We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space displacement and squeezing parameter estimation, this is achieved by introducing Expectation-Maximization (EM) based algorithms, while for phase parameter estimation an empirical Bayes method is applied. The estimated prior distribution parameters along with the observed data are used for finding the optimal Bayesian estimate of the unknown displacement, squeezing and phase parameters. Our simulation results show that the proposed algorithms have estimation performance that is very close to that of Genie Aided Bayesian estimators, that assume perfect knowledge of the prior parameters. Our proposed methods can be utilized by experimentalists to find the optimum Bayesian estimate of parameters of Gaussian quantum states by using only the observed measurements without requiring any knowledge about the prior distribution parameters.
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