Exploiting the Composite Step Strategy to the BiconjugateA-Orthogonal Residual Method for Non-Hermitian Linear Systems

The Biconjugate A-Orthogonal Residual (BiCOR) method carried out in finite precision arithmetic by means of the biconjugate A-orthonormalization procedure may possibly tend to suffer from two sources of numerical instability, known as two kinds of breakdowns, similarly to those of the Biconjugate Gradient (BCG) method. This paper naturally exploits the composite step strategy employed in the development of the composite step BCG (CSBCG) method into the BiCOR method to cure one of the breakdowns called as pivot breakdown. Analogously to the CSBCG method, the resulting interesting variant, with only a minor modification to the usual implementation of the BiCOR method, is able to avoid near pivot breakdowns and compute all the well-defined BiCOR iterates stably on the assumption that the underlying biconjugate A-orthonormalization procedure does not break down. Another benefit acquired is that it seems to be a viable algorithm providing some further practically desired smoothing of the convergence history of the norm of the residuals, which is justified by numerical experiments. In addition, the exhibited method inherits the promising advantages of the empirically observed stability and fast convergence rate of the BiCOR method over the BCG method so that it outperforms the CSBCG method to some extent

3次元座標表示の相対論的密度汎関数計算に対する新しい方法

Tohoku University萩野浩一課

Variable Selection in Linear Models with Grouped Variables

Linear mixed models have been widely used for repeated measurements, longitudinal studies, or multilevel data. The selection of random effects in linear mixed models has received much attention recently in the literature. Random effects consider dependent structure between repeatedly measured data. Due to computational challenges, the selection of grouped random effects has yet to be studied. Grouped random effects, including genetics data or categorical variables, are commonly seen in practice. We present an efficient method for selecting random effects at group levels in linear mixed models. Specifically, the proposed method employs a restricted maximum likelihood function to estimate the covariance matrix of random effects. To achieve sparse estimation and grouped random effects selection, we then introduce a new shrinkage penalty term. In addition, we extend the idea of grouped variable selection onto the latent regression model. By incorporating regression onto latent traits, latent regression models provide a way to uncover hidden influential factors from the data and make more accurate predictions. Specifically, we develop a variable selection approach for latent regression item response theory models by introducing the group LASSO penalty into the marginal log-likelihood function of observed test responses. We derive the explicit forms of updating steps for model parameters in a modified Newton-Raphson method. Our approach selects significant covariates and estimates model parameters simultaneously. For both variable selection frameworks, we perform simulation studies to evaluate the variable selection performance of the proposed methods. We then compare them to existing or naive selection methods. Additionally, we apply the proposed methods on real data sets

Multi-Observation Continuous Density Hidden Markov Models for Anomaly Detection in Full Motion Video

An increase in sensors on the battlefield produces an abundance of collected data that overwhelms the processing capability of the DoD. Automated Visual Surveillance (AVS) seeks to use machines to better exploit increased sensor data, such as by highlighting anomalies. In this thesis, we apply AVS to overhead Full Motion Video (FMV). We seek to automate the classification of soldiers in a simulated combat scenario into their agent types. To this end, we use Multi-Dimensional Continuous Density Hidden Markov Models (MOCDHMMs), a form of HMM which models a training dataset more precisely than simple HMMs. MOCDHMMs are theoretically developed but thinly applied in literature. We discover and correct three errors which occur in HMM algorithms when applied to MOCDHMMs but not when applied to simple HMMs. We offer three fixes to the errors and show analytically why they work. To show the fixes effective, we conduct experiments on three datasets: two pilot experiment datasets and a simulated combat scenario dataset. The modified MOCDHMM algorithm gives statistically significant improvement over the standard MOCDHMM: 5% improvement in accuracy for the pilot datasets and 3% for the combat scenario dataset. In addition, results suggest that increasing the number of hidden states in an MOCDHMM classifier increases the separability of the classes but also increases classifier bias. Furthermore, we find that classification based on tracked position alone is possible and that MOCDHMM classifiers are highly resistant to noise in their training data

Gene expression analysis of head and neck cancer development

Microarray analysis was performed on 32 head and neck keratinocytes cultures using Affymetrix U133A/B genechips. The panel of cultures included normal cells, mortal and immortal cultures of dysplastic keratinocytes and mortal and immortal cultures from carcinomas, all grown to a standard protocol. The overall GEP revealed that many of the well-established HNSCC molecular markers associated with motility and invasion were up-regulated in the mortal cells, particularly in the mortal carcinomas. Immortal NHSCC cells showed elevated expression of cell-cycle markers and loss of differentiation markers. In addition, a small number of common changes in gene expression in all the carcinomas, regardless of replicative fate, were identified. This included several transcription factors. A series of 49 novel gene expression changes consistently associated with immortality in dysplastic keratinocytes and SCCs were identified. The list included genes involves in cell cycle control, signalling, cellular metabolism and maintenance of cellular structure. Validation of the expression of these genes by western blot demonstrated that, in general, the protein expression of genes agreed with the RNA expression level from the microarray data. However, some heterogeneity was evident. The mortal and immortal gene expression signatures were validated by IHC in the tumours from which the cultures were derived. The tumours that gave rise to immortal cell cultures demonstrated a relatively uniform pattern of staining in relation to the novel markers of immortality. However, those tumours which gave rise to mortal cultures exhibited significant heterogeneity of gene expression pattern, with areas characteristic of both the mortal and immortal phenotype present. These novel markers give us further insight into the mechanisms and importance of keratinocytes immortalization. Surrogate markers of immortality could therefore be valuable for assessment of prognosis and therapy if confirmed in larger in vivo studies

Statistical methods for learning sparse features

With the fast development of networking, data storage, and the data collection capacity, big data are now rapidly expanding in all science and engineering domains. When dealing with such data, it is appealing if we can extract the hidden sparse structure of the data since sparse structures allow us to understand and interpret the information better. The aim of this thesis is to develop algorithms that can extract such hidden sparse structures of the data in the context of both supervised learning and unsupervised learning. In chapter 1, this thesis first examines the limitation of the classical Fisher Discriminant Analysis (FDA), a supervised dimension reduction algorithm for multi-class classification problems. This limitation has been discussed by Cui (2012), and she has proposed a new objective function in her thesis, which is named Complementary Dimension Analysis (CDA) since each sequentially added new dimension boosts the discriminative power of the reduced space. A couple of extensions of CDA are discussed in this thesis, including sparse CDA (sCDA) in which the reduced subspace involves only a small fraction of the features, and Local CDA (LCDA) that handles multimodal data more appropriately by taking the local structure of the data into consideration. A combination of sCDA and LCDA is shown to work well with real examples and can return sparse directions from data with subtle local structures. In chapter 2, this thesis considers the problem of matrix decomposition that arises in many real applications such as gene repressive identification and context mining. The goal is to retrieve a multi- layer low-rank sparse decomposition from a high dimensional data matrix. Existing algorithms are all sequential algorithms, that is, the first layer is estimated, and then remaining layers are estimated one by one, by conditioning on the previous layers. As discussed in this thesis, such sequential approaches have some limitations. A new algorithm is proposed to address those limitations, where all the layers are solved simultaneously instead of sequentially. The proposed algorithm in chapter 2 is based on a complete data matrix. In many real applications and cross-validation procedures, one needs to work with a data matrix with missing values. How to operate the proposed matrix decomposition algorithm when there exist missing values is the main focus of chapter 3. The proposed solution seems to be slightly different from some existing work such as penalized matrix decomposition (PMD). In chapter 4, this thesis considers a Bayesian approach to sparse principal component analysis (PCA). An efficient algorithm, which is based on a hybrid of Expectation-Maximization (EM) and Variational-Bayes (VB), is proposed and it can be shown to achieve selection consistency when both p and n go to infinity. Empirical studies have demonstrated the competitive performance of the proposed algorithm