorithms.

Comparison Between Supervised and Unsupervised Classifications of Neuronal Cell Types: A Case Study

In the study of neural circuits, it becomes essential to discern the different neuronal cell types that build the circuit. Traditionally, neuronal cell types have been classified using qualitative descriptors. More recently, several attempts have been made to classify neurons quantitatively, using unsupervised clustering methods. While useful, these algorithms do not take advantage of previous information known to the investigator, which could improve the classification task. For neocortical GABAergic interneurons, the problem to discern among different cell types is particularly difficult and better methods are needed to perform objective classifications. Here we explore the use of supervised classification algorithms to classify neurons based on their morphological features, using a database of 128 pyramidal cells and 199 interneurons from mouse neocortex. To evaluate the performance of different algorithms we used, as a “benchmark,” the test to automatically distinguish between pyramidal cells and interneurons, defining “ground truth” by the presence or absence of an apical dendrite. We compared hierarchical clustering with a battery of different supervised classification algorithms, finding that supervised classifications outperformed hierarchical clustering. In addition, the selection of subsets of distinguishing features enhanced the classification accuracy for both sets of algorithms. The analysis of selected variables indicates that dendritic features were most useful to distinguish pyramidal cells from interneurons when compared with somatic and axonal morphological variables. We conclude that supervised classification algorithms are better matched to the general problem of distinguishing neuronal cell types when some information on these cell groups, in our case being pyramidal or interneuron, is known a priori. As a spin‐off of this methodological study, we provide several methods to automatically distinguish neocortical pyramidal cells from interneurons, based on their morphologies.