Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper we advocate performing this task using the scattering transform, a statistical tool rooted in the mathematical properties of convolutional neural nets. This estimator can characterize a complex field without explicitly computing higher-order statistics, thus avoiding the high variance and dimensionality problems. It generates a compact set of coefficients which can be used as robust summary statistics for non-Gaussian information. It is especially suited for fields presenting localized structures and hierarchical clustering, such as the cosmological density field. To demonstrate its power, we apply this estimator to the cosmological parameter inference problem in the context of weak lensing. Using simulated convergence maps with realistic noise, the scattering transform outperforms the power spectrum and peak counts, and is on par with the state-of-the-art CNN. It retains the advantages of traditional statistical descriptors (it does not require any training nor tuning), has provable stability properties, allows to check for systematics, and importantly, the scattering coefficients are interpretable. It is a powerful and attractive estimator for observational cosmology and, in general, the study of physically-motivated fields.

中文翻译：

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使用散射变换的观测宇宙学新方法

非高斯随机场的参数估计是天体物理学和宇宙学中的常见挑战。在本文中，我们提倡使用散射变换来执行此任务，这是一种植根于卷积神经网络数学特性的统计工具。该估计器可以在不显式计算高阶统计量的情况下表征复杂字段，从而避免高方差和维数问题。它生成一组紧凑的系数，可用作非高斯信息的稳健汇总统计。它特别适用于呈现局部结构和层次聚类的领域，例如宇宙密度场。为了证明它的威力，我们将此估计器应用于弱透镜背景下的宇宙学参数推断问题。使用具有真实噪声的模拟收敛图，散射变换优于功率谱和峰值计数，并且与最先进的 CNN 相当。它保留了传统统计描述符的优点（不需要任何训练或调整），具有可证明的稳定性特性，允许检查系统性，重要的是，散射系数是可解释的。它是观测宇宙学和一般物理激励场研究的强大而有吸引力的估计器。允许检查系统性，重要的是，散射系数是可解释的。它是观测宇宙学和一般物理激励场研究的强大而有吸引力的估计器。允许检查系统性，重要的是，散射系数是可解释的。它是观测宇宙学和一般物理激励场研究的强大而有吸引力的估计器。