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The paper presents an approach to machine learning involving the use of a hybrid method in Neural ODE. The authors consider a way of the Neural ODE application with an embedded hybrid method for intelligent manipulator control in a non-deterministic environment. To reduce computational resources, the number of layers of the neural network using ODE is reduced, the solution of which is carried out by a hybrid transformation method. The hybrid method includes normalizing the system, linear transformation, and polynomial transformation. Using the hybrid method in Neural ODE can increase the learning and computation speed. The transformation method has high accuracy with low computational complexity of the algorithm. As a result of applying the hybrid method, the original nonlinear system is transformed to a simpler form. To solve the simplified transformed system, the scheme of the numerical Runge-Kutta method of the third order with an adaptive step is used. The results of the computational experiment show an increase in the speed and accuracy of the calculation. The presented approach to implementing the hybrid method in Neural ODE allows faster training of the neural network of the world model on limited data obtained from the real environment. After training on the data generated by the model of the world, a robotic arm always successfully reaches the object during subsequent interaction with the real environment. This solves the problem of the limited ability of the agent to interact when learning with the real environment in robotic systems. [ABSTRACT FROM AUTHOR]

Abstract: Incremental learning of neural networks has attracted much interest in recent years due to its wide applicability to large scale data sets and to distributed learning scenarios. Moreover, nonstationary learning paradigms have also emerged as a subarea of study in Machine Learning literature due to the problems of classical methods when dealing with data set shifts. In this paper we present an algorithm to train single layer neural networks with nonlinear output functions that take into account incremental, nonstationary and distributed learning scenarios. Moreover, it is demonstrated that introducing a regularization term into the proposed model is equivalent to choosing a particular initialization for the devised training algorithm, which may be suitable for real time systems that have to work under noisy conditions. In addition, the algorithm includes some previous models as special cases and can be used as a block component to build more complex models such as multilayer perceptrons, extending the capacity of these models to incremental, nonstationary and distributed learning paradigms. In this paper, the proposed algorithm is tested with standard data sets and compared with previous approaches, demonstrating its higher accuracy. [Copyright &y& Elsevier]

This paper considers the loopy belief propagation (LBP) algorithm applied to Gaussian graphical models. It is known for Gaussian belief propagation that, if LBP converges, LBP computes the exact posterior means but incorrect variances. In this paper, we analytically derive the posterior variances for some special structured graphs and clarify the accuracy of LBP. For the graphs of a single cycle, we derive a rigorous solution for the posterior variances and thereby find the quantity that determines the accuracy of LBP. Based on this result, we state a necessary condition for LBP convergence. The quantity above also plays an important role in graphs of a single cycle with arbitrary trees. For arbitrary topological graphs, we consider the situation where correlations between any pair of nodes are comparatively small and show analytically the principal values that determine the accuracy of LBP. [Copyright &y& Elsevier]

Nowadays, many real applications comprise data-sets where the distribution of the classes is significantly different. These data-sets are commonly known as imbalanced data-sets. Traditional classifiers are not able to deal with these kinds of data-sets because they tend to classify only majority classes, obtaining poor results for minority classes. The approaches that have been proposed to address this problem can be categorized into three types: resampling methods, algorithmic adaptations and cost sensitive techniques. Radial Basis Function Networks (RBFNs), artificial neural networks composed of local models or RBFs, have demonstrated their efficiency in different machine learning areas. Centers, widths and output weights for the RBFs must be determined when designing RBFNs. Taking into account the locally tuned response of RBFs, the objective of this paper is to study the influence of global and local paradigms on the weights training phase, within the RBFNs design methodology, for imbalanced data-sets. Least Mean Square and the Singular Value Decomposition have been chosen as representatives of local and global weights training paradigms respectively. These learning algorithms are inserted into classical RBFN design methods that are run on imbalanced data-sets and also on these data-sets preprocessed with re-balance techniques. After applying statistical tests to the results obtained, some guidelines about the RBFN design methodology for imbalanced data-sets are provided. [ABSTRACT FROM AUTHOR]

Multilayer perceptron (MLP) and support vector machine (SVM), two popular learning machines, are increasingly being used as alternatives to classical statistical models for ground-level ozone prediction. However, employing learning machines without sufficient awareness about their limitations can lead to unsatisfactory results in modeling the ozone evolving mechanism, especially during ozone formation episodes. With the spirit of literature review and justification, this paper discusses, with respect to the concerning of ozone prediction, the recently developed algorithms/technologies for treating the most prominent model-performance-degradation limitations. MLP has the “black-box” property, i.e., it hardly provides physical explanation for the trained model, overfitting and local minima problems, and SVM has parameters identification and class imbalance problems. This commentary article aims to stress that the underlying philosophy of using learning machines is by no means as trivial as simply fitting models to the data because it causes difficulties, controversies or unresolved problems. This article also aims to serve as a reference point for further technical readings for experts in relevant fields. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a new learning algorithm is proposed for the problem of simultaneous learning of a function and its derivatives as an extension of the study of error minimized extreme learning machine for single hidden layer feedforward neural networks. Our formulation leads to solving a system of linear equations and its solution is obtained by Moore–Penrose generalized pseudo-inverse. In this approach the number of hidden nodes is automatically determined by repeatedly adding new hidden nodes to the network either one by one or group by group and updating the output weights incrementally in an efficient manner until the network output error is less than the given expected learning accuracy. For the verification of the efficiency of the proposed method a number of interesting examples are considered and the results obtained with the proposed method are compared with that of other two popular methods. It is observed that the proposed method is fast and produces similar or better generalization performance on the test data. [Copyright &y& Elsevier]