Incremental neural networks for function approximation

A new strategy for incremental building of multilayer feedforward neural networks is proposed in the context of approximation of functions from R-p to R-q using noisy data. A stopping criterion based on the properties of the noise is also proposed. Experimental results for both artificial and real data are performed and two alternatives of the proposed construction strategy are compared.

Measure Fields for Function Approximation

The computation of a piecewise smooth function that approximates a finite set of data points may be decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class. The approximating function may then be computed as the optimal estimator with respect to this measure field. We give an efficient procedure for effecting both computations, and for the determination of the optimal number of components.

A Wiener model for memory high power amplifiers using B-spline function approximation

In this paper we introduce a new Wiener system modeling approach for memory high power amplifiers in communication systems using observational input/output data. By assuming that the nonlinearity in the Wiener model is mainly dependent on the input signal amplitude, the complex valued nonlinear static function is represented by two real valued B-spline curves, one for the amplitude distortion and another for the phase shift, respectively. The Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first order derivatives recursion. An illustrative example is utilized to demonstrate the efficacy of the proposed approach.

Mathematical tests about the existence and applications of PPS-wavelets in function approximation problems

Neural networks and wavelet transform have been recently seen as attractive tools for developing eficient solutions for many real world problems in function approximation. Function approximation is a very important task in environments where computation has to be based on extracting information from data samples in real world processes. So, mathematical model is a very important tool to guarantee the development of the neural network area. In this article we will introduce one series of mathematical demonstrations that guarantee the wavelets properties for the PPS functions. As application, we will show the use of PPS-wavelets in pattern recognition problems of handwritten digit through function approximation techniques.

A radial basis function network (RBFN) for function approximation

A radial basis function network (RBFN) circuit for function approximation is presented. Simulation and experimental results show that the network has good approximation capabilities. The RBFN was a squared hyperbolic secant with three adjustable parameters amplitude, width and center. To test the network a sinusoidal and sine function,vas approximated.

Comparative study between powers of sigmoid functions, MLP-backpropagation and polynomials in function approximation problems

Function approximation is a very important task in environments where the computation has to be based on extracting information from data samples in real world processes. So, the development of new mathematical model is a very important activity to guarantee the evolution of the function approximation area. In this sense, we will present the Polynomials Powers of Sigmoid (PPS) as a linear neural network. In this paper, we will introduce one series of practical results for the Polynomials Powers of Sigmoid, where we will show some advantages of the use of the powers of sigmiod functions in relationship the traditional MLP-Backpropagation and Polynomials in functions approximation problems.

Diffusion Gradient Temporal Difference for Cooperative Reinforcement Learning with Linear Function Approximation

We introduce a diffusion-based algorithm in which multiple agents cooperate to predict a common and global statevalue function by sharing local estimates and local gradient information among neighbors. Our algorithm is a fully distributed implementation of the gradient temporal difference with linear function approximation, to make it applicable to multiagent settings. Simulations illustrate the benefit of cooperation in learning, as made possible by the proposed algorithm.

A unified framework for linear function approximation of value functions in stochastic control

This paper contributes with a unified formulation that merges previ- ous analysis on the prediction of the performance ( value function ) of certain sequence of actions ( policy ) when an agent operates a Markov decision process with large state-space. When the states are represented by features and the value function is linearly approxi- mated, our analysis reveals a new relationship between two common cost functions used to obtain the optimal approximation. In addition, this analysis allows us to propose an efficient adaptive algorithm that provides an unbiased linear estimate. The performance of the pro- posed algorithm is illustrated by simulation, showing competitive results when compared with the state-of-the-art solutions.

Optimal Piecewise Linear Function Approximation for GPU-based Applications

Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind of functions often implies a very high computational cost, unacceptable in real-time applications. To alleviate this problem, functions are commonly approximated by simpler piecewise-polynomial representations. Following this idea, we propose a novel, efficient, and practical technique to evaluate complex and continuous functions using a nearly optimal design of two types of piecewise linear approximations in the case of a large budget of evaluation subintervals. To this end, we develop a thorough error analysis that yields asymptotically tight bounds to accurately quantify the approximation performance of both representations. It provides an improvement upon previous error estimates and allows the user to control the trade-off between the approximation error and the number of evaluation subintervals. To guarantee real-time operation, the method is suitable for, but not limited to, an efficient implementation in modern Graphics Processing Units (GPUs), where it outperforms previous alternative approaches by exploiting the fixed-function interpolation routines present in their texture units. The proposed technique is a perfect match for any application requiring the evaluation of continuous functions, we have measured in detail its quality and efficiency on several functions, and, in particular, the Gaussian function because it is extensively used in many areas of computer vision and cybernetics, and it is expensive to evaluate.

A new variational radial basis function approximation for inference in multivariate diffusions

In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has beneficial characteristics when estimating (hyper-)parameters. We validate our new approach on a nonlinear double well potential dynamical system.

QSAR Modeling of a Set of Pyrazinoate Esters as Antituberculosis Prodrugs

Tuberculosis is an infection caused mainly by Mycobacterium tuberculosis. A first-line antimycobacterial drug is pyrazinamide (PZA), which acts partially as a prodrug activated by a pyrazinamidase releasing the active agent, pyrazinoic acid (POA). As pyrazinoic acid presents some difficulty to cross the mycobacterial cell wall, and also the pyrazinamide-resistant strains do not express the pyrazinamidase, a set of pyrazinoic acid esters have been evaluated as antimycobacterial agents. In this work, a QSAR approach was applied to a set of forty-three pyrazinoates against M. tuberculosis ATCC 27294, using genetic algorithm function and partial least squares regression (WOLF 5.5 program). The independent variables selected were the Balaban index (I), calculated n-octanol/water partition coefficient (ClogP), van-der-Waals surface area, dipole moment, and stretching-energy contribution. The final QSAR model (N = 32, r(2) = 0.68, q(2) = 0.59, LOF = 0.25, and LSE = 0.19) was fully validated employing leave-N-out cross-validation and y-scrambling techniques. The test set (N = 11) presented an external prediction power of 73%. In conclusion, the QSAR model generated can be used as a valuable tool to optimize the activity of future pyrazinoic acid esters in the designing of new antituberculosis agents.

Molecular modeling and QSAR studies of a set of indole and benzimidazole derivatives as H(4) receptor antagonists

Histamine is an important biogenic amine, which acts with a group of four G-protein coupled receptors (GPCRs), namely H(1) to H(4) (H(1)R - H(4)R) receptors. The actions of histamine at H(4)R are related to immunological and inflammatory processes, particularly in pathophysiology of asthma, and H(4)R ligands having antagonistic properties could be helpful as antiinflammatory agents. In this work, molecular modeling and QSAR studies of a set of 30 compounds, indole and benzimidazole derivatives, as H(4)R antagonists were performed. The QSAR models were built and optimized using a genetic algorithm function and partial least squares regression (WOLF 5.5 program). The best QSAR model constructed with training set (N = 25) presented the following statistical measures: r (2) = 0.76, q (2) = 0.62, LOF = 0.15, and LSE = 0.07, and was validated using the LNO and y-randomization techniques. Four of five compounds of test set were well predicted by the selected QSAR model, which presented an external prediction power of 80%. These findings can be quite useful to aid the designing of new anti-H(4) compounds with improved biological response.

Statistical deconvolution of enthalpic energetic contributions to MHC-peptide binding affinity

Background: MHC Class I molecules present antigenic peptides to cytotoxic T cells, which forms an integral part of the adaptive immune response. Peptides are bound within a groove formed by the MHC heavy chain. Previous approaches to MHC Class I-peptide binding prediction have largely concentrated on the peptide anchor residues located at the P2 and C-terminus positions. Results: A large dataset comprising MHC-peptide structural complexes was created by remodelling pre-determined x-ray crystallographic structures. Static energetic analysis, following energy minimisation, was performed on the dataset in order to characterise interactions between bound peptides and the MHC Class I molecule, partitioning the interactions within the groove into van der Waals, electrostatic and total non-bonded energy contributions. Conclusion: The QSAR techniques of Genetic Function Approximation (GFA) and Genetic Partial Least Squares (G/PLS) algorithms were used to identify key interactions between the two molecules by comparing the calculated energy values with experimentally-determined BL50 data. Although the peptide termini binding interactions help ensure the stability of the MHC Class I-peptide complex, the central region of the peptide is also important in defining the specificity of the interaction. As thermodynamic studies indicate that peptide association and dissociation may be driven entropically, it may be necessary to incorporate entropic contributions into future calculations.

Statistical deconvolution of enthalpic energetic contributions to MHC-peptide binding affinity

Background - MHC Class I molecules present antigenic peptides to cytotoxic T cells, which forms an integral part of the adaptive immune response. Peptides are bound within a groove formed by the MHC heavy chain. Previous approaches to MHC Class I-peptide binding prediction have largely concentrated on the peptide anchor residues located at the P2 and C-terminus positions. Results - A large dataset comprising MHC-peptide structural complexes was created by re-modelling pre-determined x-ray crystallographic structures. Static energetic analysis, following energy minimisation, was performed on the dataset in order to characterise interactions between bound peptides and the MHC Class I molecule, partitioning the interactions within the groove into van der Waals, electrostatic and total non-bonded energy contributions. Conclusion - The QSAR techniques of Genetic Function Approximation (GFA) and Genetic Partial Least Squares (G/PLS) algorithms were used to identify key interactions between the two molecules by comparing the calculated energy values with experimentally-determined BL50 data. Although the peptide termini binding interactions help ensure the stability of the MHC Class I-peptide complex, the central region of the peptide is also important in defining the specificity of the interaction. As thermodynamic studies indicate that peptide association and dissociation may be driven entropically, it may be necessary to incorporate entropic contributions into future calculations.