Identification of Evolving Rule-based Models.

An approach to identification of evolving fuzzy rule-based (eR) models is proposed. eR models implement a method for the noniterative update of both the rule-base structure and parameters by incremental unsupervised learning. The rule-base evolves by adding more informative rules than those that previously formed the model. In addition, existing rules can be replaced with new rules based on ranking using the informative potential of the data. In this way, the rule-base structure is inherited and updated when new informative data become available, rather than being completely retrained. The adaptive nature of these evolving rule-based models, in combination with the highly transparent and compact form of fuzzy rules, makes them a promising candidate for modeling and control of complex processes, competitive to neural networks. The approach has been tested on a benchmark problem and on an air-conditioning component modeling application using data from an installation serving a real building. The results illustrate the viability and efficiency of the approach. (c) IEEE Transactions on Fuzzy System

The Kalman Foundations of Adaptive Least Squares: Applications to Unemployment and Inflation

Adaptive Least Squares (ALS), i.e. recursive regression with asymptotically constant gain, as proposed by Ljung (1992), Sargent (1993, 1999), and Evans and Honkapohja (2001), is an increasingly widely-used method of estimating time-varying relationships and of proxying agents’ time-evolving expectations. This paper provides theoretical foundations for ALS as a special case of the generalized Kalman solution of a Time Varying Parameter (TVP) model. This approach is in the spirit of that proposed by Ljung (1992) and Sargent (1999), but unlike theirs, nests the rigorous Kalman solution of the elementary Local Level Model, and employs a very simple, yet rigorous, initialization. Unlike other approaches, the proposed method allows the asymptotic gain to be estimated by maximum likelihood (ML). The ALS algorithm is illustrated with univariate time series models of U.S. unemployment and inflation. Because the null hypothesis that the coefficients are in fact constant lies on the boundary of the permissible parameter space, the usual regularity conditions for the chi-square limiting distribution of likelihood-based test statistics are not met. Consequently, critical values of the Likelihood Ratio test statistics are established by Monte Carlo means and used to test the constancy of the parameters in the estimated models.Kalman Filter, Adaptive Learning, Adaptive Least Squares, Time Varying Parameter Model, Natural Unemployment Rate, Inflation Forecasting

Discriminative conditional restricted Boltzmann machine for discrete choice and latent variable modelling

Conventional methods of estimating latent behaviour generally use attitudinal questions which are subjective and these survey questions may not always be available. We hypothesize that an alternative approach can be used for latent variable estimation through an undirected graphical models. For instance, non-parametric artificial neural networks. In this study, we explore the use of generative non-parametric modelling methods to estimate latent variables from prior choice distribution without the conventional use of measurement indicators. A restricted Boltzmann machine is used to represent latent behaviour factors by analyzing the relationship information between the observed choices and explanatory variables. The algorithm is adapted for latent behaviour analysis in discrete choice scenario and we use a graphical approach to evaluate and understand the semantic meaning from estimated parameter vector values. We illustrate our methodology on a financial instrument choice dataset and perform statistical analysis on parameter sensitivity and stability. Our findings show that through non-parametric statistical tests, we can extract useful latent information on the behaviour of latent constructs through machine learning methods and present strong and significant influence on the choice process. Furthermore, our modelling framework shows robustness in input variability through sampling and validation