Theory & Neural Architecture

Global Asymptotic Convergence of Nonlinear Relaxation Equations Realised Through a Recurrent Perceptron

Authors:

Danilo P Mandic,
Jonathon A. Chambers, Signal Processing Section, Department of Electrical Engineering, Imperial College, London, UK (U.K.)

Page (NA) Paper number 1041

Abstract:

Conditions for Global Asymptotic Stability (GAS) of a nonlinear relaxation equation realised by a Nonlinear Autoregressive Moving Average (NARMA) recurrent perceptron are provided. Convergence is derived through Fixed Point Iteration (FPI) techniques, based upon a contraction mapping feature of a nonlinear activation function of a neuron. Furthermore, nesting is shown to be a spatial interpretation of an FPI, which underpins a recently proposed Pipelined Recurrent Neural Network (PRNN) for nonlinear signal processing.

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A Neural Network for Data Association

Authors:

Michel Winter,
Gérard Favier,

Page (NA) Paper number 1655

Abstract:

This paper presents a new neural solution for solving the data association problem. This problem, also known as the multidimensional assignment problem, arises in data fusion systems like radar and sonar targets tracking, robotic vision... Since it leads to an NP-complete combinatorial optimization, the optimal solution can not be reached in an acceptable calculation time, and the use of approximation methods like the Lagragian relaxation is necessary. In this paper, we propose an alternative approach based on a Hopfield neural model. We show that it converges to an interesting solution that respects the constraints of the association problem. Some simulation results are presented to illustrate the behaviour of the proposed neural solution for an artificial association problem.

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Training MLPs Layer-by-layer with the Information Potential

Authors:

Dongxin Xu,
Jose C. Principe,

Page (NA) Paper number 2406

Abstract:

In the area of information processing one fundamental issue is how to measure the relationship between two variables based only on their samples. In a previous paper, the idea of Information Potential which was formulated from the so called Quadratic Mutual Information was introduced, and successfully applied to problems such as Blind Source Separation and Pose Estimation of SAR (Sythetic Aperture Radar) Images. This paper shows how information potential can be used to train a MLP (multilayer perceptron) layer-by-layer, which provides evidence that the hidden layer of a MLP serves as an "information filter" which tries to best represent the desired output in that layer in the statistical sense of mutual information.

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Time Series Prediction via Neural Network Inversion

Authors:

Lian Yan,
David J Miller,

Page (NA) Paper number 2062

Abstract:

In this work, we propose neural network inversion of a backward predictor as a technique for multi-step prediction of dynamic time series. It may be difficult to train a large network to capture the correlation that exists in some dynamic time series represented by small data sets. The new approach combines an estimate obtained from a forward predictor with an estimate obtained by inverting a backward predictor to more efficiently capture the correlation and to achieve more accurate predictions. Inversion allows us to make causal use of prediction backward in time. Also a new regularization method is developed to make neural network inversion less ill-posed. Experimental results on two benchmark series demonstrate the new approach's significant improvement over standard forward prediction, given comparable complexity.

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Partial Likelihood for Estimation of Multi-Class Posterior Probabilities

Authors:

Tülay Adali,
Hongmei Ni,
Bo Wang,

Page (NA) Paper number 2490

Abstract:

Partial likelihood (PL) provides a unified statistical framework for developing and studying adaptive techniques for nonlinear signal processing [1]. In this paper, we present the general formulation for learning posterior probabilities on the PL cost for multi-class classifier design. We show that the fundamental information-theoretic relationship for learning on the PL cost, the equivalence of likelihood maximization and relative entropy minimization, is satisfied for the multi-class case for the perceptron probability model using softmax [2] normalization. We note the inefficiency of training a softmax network and propose an efficient multi-class equalizer structure based on binary coding of the output classes. We show that the well-formed property of the PL cost [1,7] is satisfied for the softmax and the new multi-class classifier. We present simulation results to demonstrate this fact and note that though the traditional mean square error (MSE) cost uses the available information more efficiently than the PL cost for the multi-class case, the new multi-class equalizer based on binary coding is much more effective in tracking abrupt changes due to the well-formed property of the cost that it uses.

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Hybrid Sequential Monte Carlo / Kalman Methods to Train Neural Networks in Non-Stationary Environments

Authors:

João F de Freitas,
Mahesan Niranjan,
Andrew H Gee,

Page (NA) Paper number 1946

Abstract:

In this paper, we propose a novel sequential algorithm for training neural networks in non-stationary environments. The approach is based on a Monte Carlo method known as the sampling-importance resampling simulation algorithm. We derive our algorithm using a Bayesian framework, which allows us to learn the probability density functions of the network weights and outputs. Consequently, it is possible to compute various statistical estimates including centroids, modes, confidence intervals and kurtosis. The algorithm performs a global search for minima in parameter space by monitoring the errors and gradients at several points in the error surface. This global optimisation strategy is shown to perform better than local optimisation paradigms such as the extended Kalman filter.

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Reconstruction And Prediction Of Nonlinear Dynamical Systems : A Hierarchical Bayes Approach With Neural Nets

Authors:

Takashi Matsumoto,
Motoki Saito,
Yoshinori Nakajima,
Junjiro Sugi,
Hiroaki Hamagishi,

Page (NA) Paper number 2166

Abstract:

When nonlinearity is involved, time series prediction becomes a rather difficult task where the conventional linear methods have limited successes for various reasons. One of the greatest challenges stems from the fact that typical observation data is a scalar time series so that dimension of the nonlinear dynamical system (embedding dimension) is unknown. This paper proposes a Hierarchical Bayesian approach to nonlinear time series prediction problems. This class of schemes considers a family of prior distributions parameterized by hyperparameters instead of a single prior so that it enables algorithms less dependent on a particular prior. One can estimate posterior of weight parameters, hyperparameters and embedding dimension by marginalization with respect to the weight parameters and hyperparameters. The proposed scheme is tested against two examples; (i) chaotic time series, and (ii) building air-conditioning load prediction.

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Sequential Bayesian Computation of Logistic Regression Models

Authors:

Mahesan Niranjan,

Page (NA) Paper number 1868

Abstract:

The Extended Kalman Filter (EKF) algorithm for identification of a state space model is shown to be a sensible tool in estimating a Logistic Regression Model sequentially. A Gaussian probability density over the parameters of the Logistic model is propagated on a sample by sample basis. Two other approaches, the Laplace Approximation and the Variational Approximation are compared with the state space formulation. Features of the latter approach, such as the possibility of inferring noise levels by maximising the `innovation probability' are indicated. Experimental illustrations of these ideas on a synthetic problem and two real world problems are discussed.

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