I Congreso de Postgrado fcfm: ingeniería, ciencias e innovación

78 Santiago, 10 al 12 de agosto, 2022 F Í S I CA Y A S T ROF Í S I CA 05 BAYESIAN ERROR PROPAGATION FOR NEURAL-NET BASED PARAMETER INFERENCE Daniela Grandón 1 , 2 *, Elena Sellentin 2 , 3 1 Grupo de Cosmología y Astrofísica Teórica, Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile. 2 Mathematical Institute, Leiden University, Snellius Gebouw, Niels Bohrweg 1, NL-2333 CA Leiden, The Netherlands. 3 Leiden Observatory, Leiden University, Oort Gebouw, Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands. *Email: daniela.grandon@ug.uchile.cl 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 accurate theory code. ACKNOWLEDGMENTS We thank the support staff of Leiden’s ALICE High Performance Computing infrastructure. DG acknowledges finan- cial support by project ANIDPFCHA/Doctorado Nacional/2019-2119188 and thanks the Mathematical Institute of Leiden University for the hospitality during this research. REFERENCES [1] D. Grandón and E. Sellentin, Bayesian error propagation for neural-net based parameter inference, 2205.11587.