Temporal and statistical information in causal structure learning

Three experiments examined children’s and adults’ abilities to use statistical and temporal information to distinguish between common cause and causal chain structures. In Experiment 1, participants were provided with conditional probability information and/or temporal information and asked to infer the causal structure of a three-variable mechanical system that operated probabilistically. Participants of all ages preferentially relied on the temporal pattern of events in their inferences, even if this conflicted with statistical information. In Experiments 2 and 3, participants observed a series of interventions on the system, which in these experiments operated deterministically. In Experiment 2, participants found it easier to use temporal pattern information than statistical information provided as a result of interventions. In Experiment 3, in which no temporal pattern information was provided, children from 6-7 years, but not younger children, were able to use intervention information to make causal chain judgments, although they had difficulty when the structure was a common cause. The findings suggest that participants, and children in particular, may find it more difficult to use statistical information than temporal pattern information because of its demands on information processing resources. However, there may also be an inherent preference for temporal information.

Efficient Structure Learning of Bayesian Networks using Constraints

This paper addresses the problem of learning Bayesian network structures from data based on score functions that are decomposable. It describes properties that strongly reduce the time and memory costs of many known methods without losing global optimality guarantees. These properties are derived for different score criteria such as Minimum Description Length (or Bayesian Information Criterion), Akaike Information Criterion and Bayesian Dirichlet Criterion. Then a branch-and-bound algorithm is presented that integrates structural constraints with data in a way to guarantee global optimality. As an example, structural constraints are used to map the problem of structure learning in Dynamic Bayesian networks into a corresponding augmented Bayesian network. Finally, we show empirically the benefits of using the properties with state-of-the-art methods and with the new algorithm, which is able to handle larger data sets than before.

Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks

This work presents two new score functions based on the Bayesian Dirichlet equivalent uniform (BDeu) score for learning Bayesian network structures. They consider the sensitivity of BDeu to varying parameters of the Dirichlet prior. The scores take on the most adversary and the most beneficial priors among those within a contamination set around the symmetric one. We build these scores in such way that they are decomposable and can be computed efficiently. Because of that, they can be integrated into any state-of-the-art structure learning method that explores the space of directed acyclic graphs and allows decomposable scores. Empirical results suggest that our scores outperform the standard BDeu score in terms of the likelihood of unseen data and in terms of edge discovery with respect to the true network, at least when the training sample size is small. We discuss the relation between these new scores and the accuracy of inferred models. Moreover, our new criteria can be used to identify the amount of data after which learning is saturated, that is, additional data are of little help to improve the resulting model.

Advances in Learning Bayesian Networks of Bounded Treewidth

This work presents novel algorithms for learning Bayesian networks of bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed integer linear programming formulations for structure learning and treewidth computation. The approximate method consists in sampling k-trees (maximal graphs of treewidth k), and subsequently selecting, exactly or approximately, the best structure whose moral graph is a subgraph of that k-tree. The approaches are empirically compared to each other and to state-of-the-art methods on a collection of public data sets with up to 100 variables.

Learning Extended Tree Augmented Naive Structures

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds' algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). We enhance our procedure with a new score function that only takes into account arcs that are relevant to predict the class, as well as an optimization over the equivalent sample size during learning. These ideas may be useful for structure learning of Bayesian networks in general. A range of experiments shows that we obtain models with better prediction accuracy than naive Bayes and TAN, and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator (AODE). We release our implementation of ETAN so that it can be easily installed and run within Weka.

Learning Bounded Tree-Width Bayesian Networks via Sampling

Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods [12, 14] tackle the problem by using k-trees to learn the optimal Bayesian network with tree-width up to k. In this paper, we propose a sampling method to efficiently find representative k-trees by introducing an Informative score function to characterize the quality of a k-tree. The proposed algorithm can efficiently learn a Bayesian network with tree-width at most k. Experiment results indicate that our approach is comparable with exact methods, but is much more computationally efficient.

Extended Tree Augmented Naive Classifier

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds’ algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). A range of experiments show that we obtain models with better accuracy than TAN and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator.

Learning soft computing control strategies in a modular neural network architecture

Modelling and control of nonlinear dynamical systems is a challenging problem since the dynamics of such systems change over their parameter space. Conventional methodologies for designing nonlinear control laws, such as gain scheduling, are effective because the designer partitions the overall complex control into a number of simpler sub-tasks. This paper describes a new genetic algorithm based method for the design of a modular neural network (MNN) control architecture that learns such partitions of an overall complex control task. Here a chromosome represents both the structure and parameters of an individual neural network in the MNN controller and a hierarchical fuzzy approach is used to select the chromosomes required to accomplish a given control task. This new strategy is applied to the end-point tracking of a single-link flexible manipulator modelled from experimental data. Results show that the MNN controller is simple to design and produces superior performance compared to a single neural network (SNN) controller which is theoretically capable of achieving the desired trajectory. (C) 2003 Elsevier Ltd. All rights reserved.

A hierarchical multiclass support vector machine incorporated with holistic triple learning units

This paper proposes a new hierarchical learning structure, namely the holistic triple learning (HTL), for extending the binary support vector machine (SVM) to multi-classification problems. For an N-class problem, a HTL constructs a decision tree up to a depth of A leaf node of the decision tree is allowed to be placed with a holistic triple learning unit whose generalisation abilities are assessed and approved. Meanwhile, the remaining nodes in the decision tree each accommodate a standard binary SVM classifier. The holistic triple classifier is a regression model trained on three classes, whose training algorithm is originated from a recently proposed implementation technique, namely the least-squares support vector machine (LS-SVM). A major novelty with the holistic triple classifier is the reduced number of support vectors in the solution. For the resultant HTL-SVM, an upper bound of the generalisation error can be obtained. The time complexity of training the HTL-SVM is analysed, and is shown to be comparable to that of training the one-versus-one (1-vs.-1) SVM, particularly on small-scale datasets. Empirical studies show that the proposed HTL-SVM achieves competitive classification accuracy with a reduced number of support vectors compared to the popular 1-vs-1 alternative.

Fast automatic two-stage nonlinear model identification based on the extreme learning machine

It is convenient and effective to solve nonlinear problems with a model that has a linear-in-the-parameters (LITP) structure. However, the nonlinear parameters (e.g. the width of Gaussian function) of each model term needs to be pre-determined either from expert experience or through exhaustive search. An alternative approach is to optimize them by a gradient-based technique (e.g. Newton’s method). Unfortunately, all of these methods still need a lot of computations. Recently, the extreme learning machine (ELM) has shown its advantages in terms of fast learning from data, but the sparsity of the constructed model cannot be guaranteed. This paper proposes a novel algorithm for automatic construction of a nonlinear system model based on the extreme learning machine. This is achieved by effectively integrating the ELM and leave-one-out (LOO) cross validation with our two-stage stepwise construction procedure [1]. The main objective is to improve the compactness and generalization capability of the model constructed by the ELM method. Numerical analysis shows that the proposed algorithm only involves about half of the computation of orthogonal least squares (OLS) based method. Simulation examples are included to confirm the efficacy and superiority of the proposed technique.

Playful structure: a novel image of early years pedagogy for primary school classrooms

Playful structure is a new pedagogic image representing a more balanced and integrated perspective on early years pedagogy, aiming to blend apparent dichotomies and contradictions and to sustain and evolve play-based practice beyond Year 1. Playful structure invites teachers and children to initiate and maintain a degree of playfulness in the child’s whole learning experience, even when the learning intentions demand a supportive structure. Thus, playfulness becomes characteristic of the interaction between adult and the child and not just characteristic of child-initiated versus adult-initiated activities, or of play-time versus task-time. The paper is based on intensive observations and interviews with teachers in Northern Ireland who participated in a play-based and informal curriculum. This paper explains how playful structure rests on complementary processes of infusion of structure into play-based activities and infusion of playfulness into more structured activities, illustrated by cameos. ‘Infusion’ suggests the subtle blending process that allows apparent dichotomies and contradictions to be resolved in practice.

Using location-aware technology for learning Geography in a real digital space outside the classroom

The use of new mobile technologies is still in its infancy in many secondary schools and there is limited evidence of the educational and pedagogical benefits on pupils’ learning in the formal school context. This qualitative study focuses on the use of handheld devices to teach a topic in geography to an examination class. Action research combined with pupil observations and focus group interviews are used to capture the pupils’ experiences of using mediascapes. Activity Theory is used as a lens to structure the analysis of the data and to report on the cognitive and affective impact of m-learning on pupils’ academic performance in the topic. Increased attainment and the development of wider skills for lifelong learning were identified in the study. The adaptability of the majority of pupils to the technology resulted in increased levels of willingness to learn in this novel context.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

Computational learning of the conditional phase-type (C-Ph) distribution: Learning C-Ph distributions

This paper presents a new algorithm for learning the structure of a special type of Bayesian network. The conditional phase-type (C-Ph) distribution is a Bayesian network that models the probabilistic causal relationships between a skewed continuous variable, modelled by the Coxian phase-type distribution, a special type of Markov model, and a set of interacting discrete variables. The algorithm takes a dataset as input and produces the structure, parameters and graphical representations of the fit of the C-Ph distribution as output.The algorithm, which uses a greedy-search technique and has been implemented in MATLAB, is evaluated using a simulated data set consisting of 20,000 cases. The results show that the original C-Ph distribution is recaptured and the fit of the network to the data is discussed.

Learning transfer in multinational companies:Explaining inter-organisation variation

This article addresses the extent to which multinational companies (MNCs) in Ireland deploy practices aimed at the transfer of learning in their operations and the factors explaining inter-organisation variation in so doing. Using data from 260 MNCs, we find that comparatively large numbers of firms deploy practices to transfer learning in their Irish operations. Most notably, we find that almost half of all MNCs have a formal policy on organisational learning, while more than six in every ten MNCs in Ireland utilise three or more learning transfer mechanisms. In investigating inter-organisation variation with respect to these, we test a number of hypotheses involving nationality, sectoral, MNC (e.g. organisation structure) and HR factors. Our results show that the presence of international HR structures is a significant factor in explaining learning transfer in MNCs. We also find support that employment size, sector and integration between the MNC's global operations are useful variables in explaining variation in the deployment of practices on learning transfer in MNCs. © 2009 Blackwell Publishing Ltd.