Conditional density approximations with mixtures of polynomials

Mixtures of polynomials (MoPs) are a non-parametric density estimation technique especially designed for hybrid Bayesian networks with continuous and discrete variables. Algorithms to learn one- and multi-dimensional (marginal) MoPs from data have recently been proposed. In this paper we introduce two methods for learning MoP approximations of conditional densities from data. Both approaches are based on learning MoP approximations of the joint density and the marginal density of the conditioning variables, but they differ as to how the MoP approximation of the quotient of the two densities is found. We illustrate and study the methods using data sampled from known parametric distributions, and we demonstrate their applicability by learning models based on real neuroscience data. Finally, we compare the performance of the proposed methods with an approach for learning mixtures of truncated basis functions (MoTBFs). The empirical results show that the proposed methods generally yield models that are comparable to or significantly better than those found using the MoTBF-based method.

Different approaches to grounding resistance. Calculation for thin wire structures at low frequency energization

The present paper deals with the calculation of grounding resistance of an electrode composed of thin wires, that we consider here as perfect electric conductors (PEC) e.g. with null internal resistance, when buried in a soil of uniform resistivity. The potential profile at the ground surface is also calculated when the electrode is energized with low frequency current. The classic treatment by using leakage currents, called Charge Simulated Method (CSM), is compared with that using a set of steady currents along the axis of the wires, here called the Longitudinal Currents Method (LCM), to solve the Maxwell equations. The method of moments is applied to obtain a numerical approximation of the solution by using rectangular basis functions. Both methods are applied to two types of electrodes and the results are also compared with those obtained using a thirth approach, the Average Potential Method (APM), later described in the text. From the analysis performed, we can estimate a value of the error in the determination of grounding resistance as a function of the number of segments in which the electrodes are divided.

Artificial analysis of molecular marker loci linked to tree resistance response by an artificial neural network

One of the biggest challenges that software developers face is to make an accurate estimate of the project effort. Radial basis function neural networks have been used to software effort estimation in this work using NASA dataset. This paper evaluates and compares radial basis function versus a regression model. The results show that radial basis function neural network have obtained less Mean Square Error than the regression method.

Morphological classification of microtidal sand and gravel beaches

A new classification of microtidal sand and gravel beaches with very different morphologies is presented below. In 557 studied transects, 14 variables were used. Among the variables to be emphasized is the depth of the Posidonia oceanica. The classification was performed for 9 types of beaches: Type 1: Sand and gravel beaches, Type 2: Sand and gravel separated beaches, Type 3: Gravel and sand beaches, Type 4: Gravel and sand separated beaches, Type 5: Pure gravel beaches, Type 6: Open sand beaches, Type 7: Supported sand beaches, Type 8: Bisupported sand beaches and Type 9: Enclosed beaches. For the classification, several tools were used: discriminant analysis, neural networks and Support Vector Machines (SVM), the results were then compared. As there is no theory for deciding which is the most convenient neural network architecture to deal with a particular data set, an experimental study was performed with different numbers of neuron in the hidden layer. Finally, an architecture with 30 neurons was chosen. Different kernels were employed for SVM (Linear, Polynomial, Radial basis function and Sigmoid). The results obtained for the discriminant analysis were not as good as those obtained for the other two methods (ANN and SVM) which showed similar success.

Aid decision algorithms to estimate the risk in congenital heart surgery

Background and objective: In this paper, we have tested the suitability of using different artificial intelligence-based algorithms for decision support when classifying the risk of congenital heart surgery. In this sense, classification of those surgical risks provides enormous benefits as the a priori estimation of surgical outcomes depending on either the type of disease or the type of repair, and other elements that influence the final result. This preventive estimation may help to avoid future complications, or even death. Methods: We have evaluated four machine learning algorithms to achieve our objective: multilayer perceptron, self-organizing map, radial basis function networks and decision trees. The architectures implemented have the aim of classifying among three types of surgical risk: low complexity, medium complexity and high complexity. Results: Accuracy outcomes achieved range between 80% and 99%, being the multilayer perceptron method the one that offered a higher hit ratio. Conclusions: According to the results, it is feasible to develop a clinical decision support system using the evaluated algorithms. Such system would help cardiology specialists, paediatricians and surgeons to forecast the level of risk related to a congenital heart disease surgery.

Towards Accurate and Efficient Description of Excited States

Thesis (Ph.D.)--University of Washington, 2016-06

Molecular dynamics characterization of n-octyl-beta-D-glucopyranoside micelle structure in aqueous solution

n-Octyl-beta-D-glueopyranoside (OG) is a non-ionic glycolipid, which is used widely in biotechnical and biochemical applications. All-atom molecular dynamics simulations from two different initial coordinates and velocities in explicit solvent have been performed to characterize the structural behaviour of an OG aggregate at equilibrium conditions. Geometric packing properties determined from the simulations and small angle neutron scattering experiment state that OG micelles are more likely to exist in a non-spherical shape, even at the concentration range near to the critical micelle concentration (0.025 M). Despite few large deviations in the principal moment of inertia ratios, the average micelle shape calculated from both simulations is a prolate ellipsoid. The deviations at these time scales are presumably the temporary shape change of a micelle. However, the size of the micelle and the accessible surface areas were constant during the simulations with the micelle surface being rough and partially elongated. Radial distribution functions computed for the hydroxyl oxygen atoms of an OG show sharper peaks at a minimum van der Waals contact distance than the acetal oxygen, ring oxygen, and anomeric carbon atoms. This result indicates that these atoms are pointed outwards at the hydrophilic/hydrophobic interface, form hydrogen bonds with the water molecules, and thus hydrate the micelle surface effectively. (c) 2005 Elsevier Inc. All rights reserved.

On functionally-fitted Runge-Kutta methods

Functionally-fitted methods are generalizations of collocation techniques to integrate an equation exactly if its solution is a linear combination of a chosen set of basis functions. When these basis functions are chosen as the power functions, we recover classical algebraic collocation methods. This paper shows that functionally-fitted methods can be derived with less restrictive conditions than previously stated in the literature, and that other related results can be derived in a much more elegant way. The novelty in our approach is to fully retain the collocation framework without reverting back into derivations based on cumbersome Taylor series expansions.

Topographic mappings and feed-forward neural networks

This thesis is a study of the generation of topographic mappings - dimension reducing transformations of data that preserve some element of geometric structure - with feed-forward neural networks. As an alternative to established methods, a transformational variant of Sammon's method is proposed, where the projection is effected by a radial basis function neural network. This approach is related to the statistical field of multidimensional scaling, and from that the concept of a 'subjective metric' is defined, which permits the exploitation of additional prior knowledge concerning the data in the mapping process. This then enables the generation of more appropriate feature spaces for the purposes of enhanced visualisation or subsequent classification. A comparison with established methods for feature extraction is given for data taken from the 1992 Research Assessment Exercise for higher educational institutions in the United Kingdom. This is a difficult high-dimensional dataset, and illustrates well the benefit of the new topographic technique. A generalisation of the proposed model is considered for implementation of the classical multidimensional scaling (¸mds}) routine. This is related to Oja's principal subspace neural network, whose learning rule is shown to descend the error surface of the proposed ¸mds model. Some of the technical issues concerning the design and training of topographic neural networks are investigated. It is shown that neural network models can be less sensitive to entrapment in the sub-optimal global minima that badly affect the standard Sammon algorithm, and tend to exhibit good generalisation as a result of implicit weight decay in the training process. It is further argued that for ideal structure retention, the network transformation should be perfectly smooth for all inter-data directions in input space. Finally, there is a critique of optimisation techniques for topographic mappings, and a new training algorithm is proposed. A convergence proof is given, and the method is shown to produce lower-error mappings more rapidly than previous algorithms.

Efficient training of RBF networks for classification.

Radial Basis Function networks with linear outputs are often used in regression problems because they can be substantially faster to train than Multi-layer Perceptrons. For classification problems, the use of linear outputs is less appropriate as the outputs are not guaranteed to represent probabilities. We show how RBFs with logistic and softmax outputs can be trained efficiently using the Fisher scoring algorithm. This approach can be used with any model which consists of a generalised linear output function applied to a model which is linear in its parameters. We compare this approach with standard non-linear optimisation algorithms on a number of datasets.

Splines and vector splines

The thrust of this report concerns spline theory and some of the background to spline theory and follows the development in (Wahba, 1991). We also review methods for determining hyper-parameters, such as the smoothing parameter, by Generalised Cross Validation. Splines have an advantage over Gaussian Process based procedures in that we can readily impose atmospherically sensible smoothness constraints and maintain computational efficiency. Vector splines enable us to penalise gradients of vorticity and divergence in wind fields. Two similar techniques are summarised and improvements based on robust error functions and restricted numbers of basis functions given. A final, brief discussion of the application of vector splines to the problem of scatterometer data assimilation highlights the problems of ambiguous solutions.

Efficient training of RBF networks for classification

Radial Basis Function networks with linear outputs are often used in regression problems because they can be substantially faster to train than Multi-layer Perceptrons. For classification problems, the use of linear outputs is less appropriate as the outputs are not guaranteed to represent probabilities. In this paper we show how RBFs with logistic and softmax outputs can be trained efficiently using algorithms derived from Generalised Linear Models. This approach is compared with standard non-linear optimisation algorithms on a number of datasets.

Canonical solution groups of a homomorphism : manipulator kinematics, nonparametric regression and distributed object systems

The kinematic mapping of a rigid open-link manipulator is a homomorphism between Lie groups. The homomorphisrn has solution groups that act on an inverse kinematic solution element. A canonical representation of solution group operators that act on a solution element of three and seven degree-of-freedom (do!) dextrous manipulators is determined by geometric analysis. Seven canonical solution groups are determined for the seven do! Robotics Research K-1207 and Hollerbach arms. The solution element of a dextrous manipulator is a collection of trivial fibre bundles with solution fibres homotopic to the Torus. If fibre solutions are parameterised by a scalar, a direct inverse funct.ion that maps the scalar and Cartesian base space coordinates to solution element fibre coordinates may be defined. A direct inverse pararneterisation of a solution element may be approximated by a local linear map generated by an inverse augmented Jacobian correction of a linear interpolation. The action of canonical solution group operators on a local linear approximation of the solution element of inverse kinematics of dextrous manipulators generates cyclical solutions. The solution representation is proposed as a model of inverse kinematic transformations in primate nervous systems. Simultaneous calibration of a composition of stereo-camera and manipulator kinematic models is under-determined by equi-output parameter groups in the composition of stereo-camera and Denavit Hartenberg (DH) rnodels. An error measure for simultaneous calibration of a composition of models is derived and parameter subsets with no equi-output groups are determined by numerical experiments to simultaneously calibrate the composition of homogeneous or pan-tilt stereo-camera with DH models. For acceleration of exact Newton second-order re-calibration of DH parameters after a sequential calibration of stereo-camera and DH parameters, an optimal numerical evaluation of DH matrix first order and second order error derivatives with respect to a re-calibration error function is derived, implemented and tested. A distributed object environment for point and click image-based tele-command of manipulators and stereo-cameras is specified and implemented that supports rapid prototyping of numerical experiments in distributed system control. The environment is validated by a hierarchical k-fold cross validated calibration to Cartesian space of a radial basis function regression correction of an affine stereo model. Basic design and performance requirements are defined for scalable virtual micro-kernels that broker inter-Java-virtual-machine remote method invocations between components of secure manageable fault-tolerant open distributed agile Total Quality Managed ISO 9000+ conformant Just in Time manufacturing systems.

The impact of architecture on the performance of artificial neural networks

A number of researchers have investigated the impact of network architecture on the performance of artificial neural networks. Particular attention has been paid to the impact on the performance of the multi-layer perceptron of architectural issues, and the use of various strategies to attain an optimal network structure. However, there are still perceived limitations with the multi-layer perceptron and networks that employ a different architecture to the multi-layer perceptron have gained in popularity in recent years, particularly, networks that implement a more localised solution, where the solution in one area of the problem space does not impact, or has a minimal impact, on other areas of the space. In this study, we discuss the major architectural issues affecting the performance of a multi-layer perceptron, before moving on to examine in detail the performance of a new localised network, namely the bumptree. The work presented here examines the impact on the performance of artificial neural networks of employing alternative networks to the long established multi-layer perceptron. In particular, networks that impose a solution where the impact of each parameter in the final network architecture has a localised impact on the problem space being modelled are examined. The alternatives examined are the radial basis function and bumptree neural networks, and the impact of architectural issues on the performance of these networks is examined. Particular attention is paid to the bumptree, with new techniques for both developing the bumptree structure and employing this structure to classify patterns being examined.

On the Error-Free Computation of Fast Cosine Transform

We extend our previous work into error-free representations of transform basis functions by presenting a novel error-free encoding scheme for the fast implementation of a Linzer-Feig Fast Cosine Transform (FCT) and its inverse. We discuss an 8x8 L-F scaled Discrete Cosine Transform where the architecture uses a new algebraic integer quantization of the 1-D radix-8 DCT that allows the separable computation of a 2-D DCT without any intermediate number representation conversions. The resulting architecture is very regular and reduces latency by 50% compared to a previous error-free design, with virtually the same hardware cost.