Empirical Gaussian Processes

• URL: http://arxiv.org/abs/2602.12082v1
• Date: Thu, 12 Feb 2026 15:39:08 GMT
• Title: Empirical Gaussian Processes
• Authors: Jihao Andreas Lin, Sebastian Ament, Louis C. Tiao, David Eriksson, Maximilian Balandat, Eytan Bakshy,
• Abstract summary: Empirical GPs are a principled framework for constructing flexible, data-driven GP priors.<n>We show that Empirical GPs achieve competitive performance on learning curve extrapolation and time series forecasting benchmarks.
• Score: 18.40952262882312
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Gaussian processes (GPs) are powerful and widely used probabilistic regression models, but their effectiveness in practice is often limited by the choice of kernel function. This kernel function is typically handcrafted from a small set of standard functions, a process that requires expert knowledge, results in limited adaptivity to data, and imposes strong assumptions on the hypothesis space. We study Empirical GPs, a principled framework for constructing flexible, data-driven GP priors that overcome these limitations. Rather than relying on standard parametric kernels, we estimate the mean and covariance functions empirically from a corpus of historical observations, enabling the prior to reflect rich, non-trivial covariance structures present in the data. Theoretically, we show that the resulting model converges to the GP that is closest (in KL-divergence sense) to the real data generating process. Practically, we formulate the problem of learning the GP prior from independent datasets as likelihood estimation and derive an Expectation-Maximization algorithm with closed-form updates, allowing the model handle heterogeneous observation locations across datasets. We demonstrate that Empirical GPs achieve competitive performance on learning curve extrapolation and time series forecasting benchmarks.

Related papers

• Compactly-supported nonstationary kernels for computing exact Gaussian processes on big data [3.8836840455173625]
  The Gaussian process (GP) is a widely used machine learning method with implicit uncertainty characterization.<n>Traditional implementations of GPs involve stationary kernels that limit their flexibility.<n>We derive an alternative kernel that can discover and encode both sparsity and nonstationarity.
  arXiv  Detail & Related papers  (2024-11-07T20:07:21Z)
• Inference at the data's edge: Gaussian processes for modeling and inference under model-dependency, poor overlap, and extrapolation [0.0]
  The Gaussian Process (GP) is a flexible non-linear regression approach. It provides a principled approach to handling our uncertainty over predicted (counterfactual) values. This is especially valuable under conditions of extrapolation or weak overlap.
  arXiv  Detail & Related papers  (2024-07-15T05:09:50Z)
• Bayesian Gaussian Process ODEs via Double Normalizing Flows [27.015257976208737]
  We introduce normalizing flows to re parameterize the ODE vector field, resulting in a data-driven prior distribution.<n>We also apply normalizing flows to the posterior inference of GP ODEs to resolve the issue of strong mean-field assumptions.<n>We validate the effectiveness of our approach on simulated dynamical systems and real-world human motion data.
  arXiv  Detail & Related papers  (2023-09-17T09:28:47Z)
• FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels [82.53569355337586]
  This work offers an efficient solution to temporal point processes inference using general parametric kernels with finite support. The method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG) Results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.
  arXiv  Detail & Related papers  (2022-10-10T12:35:02Z)
• Robust and Adaptive Temporal-Difference Learning Using An Ensemble of Gaussian Processes [70.80716221080118]
  The paper takes a generative perspective on policy evaluation via temporal-difference (TD) learning. The OS-GPTD approach is developed to estimate the value function for a given policy by observing a sequence of state-reward pairs. To alleviate the limited expressiveness associated with a single fixed kernel, a weighted ensemble (E) of GP priors is employed to yield an alternative scheme.
  arXiv  Detail & Related papers  (2021-12-01T23:15:09Z)
• 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)
• Incremental Ensemble Gaussian Processes [53.3291389385672]
  We propose an incremental ensemble (IE-) GP framework, where an EGP meta-learner employs an it ensemble of GP learners, each having a unique kernel belonging to a prescribed kernel dictionary. With each GP expert leveraging the random feature-based approximation to perform online prediction and model update with it scalability, the EGP meta-learner capitalizes on data-adaptive weights to synthesize the per-expert predictions. The novel IE-GP is generalized to accommodate time-varying functions by modeling structured dynamics at the EGP meta-learner and within each GP learner.
  arXiv  Detail & Related papers  (2021-10-13T15:11:25Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)
• Learning Inconsistent Preferences with Gaussian Processes [14.64963271587818]
  We revisit widely used preferential Gaussian processes by Chu et al.(2005) and challenge their modelling assumption that imposes rankability of data items via latent utility function values. We propose a generalisation of pgp which can capture more expressive latent preferential structures in the data. Our experimental findings support the conjecture that violations of rankability are ubiquitous in real-world preferential data.
  arXiv  Detail & Related papers  (2020-06-06T11:57:45Z)
• 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)

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.