# Uniform Risk Bounds for Learning with Dependent Data Sequences

arXiv: https://arxiv.org/abs/2303.11650 · HTML: https://mlsanity.com/paper/2303.11650/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 12 of 12)

- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Learning without Concentration](https://mlsanity.com/paper/1401.0304/) (2014)
- [Relative Deviation Learning Bounds and Generalization with Unbounded Loss Functions](https://mlsanity.com/paper/1310.5796/) (2013)
- [Learning without Concentration for General Loss Functions](https://mlsanity.com/paper/1410.3192/) (2014)
- [Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs](https://mlsanity.com/paper/1307.0345/) (2013)
- [Tight Lower Bound on the Probability of a Binomial Exceeding its Expectation](https://mlsanity.com/paper/1306.1433/) (2013)
- [Relative Deviation Margin Bounds](https://mlsanity.com/paper/2006.14950/) (2020)
- [Error Bounds for Piecewise Smooth and Switching Regression](https://mlsanity.com/paper/1707.07938/) (2017)
- [Risk Bounds for Learning Multiple Components with Permutation-Invariant Losses](https://mlsanity.com/paper/1904.07594/) (2019)
- [Margin theory for the scenario-based approach to robust optimization in high dimension](https://mlsanity.com/paper/2303.03891/) (2023)

## Built on by (most cited first, 1 of 1)

- [Data Quality in Edge Machine Learning: A State-of-the-Art Survey](https://mlsanity.com/paper/2406.02600/) (2024)

## Abstract (arXiv)

This paper extends standard results from learning theory with independent data to sequences of dependent data. Contrary to most of the literature, we do not rely on mixing arguments or sequential measures of complexity and derive uniform risk bounds with classical proof patterns and capacity measures. In particular, we show that the standard classification risk bounds based on the VC-dimension hold in the exact same form for dependent data, and further provide Rademacher complexity-based bounds, that remain unchanged compared to the standard results for the identically and independently distributed case. Finally, we show how to apply these results in the context of scenario-based optimization in order to compute the sample complexity of random programs with dependent constraints.