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On Signal-to-Noise Ratio Issues in Variational Inference for Deep Gaussian Processes
Tim G. J. Rudner · Oscar Key · Yarin Gal · Tom Rainforth

Thu Jul 22 05:40 AM -- 05:45 AM (PDT) @ None

We show that the gradient estimates used in training Deep Gaussian Processes (DGPs) with importance-weighted variational inference are susceptible to signal-to-noise ratio (SNR) issues. Specifically, we show both theoretically and via an extensive empirical evaluation that the SNR of the gradient estimates for the latent variable's variational parameters decreases as the number of importance samples increases. As a result, these gradient estimates degrade to pure noise if the number of importance samples is too large. To address this pathology, we show how doubly-reparameterized gradient estimators, originally proposed for training variational autoencoders, can be adapted to the DGP setting and that the resultant estimators completely remedy the SNR issue, thereby providing more reliable training. Finally, we demonstrate that our fix can lead to consistent improvements in the predictive performance of DGP models.

Author Information

Tim G. J. Rudner (University of Oxford)

I am a PhD Candidate in the Department of Computer Science at the University of Oxford, where I conduct research on probabilistic machine learning with Yarin Gal and Yee Whye Teh. My research interests span **Bayesian deep learning**, **variational inference**, and **reinforcement learning**. I am particularly interested in uncertainty quantification in deep learning, reinforcement learning as probabilistic inference, and probabilistic transfer learning. I am also a **Rhodes Scholar** and an **AI Fellow** at Georgetown University's Center for Security and Emerging Technology.

Oscar Key (UCL)
Yarin Gal (University of Oxford)
Tom Rainforth (University of Oxford)

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