# Statistical Estimation from Dependent Data

arXiv: https://arxiv.org/abs/2107.09773 · HTML: https://mlsanity.com/paper/2107.09773/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 20 Jul 2021.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Learning from weakly dependent data under Dobrushin's condition](https://mlsanity.com/paper/1906.09247/) (2019)
- [Predictive PAC Learning and Process Decompositions](https://mlsanity.com/paper/1309.4859/) (2013)
- [Regression from Dependent Observations](https://mlsanity.com/paper/1905.03353/) (2019)
- [Concentration of Multilinear Functions of the Ising Model with Applications to Network Data](https://mlsanity.com/paper/1710.04170/) (2017)
- [Optimal Single Sample Tests for Structured versus Unstructured Network Data](https://mlsanity.com/paper/1802.06186/) (2018)
- [Worst-Case Analysis for Randomly Collected Data](https://mlsanity.com/paper/1911.03605/) (2019)

## Built on by (most cited first, 9 of 9)

- [On Empirical Risk Minimization with Dependent and Heavy-Tailed Data](https://mlsanity.com/paper/2109.02224/) (2021)
- [On counterfactual inference with unobserved confounding](https://mlsanity.com/paper/2211.08209/) (2022)
- [Learning and Testing Latent-Tree Ising Models Efficiently](https://mlsanity.com/paper/2211.13291/) (2022)
- [Learning Hard-Constrained Models with One Sample](https://mlsanity.com/paper/2311.03332/) (2023)
- [Benign Overfitting in Time Series Linear Models with Over-Parameterization](https://mlsanity.com/paper/2204.08369/) (2022)
- [Estimating Ising Models in Total Variation Distance](https://mlsanity.com/paper/2511.21008/) (2025)
- [Learning the Inverse Temperature of Ising Models under Hard Constraints using One Sample](https://mlsanity.com/paper/2509.20993/) (2025)
- [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)

We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected on a spatial domain, a temporal domain, or a social network, which induce dependencies. We model these dependencies in the language of Markov Random Fields and, importantly, allow these dependencies to be substantial, i.e do not assume that the Markov Random Field capturing these dependencies is in high temperature. As our main contribution we provide algorithms and statistically efficient estimation rates for this model, giving several instantiations of our bounds in logistic regression, sparse logistic regression, and neural network settings with dependent data. Our estimation guarantees follow from novel results for estimating the parameters (i.e. external fields and interaction strengths) of Ising models from a em single sample. We evaluate our estimation approach on real networked data, showing that it outperforms standard regression approaches that ignore dependencies, across three text classification datasets: Cora, Citeseer and Pubmed.