Robust and Conjugate Gaussian Process Regression

• URL: http://arxiv.org/abs/2311.00463v2
• Date: Mon, 3 Jun 2024 10:07:13 GMT
• Title: Robust and Conjugate Gaussian Process Regression
• Authors: Matias Altamirano, François-Xavier Briol, Jeremias Knoblauch,
• Abstract summary: We show how to perform robust and conjugate Gaussian process (RCGP) regression at virtually no additional cost using generalised Bayesian inference. RCGP is particularly versatile as it enables exact conjugate closed form updates in all settings where standard GPs admit them.
• Score: 6.417777780911224
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To enable closed form conditioning, a common assumption in Gaussian process (GP) regression is independent and identically distributed Gaussian observation noise. This strong and simplistic assumption is often violated in practice, which leads to unreliable inferences and uncertainty quantification. Unfortunately, existing methods for robustifying GPs break closed-form conditioning, which makes them less attractive to practitioners and significantly more computationally expensive. In this paper, we demonstrate how to perform provably robust and conjugate Gaussian process (RCGP) regression at virtually no additional cost using generalised Bayesian inference. RCGP is particularly versatile as it enables exact conjugate closed form updates in all settings where standard GPs admit them. To demonstrate its strong empirical performance, we deploy RCGP for problems ranging from Bayesian optimisation to sparse variational Gaussian processes.

Related papers

• Non-Gaussian Process Regression [0.0]
  We extend the GP framework into a new class of time-changed GPs that allow for straightforward modelling of heavy-tailed non-Gaussian behaviours. We present Markov chain Monte Carlo inference procedures for this model and demonstrate the potential benefits.
  arXiv  Detail & Related papers  (2022-09-07T13:08:22Z)
• Non-Gaussian Gaussian Processes for Few-Shot Regression [71.33730039795921]
  We propose an invertible ODE-based mapping that operates on each component of the random variable vectors and shares the parameters across all of them. NGGPs outperform the competing state-of-the-art approaches on a diversified set of benchmarks and applications.
  arXiv  Detail & Related papers  (2021-10-26T10:45:25Z)
• Stochastic Training is Not Necessary for Generalization [57.04880404584737]
  It is widely believed that the implicit regularization of gradient descent (SGD) is fundamental to the impressive generalization behavior we observe in neural networks. In this work, we demonstrate that non-stochastic full-batch training can achieve strong performance on CIFAR-10 that is on-par with SGD.
  arXiv  Detail & Related papers  (2021-09-29T00:50:00Z)
• Scalable Variational Gaussian Processes via Harmonic Kernel Decomposition [54.07797071198249]
  We introduce a new scalable variational Gaussian process approximation which provides a high fidelity approximation while retaining general applicability. We demonstrate that, on a range of regression and classification problems, our approach can exploit input space symmetries such as translations and reflections. Notably, our approach achieves state-of-the-art results on CIFAR-10 among pure GP models.
  arXiv  Detail & Related papers  (2021-06-10T18:17:57Z)
• On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach [0.76146285961466]
  Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. We propose a pseudo-marginal (PM) scheme that offers exact inference as well as computational gains through doubly estimators for the likelihood and large datasets.
  arXiv  Detail & Related papers  (2021-03-04T20:48:29Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• Likelihood-Free Inference with Deep Gaussian Processes [70.74203794847344]
  Surrogate models have been successfully used in likelihood-free inference to decrease the number of simulator evaluations. We propose a Deep Gaussian Process (DGP) surrogate model that can handle more irregularly behaved target distributions. Our experiments show how DGPs can outperform GPs on objective functions with multimodal distributions and maintain a comparable performance in unimodal cases.
  arXiv  Detail & Related papers  (2020-06-18T14:24:05Z)
• SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives [86.01677297601624]
  We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
  arXiv  Detail & Related papers  (2020-03-05T14:33:20Z)
• Transport Gaussian Processes for Regression [0.22843885788439797]
  We propose a methodology to construct processes, which include GPs, warped GPs, Student-t processes and several others. Our approach is inspired by layers-based models, where each proposed layer changes a specific property over the generated process. We validate the proposed model through experiments with real-world data.
  arXiv  Detail & Related papers  (2020-01-30T17:44:21Z)
• Sequential Gaussian Processes for Online Learning of Nonstationary Functions [9.997259201098602]
  We propose a sequential Monte Carlo algorithm to fit infinite mixtures of GPs that capture non-stationary behavior while allowing for online, distributed inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the presence of non-stationarity in time-series data.
  arXiv  Detail & Related papers  (2019-05-24T02:29:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.