Hidden Markov models have become a popular tool for modeling long-term investment guarantees. Many different variations of hidden Markov models have been proposed over the past decades for modeling indexes such as the S&P 500, and they capture the tail risk inherent in the market to varying degrees. However, goodness-of-fit testing, such as residual-based testing, for hidden Markov models is a relatively undeveloped area of research. This work focuses on hidden Markov model assessment, and develops a stochastic approach to deriving a residual set that is ideal for standard residual tests. This result allows hidden-state models to be tested for goodness-of-fit with the well developed testing strategies for single-state models. This work also focuses on parameter uncertainty for the popular long-term equity hidden Markov models. There is a special focus on underlying states that represent lower returns and higher volatility in the market, as these states can have the largest impact on investment guarantee valuation. A Bayesian approach for the hidden Markov models is applied to address the issue of parameter uncertainty and the impact it can have on investment guarantee models. Also in this thesis, the areas of portfolio optimization and portfolio replication under a hidden Markov model setting are further developed. Different strategies for optimization and portfolio hedging under hidden Markov models are presented and compared using real world data. The impact of parameter uncertainty, particularly with model parameters that are connected with higher market volatility, is once again a focus, and the effects of not taking parameter uncertainty into account when optimizing or hedging in a hidden Markov are demonstrated.

In this thesis, methods for achieving finer scale multi-spectral classification through the use of super resolution (SR) techniques are investigated. A new super resolution algorithm Maximum a Posteriori based on the universal hidden Markov tree model (MAP-uHMT) is developed which can be applied successfully to super-resolve each multi-spectral channel before classification by standard methods. It is believed that this is the first time that a true super resolution algorithm has been applied to multi-spectral classification, and results are shown to be excellent. Image registration is an important step for SR in which misalignment can be measured for each of many low resolution images; therefore, a new and computationally efficient image registration is developed for this particular application. This improved elastic image registration method can deal with a global affine warping and local shift translations based on coarse to fine pyramid levels. The experimental results show that it can provide good registration accuracy in less computational time than comparable methods. Maximum a posteriori (MAP) is adopted to deal with the ill-conditioned problem of super resolution, wherein a prior is constructed based on the universal hidden Markov tree (uHMT) model in the wavelet domain. In order to test this prior for MAP estimation, it is first tested in the simpler and typically ill-conditioned problem of image denoising. Experimental results illustrate that this new image denoising method achieves good performance for the test images. The new prior is then extended to SR. By combining with the new elastic image registration algorithm, MAP-uHMT can super resolve both some natural video frames and remote sensing images. Test results with both synthetic data and real data show that this method achieves super resolution both visually and quantitatively. In order to show that MAPuHMT is also applicable more widely, it is tested on a sequence of long-range surveillance images captured under conditions of atmospheric turbulence distortion. The results suggest that super resolution may have been achieved in this application also.

In this thesis, we consider a robust state estimation problem for discrete-time, homogeneous, first-order, finite-state finite-alphabet hidden Markov models (HMMs). Based on Kolmogorov's Theorem on the existence of a process, we first present the Kolmogorov model for the HMMs under consideration. A new change of measure is introduced. The statistical properties of the Kolmogorov representation of an HMM are discussed on the canonical probability space. A special Kolmogorov measure is constructed. Meanwhile, the ergodicity of two expanded Markov chains is investigated. In order to describe the uncertainty of HMMs, we study probability distance problems based on the Kolmogorov model of HMMs. Using a change of measure technique, the relative entropy and the relative entropy rate as probability distances between HMMs, are given in terms of the HMM parameters. Also, we obtain a new expression for a probability distance considered in the existing literature such that we can use an information state method to calculate it. Furthermore, we introduce regular conditional relative entropy as an a posteriori probability distance to measure the discrepancy between HMMs when a realized observation sequence is given. A representation of the regular conditional relative entropy is derived based on the Radon-Nikodym derivative. Then a recursion for the regular conditional relative entropy is obtained using an information state method. Meanwhile, the well-known duality relationship between free energy and relative entropy is extended to the case of regular conditional relative entropy given a sub-[special character]-algebra. Finally, regular conditional relative entropy constraints are defined based on the study of the probability distance problem. Using a Lagrange multiplier technique and the duality relationship for regular conditional relative entropy, a finite horizon robust state estimator for HMMs with regular conditional relative entropy constraints is derived. A complete characterization of the solution to the robust state estimation problem is also presented.

In this thesis, we consider a robust state estimation problem for discrete-time, homogeneous, first-order, finite-state finite-alphabet hidden Markov models (HMMs). Based on Kolmogorov's Theorem on the existence of a process, we first present the Kolmogorov model for the HMMs under consideration. A new change of measure is introduced. The statistical properties of the Kolmogorov representation of an HMM are discussed on the canonical probability space. A special Kolmogorov measure is constructed. Meanwhile, the ergodicity of two expanded Markov chains is investigated. In order to describe the uncertainty of HMMs, we study probability distance problems based on the Kolmogorov model of HMMs. Using a change of measure technique, the relative entropy and the relative entropy rate as probability distances between HMMs, are given in terms of the HMM parameters. Also, we obtain a new expression for a probability distance considered in the existing literature such that we can use an information state method to calculate it. Furthermore, we introduce regular conditional relative entropy as an a posteriori probability distance to measure the discrepancy between HMMs when a realized observation sequence is given. A representation of the regular conditional relative entropy is derived based on the Radon-Nikodym derivative. Then a recursion for the regular conditional relative entropy is obtained using an information state method. Meanwhile, the well-known duality relationship between free energy and relative entropy is extended to the case of regular conditional relative entropy given a sub-[special character]-algebra. Finally, regular conditional relative entropy constraints are defined based on the study of the probability distance problem. Using a Lagrange multiplier technique and the duality relationship for regular conditional relative entropy, a finite horizon robust state estimator for HMMs with regular conditional relative entropy constraints is derived. A complete characterization of the solution to the robust state estimation problem is also presented.

ABSTRACT OF THE DISSERTATION OF Yonglian Wang, for Doctor of Philosophy degree in Electrical and Computer Engineering, presented on May 19, 2009, at Southern Illinois University- Carbondale. TITLE: SPEECH RECOGNITION UNDER STRESS MAJOR PROFESSOR: Dr. Nazeih M. Botros In this dissertation, three techniques, Dynamic Time Warping (DTW), Hidden Markov Models (HMM), and Hidden Control Neural Network (HCNN) are utilized to realize talker-independent isolated word recognition. DTW is a technique utilized to measure the distance between two input patterns or vectors; HMM is a tool utilized to model speech signals using stochastic process in five states to compare the similarity between signals; and HCNN calculates the errors between actual output and target output and it is mainly built for the stress compensated speech recognition. When stress (Angry, Question and Soft) is induced into the normal talking speech, speech recognition performance degrades greatly. Therefore hypothesis driven approach, a stress compensation technique is introduced to cancel the distortion caused by stress. The database for this research is SUSAS (Speech under Simulated and Actual Stress) which includes five domains encompassing a wide variety of stress, 16,000 isolated-word speech signal samples available from 44 speakers. Another database, called TIMIT (10 speakers and 6300 sentences in total) is used as a minor in DTW algorithm. The words used for speech recognition are speaker-independent. The characteristic feature analysis has been carried out in three domains: pitch, intensity， and glottal spectrum. The results showed that speech spoken under angry and question stress indicates extremely wide fluctuations with average higher pitch, higher RMS intensity, and more energy compared to neutral. In contrast, the soft talking style has lower pitch, lower RMS intensity, and less energy compared to neutral. The Linear Predictive Coding (LPC) cepstral feature analysis is used to obtain the observation vector and the input vector for DTW, HMM, and stress compensation. Both HMM and HCNN consist of training and recognition stages. Training stage is to form references, while recognition stage is to compare an unknown word against all the reference models. The unknown word is recognized by the model with highest similarity. Our results showed that HMM technique can achieve 91% recognition rate for Normal speech; however, the recognition rate dropped to 60% for Angry stress condition, 65% for Question stress condition, and 76% for Soft stress condition. After compensation was applied for the cepstral tilts, the recognition rate increased by 10% for Angry stress condition, 8% for Question stress condition, and 4% for Soft stress condition. Finally, HCNN technique increased the recognition rate to 90% for Angry stress condition and it also differentiated the Angry stress from other stress group.

by Zhou, Shengli. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 70-75). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of Gesture Recognition --- p.1 / Chapter 1.2 --- HCI System --- p.2 / Chapter 1.2.1 --- Vision Based HCI System --- p.2 / Chapter 1.2.2 --- Accelerometer Based HCI System --- p.4 / Chapter 1.3 --- Pattern Recognition Methods --- p.6 / Chapter 1.4 --- Thesis Outline --- p.7 / Chapter Chapter 2 --- 2D Hand-Written Character Recognition --- p.8 / Chapter 2.1 --- Introduction to Accelerometer Based Hand-Written Character Recognition --- p.8 / Chapter 2.1.1 --- Character Recognition Based on Trajectory Reconstruction --- p.9 / Chapter 2.1.2 --- Character Recognition Based on Classification --- p.10 / Chapter 2.2 --- Neural Network --- p.11 / Chapter 2.2.1 --- Mathematical Model of Neural Network (NN) --- p.11 / Chapter 2.2.2 --- Types of Neural Network Learning --- p.13 / Chapter 2.2.3 --- Self-Organizing Maps (SOMs) --- p.14 / Chapter 2.2.4 --- Properties of Neural Network --- p.16 / Chapter 2.3 --- Experimental Setup --- p.17 / Chapter 2.4 --- Configuration of Sensing Mote --- p.18 / Chapter 2.5 --- Data Acquisition Methods --- p.19 / Chapter 2.6 --- Data Preprocessing Methods --- p.20 / Chapter 2.6.1 --- Fast Fourier Transform (FFT) --- p.21 / Chapter 2.6.2 --- Discrete Cosine Transform (DCT) --- p.23 / Chapter 2.6.3 --- Problem Analysis --- p.25 / Chapter 2.7 --- Hand-written Character Classification using SOMs --- p.26 / Chapter 2.7.1 --- Recognition of All Characters in the Same Group --- p.27 / Chapter 2.7.2 --- Recognize the Numbers and Letters Respectively --- p.28 / Chapter 2.8 --- Conclusion --- p.29 / Chapter Chapter 3 --- Human Gesture Recognition --- p.32 / Chapter 3.1 --- Introduction to Human Gesture Recognition --- p.32 / Chapter 3.1.1 --- Dynamic Gesture Recognition --- p.32 / Chapter 3.1.2 --- Hidden Markov Models (HMMs) --- p.33 / Chapter 3.1.2.1 --- Applications of HMMs --- p.34 / Chapter 3.1.2.2 --- Training Algorithm --- p.35 / Chapter 3.1.2.3 --- Recognition Algorithm --- p.35 / Chapter 3.2 --- System Architecture --- p.36 / Chapter 3.2.1 --- Experimental Devices --- p.36 / Chapter 3.2.2 --- Data Acquisition Methods --- p.38 / Chapter 3.2.3 --- System Work Flow --- p.39 / Chapter 3.3 --- Real-Time Gesture Spotting --- p.40 / Chapter 3.3.1 --- Introduction --- p.40 / Chapter 3.3.2 --- Gesture Segmentation Based on Standard Deviation Calculation --- p.42 / Chapter 3.3.3 --- Evaluation of Gesture Spotting Program --- p.47 / Chapter 3.4 --- Comparison of Data Processing Methods --- p.48 / Chapter 3.4.1 --- Discrete Cosine Transform (DCT) --- p.48 / Chapter 3.4.2 --- Discrete Wavelet Transform (DWT) --- p.49 / Chapter 3.4.3 --- Zero Bias Compensation and Filtering (ZBC&F) --- p.51 / Chapter 3.4.4 --- Comparison of Experimental Results --- p.52 / Chapter 3.5 --- Data Base Setup --- p.53 / Chapter 3.6 --- Experimental Results Based on the Database Obtained from Ten Test Subjects --- p.53 / Chapter 3.6.1 --- Experimental Results when Gestures are Manually and Automatically “cut´ح --- p.54 / Chapter 3.6.2 --- The Influence of Number of Dominant Frequencies on Recognition --- p.55 / Chapter 3.6.3 --- The Influence of Sampling Frequencies on Recognition --- p.59 / Chapter 3.6.4 --- Influence of Number of Test Subjects on Recognition --- p.62 / Chapter 3.6.4.1 --- Experimental Results When Training and Testing Subjects Are Overlaped --- p.61 / Chapter 3.6.4.2 --- Experimental Results When Training and Testing Subjects Are Not Overlap --- p.62 / Chapter 3.6.4.3 --- Discussion --- p.65 / Chapter Chapter 4 --- Conclusion --- p.68 / Bibliography --- p.70

O Processamento de Linguagem Natural (PLN) é uma área da Ciência da Computação, que vem tentando, ao longo dos anos, aperfeiçoar a comunicação entre o homem e o computador. Varias técnicas tem sido utilizadas para aperfeiçoar esta comunicação, entre elas a aplicação de métodos estatísticos. Estes métodos tem sido usados por pesquisadores de PLN, com um crescente sucesso e uma de suas maiores vantagens é a possibilidade do tratamento de textos irrestritos. Em particular, a aplicação dos métodos estatísticos, na marcação automática de "corpus" com categorias morfo-sintáticas, tem se mostrado bastante promissora, obtendo resultados surpreendentes. Assim sendo, este trabalho descreve o processo de marcação automática de categorias morfo-sintáticas. Inicialmente, são apresentados e comparados os principais métodos aplicados a marcação automática: os métodos baseados em regras e os métodos estatísticos. São descritos os principais formalismos e técnicas usadas para esta finalidade pelos métodos estatísticos. E introduzida a marcação automática para a Língua Portuguesa, algo até então inédito. O objetivo deste trabalho é fazer um estudo detalhado e uma avaliação do sistema rotulador de categorias morfo-sintáticas, a fim de que se possa definir um padrão no qual o sistema apresente a mais alta precisão possível. Para efetuar esta avaliação, são especificados alguns critérios: a qualidade do "corpus" de treinamento, o seu tamanho e a influencia das palavras desconhecidas. A partir dos resultados obtidos, espera-se poder aperfeiçoar o sistema rotulador, de forma a aproveitar, da melhor maneira possível, os recursos disponíveis para a Língua Portuguesa. / Natural Language Processing (NLP) is an area of Computer Sciences, that have been trying to improve communication between human beings and computers. A number of different techniques have been used to improve this communication and among them, the use of stochastic methods. These methods have successfully being used by NLP researchers and one of their most remarkable advantages is that they are able to deal with unrestricted texts. Namely, the use of stochastic methods for part-of-speech tagging has achieving some extremely good results. Thus, this work describes the process of part-of-speech tagging. At first, we present and compare the main tagging methods: the rule-based methods and the stochastic ones. We describe the main stochastic tagging formalisms and techniques for part-of-speech tagging. We also introduce part-of-speech tagging for the Portuguese Language. The main purpose of this work is to study and evaluate a part-of-speech tagger system in order to establish a pattern in which it is possible to achieve the greatest accuracy. To perform this evaluation, several parameters were set: the corpus quality, its size and the relation between unknown words and accuracy. The results obtained will be used to improve the tagger, in order to use better the available Portuguese Language resources.

O Processamento de Linguagem Natural (PLN) é uma área da Ciência da Computação, que vem tentando, ao longo dos anos, aperfeiçoar a comunicação entre o homem e o computador. Varias técnicas tem sido utilizadas para aperfeiçoar esta comunicação, entre elas a aplicação de métodos estatísticos. Estes métodos tem sido usados por pesquisadores de PLN, com um crescente sucesso e uma de suas maiores vantagens é a possibilidade do tratamento de textos irrestritos. Em particular, a aplicação dos métodos estatísticos, na marcação automática de "corpus" com categorias morfo-sintáticas, tem se mostrado bastante promissora, obtendo resultados surpreendentes. Assim sendo, este trabalho descreve o processo de marcação automática de categorias morfo-sintáticas. Inicialmente, são apresentados e comparados os principais métodos aplicados a marcação automática: os métodos baseados em regras e os métodos estatísticos. São descritos os principais formalismos e técnicas usadas para esta finalidade pelos métodos estatísticos. E introduzida a marcação automática para a Língua Portuguesa, algo até então inédito. O objetivo deste trabalho é fazer um estudo detalhado e uma avaliação do sistema rotulador de categorias morfo-sintáticas, a fim de que se possa definir um padrão no qual o sistema apresente a mais alta precisão possível. Para efetuar esta avaliação, são especificados alguns critérios: a qualidade do "corpus" de treinamento, o seu tamanho e a influencia das palavras desconhecidas. A partir dos resultados obtidos, espera-se poder aperfeiçoar o sistema rotulador, de forma a aproveitar, da melhor maneira possível, os recursos disponíveis para a Língua Portuguesa. / Natural Language Processing (NLP) is an area of Computer Sciences, that have been trying to improve communication between human beings and computers. A number of different techniques have been used to improve this communication and among them, the use of stochastic methods. These methods have successfully being used by NLP researchers and one of their most remarkable advantages is that they are able to deal with unrestricted texts. Namely, the use of stochastic methods for part-of-speech tagging has achieving some extremely good results. Thus, this work describes the process of part-of-speech tagging. At first, we present and compare the main tagging methods: the rule-based methods and the stochastic ones. We describe the main stochastic tagging formalisms and techniques for part-of-speech tagging. We also introduce part-of-speech tagging for the Portuguese Language. The main purpose of this work is to study and evaluate a part-of-speech tagger system in order to establish a pattern in which it is possible to achieve the greatest accuracy. To perform this evaluation, several parameters were set: the corpus quality, its size and the relation between unknown words and accuracy. The results obtained will be used to improve the tagger, in order to use better the available Portuguese Language resources.

abstract: With the rapid development of mobile sensing technologies like GPS, RFID, sensors in smartphones, etc., capturing position data in the form of trajectories has become easy. Moving object trajectory analysis is a growing area of interest these days owing to its applications in various domains such as marketing, security, traffic monitoring and management, etc. To better understand movement behaviors from the raw mobility data, this doctoral work provides analytic models for analyzing trajectory data. As a first contribution, a model is developed to detect changes in trajectories with time. If the taxis moving in a city are viewed as sensors that provide real time information of the traffic in the city, a change in these trajectories with time can reveal that the road network has changed. To detect changes, trajectories are modeled with a Hidden Markov Model (HMM). A modified training algorithm, for parameter estimation in HMM, called m-BaumWelch, is used to develop likelihood estimates under assumed changes and used to detect changes in trajectory data with time. Data from vehicles are used to test the method for change detection. Secondly, sequential pattern mining is used to develop a model to detect changes in frequent patterns occurring in trajectory data. The aim is to answer two questions: Are the frequent patterns still frequent in the new data? If they are frequent, has the time interval distribution in the pattern changed? Two different approaches are considered for change detection, frequency-based approach and distribution-based approach. The methods are illustrated with vehicle trajectory data. Finally, a model is developed for clustering and outlier detection in semantic trajectories. A challenge with clustering semantic trajectories is that both numeric and categorical attributes are present. Another problem to be addressed while clustering is that trajectories can be of different lengths and also have missing values. A tree-based ensemble is used to address these problems. The approach is extended to outlier detection in semantic trajectories. / Dissertation/Thesis / Ph.D. Industrial Engineering 2012

abstract: Structural integrity is an important characteristic of performance for critical components used in applications such as aeronautics, materials, construction and transportation. When appraising the structural integrity of these components, evaluation methods must be accurate. In addition to possessing capability to perform damage detection, the ability to monitor the level of damage over time can provide extremely useful information in assessing the operational worthiness of a structure and in determining whether the structure should be repaired or removed from service. In this work, a sequential Bayesian approach with active sensing is employed for monitoring crack growth within fatigue-loaded materials. The monitoring approach is based on predicting crack damage state dynamics and modeling crack length observations. Since fatigue loading of a structural component can change while in service, an interacting multiple model technique is employed to estimate probabilities of different loading modes and incorporate this information in the crack length estimation problem. For the observation model, features are obtained from regions of high signal energy in the time-frequency plane and modeled for each crack length damage condition. Although this observation model approach exhibits high classification accuracy, the resolution characteristics can change depending upon the extent of the damage. Therefore, several different transmission waveforms and receiver sensors are considered to create multiple modes for making observations of crack damage. Resolution characteristics of the different observation modes are assessed using a predicted mean squared error criterion and observations are obtained using the predicted, optimal observation modes based on these characteristics. Calculation of the predicted mean square error metric can be computationally intensive, especially if performed in real time, and an approximation method is proposed. With this approach, the real time computational burden is decreased significantly and the number of possible observation modes can be increased. Using sensor measurements from real experiments, the overall sequential Bayesian estimation approach, with the adaptive capability of varying the state dynamics and observation modes, is demonstrated for tracking crack damage. / Dissertation/Thesis / Ph.D. Electrical Engineering 2013