# Non-parametric Sparse Additive Auto-regressive Network Models

arXiv: https://arxiv.org/abs/1801.07644 · HTML: https://mlsanity.com/paper/1801.07644/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2018.

## Built on by (most cited first, 2 of 2)

- [Nystr"om Regularization for Time Series Forecasting](https://mlsanity.com/paper/2111.07109/) (2021)
- [Improved Prediction and Network Estimation Using the Monotone Single Index Multi-variate Autoregressive Model](https://mlsanity.com/paper/2106.14630/) (2021)

## Abstract (arXiv)

Consider a multi-variate time series (Xt)t=0T where Xt ∈ ℝd which may represent spike train responses for multiple neurons in a brain, crime event data across multiple regions, and many others. An important challenge associated with these time series models is to estimate an influence network between the d variables, especially when the number of variables d is large meaning we are in the high-dimensional setting. Prior work has focused on parametric vector auto-regressive models. However, parametric approaches are somewhat restrictive in practice. In this paper, we use the non-parametric sparse additive model (SpAM) framework to address this challenge. Using a combination of β and φ-mixing properties of Markov chains and empirical process techniques for reproducing kernel Hilbert spaces (RKHSs), we provide upper bounds on mean-squared error in terms of the sparsity s, logarithm of the dimension log d, number of time points T, and the smoothness of the RKHSs. Our rates are sharp up to logarithm factors in many cases. We also provide numerical experiments that support our theoretical results and display potential advantages of using our non-parametric SpAM framework for a Chicago crime dataset.