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Factor analysis is a critical component of high dimensional biological dataanalysis. However, modern biological data contain two key features thatirrevocably corrupt existing methods. First, these data, which includelongitudinal, multi-treatment and multi-tissue data, contain samples that breakcritical independence requirements necessary for the utilization of prevailingmethods. Second, biological data contain factors with large, moderate and smallsignal strengths, and therefore violate the ubiquitous "pervasive factor"assumption essential to the performance of many methods. In this work, Idevelop a novel statistical framework to perform factor analysis and interpretits results in data with dependent observations and factors whose signalstrengths span several orders of magnitude. I then prove that my methodologycan be used to solve many important and previously unsolved problems thatroutinely arise when analyzing dependent biological data, including highdimensional covariance estimation, subspace recovery, latent factorinterpretation and data denoising. Additionally, I show that my estimator forthe number of factors overcomes both the notorious "eigenvalue shadowing"problem, as well as the biases due to the pervasive factor assumption thatplague existing estimators. Simulated and real data demonstrate the superiorperformance of my methodology in practice.

Factor analysis in high dimensional biological data with dependent observations