Non-negative DAG Learning from Time-Series Data

TL;DR

This paper introduces a convex optimization approach for learning non-negative DAG structures from multivariate time-series data modeled by SVARM, ensuring global optimality and improved performance over existing methods.

Contribution

It proposes a novel convex formulation for non-negative DAG learning from time-series data, enabling efficient and globally optimal solutions.

Findings

Outperforms existing methods on synthetic data

Guarantees global optimality due to convex formulation

Effective in capturing instantaneous causal dependencies

Abstract

This work aims to learn the directed acyclic graph (DAG) that captures the instantaneous dependencies underlying a multivariate time series. The observed data follow a linear structural vector autoregressive model (SVARM) with both instantaneous and time-lagged dependencies, where the instantaneous structure is modeled by a DAG to reflect potential causal relationships. While recent continuous relaxation approaches impose acyclicity through smooth constraint functions involving powers of the adjacency matrix, they lead to non-convex optimization problems that are challenging to solve. In contrast, we assume that the underlying DAG has only non-negative edge weights, and leverage this additional structure to impose acyclicity via a convex constraint. This enables us to cast the problem of non-negative DAG recovery from multivariate time-series data as a convex optimization problem in abstract form, which we solve using the method of multipliers. Crucially, the convex formulation guarantees global optimality of the solution. Finally, we assess the performance of the proposed method on synthetic time-series data, where it outperforms existing alternatives.