Parameter Magnitude-Based Information Criterion in Identification of Discrete-Time Dynamic System / Md Fahmi Abd Samad and Abdul Rahman Mohd Nasir

Information criterion is an important factor for model structure selection in system identification. It is used to determine the optimality of a particular model structure with the aim of selecting an adequate model. A good information criterion not only evaluate predictive accuracy but also the parsimony of model. There are many information criterions those are widely used such as Akaike information criterion (AIC), corrected Akaike information criterion (AICc) and Bayesian information criterion (BIC). This paper introduces a new parameter-magnitude based information criterion (PMIC2) for identification of linear and non-linear discrete time model. It presents a study on comparison between AIC, AICc, BIC and PMIC2 in selecting the correct model structure for simulated models. This shall be tested using computational software on a number of simulated systems in the form of discrete-time models of various lag orders and number of terms/variables. It is shown that PMIC2 performed in optimum model structure selection better than AIC, AICc and BIC

Parameter Magnitude-Based Information Criterion In Identification Of Discrete-Time Dynamic System

Information criterion is an important factor for model structure selection in system identification. It is used to determine the optimality of a particular model structure with the aim of selecting an adequate model. A good information criterion not only evaluate predictive accuracy but also the parsimony of model. There are many information criterions those are widely used such as Akaike information criterion (AIC), corrected Akaike information criterion (AICc) and Bayesian information criterion (BIC). This paper introduces a new parameter-magnitude based information criterion (PMIC2) for identification of linear and non-linear discrete time model. It presents a study on comparison between AIC, AICc, BIC and PMIC2 in selecting the correct model structure for simulated models. This shall be tested using computational software on a number of simulated systems in the form of discrete-time models of various lag orders and number of terms/variables. It is shown that PMIC2 performed in optimum model structure selection better than AIC, AICc and BIC

On accuracy of PDF divergence estimators and their applicability to representative data sampling

Generalisation error estimation is an important issue in machine learning. Cross-validation traditionally used for this purpose requires building multiple models and repeating the whole procedure many times in order to produce reliable error estimates. It is however possible to accurately estimate the error using only a single model, if the training and test data are chosen appropriately. This paper investigates the possibility of using various probability density function divergence measures for the purpose of representative data sampling. As it turned out, the first difficulty one needs to deal with is estimation of the divergence itself. In contrast to other publications on this subject, the experimental results provided in this study show that in many cases it is not possible unless samples consisting of thousands of instances are used. Exhaustive experiments on the divergence guided representative data sampling have been performed using 26 publicly available benchmark datasets and 70 PDF divergence estimators, and their results have been analysed and discussed

Detection of complex point targets with distributed assets in a MIMO radar system

The report explores the problem of detecting complex point target models in a MIMO radar system. A complex point target is a mathematical and statistical model for a radar target that is not resolved in space, but exhibits varying complex reflectivity across the different bistatic view angles. The complex reflectivity can be modeled as a complex stochastic process whose index set is the set of all the bistatic view angles, and the parameters of the stochastic process follow from an analysis of a target model comprising a number of ideal point scatterers randomly located within some radius of the targets center of mass. The proposed complex point targets may be applicable to statistical inference in multistatic or MIMO radar system. Six different target models are summarized here – three 2-dimensional (Gaussian, Uniform Square, and Uniform Circle) and three 3-dimensional (Gaussian, Uniform Cube, and Uniform Sphere). They are assumed to have different distributions on the location of the point scatterers within the target. We develop data models for the received signals from such targets in the MIMO radar system with distributed assets and partially correlated signals, and consider the resulting detection problem which reduces to the familiar Gauss-Gauss detection problem. We illustrate that the target parameter and transmit signal have an influence on the detector performance through target extent and the SNR respectively. A series of the receiver operator characteristic (ROC) curves are generated to notice the impact on the detector for varying SNR. Kullback–Leibler (KL) divergence is applied to obtain the approximate mean difference between density functions the scatterers assume inside the target models to show the change in the performance of the detector with target extent of the point scatterers

Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison

Within path sampling framework, we show that probability distribution divergences, such as the Chernoff information, can be estimated via thermodynamic integration. The Boltzmann-Gibbs distribution pertaining to different Hamiltonians is implemented to derive tempered transitions along the path, linking the distributions of interest at the endpoints. Under this perspective, a geometric approach is feasible, which prompts intuition and facilitates tuning the error sources. Additionally, there are direct applications in Bayesian model evaluation. Existing marginal likelihood and Bayes factor estimators are reviewed here along with their stepping-stone sampling analogues. New estimators are presented and the use of compound paths is introduced