# Improved Prediction and Network Estimation Using the Monotone Single Index Multi-variate Autoregressive Model

arXiv: https://arxiv.org/abs/2106.14630 · HTML: https://mlsanity.com/paper/2106.14630/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 55 references that are in the map.
- First posted on arXiv 28 Jun 2021.

## Builds on (most cited first, 8 of 8)

- [On Iterative Hard Thresholding Methods for High-dimensional M-Estimation](https://mlsanity.com/paper/1410.5137/) (2014)
- [Between hard and soft thresholding: optimal iterative thresholding algorithms](https://mlsanity.com/paper/1804.08841/) (2018)
- [Inference of High-dimensional Autoregressive Generalized Linear Models](https://mlsanity.com/paper/1605.02693/) (2016)
- [Non-parametric Sparse Additive Auto-regressive Network Models](https://mlsanity.com/paper/1801.07644/) (2018)
- [Convergence guarantee for the sparse monotone single index model](https://mlsanity.com/paper/2105.07587/) (2021)
- [Network Estimation from Point Process Data](https://mlsanity.com/paper/1802.04838/) (2018)
- [Estimating Network Structure from Incomplete Event Data](https://mlsanity.com/paper/1811.02979/) (2018)
- [High-Dimensional Bernoulli Autoregressive Process with Long-Range Dependence](https://mlsanity.com/paper/1903.09631/) (2019)

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

- [Learning with little mixing](https://mlsanity.com/paper/2206.08269/) (2022)

## Abstract (arXiv)

Network estimation from multi-variate point process or time series data is a problem of fundamental importance. Prior work has focused on parametric approaches that require a known parametric model, which makes estimation procedures less robust to model mis-specification, non-linearities and heterogeneities. In this paper, we develop a semi-parametric approach based on the monotone single-index multi-variate autoregressive model (SIMAM) which addresses these challenges. We provide theoretical guarantees for dependent data and an alternating projected gradient descent algorithm. Significantly we do not explicitly assume mixing conditions on the process (although we do require conditions analogous to restricted strong convexity) and we achieve rates of the form O(T^-frac13 √slog(TM)) (optimal in the independent design case) where s is the threshold for the maximum in-degree of the network that indicates the sparsity level, M is the number of actors and T is the number of time points. In addition, we demonstrate the superior performance both on simulated data and two real data examples where our SIMAM approach out-performs state-of-the-art parametric methods both in terms of prediction and network estimation.