# Learning from weakly dependent data under Dobrushin's condition

arXiv: https://arxiv.org/abs/1906.09247 · HTML: https://mlsanity.com/paper/1906.09247/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

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

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- [Benign Overfitting in Time Series Linear Models with Over-Parameterization](https://mlsanity.com/paper/2204.08369/) (2022)
- [Diversity-enhancing Generative Network for Few-shot Hypothesis Adaptation](https://mlsanity.com/paper/2307.05948/) (2023)
- [Exponential Weights Algorithms for Selective Learning](https://mlsanity.com/paper/2106.15662/) (2021)
- [Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Models](https://mlsanity.com/paper/2206.02455/) (2022)
- [Causal Inference for Sequential Settings under Interference and Latent Confounding](https://mlsanity.com/paper/2607.14940/) (2026)

## Abstract (arXiv)

Statistical learning theory has largely focused on learning and generalization given independent and identically distributed (i.i.d.) samples. Motivated by applications involving time-series data, there has been a growing literature on learning and generalization in settings where data is sampled from an ergodic process. This work has also developed complexity measures, which appropriately extend the notion of Rademacher complexity to bound the generalization error and learning rates of hypothesis classes in this setting. Rather than time-series data, our work is motivated by settings where data is sampled on a network or a spatial domain, and thus do not fit well within the framework of prior work. We provide learning and generalization bounds for data that are complexly dependent, yet their distribution satisfies the standard Dobrushin's condition. Indeed, we show that the standard complexity measures of Gaussian and Rademacher complexities and VC dimension are sufficient measures of complexity for the purposes of bounding the generalization error and learning rates of hypothesis classes in our setting. Moreover, our generalization bounds only degrade by constant factors compared to their i.i.d. analogs, and our learnability bounds degrade by log factors in the size of the training set.