The Hamiltonian Monte Carlo Method Based On Differential Privacy

The Monte Carlo algorithm on the minibatch dataset makes it possible to select the minibatch data at random and use the Monte Carlo method for Bayesian learning of model parameters.In this paper,the Hamiltonian Monte Carlo simulation algorithm on the subsample data achieves privacy protection by randomly selecting the subsample of the data set and clipping the logarithmic likelihood of the two adjacent steps of the Markov chain.This method can not only avoid the problem of gradient perturbation,but also be applicable to the parameter learning of any model.The algorithm is based on the decomposition of Barker's acceptance function to correct the random errors of minibatch data and full data.Through analysis,it is concluded that this algorithm can effectively protect data privacy even for random selection of subsample data sets.In a binary Gaussian mixed model,the experimental results demonstrate the robustness of the proposed algorithm,and the algorithm performs well in the case of privacy.The Barker acceptance function HMC algorithm on the subsample data set can replace the whole data for parameter learning,and the effect of parameter learning is not weakened,and it has good robustness.