# Latent variable modeling with random features

arXiv: https://arxiv.org/abs/2006.11145 · HTML: https://mlsanity.com/paper/2006.11145/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [Sequential Estimation of Gaussian Process-based Deep State-Space Models](https://mlsanity.com/paper/2301.12528/) (2023)
- [Bayesian Non-linear Latent Variable Modeling via Random Fourier Features](https://mlsanity.com/paper/2306.08352/) (2023)
- [Preventing Model Collapse in Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2404.01697/) (2024)
- [Nonnegative spatial factorization](https://mlsanity.com/paper/2110.06122/) (2021)
- [Sparse Infinite Random Feature Latent Variable Modeling](https://mlsanity.com/paper/2205.09909/) (2022)
- [Multi-View Oriented GPLVM: Expressiveness and Efficiency](https://mlsanity.com/paper/2502.08253/) (2025)
- [Scalable Random Feature Latent Variable Models](https://mlsanity.com/paper/2410.17700/) (2024)
- [Amortized Structured Stochastic Variational Inference for Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2610.03647/) (2026)

## Abstract (arXiv)

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.