On the complexity of solving polytree-shaped limited memory influence diagrams with binary variables

Influence diagrams are intuitive and concise representations of structured decision problems. When the problem is non-Markovian, an optimal strategy can be exponentially large in the size of the diagram. We can avoid the inherent intractability by constraining the size of admissible strategies, giving rise to limited memory influence diagrams. A valuable question is then how small do strategies need to be to enable efficient optimal planning. Arguably, the smallest strategies one can conceive simply prescribe an action for each time step, without considering past decisions or observations. Previous work has shown that finding such optimal strategies even for polytree-shaped diagrams with ternary variables and a single value node is NP-hard, but the case of binary variables was left open. In this paper we address such a case, by first noting that optimal strategies can be obtained in polynomial time for polytree-shaped diagrams with binary variables and a single value node. We then show that the same problem is NP-hard if the diagram has multiple value nodes. These two results close the fixed-parameter complexity analysis of optimal strategy selection in influence diagrams parametrized by the shape of the diagram, the number of value nodes and the maximum variable cardinality.

A two-stage algorithm for identification of nonlinear dynamic systems

This paper investigates the two-stage stepwise identification for a class of nonlinear dynamic systems that can be described by linear-in-the-parameters models, and the model has to be built from a very large pool of basis functions or model terms. The main objective is to improve the compactness of the model that is obtained by the forward stepwise methods, while retaining the computational efficiency. The proposed algorithm first generates an initial model using a forward stepwise procedure. The significance of each selected term is then reviewed at the second stage and all insignificant ones are replaced, resulting in an optimised compact model with significantly improved performance. The main contribution of this paper is that these two stages are performed within a well-defined regression context, leading to significantly reduced computational complexity. The efficiency of the algorithm is confirmed by the computational complexity analysis, and its effectiveness is demonstrated by the simulation results.

A Hybrid Forward Algorithm for RBF Neural Network Construction

This paper proposes a novel hybrid forward algorithm (HFA) for the construction of radial basis function (RBF) neural networks with tunable nodes. The main objective is to efficiently and effectively produce a parsimonious RBF neural network that generalizes well. In this study, it is achieved through simultaneous network structure determination and parameter optimization on the continuous parameter space. This is a mixed integer hard problem and the proposed HFA tackles this problem using an integrated analytic framework, leading to significantly improved network performance and reduced memory usage for the network construction. The computational complexity analysis confirms the efficiency of the proposed algorithm, and the simulation results demonstrate its effectiveness

A novel continuous forward algorithm for RBF neural modelling

A continuous forward algorithm (CFA) is proposed for nonlinear modelling and identification using radial basis function (RBF) neural networks. The problem considered here is simultaneous network construction and parameter optimization, well-known to be a mixed integer hard one. The proposed algorithm performs these two tasks within an integrated analytic framework, and offers two important advantages. First, the model performance can be significantly improved through continuous parameter optimization. Secondly, the neural representation can be built without generating and storing all candidate regressors, leading to significantly reduced memory usage and computational complexity. Computational complexity analysis and simulation results confirm the effectiveness.

A fast multi-output RBF neural network construction method

This paper investigates the center selection of multi-output radial basis function (RBF) networks, and a multi-output fast recursive algorithm (MFRA) is proposed. This method can not only reveal the significance of each candidate center based on the reduction in the trace of the error covariance matrix, but also can estimate the network weights simultaneously using a back substitution approach. The main contribution is that the center selection procedure and the weight estimation are performed within a well-defined regression context, leading to a significantly reduced computational complexity. The efficiency of the algorithm is confirmed by a computational complexity analysis, and simulation results demonstrate its effectiveness. (C) 2010 Elsevier B.V. All rights reserved.

Two-stage mixed discrete-continuous identification of radial basis function (RBF) neural models for nonlinear systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous; identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.

An Efficient LS-SVM-Based Method for Fuzzy System Construction

This paper proposes an efficient learning mechanism to build fuzzy rule-based systems through the construction of sparse least-squares support vector machines (LS-SVMs). In addition to the significantly reduced computational complexity in model training, the resultant LS-SVM-based fuzzy system is sparser while offers satisfactory generalization capability over unseen data. It is well known that the LS-SVMs have their computational advantage over conventional SVMs in the model training process; however, the model sparseness is lost, which is the main drawback of LS-SVMs. This is an open problem for the LS-SVMs. To tackle the nonsparseness issue, a new regression alternative to the Lagrangian solution for the LS-SVM is first presented. A novel efficient learning mechanism is then proposed in this paper to extract a sparse set of support vectors for generating fuzzy IF-THEN rules. This novel mechanism works in a stepwise subset selection manner, including a forward expansion phase and a backward exclusion phase in each selection step. The implementation of the algorithm is computationally very efficient due to the introduction of a few key techniques to avoid the matrix inverse operations to accelerate the training process. The computational efficiency is also confirmed by detailed computational complexity analysis. As a result, the proposed approach is not only able to achieve the sparseness of the resultant LS-SVM-based fuzzy systems but significantly reduces the amount of computational effort in model training as well. Three experimental examples are presented to demonstrate the effectiveness and efficiency of the proposed learning mechanism and the sparseness of the obtained LS-SVM-based fuzzy systems, in comparison with other SVM-based learning techniques.

A novel forward gene selection algorithm for microarray data

This paper investigates the gene selection problem for microarray data with small samples and variant correlation. Most existing algorithms usually require expensive computational effort, especially under thousands of gene conditions. The main objective of this paper is to effectively select the most informative genes from microarray data, while making the computational expenses affordable. This is achieved by proposing a novel forward gene selection algorithm (FGSA). To overcome the small samples' problem, the augmented data technique is firstly employed to produce an augmented data set. Taking inspiration from other gene selection methods, the L2-norm penalty is then introduced into the recently proposed fast regression algorithm to achieve the group selection ability. Finally, by defining a proper regression context, the proposed method can be fast implemented in the software, which significantly reduces computational burden. Both computational complexity analysis and simulation results confirm the effectiveness of the proposed algorithm in comparison with other approaches

Approximating Credal Network Inferences by Linear Programming

An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to very accurate inferences. The approach can also be specialized to classification with credal networks based on the maximality criterion. A complexity analysis for both the problem and the algorithm is reported together with numerical experiments, which confirm the good performance of the method. While the inner approximation produced by the algorithm gives rise to a classifier which might return a subset of the optimal class set, preliminary empirical results suggest that the accuracy of the optimal class set is seldom affected by the approximate probabilities

Measuring icon complexity: An automated analysis

Measures of icon designs rely heavily on surveys of the perceptions of population samples. Thus, measuring the extent to which changes in the structure of an icon will alter its perceived complexity can be costly and slow. An automated system capable of producing reliable estimates of perceived complexity could reduce development costs and time. Measures of icon complexity developed by Garcia, Badre, and Stasko (1994) and McDougall, Curry, and de Bruijn (1999) were correlated with six icon properties measured using Matlab (MathWorks, 2001) software, which uses image-processing techniques to measure icon properties. The six icon properties measured were icon foreground, the number of objects in an icon, the number of holes in those objects, and two calculations of icon edges and homogeneity in icon structure. The strongest correlates with human judgments of perceived icon complexity (McDougall et al., 1999) were structural variability (r(s) = .65) and edge information (r(s) =.64).

Low Complexity Spectral Analysis of Heart-Rate-Variability through a Wavelet based FFT

In this paper, a low complexity system for spectral analysis of heart rate variability (HRV) is presented. The main idea of the proposed approach is the implementation of the Fast-Lomb periodogram that is a ubiquitous tool in spectral analysis, using a wavelet based Fast Fourier transform. Interestingly we show that the proposed approach enables the classification of processed data into more and less significant based on their contribution to output quality. Based on such a classification a percentage of less-significant data is being pruned leading to a significant reduction of algorithmic complexity with minimal quality degradation. Indeed, our results indicate that the proposed system can achieve up-to 45% reduction in number of computations with only 4.9% average error in the output quality compared to a conventional FFT based HRV system.

Performance Analysis of a Low Complexity Detector for MCIK-OFDM over TWDP Fading

This letter analyzes the performance of a low complexity detection scheme for a multi-carrier index keying (MCIK) with orthogonal frequency division multiplexing (OFDM) system over two-wave with diffused power (TWDP) fading channels. A closed-form expression for the average pairwise error probability (PEP) over TWDP fading channels is derived. This expression is used to analyze the performance of MCIK-OFDM in moderate, severe and extreme fading conditions. The presented results provide an insight on the performance of MCIK-OFDM for wireless communication systems that operate in enclosed metallic structures such as in-vehicular device-to-device (D2D) wireless networks.

A method to bridge the gap between breadth and depth in IS narrative analysis

A method extending narrative analysis with grounded theory analysis is proposed to bridge the gap between breadth and depth in IS narrative research. The purpose of the method is not to develop a theory but to make narrative analysis more accessible, transparent and accountable; and the resultant narrative more contextually grounded. The method is aimed particularly at inexperienced narrative researchers who currently lack guidance through the complexity of narrative analysis, but may also benefit experienced narrative researchers who may not be familiar with the applicability of grounded theory tools and techniques in this area.