# Neutral Networks and Invariant Causal Prediction – University of Copenhagen

Department of Mathematical Sciences > Calendar > Events > Neutral Networks and I...

# Neutral Networks and Invariant Causal Prediction

Specialeforsvar ved Matthias Pertzsch Stahlberg

Titel: Neutral Networks and Invariant Causal Prediction

Abstract:  In many aspects, inferring the underlying cause-effect relationships in a system of variables is of great interest. Inferring the underlying causes of one of the variables in such a system makes us able to accurately predict the outcome of this variable even if we actively make changes to one or more of the remaining variables. In the literature, a variety of methods for inferring the underlying causes of a given target variable have been proposed. One of these is the method of invariant causal prediction (ICP) (Peters et al., 2016), which exploits the invariance of a prediction under a causal model using data from different so-called environments or interventional settings. Peters et al. (2016) mainly focus on the linear case whereas Heinze-Deml et al. (2017) focus on the non-linear case. In this thesis, we propose to apply the method of ICP together with feedforward neural networks (FNNs) (e.g. Goodfellow et al., 2016, Hastie et al., 2009) for inferring the direct causes of a given target variable of interest. Through a simulation study, we find that the proposed method is able to correctly identify the direct causes. Here we also find that the proposed method achieves the correct type I error rate as well as a good level of statistical power. We stress that it is of great importance that the hyperparameters of the FNN for fitting the data are set appropriately on before-hand since the proposed method does not work as desired when using an FNN, which results in either under or overfitting of the data. We then try to apply the proposed method for inferring the underlying causes of the under-five mortality rate using data provided by The World Bank. In conclusion, the proposed method discovers that the differenced urban population growth is a direct cause of the differenced under-five mortality rate.

Vejleder: Jonas Martin Peters
Censor:   Alexander Sokol, Nordea