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1.  Joint Adaptive Mean-Variance Regularization and Variance Stabilization of High Dimensional Data 
The paper addresses a common problem in the analysis of high-dimensional high-throughput “omics” data, which is parameter estimation across multiple variables in a set of data where the number of variables is much larger than the sample size. Among the problems posed by this type of data are that variable-specific estimators of variances are not reliable and variable-wise tests statistics have low power, both due to a lack of degrees of freedom. In addition, it has been observed in this type of data that the variance increases as a function of the mean. We introduce a non-parametric adaptive regularization procedure that is innovative in that : (i) it employs a novel “similarity statistic”-based clustering technique to generate local-pooled or regularized shrinkage estimators of population parameters, (ii) the regularization is done jointly on population moments, benefiting from C. Stein's result on inadmissibility, which implies that usual sample variance estimator is improved by a shrinkage estimator using information contained in the sample mean. From these joint regularized shrinkage estimators, we derived regularized t-like statistics and show in simulation studies that they offer more statistical power in hypothesis testing than their standard sample counterparts, or regular common value-shrinkage estimators, or when the information contained in the sample mean is simply ignored. Finally, we show that these estimators feature interesting properties of variance stabilization and normalization that can be used for preprocessing high-dimensional multivariate data. The method is available as an R package, called ‘MVR’ (‘Mean-Variance Regularization’), downloadable from the CRAN website.
doi:10.1016/j.csda.2012.01.012
PMCID: PMC3375876  PMID: 22711950
Bioinformatics; Inadmissibility; Regularization; Shrinkage Estimators; Normalization; Variance Stabilization
2.  Genomic Promoter Analysis Predicts Functional Transcription Factor Binding 
Advances in Bioinformatics  2008;2008:369830.
Background. The computational identification of functional transcription factor binding sites (TFBSs) remains a major challenge of computational biology. Results. We have analyzed the conserved promoter sequences for the complete set of human RefSeq genes using our conserved transcription factor binding site (CONFAC) software. CONFAC identified 16296 human-mouse ortholog gene pairs, and of those pairs, 9107 genes contained conserved TFBS in the 3 kb proximal promoter and first intron. To attempt to predict in vivo occupancy of transcription factor binding sites, we developed a novel marginal effect isolator algorithm that builds upon Bayesian methods for multigroup TFBS filtering and predicted the in vivo occupancy of two transcription factors with an overall accuracy of 84%. Conclusion. Our analyses show that integration of chromatin immunoprecipitation data with conserved TFBS analysis can be used to generate accurate predictions of functional TFBS. They also show that TFBS cooccurrence can be used to predict transcription factor binding to promoters in vivo.
doi:10.1155/2008/369830
PMCID: PMC2768302  PMID: 19865592
3.  Local sparse bump hunting reveals molecular heterogeneity of colon tumors‡ 
Statistics in medicine  2011;31(0):1203-1220.
The question of molecular heterogeneity and of tumoral phenotype in cancer remains unresolved. To understand the underlying molecular basis of this phenomenon, we analyzed genome-wide expression data of colon cancer metastasis samples, as these tumors are the most advanced and hence would be anticipated to be the most likely heterogeneous group of tumors, potentially exhibiting the maximum amount of genetic heterogeneity. Casting a statistical net around such a complex problem proves difficult because of the high dimensionality and multi-collinearity of the gene expression space, combined with the fact that genes act in concert with one another and that not all genes surveyed might be involved. We devise a strategy to identify distinct subgroups of samples and determine the genetic/molecular signature that defines them. This involves use of the local sparse bump hunting algorithm, which provides a much more optimal and biologically faithful transformed space within which to search for bumps. In addition, thanks to the variable selection feature of the algorithm, we derived a novel sparse gene expression signature, which appears to divide all colon cancer patients into two populations: a population whose expression pattern can be molecularly encompassed within the bump and an outlier population that cannot be. Although all patients within any given stage of the disease, including the metastatic group, appear clinically homogeneous, our procedure revealed two subgroups in each stage with distinct genetic/molecular profiles. We also discuss implications of such a finding in terms of early detection, diagnosis and prognosis.
doi:10.1002/sim.4389
PMCID: PMC3668571  PMID: 22052459
local sparse bump hunting; mixture density; class discovery; colon cancer patient subtyping; early diagnosis and prognosis
4.  Local Sparse Bump Hunting 
The search for structures in real datasets e.g. in the form of bumps, components, classes or clusters is important as these often reveal underlying phenomena leading to scientific discoveries. One of these tasks, known as bump hunting, is to locate domains of a multidimensional input space where the target function assumes local maxima without pre-specifying their total number. A number of related methods already exist, yet are challenged in the context of high dimensional data. We introduce a novel supervised and multivariate bump hunting strategy for exploring modes or classes of a target function of many continuous variables. This addresses the issues of correlation, interpretability, and high-dimensionality (p ≫ n case), while making minimal assumptions. The method is based upon a divide and conquer strategy, combining a tree-based method, a dimension reduction technique, and the Patient Rule Induction Method (PRIM). Important to this task, we show how to estimate the PRIM meta-parameters. Using accuracy evaluation procedures such as cross-validation and ROC analysis, we show empirically how the method outperforms a naive PRIM as well as competitive non-parametric supervised and unsupervised methods in the problem of class discovery. The method has practical application especially in the case of noisy high-throughput data. It is applied to a class discovery problem in a colon cancer micro-array dataset aimed at identifying tumor subtypes in the metastatic stage. Supplemental Materials are available online.
doi:10.1198/jcgs.2010.09029
PMCID: PMC3293195  PMID: 22399839
mode/class discovery; patient rule induction method; sparse principal components; clustering; classification; density estimation
5.  Genomic Promoter Analysis Predicts Functional Transcription Factor Binding 
Advances in bioinformatics  2008;2008:3698301-3698309.
Background
The computational identification of functional transcription factor binding sites (TFBSs) remains a major challenge of computational biology.
Results
We have analyzed the conserved promoter sequences for the complete set of human RefSeq genes using our conserved transcription factor binding site (CONFAC) software. CONFAC identified 16296 human-mouse ortholog gene pairs, and of those pairs, 9107 genes contained conserved TFBS in the 3 kb proximal promoter and first intron. To attempt to predict in vivo occupancy of transcription factor binding sites, we developed a novel marginal effect isolator algorithm that builds upon Bayesian methods for multigroup TFBS filtering and predicted the in vivo occupancy of two transcription factors with an overall accuracy of 84%.
Conclusion
Our analyses show that integration of chromatin immunoprecipitation data with conserved TFBS analysis can be used to generate accurate predictions of functional TFBS. They also show that TFBS cooccurrence can be used to predict transcription factor binding to promoters in vivo.
doi:10.1155/2008/369830
PMCID: PMC2768302  PMID: 19865592
6.  Studying genetic determinants of natural variation in human gene expression using Bayesian ANOVA 
BMC Proceedings  2007;1(Suppl 1):S115.
Standard genetic mapping techniques scan chromosomal segments for location of genetic linkage and association signals. The majority of these methods consider only correlations at single markers and/or phenotypes with explicit detailing of the genetic structure. These methods tend to be limited by their inability to consider the effect of large numbers of model variables jointly. In contrast, we propose a Bayesian analysis of variance (ANOVA) method to categorize individuals based on similarity of multidimensional profiles and attempt to analyze all variables simultaneously. Using Problem 1 of the Genetic Analysis Workshop 15 data set, we demonstrate the method's utility for joint analysis of gene expression levels and single-nucleotide polymorphism genotypes. We show that the method extracts similar information to that of previous genetic mapping analyses, and suggest extensions of the method for mining unique information not previously found.
PMCID: PMC2367590  PMID: 18466456
7.  Statistical Redundancy Testing for Improved Gene Selection in Cancer Classification Using Microarray Data 
Cancer Informatics  2007;3:29-41.
In gene selection for cancer classification using microarray data, we define an eigenvalue-ratio statistic to measure a gene’s contribution to the joint discriminability when this gene is included into a set of genes. Based on this eigenvalue-ratio statistic, we define a novel hypothesis testing for gene statistical redundancy and propose two gene selection methods. Simulation studies illustrate the agreement between statistical redundancy testing and gene selection methods. Real data examples show the proposed gene selection methods can select a compact gene subset which can not only be used to build high quality cancer classifiers but also show biological relevance.
PMCID: PMC2675847  PMID: 19455233
gene selection; microarray; cancer classification; statistical redundancy
8.  BAMarray™: Java software for Bayesian analysis of variance for microarray data 
BMC Bioinformatics  2006;7:59.
Background
DNA microarrays open up a new horizon for studying the genetic determinants of disease. The high throughput nature of these arrays creates an enormous wealth of information, but also poses a challenge to data analysis. Inferential problems become even more pronounced as experimental designs used to collect data become more complex. An important example is multigroup data collected over different experimental groups, such as data collected from distinct stages of a disease process. We have developed a method specifically addressing these issues termed Bayesian ANOVA for microarrays (BAM). The BAM approach uses a special inferential regularization known as spike-and-slab shrinkage that provides an optimal balance between total false detections and total false non-detections. This translates into more reproducible differential calls. Spike and slab shrinkage is a form of regularization achieved by using information across all genes and groups simultaneously.
Results
BAMarray™ is a graphically oriented Java-based software package that implements the BAM method for detecting differentially expressing genes in multigroup microarray experiments (up to 256 experimental groups can be analyzed). Drop-down menus allow the user to easily select between different models and to choose various run options. BAMarray™ can also be operated in a fully automated mode with preselected run options. Tuning parameters have been preset at theoretically optimal values freeing the user from such specifications. BAMarray™ provides estimates for gene differential effects and automatically estimates data adaptive, optimal cutoff values for classifying genes into biological patterns of differential activity across experimental groups. A graphical suite is a core feature of the product and includes diagnostic plots for assessing model assumptions and interactive plots that enable tracking of prespecified gene lists to study such things as biological pathway perturbations. The user can zoom in and lasso genes of interest that can then be saved for downstream analyses.
Conclusion
BAMarray™ is user friendly platform independent software that effectively and efficiently implements the BAM methodology. Classifying patterns of differential activity is greatly facilitated by a data adaptive cutoff rule and a graphical suite. BAMarray™ is licensed software freely available to academic institutions. More information can be found at .
doi:10.1186/1471-2105-7-59
PMCID: PMC1382258  PMID: 16466568

Results 1-8 (8)