Discriminant feature analysis for pattern recognition

Ph.DDOCTOR OF PHILOSOPH

Model combination by decomposition and aggregation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2004.Includes bibliographical references (p. 265-282).This thesis focuses on a general problem in statistical modeling, namely model combination. It proposes a novel feature-based model combination method to improve model accuracy and reduce model uncertainty. In this method, a set of candidate models are first decomposed into a group of components or features and then components are selected and aggregated into a composite model based on data. However, in implementing this new method, some central challenges have to be addressed, which include candidate model choice, component selection, data noise modeling, model uncertainty reduction and model locality. In order to solve these problems, some new methods are put forward. In choosing candidate models, some criteria are proposed including accuracy, diversity, independence as well as completeness and then corresponding quantitative measures are designed to quantify these criteria, and finally an overall preference score is generated for each model in the pool. Principal component analysis (PCA) and independent component analysis (ICA) are applied to decompose candidate models into components and multiple linear regression is employed to aggregate components into a composite model.(cont.) In order to reduce model structure uncertainty, a new concept of fuzzy variable selection is introduced to carry out component selection, which is able to combine the interpretability of classical variable selection and the stability of shrinkage estimators. In dealing with parameter estimation uncertainty, exponential power distribution is proposed to model unknown non-Gaussian noise and parametric weighted least-squares method is devise to estimate parameters in the context of non-Gaussian noise. These two methods are combined to work together to reduce model uncertainty, including both model structure uncertainty and parameter uncertainty. To handle model locality, i.e. candidate models do not work equally well over different regions, the adaptive fuzzy mixture of local ICA models is developed. Basically, it splits the entire input space into domains, build local ICA models within each sub-region and then combine them into a mixture model. Many different experiments are carried out to demonstrate the performance of this novel method. Our simulation study and comparison show that this new method meets our goals and outperforms existing methods in most situations.by Mingyang Xu.Ph.D

Data-driven methods for the assessment and improvement of forecasts

This thesis uses data-driven techniques to analyse and assess both point and probability forecasts within a prequential framework. Point forecasts are assessed using recursive residuals. Examination of the properties of the recursive residual found them to be unique to this residual. Recursive residuals for the hidden state of HMM are also defined by taking the difference between the one step ahead forecast and the forecast's filtered update. The quality of forecasts generated from different models can be assessed by comparing the information content in their corresponding residuals. When faced with model to correct this misspecification it is shown how this residual can be modelled to correct this misspecification, thereby improving forecasts. It is also shown how the residual content can be used to judge the predictive sufficiency of alternative forecasting methods. Using the theory of probability forecasting, the technique of forecasting assessment by calibration is extended to HMM's to assess how well the one step ahead forecast is explained by its filtered update. A test statistic to test the empirical calibration of the forecasts is also defined and applied to the real world problem of CpG island detection in Human DNA sequences. The distribution of the test statistic is investigated using a prequential frame of reference and is found to be N(0.1). Calibration of HMMs is also examined using smoothed predictions and cross- validation forecasts. A test statistic is defined for this scenario and the its distribution is examined using a cross- validation frame of reference. A prequential estimation algorithm for HMMs is also developed