Browsing by Subject "EM algorithm"
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Item Model-based Pre-processing in Protein Mass Spectrometry(2011-02-22) Wagaman, John C.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.Item On adaptive transmission, signal detection and channel estimation for multiple antenna systems(Texas A&M University, 2004-11-15) Xie, YongzheThis research concerns analysis of system capacity, development of adaptive transmission schemes with known channel state information at the transmitter (CSIT) and design of new signal detection and channel estimation schemes with low complexity in some multiple antenna systems. We first analyze the sum-rate capacity of the downlink of a cellular system with multiple transmit antennas and multiple receive antennas assuming perfect CSIT. We evaluate the ergodic sum-rate capacity and show how the sum-rate capacity increases as the number of users and the number of receive antennas increases. We develop upper and lower bounds on the sum-rate capacity and study various adaptive MIMO schemes to achieve, or approach, the sum-rate capacity. Next, we study the minimum outage probability transmission schemes in a multiple-input-single-output (MISO) flat fading channel assuming partial CSIT. Considering two special cases: the mean feedback and the covariance feedback, we derive the optimum spatial transmission directions and show that the associated optimum power allocation scheme, which minimizes the outage probability, is closely related to the target rate and the accuracy of the CSIT. Since CSIT is obtained at the cost of feedback bandwidth, we also consider optimal allocation of bandwidth between the data channel and the feedback channel in order to maximize the average throughput of the data channel in MISO, flat fading, frequency division duplex (FDD) systems. We show that beamforming based on feedback CSI can achieve an average rate larger than the capacity without CSIT under a wide range of mobility conditions. We next study a SAGE-aided List-BLAST detection scheme for MIMO systems which can achieve performance close to that of the maximum-likelihood detector with low complexity. Finally, we apply the EM and SAGE algorithms in channel estimation for OFDM systems with multiple transmit antennas and compare them with a recently proposed least-squares based estimation algorithm. The EM and SAGE algorithms partition the problem of estimating a multi-input channel into independent channel estimation for each transmit-receive antenna pair, therefore avoiding the matrix inversion encountered in the joint least-squares estimation.Item Topics on Regularization of Parameters in Multivariate Linear Regression(2012-02-14) Chen, LianfuMy dissertation mainly focuses on the regularization of parameters in the multivariate linear regression under different assumptions on the distribution of the errors. It consists of two topics where we develop iterative procedures to construct sparse estimators for both the regression coefficient and scale matrices simultaneously, and a third topic where we develop a method for testing if the skewness parameter in the skew-normal distribution is parallel to one of the eigenvectors of the scale matrix. In the first project, we propose a robust procedure for constructing a sparse estimator of a multivariate regression coefficient matrix that accounts for the correlations of the response variables. Robustness to outliers is achieved using heavy-tailed t distributions for the multivariate response, and shrinkage is introduced by adding to the negative log-likelihood l1 penalties on the entries of both the regression coefficient matrix and the precision matrix of the responses. Taking advantage of the hierarchical representation of a multivariate t distribution as the scale mixture of normal distributions and the EM algorithm, the optimization problem is solved iteratively where at each EM iteration suitably modified multivariate regression with covariance estimation (MRCE) algorithms proposed by Rothman, Levina and Zhu are used. We propose two new optimization algorithms for the penalized likelihood, called MRCEI and MRCEII, which differ from MRCE in the way that the tuning parameters for the two matrices are selected. Estimating the degrees of freedom when penalizing the entries of the matrices presents new computational challenges. A simulation study and real data analysis demonstrate that the MRCEII, which selects the tuning parameter of the precision matrix of the multiple responses using the Cp criterion, generally does the best among all methods considered in terms of the prediction error, and MRCEI outperforms the MRCE methods when the regression coefficient matrix is less sparse. The second project is motivated by the existence of the skewness in the data for which the symmetric distribution assumption on the errors does not hold. We extend the procedure we have proposed to the case where the errors in the multivariate linear regression follow a multivariate skew-normal or skew-t distribution. Based on the convenient representation of skew-normal and skew-t as well as the EM algorithm, we develop an optimization algorithm, called MRST, to iteratively minimize the negative penalized log-likelihood. We also carry out a simulation study to assess the performance of the method and illustrate its application with one real data example. In the third project, we discuss the asymptotic distributions of the eigenvalues and eigenvectors for the MLE of the scale matrix in a multivariate skew-normal distribution. We propose a statistic for testing whether the skewness vector is proportional to one of the eigenvectors of the scale matrix based on the likelihood ratio. Under the alternative, the likelihood is maximized numerically with two different ways of parametrization for the scale matrix: Modified Cholesky Decomposition (MCD) and Givens Angle. We conduct a simulation study and show that the statistic obtained using Givens Angle parametrization performs well and is more reliable than that obtained using MCD.