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Eindhoven SPOR seminar
Apr 26, 15:45 - 16:45
Karl Rohe (UW Madison)
Vintage Factor Analysis with Varimax Performs Statistical Inference
Psychologists developed Multiple Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors. In this form of factor analysis, the Varimax "factor rotation" is a key step to make the factors interpretable. Charles Spearman and many others objected to factor rotations because the factors seem to be rotationally invariant. This is an historical enigma because factor rotations have survived and are widely popular because, empirically, they often make factors easier to interpret. We argue that the rotation makes the factors easier to interpret because, in fact, the Varimax factor rotation performs statistical inference. We show that Principal Components Analysis (PCA) with the Varimax rotation provides a unified spectral estimation strategy for a broad class of modern factor models, including the Stochastic Blockmodel and a natural variation of Latent Dirichlet Allocation (i.e., "topic modeling"). In addition, we show that Thurstone's widely employed sparsity diagnostics implicitly assess a key "leptokurtic" condition that makes the rotation statistically identifiable in these models. Taken together, this shows that the know-how of Vintage Factor Analysis performs statistical inference, reversing nearly a century of statistical thinking on the topic. With a sparse eigensolver, PCA with Varimax is both fast and stable. Combined with Thurstone's straightforward diagnostics, this vintage approach is suitable for a wide array of modern applications. See https://arxiv.org/abs/2004.05387
This talk will be held fully online; you are welcome to attend the talk via Zoom. The Zoom link is attached to the bottom of this invitation.
For upcoming events of the SPOR seminar, as well as a history of previous talks, see: https://www.eurandom.tue.nl/eindhoven-spor-seminar/. Recordings of earlier talks are available upon request.