Differentiable Predictions for Large Scale Structure with SHAMNet

The Open Journal of Astrophysics, vol. 5

Abstract

Neural nets have become popular to accelerate parameter inferences, especially for the upcoming generation of galaxy surveys in cosmology. As neural nets are approximative by nature, a recurrent question has been how to propagate the neural net's approximation error, in order to avoid biases in the parameter inference. We present a Bayesian solution to propagating a neural net's approximation error and thereby debiasing parameter inference. We exploit that a neural net reports its approximation errors during the validation phase. We capture the thus reported approximation errors via the highest-order summary statistics, allowing us to eliminate the neural net's bias during inference, and propagating its uncertainties. We demonstrate that our method is quickly implemented and successfully infers parameters even for strongly biased neural nets. In summary, our method provides the missing element to judge the accuracy of a posterior if it cannot be computed based on an infinitely accurately theory code.

Authors 2

1. Daniela Grandón Aachen Mathematical Institute Leiden Observatory

   Leiden University · University of Chile · Leiden Observatory

   Affiliation as printed

   Grupo de Cosmología y Astrofísica Teórica , Departamento de Física , FCFM , Universidad de Chile , Blanco Encalada 2008 , Santiago , Chile

   Mathematical Institute , Leiden University , Snellius Gebouw , Niels Bohrweg 1 , NL-2333 CA Leiden , The Netherlands

   Grupo de Cosmología y Astrofísica Teórica, Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile

   Leiden Observatory, Leiden University, Oort Gebouw, Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands

   Mathematical Institute, Leiden University, Snellius Gebouw, Niels Bohrweg 1, NL-2333 CA Leiden, The Netherlands

2. Elena Sellentin Aachen Leiden Observatory Mathematical Institute

   Leiden University · University of Chile · Leiden Observatory

   Affiliation as printed

   Leiden Observatory , Leiden University , Oort Gebouw , Niels Bohrweg 2 , NL-2333 CA Leiden , The Netherlands

   Mathematical Institute , Leiden University , Snellius Gebouw , Niels Bohrweg 1 , NL-2333 CA Leiden , The Netherlands

   Grupo de Cosmología y Astrofísica Teórica, Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile

   Leiden Observatory, Leiden University, Oort Gebouw, Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands

   Mathematical Institute, Leiden University, Snellius Gebouw, Niels Bohrweg 1, NL-2333 CA Leiden, The Netherlands