Latent variable modeling with random features
This provides a flexible tool for nonlinear dimension reduction in fields like neuroscience and computer vision, though it is incremental as it builds on existing random feature approximations.
The authors tackled the challenge of generalizing Gaussian process-based latent variable models to non-Gaussian data by developing random feature latent variable models (RFLVMs), which enable computationally tractable nonlinear dimension reduction for various data types and produce results comparable to state-of-the-art methods.
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.