Sparse estimation of parameter support sets for generalized vector autoregressions by resampling and model aggregation

TL;DR

This paper introduces a resampling and model aggregation approach for accurately estimating the support set of nonzero parameters in sparse generalized vector autoregressive models, with applications in network recovery and ecological data analysis.

Contribution

The paper proposes a novel support estimation method that combines LASSO on data subsamples with aggregation, improving accuracy over traditional LASSO approaches.

Findings

Our method outperforms benchmark LASSO-based techniques in simulations.

The approach effectively recovers network structures in GVAR models.

Application to paleoclimatology data demonstrates practical utility.

Abstract

The central problem we address in this work is estimation of the parameter support set S, the set of indices corresponding to nonzero parameters, in the context of a sparse parametric likelihood model for discrete multivariate time series. We develop an algorithm that performs the estimation by aggregating support sets obtained by applying the LASSO to data subsamples. Our approach is to identify several candidate models and estimate S by selecting common parameters, thus "aggregating" candidate models. While our method is broadly applicable to any selection problem, we focus on the generalized vector autoregressive (GVAR) model class, and particularly the Poisson case, emphasizing applications in network recovery from discrete multivariate time series. We propose benchmark methods based on the LASSO, develop simulation strategies for GVAR processes, and present empirical results demonstrating the superior performance of our method. Additionally, we present an application estimating ecological interaction networks from paleoclimatology data.