# A chain rule for the expected suprema of Gaussian processes

arXiv: https://arxiv.org/abs/1411.2635 · HTML: https://mlsanity.com/paper/1411.2635/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2014.

## Built on by (most cited first, 13 of 13)

- [Sharing Knowledge in Multi-Task Deep Reinforcement Learning](https://mlsanity.com/paper/2401.09561/) (2024)
- [A Theory of Multimodal Learning](https://mlsanity.com/paper/2309.12458/) (2023)
- [Learning an Explicit Hyperparameter Prediction Function Conditioned on Tasks](https://mlsanity.com/paper/2107.02378/) (2021)
- [Mastering Long-Tail Complexity on Graphs: Characterization, Learning, and Generalization](https://mlsanity.com/paper/2305.09938/) (2023)
- [Nonlinear Meta-Learning Can Guarantee Faster Rates](https://mlsanity.com/paper/2307.10870/) (2023)
- [On Generalization Bounds for Neural Networks with Low Rank Layers](https://mlsanity.com/paper/2411.13733/) (2024)
- [Provable Pathways: Learning Multiple Tasks over Multiple Paths](https://mlsanity.com/paper/2303.04338/) (2023)
- [Statistical learning on measures: an application to persistence diagrams](https://mlsanity.com/paper/2303.08456/) (2023)
- [Deep Safe Multi-Task Learning](https://mlsanity.com/paper/2111.10601/) (2021)
- [A Chain Rule for the Expected Suprema of Bernoulli Processes](https://mlsanity.com/paper/2304.14474/) (2023)
- [Bridging Lifelong and Multi-Task Representation Learning via Algorithm and Complexity Measure](https://mlsanity.com/paper/2511.01847/) (2025)
- [Representative Action Selection for Large Action Space: From Bandits to MDPs](https://mlsanity.com/paper/2511.22104/) (2025)
- [Sample Complexity of Scientific Discovery: PAC Learnability of Compositional Function Trees](https://mlsanity.com/paper/2606.29331/) (2026)

## Abstract (arXiv)

The expected supremum of a Gaussian process indexed by the image of an index set under a function class is bounded in terms of separate properties of the index set and the function class. The bound is relevant to the estimation of nonlinear transformations or the analysis of learning algorithms whenever hypotheses are chosen from composite classes, as is the case for multi-layer models.