Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
High-Dimensional Gaussian Process Inference with Derivatives
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Exploit the Kronecker-plus-low-rank structure of derivative Gram matrices | Exact GP inference with gradient observations · Low-data regime (N<D) | inference computational complexity: \mathcal{O}(N^3 D^3) -> \mathcal{O}(N^2 D + (N^2)^3) | Helped |
| Use the analytical solution for the second-order polynomial kernel | Structured gradient GP inference for probabilistic linear algebra · Quadratic optimization / probabilistic linear algebra | inference computational complexity: \mathcal{O}(N^2 D + (N^2)^3) -> \mathcal{O}(N^2 D + N^3) | Helped |
| Use implicit exact matrix-vector products with an iterative solver instead of constructing the full Gram matrix | Gradient GP inference · 100-dimensional relaxed Rosenbrock function | memory: from \mathcal{O}((ND)^2) to \mathcal{O}(N^2 + ND) | Helped |
| Replace true gradients with a GP gradient surrogate after an initial training phase | HMC · 100-dimensional synthetic target | acceptance rate: 0.46 ± 0.02 -> 0.50 ± 0.02 | Mixed |
| Use only gradient observations, without function evaluations, to train the HMC surrogate | GPG-HMC · 100-dimensional synthetic target | true gradient evaluations: N=10 | Helped |
| Use reversed inference to predict the optimizer from gradient observations | GP-based optimization · 100-dimensional quadratic optimization | convergence | No clear effect |
| Use GP Hessian inference with a fixed c=0 | GP-based optimization · 100-dimensional quadratic optimization | convergence | Hurt |
| Use GP-based Hessian or optimizer inference with an RBF kernel | GP-based optimization · 100-dimensional relaxed Rosenbrock function | convergence | No clear effect |
Closest papers by meaning
- Scaling Gaussian Processes with Derivative Information Using Variational Inference (NeurIPS 2021 · similarity 0.92)
- Scalable Derivative Gaussian Processes via Exact Gradient Reduction (NeurIPS 2026 · similarity 0.91)
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- Variational Inference for Gaussian Process Models with Linear Complexity (NeurIPS 2017 · similarity 0.89)
- Standard Gaussian Process is All You Need for High-Dimensional Bayesian Optimization (ICLR 2025 · similarity 0.86)
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