Latent variable modeling with random features

• URL: http://arxiv.org/abs/2006.11145v1
• Date: Fri, 19 Jun 2020 14:12:05 GMT
• Title: Latent variable modeling with random features
• Authors: Gregory W. Gundersen, Michael Minyi Zhang, Barbara E. Engelhardt
• Abstract summary: We develop a family of nonlinear dimension reduction models that are easily to non-Gaussian data likelihoods. Our generalized RFLVMs produce results comparable with other state-of-the-art dimension reduction methods.
• Score: 7.856578780790166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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