宇宙学推断用数据压缩方法选择指南
A guide to choosing data compression methods for cosmological inference
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中文总结 AI 辅助
该研究提供宇宙学推断用数据压缩方法选择指南，分类不同压缩方法，以弱引力透镜功率谱为数据测试，发现MOPED等可实现无损压缩，还给出MOPED和CCA的应用策略。
中文摘要 AI 辅助
我们提供一份教学指南，帮助研究人员为宇宙学推断和数值协方差估计选择合适的压缩方法，平衡信息损失与复杂度之间的关系。我们描述了文献中使用的方法，按损失函数的形式（费舍尔信息、互信息或均方误差）以及线性或非线性进行分类。我们详细研究了线性压缩方法：大规模优化参数估计与数据压缩（MOPED）、典型相关分析（CCA）、主成分分析和线性神经网络。我们还研究了基于具有相似架构但不同损失函数的神经网络的简单非线性方法。我们使用层析弱引力透镜功率谱作为示例数据向量，从压缩数据中推导宇宙学参数Ω_m、σ_8、w_0和w_a的约束条件。对于我们的性能指标（FoM），我们使用费舍尔矩阵的对数行列式，它能很好地近似完整后验的协方差。MOPED和基于费舍尔信息的线性神经网络均实现了无损压缩。优化互信息的损失函数的神经网络最多达到未压缩FoM的84%，最小化均方误差的神经网络最多达到72%。我们展示了如何确定即使在基准宇宙学不确定的情况下MOPED是否仍能保留信息，并演示了一种CCA策略，该策略产生的FoM接近MOPED的FoM，同时仅需要大致了解后验质量的主要位置。
英文摘要
We provide a pedagogical guide to help researchers choose an appropriate compression method for cosmological inference and numerical covariance estimation, trading off the balance between information loss and complexity. We describe methods used in the literature, categorising them by the form of the loss function -- Fisher information, mutual information, or mean squared error -- and by whether they are linear or non-linear. We consider in detail the linear compression methods: massively optimised parameter estimation and data compression (MOPED), canonical correlation analysis (CCA), principal component analysis, and linear neural networks. We also investigate simple non-linear methods based on neural networks with similar architectures but different loss functions. We use tomographic weak lensing power spectra as example data vectors, deriving constraints on the cosmological parameters $Ω_\mathrm{m}$, $σ_8$, $w_0$ and $w_a$ from compressed data. For our figure of merit (FoM) we use the log determinant of the Fisher matrix, which approximates the covariance of the full posterior well. MOPED and a Fisher information-based linear neural network both achieve lossless compression. Neural networks with loss functions which optimise mutual information achieve at most 84 per cent of the uncompressed FoM and those which minimise mean squared errors achieve at most 72 per cent. We show how to determine whether MOPED will retain information even if the fiducial cosmology is not known with certainty, and demonstrate a strategy for CCA which results in an FoM close to that of MOPED while requiring only an approximate idea of where the bulk of the posterior mass is located.
