# Inference of High-dimensional Autoregressive Generalized Linear Models

arXiv: https://arxiv.org/abs/1605.02693 · HTML: https://mlsanity.com/paper/1605.02693/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2016.

## Built on by (most cited first, 4 of 4)

- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [Majorizing Measures, Sequential Complexities, and Online Learning](https://mlsanity.com/paper/2102.01729/) (2021)
- [Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systems](https://mlsanity.com/paper/2105.11558/) (2021)
- [Improved Prediction and Network Estimation Using the Monotone Single Index Multi-variate Autoregressive Model](https://mlsanity.com/paper/2106.14630/) (2021)

## Abstract (arXiv)

Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector could correspond to a different node in a network, and the parameters of an autoregressive model would correspond to the impact of the network structure on the time series evolution. Often these models are used successfully in practice to learn the structure of social, epidemiological, financial, or biological neural networks. However, little is known about statistical guarantees on estimates of such models in non-Gaussian settings. This paper addresses the inference of the autoregressive parameters and associated network structure within a generalized linear model framework that includes Poisson and Bernoulli autoregressive processes. At the heart of this analysis is a sparsity-regularized maximum likelihood estimator. While sparsity-regularization is well-studied in the statistics and machine learning communities, those analysis methods cannot be applied to autoregressive generalized linear models because of the correlations and potential heteroscedasticity inherent in the observations. Sample complexity bounds are derived using a combination of martingale concentration inequalities and modern empirical process techniques for dependent random variables. These bounds, which are supported by several simulation studies, characterize the impact of various network parameters on estimator performance.