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Vintage Factor Analysis with Varimax Performs Statistical Inference

Tuesday, April 27, 2021 - 11:00 to 12:00
Karl Rohe, Associate Professor of Statistics at the University of Wisconsin–Madison
Statistics Seminar
Zoom

To join via Zoom: To join this seminar, please request Zoom connection details from headsec [at] stat.ubc.ca.

Post-seminar Q&A: Graduate students are invited to stay after the seminar for a Q&A session with the speaker (~12pm–12:30pm PST).

Abstract: Vintage Factor Analysis is nearly a century old and remains popular today with practitioners. A key step, the factor rotation, is historically controversial because it appears to be unidentifiable. This controversy goes back as far as Charles Spearman. The unidentifiability is still reported in all modern multivariate textbooks. This talk will overturn this controversy and provide a positive theory for PCA with a varimax rotation. Just as sparsity helps to find a solution in p>n regression, we show that sparsity resolves the rotational invariance of factor analysis. PCA + varimax is fast to compute and provides a unified spectral estimation strategy for Stochastic Blockmodels, topic models (LDA), and nonnegative matrix factorization. Moreover, the estimator is consistent for an even broader class of models and the old factor analysis diagnostics (which have been used for nearly a century) assess the identifiability.  https://arxiv.org/abs/2004.05387