The EM Algorithm and the Rise of Computational Biology

In the past decade computational biology has grown from a cottage industry with a handful of researchers to an attractive interdisciplinary field, catching the attention and imagination of many quantitatively-minded scientists. Of interest to us is the key role played by the EM algorithm during this transformation. We survey the use of the EM algorithm in a few important computational biology problems surrounding the "central dogma"; of molecular biology: from DNA to RNA and then to proteins. Topics of this article include sequence motif discovery, protein sequence alignment, population genetics, evolutionary models and mRNA expression microarray data analysis.Comment: Published in at http://dx.doi.org/10.1214/09-STS312 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Large Covariance Estimation by Thresholding Principal Orthogonal Complements

This paper deals with the estimation of a high-dimensional covariance with a conditional sparsity structure and fast-diverging eigenvalues. By assuming sparse error covariance matrix in an approximate factor model, we allow for the presence of some cross-sectional correlation even after taking out common but unobservable factors. We introduce the Principal Orthogonal complEment Thresholding (POET) method to explore such an approximate factor structure with sparsity. The POET estimator includes the sample covariance matrix, the factor-based covariance matrix (Fan, Fan, and Lv, 2008), the thresholding estimator (Bickel and Levina, 2008) and the adaptive thresholding estimator (Cai and Liu, 2011) as specific examples. We provide mathematical insights when the factor analysis is approximately the same as the principal component analysis for high-dimensional data. The rates of convergence of the sparse residual covariance matrix and the conditional sparse covariance matrix are studied under various norms. It is shown that the impact of estimating the unknown factors vanishes as the dimensionality increases. The uniform rates of convergence for the unobserved factors and their factor loadings are derived. The asymptotic results are also verified by extensive simulation studies. Finally, a real data application on portfolio allocation is presented

Computer Analysis of Architecture Using Automatic Image Understanding

In the past few years, computer vision and pattern recognition systems have been becoming increasingly more powerful, expanding the range of automatic tasks enabled by machine vision. Here we show that computer analysis of building images can perform quantitative analysis of architecture, and quantify similarities between city architectural styles in a quantitative fashion. Images of buildings from 18 cities and three countries were acquired using Google StreetView, and were used to train a machine vision system to automatically identify the location of the imaged building based on the image visual content. Experimental results show that the automatic computer analysis can automatically identify the geographical location of the StreetView image. More importantly, the algorithm was able to group the cities and countries and provide a phylogeny of the similarities between architectural styles as captured by StreetView images. These results demonstrate that computer vision and pattern recognition algorithms can perform the complex cognitive task of analyzing images of buildings, and can be used to measure and quantify visual similarities and differences between different styles of architectures. This experiment provides a new paradigm for studying architecture, based on a quantitative approach that can enhance the traditional manual observation and analysis. The source code used for the analysis is open and publicly available