论文标题
贝叶斯参数估计的机器学习方法
A machine learning approach to Bayesian parameter estimation
论文作者
论文摘要
贝叶斯估计是量子传感器运行的强大理论范例。但是，用于统计推断的贝叶斯方法通常会遭受要求的校准要求，迄今已将其用于原则证明实验的使用。在这项理论研究中，我们将参数估计作为一项分类任务，并使用人工神经网络有效执行贝叶斯估计。我们表明，网络的后验分布集中在逆Fisher信息给出的不确定性内的参数的真实（未知）值，代表给定设备的最终灵敏度极限。当仅提供有限数量的校准测量值时，我们的基于机器学习的过程优于标准校准方法。因此，我们的工作为贝叶斯量子传感器铺平了道路，这些传感器可以从有效的优化方法中受益，例如在自适应方案中，并利用复杂的非古典状态。这些功能可以显着增强未来设备的敏感性。
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its use to proof-of-principle experiments. In this theoretical study, we formulate parameter estimation as a classification task and use artificial neural networks to efficiently perform Bayesian estimation. We show that the network's posterior distribution is centered at the true (unknown) value of the parameter within an uncertainty given by the inverse Fisher information, representing the ultimate sensitivity limit for the given apparatus. When only a limited number of calibration measurements are available, our machine-learning based procedure outperforms standard calibration methods. Thus, our work paves the way for Bayesian quantum sensors which can benefit from efficient optimization methods, such as in adaptive schemes, and take advantage of complex non-classical states. These capabilities can significantly enhance the sensitivity of future devices.
