# Estimation Rates for Sparse Linear Cyclic Causal Models

## TL;DR

This paper analyzes the statistical estimation rates for sparse linear cyclic causal models, introducing a new estimator and comparing it to existing methods, with theoretical and empirical insights.

## Contribution

It presents a novel two-step penalized maximum likelihood estimator and establishes its near minimax optimality for sparse cyclic causal graphs.

## Key findings

- The new estimator outperforms LLC in synthetic experiments.
- Asymptotic near minimax optimality is proven for the maximum likelihood estimator.
- Practical advantages are demonstrated through numerical experiments.

## Abstract

Causal models are important tools to understand complex phenomena and predict the outcome of controlled experiments, also known as interventions. In this work, we present statistical rates of estimation for linear cyclic causal models under the assumption of homoscedastic Gaussian noise by analyzing both the LLC estimator introduced by Hyttinen, Eberhardt and Hoyer and a novel two-step penalized maximum likelihood estimator. We establish asymptotic near minimax optimality for the maximum likelihood estimator over a class of sparse causal graphs in the case of near-optimally chosen interventions. Moreover, we find evidence for practical advantages of this estimator compared to LLC in synthetic numerical experiments.