# Generalization for slowly mixing processes

arXiv: https://arxiv.org/abs/2305.00977 · HTML: https://mlsanity.com/paper/2305.00977/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 40 references that are in the map.
- First posted on arXiv 28 Apr 2023.

## Builds on (most cited first, 10 of 10)

- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Exactly Computing the Local Lipschitz Constant of ReLU Networks](https://mlsanity.com/paper/2003.01219/) (2020)
- [Near optimal finite time identification of arbitrary linear dynamical systems](https://mlsanity.com/paper/1812.01251/) (2018)
- [Relating Adversarially Robust Generalization to Flat Minima](https://mlsanity.com/paper/2104.04448/) (2021)
- [Learning nonlinear dynamical systems from a single trajectory](https://mlsanity.com/paper/2004.14681/) (2020)
- [Mixing time estimation in reversible Markov chains from a single sample path](https://mlsanity.com/paper/1708.07367/) (2017)
- [Estimating the Mixing Time of Ergodic Markov Chains](https://mlsanity.com/paper/1902.01224/) (2019)
- [Predictive PAC Learning and Process Decompositions](https://mlsanity.com/paper/1309.4859/) (2013)
- [Statistical Estimation of Ergodic Markov Chain Kernel over Discrete State Space](https://mlsanity.com/paper/1809.05014/) (2018)

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

- [Sharp Rates in Dependent Learning Theory: Avoiding Sample Size Deflation for the Square Loss](https://mlsanity.com/paper/2402.05928/) (2024)

## Abstract (arXiv)

A bound uniform over various loss-classes is given for data generated by stationary and phi-mixing processes, where the mixing time (the time needed to obtain approximate independence) enters the sample complexity only in an additive way. For slowly mixing processes this can be a considerable advantage over results with multiplicative dependence on the mixing time. The admissible loss-classes include functions with prescribed Lipschitz norms or smoothness parameters. The bound can also be applied to be uniform over unconstrained loss-classes, where it depends on local Lipschitz properties of the function on the sample path.