宇宙学统计推断的降维技术
Dimensionality Reduction Techniques for Statistical Inference in Cosmology
AI总结：
针对宇宙学参数统计推断中的数据压缩需求，通过理论分析与模拟弱透镜数据实验，提出e-MOPED和改编CCA两种线性降维方法，在减少计算资源的同时提升参数约束优值，还给出改进所有方法的两项建议。
摘要：
我们探索用于宇宙学参数统计推断的线性和非线性降维技术。鉴于压缩宇宙学中日益复杂的数据向量的重要性，我们解决影响所实现约束能力的问题，例如：当前使用的方法是否有效无损？非线性方法（通常基于神经网络）在什么条件下优于线性方法？通过理论分析和模拟弱透镜数据向量的实验，我们比较了三种标准线性方法和基于神经网络的方法。我们提出两种线性方法，它们在使用更少计算资源的情况下优于所有其他方法：一种称为e-MOPED的MOPED算法变体，以及典型相关分析（CCA）的改编版。e-MOPED和CCA均利用覆盖全参数空间的模拟，并依赖数据向量对目标参数的敏感性。与文献中使用的压缩方法相比，我们获得的增益显著：在包含统计和系统误差的真实模拟推理分析中，$Ω_m$和$S_8$的优值（Figure of Merit）提升高达30%。我们还推荐两种改进所有方法性能的修改：首先，在压缩数据向量中包含可能不针对关键参数但因相关性仍增强约束的分量，优值增益超过20%；其次，分别压缩高斯和非高斯统计量，我们的分析中包含了每种类型的两个汇总统计量。
英文摘要：
We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions that impact the constraining power achieved, such as: Are currently used methods effectively lossless? Under what conditions do nonlinear methods, typically based on neural nets, outperform linear methods? Through theoretical analysis and experiments with simulated weak lensing data vectors we compare three standard linear methods and neural network based methods. We propose two linear methods that outperform all others while using less computational resources: a variation of the MOPED algorithm we call e-MOPED and an adaptation of Canonical Correlation Analysis (CCA), which is a method new to cosmology but well known in statistics. Both e-MOPED and CCA utilize simulations spanning the full parameter space, and rely on the sensitivity of the data vector to the parameters of interest. The gains we obtain are significant compared to compression methods used in the literature: up to 30% in the Figure of Merit for $Ω_m$ and $S_8$ in a realistic Simulation Based Inference analysis that includes statistical and systematic errors. We also recommend two modifications that improve the performance of all methods: First, include components in the compressed data vector that may not target the key parameters but still enhance the constraints on due to their correlations. The gain is significant, above 20% in the Figure of Merit. Second, compress Gaussian and non-Gaussian statistics separately -- we include two summary statistics of each type in our analysis.
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