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Title: Latent variable modeling with random features
Gaussian process-based latent variable models are flexible and theoretically grounded tools for nonlinear dimension reduction, but generalizing to non-Gaussian data likelihoods within this nonlinear framework is statistically challenging. Here, we use random features to develop a family of nonlinear dimension reduction models that are easily extensible to non-Gaussian data likelihoods; we call these random feature latent variable models (RFLVMs). By approximating a nonlinear relationship between the latent space and the observations with a function that is linear with respect to random features, we induce closed-form gradients of the posterior distribution with respect to the latent variable. This allows the RFLVM framework to support computationally tractable nonlinear latent variable models for a variety of data likelihoods in the exponential family without specialized derivations. Our generalized RFLVMs produce results comparable with other state-of-the-art dimension reduction methods on diverse types of data, including neural spike train recordings, images, and text data.
Michael Zhang is currently an assistant professor since January 2021 in the Department of Statistics and Actuarial Science at the University of Hong Kong. His research interests include statistical machine learning, scalable inference and Bayesian non-parametrics. Michael Zhang was a post-doctoral researcher at Princeton University under the supervision of Profs. Barbara Engelhardt and Brandon Stewart and earned a Ph.D. in statistics at the University of Texas at Austin where he was advised by Prof. Sinead Williamson.