Multivariate Models and Algorithms for Learning Correlation Structures from Replicated Molecular Profiling Data

Advances in high-throughput data acquisition technologies, e.g. microarray and next-generation sequencing, have resulted in the production of a myriad amount of molecular profiling data. Consequently, there has been an increasing interest in the development of computational methods to uncover gene association patterns underlying such data, e.g. gene clustering (Medvedovic & Sivaganesan, 2002; Medvedovic et al., 2004), inference of gene association networks (Altay and Emmert-Streib, 2010; Butte & Kohane, 2000; Zhu et al., 2005), sample classification (Yeung & Bumgarner, 2005) and detection of differentially expressed genes (Sartor et al., 2006). However, outcome of any bioinformatics analysis is directly influenced by the quality of molecular profiling data, which are often contaminated with excessive noise. Replication is a frequently used strategy to account for the noise introduced at various stages of a biomedical experiment and to achieve a reliable discovery of the underlying biomolecular activities. Particularly, estimation of the correlation structure of a gene set arises naturally in many pattern analyses of replicated molecular profiling data. In both supervised and unsupervised learning, performance of various data analysis methods, e.g. linear and quadratic discriminate analysis (Hastie et al., 2009), correlation-based hierarchial clustering (Eisen et al., 1998; de Hoon et al., 2004; Yeung et al., 2003) and co-expression networking (Basso et al., 2005; Boscolo et al., 2008) relies on an accurate estimate of the true correlation structure. The existing MLE (maximum likelihood estimate) based approaches to the estimation of correlation structure do not automatically accommodate replicated measurements. Often, an ad hoc step of data preprocessing by averaging (either weighted, unweighted or something in between) is used to reduce the multivariate structure of replicated data into bivariate one (Hughes et al., 2000; Yao et al., 2008; Yeung et al., 2003). Averaging is not completely satisfactory as it creates a strong bias while reducing the variance among replicates with diverse magnitudes. Moreover, averaging may lead to a significant amount of information loss, e.g. it may wipe out important patterns of small magnitudes or cancel out opposite patterns of similar magnitudes. Thus, it is necessary to design multivariate correlation estimators by treating each replicate exclusively as a random variable. In general, the experimental design that specifies replication mechanism of a gene set may be unknown 3