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Continuous-depth Deep Gaussian Processes

The paper proposes a continuous-depth formulation for Deep Gaussian Processes (DGPs), treating depth as a latent continuous evolution rather than a discrete stack. It introduces two instantiations—CDGP, which applies a GP prior directly to the state–depth drift, and FlowDGP, which uses a flow-evolved prior to capture richer depth dependence at lower training cost. Experiments on synthetic, benchmark, and large-scale regression tasks demonstrate that residual DGP improves over plain DGP, while CDGP and FlowDGP offer stronger performance across the studied regimes.

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arXiv Machine Learning
Oct 23

Continuous-depth Deep Gaussian Processes

The paper introduces a continuous-depth formulation of Deep Gaussian Processes (DGPs), treating depth as a latent continuous evolution rather than a discrete stack. It proposes two instantiations—CDGP, which applies a GP prior directly to the state–depth drift, and FlowDGP, which uses a flow-evolved prior to capture richer depth dependence at lower training cost. Experiments on synthetic, benchmark, and large-scale regression tasks demonstrate that residual DGP outperforms plain DGP, while CDGP and FlowDGP provide stronger overall performance across the studied regimes.

By Ying Li, Sanyou Wu, Zi Yang, Qiaochu Xu, Yuhao Liu, Zhidi Lin, Michael Minyi Zhang, Petar Djuric, Alexandre H. Thiery
benchmarks
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arXiv Machine Learning
Sep 14

Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization

The paper investigates nonlinear dimensionality reduction for Bayesian optimisation (BO) by transforming high‑dimensional black‑box optimisation problems into a sequence of low‑dimensional latent‑space BO (LSBO) tasks. It extends earlier linear embedding approaches by using variational autoencoders (VAEs), deep metric loss, and adaptive retraining to better capture nonlinear structure, and couples LSBO with sequential domain reduction (SDR‑LSBO) to progressively narrow search domains. Experiments on GPU‑accelerated BoTorch with Matérn‑5/2 Gaussian‑process surrogates show that VAE‑based LSBO outperforms adaptive linear embeddings, and the authors provide a theoretical analysis of latent‑space error versus representation gap under PAC‑Bayes conditions.

By Luo Long, Coralia Cartis, Paz Fink Shustin
ragdiffusionbenchmarks
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arXiv Machine Learning
Oct 7

Generalized Matheron Variational Implicit Processes

Generalized Matheron Variational Implicit Processes (GMVIP) provide a pathwise variational family for posterior inference with implicit-process priors, such as Bayesian neural networks and stochastic simulators. For Gaussian‑process priors, GMVIP reproduces the standard inducing‑variable variational GP construction, while for general implicit priors it preserves the prior mean and covariance in the population limit. The method constructs posterior samples by drawing a function from the prior and applying a correction anchored at inducing inputs, with the correction determined directly from prior samples, and achieves a tractable coefficient‑space Kullback‑Leibler divergence. Experiments on regression, classification, and forecasting demonstrate that GMVIP is broadly competitive with existing methods.

By Luis A. Ortega, Andr\'es R. Masegosa, Thomas D. Nielsen
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