宇宙学参数估计的边学边加速度
Learn-As-You-Go Acceleration of Cosmological Parameter Estimates
摘要：
宇宙学分析可以通过使用训练集来近似缓慢的计算来加速，该训练集可以是预先计算的或动态生成的。然而，这种方法只有在近似值被很好地理解和控制的情况下才是安全的。本文调查了与使用基于机器学习的仿真策略加速宇宙学参数估计相关的问题。我们描述了一种在Cosmo++代码中实现的随走随学算法，并且（1）在同时估计后验概率的同时训练仿真器;（2）识别不可靠的估计，如果必要的话计算精确的数值似然;（3）随着计算的进行，逐步学习和更新误差模型。我们明确地描述和模拟的仿真误差，并显示如何将其传播到后验概率。我们应用这些技术的普朗克似然和计算$Λ$ CDM后验概率。在没有预定义训练集的情况下，计算显着加速，并且后验概率中的不确定性低于统计波动。我们已经得到了一个加速因子$6.5$的大都会黑斯廷斯和$3.5$的巢式抽样。最后，我们讨论了可信误差模型的一般要求，并展示了如何实时更新它们。
英文摘要：
Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitly describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of $Λ$CDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of $6.5$ for Metropolis-Hastings and $3.5$ for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.
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