Der technologische Fortschritt ermöglicht es heute, die moleculare Konfiguration einzelner Zellen oder ganzer Gewebeproben zu untersuchen. Solche in großen Mengen produzierten hochdimensionalen Omics-Daten aus der Molekularbiologie lassen sich zu immer niedrigeren Kosten erzeugen und werden so immer häufiger auch in klinischen Fragestellungen eingesetzt. Personalisierte Diagnose oder auch die Vorhersage eines Behandlungserfolges auf der Basis solcher Hochdurchsatzdaten stellen eine moderne Anwendung von Techniken aus dem maschinellen Lernen dar. In der Praxis werden klinische Parameter, wie etwa der Gesundheitszustand oder die Nebenwirkungen einer Therapie, häufig auf einer ordinalen Skala erhoben (beispielsweise gut, normal, schlecht). Es ist verbreitet, Klassifikationsproblme mit ordinal skaliertem Endpunkt wie generelle Mehrklassenproblme zu behandeln und somit die Information, die in der Ordnung zwischen den Klassen enthalten ist, zu ignorieren. Allerdings kann das Vernachlässigen dieser Information zu einer verminderten Klassifikationsgüte führen oder sogar eine ungünstige ungeordnete Klassifikation erzeugen. Klassische Ansätze, einen ordinal skalierten Endpunkt direkt zu modellieren, wie beispielsweise mit einem kumulativen Linkmodell, lassen sich typischerweise nicht auf hochdimensionale Daten anwenden. Wir präsentieren in dieser Arbeit hierarchical twoing (hi2) als einen Algorithmus für die Klassifikation hochdimensionler Daten in ordinal Skalierte Kategorien. hi2 nutzt die Mächtigkeit der sehr gut verstandenen binären Klassifikation, um auch in ordinale Kategorien zu klassifizieren. Eine Opensource-Implementierung von hi2 ist online verfügbar. In einer Vergleichsstudie zur Klassifikation von echten wie von simulierten Daten mit ordinalem Endpunkt produzieren etablierte Methoden, die speziell für geordnete Kategorien entworfen wurden, nicht generell bessere Ergebnisse als state-of-the-art nicht-ordinale Klassifikatoren. Die Fähigkeit eines Algorithmus, mit hochdimensionalen Daten umzugehen, dominiert die Klassifikationsleisting. Wir zeigen, dass unser Algorithmus hi2 konsistent gute Ergebnisse erzielt und in vielen Fällen besser abschneidet als die anderen Methoden.

Time series is one of the main research objects in the field of data mining. Visualization is an important mechanism to present processed time series for further analysis by users. In recent years researchers have designed a number of sophisticated visualization techniques for time series. However, most of these techniques focus on the static format, trying to encode the maximal amount of information through one image or plot. We propose the pixel video technique, a visualization technique displaying data in video format. Using pixel video technique, a hierarchal dimension cluster tree for generating the similarity order of dimensions is first constructed, each frame image is generated according to pixeloriented techniques displaying the data in the form of a video.

archives@tulane.edu / Modern biomedical studies often collect multiple types of high-dimensional data on a common set of objects. A representative model for the integrative analysis of multiple data types is to decompose each data matrix into a low-rank common-source matrix generated by latent factors shared across all data types, a low-rank distinctive-source matrix corresponding to each data type, and an additive noise matrix. We propose a novel decomposition method, called the decomposition-based generalized canonical correlation analysis, which appropriately defines those matrices by imposing a desirable orthogonality constraint on distinctive latent factors that aims to sufficiently capture the common latent factors. To further delineate the common and distinctive patterns between two data types, we propose another new decomposition method, called the common and distinctive pattern analysis. This method takes into account the common and distinctive information between the coefficient matrices of the common latent factors. We develop consistent estimation approaches for both proposed decompositions under high-dimensional settings, and demonstrate their finite-sample performance via extensive simulations. We illustrate the superiority of proposed methods over the state of the arts by real-world data examples obtained from The Cancer Genome Atlas and Human Connectome Project. / 1 / Zhe Qu

No description available.

Hierarchical clustering algorithms are common tools for simplifying, exploring and analyzing datasets in many areas of research. For flow cytometry, a specific variant of agglomerative clustering has been proposed, that uses cluster linkage based on Mahalanobis distance to produce results better suited for the domain. Applicability of this clustering algorithm is currently limited by its relatively high computational complexity, which does not allow it to scale to common cytometry datasets. This thesis describes a specialized, GPU-accelerated version of the Mahalanobis-average linked hierarchical clustering, which improves the algorithm performance by several orders of magnitude, thus allowing it to scale to much larger datasets. The thesis provides an overview of current hierarchical clustering algorithms, and details the construction of the variant used on GPU. The result is benchmarked on publicly available high-dimensional data from mass cytometry.

No description available.

Master of Science / Department of Statistics / Kun Chen / We study the composite group bridge penalized regression methods for conducting bilevel variable selection in high dimensional linear regression models with a diverging number of predictors. The proposed method combines the ideas of bridge regression (Huang et al., 2008a) and group bridge regression (Huang et al., 2009), to achieve variable selection consistency in both individual and group levels simultaneously, i.e., the important groups and the important individual variables within each group can both be correctly identi ed with probability approaching to one as the sample size increases to in nity. The method takes full advantage of the prior grouping information, and the established bi-level oracle properties ensure that the method is immune to possible group misidenti cation. A related adaptive group bridge estimator, which uses adaptive penalization for improving bi-level selection, is also investigated. Simulation studies show that the proposed methods have superior performance in comparison to many existing methods.

Doctor of Philosophy / Department of Statistics / Suzanne Dubnicka / DNA barcodes are short strands of nucleotide bases taken from the cytochrome c oxidase subunit 1 (COI) of the mitochondrial DNA (mtDNA). A single barcode may have the form C C G G C A T A G T A G G C A C T G . . . and typically ranges in length from 255 to around 700 nucleotide bases. Unlike nuclear DNA (nDNA), mtDNA remains largely unchanged as it is passed from mother to offspring. It has been proposed that these barcodes may be used as a method of differentiating between biological species (Hebert, Ratnasingham, and deWaard 2003). While this proposal is sharply debated among some taxonomists (Will and Rubinoff 2004), it has gained momentum and attention from biologists. One issue at the heart of the controversy is the use of genetic distance measures as a tool for species differentiation. Current methods of species classification utilize these distance measures that are heavily dependent on both evolutionary model assumptions as well as a clearly defined "gap" between intra- and interspecies variation (Meyer and Paulay 2005). We point out the limitations of such distance measures and propose a character-based method of species classification which utilizes an application of Bayes' rule to overcome these deficiencies. The proposed method is shown to provide accurate species-level classification. The proposed methods also provide answers to important questions not addressable with current methods.

<p>A significant hurdle for analyzing big data is the lack of effective technology and statistical inference methods. A popular approach for analyzing data with large sample is subsampling. Many subsampling probabilities have been introduced in literature (Ma, \emph{et al.}, 2015) for linear model. In this dissertation, we focus on generalized estimating equations (GEE) with big data and derive the asymptotic normality for the estimator without resampling and estimator with resampling. We also give the asymptotic representation of the bias of estimator without resampling and estimator with resampling. we show that bias becomes significant when the data is of high-dimensional. We also present a novel subsampling method called A-optimal which is derived by minimizing the trace of some dispersion matrices (Peng and Tan, 2018). We derive the asymptotic normality of the estimator based on A-optimal subsampling methods. We conduct extensive simulations on large sample data with high dimension to evaluate the performance of our proposed methods using MSE as a criterion. High dimensional data are further investigated and we show through simulations that minimizing the asymptotic variance does not imply minimizing the MSE as bias not negligible. We apply our proposed subsampling method to analyze a real data set, gas sensor data which has more than four millions data points. In both simulations and real data analysis, our A-optimal method outperform the traditional uniform subsampling method.</p>

This thesis provides novel methodology for statistical analysis of paired high-dimensional genomic data, with the aimto identify gene interactions specific to each group of samples as well as the gene connections that change between the two classes of observations. An example of such groups can be patients under two medical conditions, in which the estimation of gene interaction networks is relevant to biologists as part of discerning gene regulatory mechanisms that control a disease process like, for instance, cancer. We construct these interaction networks fromdata by considering the non-zero structure of correlationmatrices, which measure linear dependence between random variables, and their inversematrices, which are commonly known as precision matrices and determine linear conditional dependence instead. In this regard, we study three statistical problems related to the testing, single estimation and joint estimation of (conditional) dependence structures. Firstly, we develop hypothesis testingmethods to assess the equality of two correlation matrices, and also two correlation sub-matrices, corresponding to two classes of samples, and hence the equality of the underlying gene interaction networks. We consider statistics based on the average of squares, maximum and sum of exceedances of sample correlations, which are suitable for both independent and paired observations. We derive the limiting distributions for the test statistics where possible and, for practical needs, we present a permuted samples based approach to find their corresponding non-parametric distributions. Cases where such hypothesis testing presents enough evidence against the null hypothesis of equality of two correlation matrices give rise to the problem of estimating two correlation (or precision) matrices. However, before that we address the statistical problem of estimating conditional dependence between random variables in a single class of samples when data are high-dimensional, which is the second topic of the thesis. We study the graphical lasso method which employs an L1 penalized likelihood expression to estimate the precision matrix and its underlying non-zero graph structure. The lasso penalization termis given by the L1 normof the precisionmatrix elements scaled by a regularization parameter, which determines the trade-off between sparsity of the graph and fit to the data, and its selection is our main focus of investigation. We propose several procedures to select the regularization parameter in the graphical lasso optimization problem that rely on network characteristics such as clustering or connectivity of the graph. Thirdly, we address the more general problem of estimating two precision matrices that are expected to be similar, when datasets are dependent, focusing on the particular case of paired observations. We propose a new method to estimate these precision matrices simultaneously, a weighted fused graphical lasso estimator. The analogous joint estimation method concerning two regression coefficient matrices, which we call weighted fused regression lasso, is also developed in this thesis under the same paired and high-dimensional setting. The two joint estimators maximize penalized marginal log likelihood functions, which encourage both sparsity and similarity in the estimated matrices, and that are solved using an alternating direction method of multipliers (ADMM) algorithm. Sparsity and similarity of thematrices are determined by two tuning parameters and we propose to choose them by controlling the corresponding average error rates related to the expected number of false positive edges in the estimated conditional dependence networks. These testing and estimation methods are implemented within the R package ldstatsHD, and are applied to a comprehensive range of simulated data sets as well as to high-dimensional real case studies of genomic data. We employ testing approaches with the purpose of discovering pathway lists of genes that present significantly different correlation matrices on healthy and unhealthy (e.g., tumor) samples. Besides, we use hypothesis testing problems on correlation sub-matrices to reduce the number of genes for estimation. The proposed joint estimation methods are then considered to find gene interactions that are common between medical conditions as well as interactions that vary in the presence of unhealthy tissues.