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

TL;DR

This paper introduces a semi-parametric monotone single-index multivariate autoregressive model (SIMAM) that improves network estimation from time series data, offering theoretical guarantees and superior empirical performance over existing parametric methods.

Contribution

The paper develops a novel semi-parametric SIMAM approach with theoretical guarantees and an efficient algorithm, addressing limitations of parametric models in network estimation.

Findings

Achieves optimal convergence rates for dependent data.

Outperforms state-of-the-art parametric methods in simulations.

Demonstrates superior real-data prediction and network estimation.

Abstract

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 $O(T^{-\frac{1}{3}} \sqrt{s\log(TM)})$ (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.