A Quadratically Regularized Functional Canonical Correlation Analysis for Identifying the Global Structure of Pleiotropy with NGS Data

Investigating the pleiotropic effects of genetic variants can increase statistical power, provide important information to achieve deep understanding of the complex genetic structures of disease, and offer powerful tools for designing effective treatments with fewer side effects. However, the current multiple phenotype association analysis paradigm lacks breadth (number of phenotypes and genetic variants jointly analyzed at the same time) and depth (hierarchical structure of phenotype and genotypes). A key issue for high dimensional pleiotropic analysis is to effectively extract informative internal representation and features from high dimensional genotype and phenotype data. To explore multiple levels of representations of genetic variants, learn their internal patterns involved in the disease development, and overcome critical barriers in advancing the development of novel statistical methods and computational algorithms for genetic pleiotropic analysis, we proposed a new framework referred to as a quadratically regularized functional CCA (QRFCCA) for association analysis which combines three approaches: (1) quadratically regularized matrix factorization, (2) functional data analysis and (3) canonical correlation analysis (CCA). Large-scale simulations show that the QRFCCA has a much higher power than that of the nine competing statistics while retaining the appropriate type 1 errors. To further evaluate performance, the QRFCCA and nine other statistics are applied to the whole genome sequencing dataset from the TwinsUK study. We identify a total of 79 genes with rare variants and 67 genes with common variants significantly associated with the 46 traits using QRFCCA. The results show that the QRFCCA substantially outperforms the nine other statistics.Comment: 64 pages including 12 figure

A Comparison of Relaxations of Multiset Cannonical Correlation Analysis and Applications

Canonical correlation analysis is a statistical technique that is used to find relations between two sets of variables. An important extension in pattern analysis is to consider more than two sets of variables. This problem can be expressed as a quadratically constrained quadratic program (QCQP), commonly referred to Multi-set Canonical Correlation Analysis (MCCA). This is a non-convex problem and so greedy algorithms converge to local optima without any guarantees on global optimality. In this paper, we show that despite being highly structured, finding the optimal solution is NP-Hard. This motivates our relaxation of the QCQP to a semidefinite program (SDP). The SDP is convex, can be solved reasonably efficiently and comes with both absolute and output-sensitive approximation quality. In addition to theoretical guarantees, we do an extensive comparison of the QCQP method and the SDP relaxation on a variety of synthetic and real world data. Finally, we present two useful extensions: we incorporate kernel methods and computing multiple sets of canonical vectors

Linking Image and Text with 2-Way Nets

Linking two data sources is a basic building block in numerous computer vision problems. Canonical Correlation Analysis (CCA) achieves this by utilizing a linear optimizer in order to maximize the correlation between the two views. Recent work makes use of non-linear models, including deep learning techniques, that optimize the CCA loss in some feature space. In this paper, we introduce a novel, bi-directional neural network architecture for the task of matching vectors from two data sources. Our approach employs two tied neural network channels that project the two views into a common, maximally correlated space using the Euclidean loss. We show a direct link between the correlation-based loss and Euclidean loss, enabling the use of Euclidean loss for correlation maximization. To overcome common Euclidean regression optimization problems, we modify well-known techniques to our problem, including batch normalization and dropout. We show state of the art results on a number of computer vision matching tasks including MNIST image matching and sentence-image matching on the Flickr8k, Flickr30k and COCO datasets.Comment: 14 pages, 2 figures, 6 table