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Mass spectrometry is an analytical technique commonly used for determining elemental composition in a substance sample. For this purpose, the sample is placed into some liquid solution called liquid matrix. Unfortunately, the spectrum of the sample is not observable separate from that of the solution. Thus, it is desired to distinguish the sample spectrum. The analysis is usually based on the comparison of the mixed spectrum with the one of the sole solution. Introducing the missing information about the origin of observed spectrum peaks, the author obtains a classic set up for the Expectation-Maximization (EM) algorithm. The author proposed a mixture modeling the spectrum of the liquid solution as well as that of the sample. A bell-shaped probability mass function obtained by discretization of the univariate Gaussian probability density function was proposed or serving as a mixture component. The E- and M- steps were derived under the proposed model. The corresponding R program is written and tested on a small but challenging simulation example. Varying the number of mixture components for the liquid matrix and sample, the author found the correct model according to Bayesian Information Criterion. The initialization of the EM algorithm is a difficult standalone problem that was successfully resolved for this case. The author presents the findings and provides results from the simulation example as well as corresponding illustrations supporting the conclusions.

With the growth of computer power, Digital Image Processing plays a more and more important role in the modern world, including the field of industry, medical, communications, spaceflight technology etc. As a sub-field, Interactive Image Processing emphasizes particularly on the communications between machine and human. The basic flowchart is definition of object, analysis and training phase, recognition and feedback. Generally speaking, the core issue is how we define the interesting object and track them more accurately in order to complete the interaction process successfully. This thesis proposes a novel dynamic simulation scheme for interactive image processing. The work consists of two main parts: Hand Motion Detection and Hand Gesture recognition. Within a hand motion detection processing, movement of hand will be identified and extracted. In a specific detection period, the current image is compared with the previous image in order to generate the difference between them. If the generated difference exceeds predefined threshold alarm, a typical hand motion movement is detected. Furthermore, in some particular situations, changes of hand gesture are also desired to be detected and classified. This task requires features extraction and feature comparison among each type of gestures. The essentials of hand gesture are including some low level features such as color, shape etc. Another important feature is orientation histogram. Each type of hand gestures has its particular representation in the domain of orientation histogram. Because Gaussian Mixture Model has great advantages to represent the object with essential feature elements and the Expectation-Maximization is the efficient procedure to compute the maximum likelihood between testing images and predefined standard sample of each different gesture, the comparability between testing image and samples of each type of gestures will be estimated by Expectation-Maximization algorithm in Gaussian Mixture Model. The performance of this approach in experiments shows the proposed method works well and accurately.

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With the ever increasing deployment and usage of gigabit networks, traditional network anomaly detection based intrusion detection systems have not scaled accordingly. Most, if not all, systems deployed assume the availability of complete and clean data for the purpose of intrusion detection. We contend that this assumption is not valid. Factors like noise in the audit data, mobility of the nodes, and the large amount of data generated by the network make it difficult to build a normal traffic profile of the network for the purpose of anomaly detection. From this perspective, the leitmotif of the research effort described in this dissertation is the design of a novel intrusion detection system that has the capability to detect intrusions with high accuracy even when complete audit data is not available. In this dissertation, we take a holistic approach to anomaly detection to address the threats posed by network based denial-of-service attacks by proposing improvements in every step of the intrusion detection process. At the data collection phase, we have implemented an adaptive sampling scheme that intelligently samples incoming network data to reduce the volume of traffic sampled, while maintaining the intrinsic characteristics of the network traffic. A Bloom filters based fast flow aggregation scheme is employed at the data pre-processing stage to further reduce the response time of the anomaly detection scheme. Lastly, this dissertation also proposes an expectation-maximization algorithm based anomaly detection scheme that uses the sampled audit data to detect intrusions in the incoming network traffic. / Ph. D.

Computational biology currently faces challenges in a big data world with thousands of data samples across multiple disease types including cancer. The challenging problem is how to extract biologically meaningful information from large-scale genomic data. Next-generation Sequencing (NGS) can now produce high quality data at DNA and RNA levels. However, in cells there exist a lot of non-specific (background) signals that affect the detection accuracy of true (foreground) signals. In this dissertation work, under Bayesian framework, we aim to develop and apply approaches to learn the distribution of genomic signals in each type of NGS data for reliable identification of specific foreground signals. We propose a novel Bayesian approach (ChIP-BIT) to reliably detect transcription factor (TF) binding sites (TFBSs) within promoter or enhancer regions by jointly analyzing the sample and input ChIP-seq data for one specific TF. Specifically, a Gaussian mixture model is used to capture both binding and background signals in the sample data; and background signals are modeled by a local Gaussian distribution that is accurately estimated from the input data. An Expectation-Maximization algorithm is used to learn the model parameters according to the distributions on binding signal intensity and binding locations. Extensive simulation studies and experimental validation both demonstrate that ChIP-BIT has a significantly improved performance on TFBS detection over conventional methods, particularly on weak binding signal detection. To infer cis-regulatory modules (CRMs) of multiple TFs, we propose to develop a Bayesian integration approach, namely BICORN, to integrate ChIP-seq and RNA-seq data of the same tissue. Each TFBS identified from ChIP-seq data can be either a functional binding event mediating target gene transcription or a non-functional binding. The functional bindings of a set of TFs usually work together as a CRM to regulate the transcription processes of a group of genes. We develop a Gibbs sampling approach to learn the distribution of CRMs (a joint distribution of multiple TFs) based on their functional bindings and target gene expression. The robustness of BICORN has been validated on simulated regulatory network and gene expression data with respect to different noise settings. BICORN is further applied to breast cancer MCF-7 ChIP-seq and RNA-seq data to identify CRMs functional in promoter or enhancer regions. In tumor cells, the normal regulatory mechanism may be interrupted by genome mutations, especially those somatic mutations that uniquely occur in tumor cells. Focused on a specific type of genome mutation, structural variation (SV), we develop a novel pattern-based probabilistic approach, namely PSSV, to identify somatic SVs from whole genome sequencing (WGS) data. PSSV features a mixture model with hidden states representing different mutation patterns; PSSV can thus differentiate heterozygous and homozygous SVs in each sample, enabling the identification of those somatic SVs with a heterozygous status in the normal sample and a homozygous status in the tumor sample. Simulation studies demonstrate that PSSV outperforms existing tools. PSSV has been successfully applied to breast cancer patient WGS data for identifying somatic SVs of key factors associated with breast cancer development. In this dissertation research, we demonstrate the advantage of the proposed distributional learning-based approaches over conventional methods for NGS data analysis. Distributional learning is a very powerful approach to gain biological insights from high quality NGS data. Successful applications of the proposed Bayesian methods to breast cancer NGS data shed light on underlying molecular mechanisms of breast cancer, enabling biologists or clinicians to identify major cancer drivers and develop new therapeutics for cancer treatment. / Ph. D.

Many common statistical techniques for modeling multidimensional dynamic data sets can be seen as variants of one (or multiple) underlying linear/nonlinear model(s). These statistical techniques fall into two broad categories of supervised and unsupervised learning. The emphasis of this dissertation is on unsupervised learning under multiple generative models. For linear models, this has been achieved by collective observations and derivations made by previous authors during the last few decades. Factor analysis, polynomial chaos expansion, principal component analysis, gaussian mixture clustering, vector quantization, and Kalman filter models can all be unified as some variations of unsupervised learning under a single basic linear generative model. Hidden Markov modeling (HMM), however, is categorized as an unsupervised learning under multiple linear/nonlinear generative models. This dissertation is primarily focused on hidden Markov models (HMMs). On the first half of this dissertation we study enhancements on the theory of hidden Markov modeling. These include three branches: 1) a robust as well as a closed-form parameter estimation solution to the expectation maximization (EM) process of HMMs for the case of elliptically symmetrical densities; 2) a two-step HMM, with a combined state sequence via an extended Viterbi algorithm for smoother state estimation; and 3) a duration-dependent HMM, for estimating the expected residency frequency on each state. Then, the second half of the dissertation studies three novel applications of these methods: 1) the applications of Markov switching models on the Bifurcation Theory in nonlinear dynamics; 2) a Game Theory application of HMM, based on fundamental theory of card counting and an example on the game of Baccarat; and 3) Trust modeling and the estimation of trustworthiness metrics in cyber security systems via Markov switching models. As a result of the duration dependent HMM, we achieved a better estimation for the expected duration of stay on each regime. Then by robust and closed form solution to the EM algorithm we achieved robustness against outliers in the training data set as well as higher computational efficiency in the maximization step of the EM algorithm. By means of the two-step HMM we achieved smoother probability estimation with higher likelihood than the standard HMM. / Ph. D.

This thesis investigates the application of Hidden Markov Models (HMMs) to model financial volatility-regimes and presents a parameter learning approach using real-world data. Although HMMs as regime-switching models are established, empirical studies regarding the parameter estimation of such models remain limited. We address this issue by creating a systematic approach (algorithm) for parameter learning using Python programming and the hmmlearn library. The algorithm works by initializing a wide range of random parameter values for an HMM and maximizing the log-likelihood of an observation sequence, obtained from market data, using expectation-maximization; the optimal number of volatility regimes for the HMM is determined using information criterion. By training models on historical market and volatility index data, we found that a discrete model is favored for volatility modeling and option pricing due to its low complexity and high customizability, and a Gaussian model is favored for asset allocation and price simulation due to its ability to model market regimes. However, practical applications of these models were not researched, and thus, require further studies to test and calibrate.