Over the years analysts have used the EM algorithm to obtain maximum likelihood estimates from incomplete data for various models. The general algorithm admits several appealing properties such as strong global convergence; however, the rate of convergence is linear which in some cases may be unacceptably slow. This work is primarily concerned with applying Anderson acceleration to the EM algorithm for Gaussian mixture models (GMM) in hopes of alleviating slow convergence. As preamble we provide a review of maximum likelihood estimation and derive the EM algorithm in detail. The iterates that correspond to the GMM are then formulated and examples are provided. These examples show how faster convergence is experienced when the data are well separated, whereas much slower convergence is seen whenever the sample is poorly separated. The Anderson acceleration method is then presented, and its connection to the EM algorithm is discussed. The work is then concluded by applying Anderson acceleration to the EM algorithm which results in reducing the number of iterations required to obtain convergence.

The objective of this project is to determine whether utilizing an EM Algorithm to fit a Gaussian mixed model distribution model provides needed accuracy in identifying the number of defective parts per million when the overall population is made up of multiple independent runs or lots. The other option is approximating using standard software tools and common known techniques available to a process, industrial or quality engineer. These tools and techniques provide methods utilizing familiar distributions and statistical process control methods widely understood. This paper compares these common methods with an EM Algorithm programmed in R using a dataset of actual measurements for length of manufactured product. / text

With the onset of large-scale gene expression profiling, many researchers have turned their attention toward biological process modeling and system identification. The abundance of data available, while inspiring, is also daunting to interpret. Following the initial work of Rangel et al., we propose a linear model for identifying the biological model behind the data and utilize a modification of the Expectation-Maximization algorithm for training it. With our model, we explore some commonly accepted assumptions concerning sampling, discretization, and state transformations. Also, we illuminate the model complexities and interpretation difficulties caused by unknown state transformations and propose some solutions for resolving these problems. Finally, we elucidate the advantages and limitations of our linear state-space model with simulated data from several nonlinear networks. / Master of Science

Two different types of switching mechanism are considered in this thesis; one is featured with abrupt/sudden switching while the other one shows gradual changing behavior in its dynamics. It is shown that, through the comparison of the identification results from the proposed method and a benchmark method, the proposed robust identification method can achieve better performance when dealing with the data set mixed with outliers. To model the switched systems exhibiting gradual or smooth transition among different local models, in addition to estimating the local sub-systems parameters, a smooth validity (an exponential function) function is introduced to combine all the local models so that throughout the working range of the gradual switched system, the dynamics of the nonlinear process can be appropriately approximated. Verification results on a simulated numerical example and CSTR process confirm the effectiveness of the proposed Linear Parameter Varying (LPV) identification algorithm. / Process Control

In this thesis, we consider the problem of distributed detection problem in cooperative communication networks when the channel state information (CSI) is unknown. The amplify-and-forward relay strategy is considered in this thesis. Since the CSI is assumed to be unknown to the system, the joint detection and estimation approach is considered in this work. The proposed scheme in this work differs from existing joint detection and estimation schemes in that it utilizes a distributed approach, which exploits node cooperation and achieves a better system performance in cooperative communication networks. Moreover, by contrast to the existing channel estimation and symbol detection schemes, the proposed scheme is mainly developed based on the assumption that the data communication from the source to each relay node is to undergo a correlated fading channel. We derive the joint detection and estimation rules for our problem using the expectation-maximum (EM) algorithm. Simulation results show that the proposed scheme can perform well. Moreover, the obtained results show that the proposed iteration algorithm converges very fast, which implies the proposed scheme can work well in real-time applications.

The discovery of proteomic information through the use of mass spectrometry (MS) has been an active area of research in the diagnosis and prognosis of many types of cancer. This process involves feature selection through peak detection but is often complicated by many forms of non-biologicalbias. The need to extract biologically relevant peak information from MS data has resulted in the development of statistical techniques to aid in spectra pre-processing. Baseline estimation and normalization are important pre-processing steps because the subsequent quantification of peak heights depends on this baseline estimate. This dissertation introduces a mixture model to estimate the baseline and peak heights simultaneously through the expectation-maximization (EM) algorithm and a penalized likelihood approach. Our model-based pre-processing performs well in the presence of raw, unnormalized data, with few subjective inputs. We also propose a model-based normalization solution for use in subsequent classification procedures, where misclassification results compare favorably with existing methods of normalization. The performance of our pre-processing method is evaluated using popular matrix-assisted laser desorption and ionization (MALDI) and surface-enhanced laser desorption and ionization (SELDI) datasets as well as through simulation.

First, we study a Poisson model a polluted random screen. In this model, the defects on random screen are assumed Poisson-distribution and overlapped. The transmittance effects of overlapping defects are multiplicative. We can compute the autocorrelation function of the screen is obtained by defects' density, radius, and transmittance. Using the autocorrelation function, we then restore the telescope astronomy images. These image signals are generally degraded by their propagation through the random scattering in atmosphere. To restore the images, we estimate the three key parameters by three methods. They are expectation- maximization (EM) method and two Maximum-Entropy (ME) methods according to two different definitions. The restoration are successful and demonstrated in this thesis.

The expectation-maximization (EM) algorithm is a widely utilized approach to max- imum likelihood estimation in the presence of missing data, this thesis focuses on its application within the model-based clustering framework. The performance of the EM algorithm can be highly dependent on how the algorithm is initialized. Several ways of initializing the EM algorithm have been proposed, however, the best method to use for initialization remains a somewhat controversial topic. From an attempt to obtain a superior method of initializing the EM algorithm, comes the concept of using multiple existing methods together in what will be called a `voting' procedure. This procedure will use several common initialization methods to cluster the data, then a nal starting ^zig matrix will be obtained in two ways. The hard `voting' method follows a majority rule, whereas the soft `voting' method takes an average of the multiple group memberships. The nal ^zig matrix obtained from both methods will dictate the starting values of ^ g; ^ g; and ^ g used to initialize the EM algorithm.

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