ANNZ+: an enhanced photometric redshift estimation algorithm with applications on the PAU Survey

TL;DR

ANNZ+ enhances photometric redshift estimation by integrating new activation functions and testing robustness across various galaxy samples, achieving significant accuracy improvements and outperforming its predecessor, ANNZ2.

Contribution

The paper introduces ANNZ+, an upgraded version of the classic ANNZ algorithm, with new activation functions and extensive testing, maintaining its relevance and competitiveness in modern photometric redshift estimation.

Findings

Tanh and Leaky ReLU provide stable, consistent results.

ANNZ+ improves accuracy by over 1% on SDSS data.

Outperforms ANNZ2 by 44% in RMS error on PAUS dataset.

Abstract

ANNZ is a fast and simple algorithm which utilises artificial neural networks (ANNs), it was known as one of the pioneers of machine learning approaches to photometric redshift estimation decades ago. We enhanced the algorithm by introducing new activation functions like tanh, softplus, SiLU, Mish and ReLU variants; its new performance is then vigorously tested on legacy samples like the Luminous Red Galaxy (LRG) and Stripe-82 samples from SDSS, as well as modern galaxy samples like the Physics of the Accelerating Universe Survey (PAUS). This work focuses on testing the robustness of activation functions with respect to the choice of ANN architectures, particularly on its depth and width, in the context of galaxy photometric redshift estimation. Our upgraded algorithm, which we named ANNZ+, shows that the tanh and Leaky ReLU activation functions provide more consistent and stable results across deeper and wider architectures with > 1 per cent improvement in root-mean-square error ($\sigma_{\textrm{RMS}}$) and 68th percentile error ($\sigma_{68}$) when tested on SDSS data sets. While assessing its capabilities in handling high dimensional inputs, we achieved an improvement of 11 per cent in $\sigma_{\textrm{RMS}}$ and 6 per cent in $\sigma_{68}$ with the tanh activation function when tested on the 40-narrowband PAUS dataset; it even outperformed ANNZ2, its supposed successor, by 44 per cent in $\sigma_{\textrm{RMS}}$. This justifies the effort to upgrade the 20-year-old ANNZ, allowing it to remain viable and competitive within the photo-z community today. The updated algorithm ANNZ+ is publicly available at https://github.com/imdadmpt/ANNzPlus.