Covariate assisted screening and estimation

Consider a linear model $Y=X\beta+z$, where $X=X_{n,p}$ and $z\sim N(0,I_n)$. The vector $\beta$ is unknown but is sparse in the sense that most of its coordinates are $0$. The main interest is to separate its nonzero coordinates from the zero ones (i.e., variable selection). Motivated by examples in long-memory time series (Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer]) and the change-point problem (Bhattacharya [In Change-Point Problems (South Hadley, MA, 1992) (1994) 28-56 IMS]), we are primarily interested in the case where the Gram matrix $G=X'X$ is nonsparse but sparsifiable by a finite order linear filter. We focus on the regime where signals are both rare and weak so that successful variable selection is very challenging but is still possible. We approach this problem by a new procedure called the covariate assisted screening and estimation (CASE). CASE first uses a linear filtering to reduce the original setting to a new regression model where the corresponding Gram (covariance) matrix is sparse. The new covariance matrix induces a sparse graph, which guides us to conduct multivariate screening without visiting all the submodels. By interacting with the signal sparsity, the graph enables us to decompose the original problem into many separated small-size subproblems (if only we know where they are!). Linear filtering also induces a so-called problem of information leakage, which can be overcome by the newly introduced patching technique. Together, these give rise to CASE, which is a two-stage screen and clean [Fan and Song Ann. Statist. 38 (2010) 3567-3604; Wasserman and Roeder Ann. Statist. 37 (2009) 2178-2201] procedure, where we first identify candidates of these submodels by patching and screening, and then re-examine each candidate to remove false positives.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1243 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Recent Advances in Text Analysis

Text analysis is an interesting research area in data science and has various applications, such as in artificial intelligence, biomedical research, and engineering. We review popular methods for text analysis, ranging from topic modeling to the recent neural language models. In particular, we review Topic-SCORE, a statistical approach to topic modeling, and discuss how to use it to analyze MADStat - a dataset on statistical publications that we collected and cleaned. The application of Topic-SCORE and other methods on MADStat leads to interesting findings. For example, $11$ representative topics in statistics are identified. For each journal, the evolution of topic weights over time can be visualized, and these results are used to analyze the trends in statistical research. In particular, we propose a new statistical model for ranking the citation impacts of $11$ topics, and we also build a cross-topic citation graph to illustrate how research results on different topics spread to one another. The results on MADStat provide a data-driven picture of the statistical research in $1975$--$2015$, from a text analysis perspective

fREDUCE: Detection of degenerate regulatory elements using correlation with expression

<p>Abstract</p> <p>Background</p> <p>The precision of transcriptional regulation is made possible by the specificity of physical interactions between transcription factors and their cognate binding sites on DNA. A major challenge is to decipher transcription factor binding sites from sequence and functional genomic data using computational means. While current methods can detect strong binding sites, they are less sensitive to degenerate motifs.</p> <p>Results</p> <p>We present fREDUCE, a computational method specialized for the detection of weak or degenerate binding motifs from gene expression or ChIP-chip data. fREDUCE is built upon the widely applied program REDUCE, which elicits motifs by global statistical correlation of motif counts with expression data. fREDUCE introduces several algorithmic refinements that allow efficient exhaustive searches of oligonucleotides with a specified number of degenerate IUPAC symbols. On yeast ChIP-chip benchmarks, fREDUCE correctly identified motifs and their degeneracies with accuracies greater than its predecessor REDUCE as well as other known motif-finding programs. We have also used fREDUCE to make novel motif predictions for transcription factors with poorly characterized binding sites.</p> <p>Conclusion</p> <p>We demonstrate that fREDUCE is a valuable tool for the prediction of degenerate transcription factor binding sites, especially from array datasets with weak signals that may elude other motif detection methods.</p