This repository contains the codes for reproducing the numerical results in the paper entitled

Bayesian Frequency Estimation Under Local Differential Privacy With an Adaptive Randomized Response Mechanism

by Soner Aydın, Sinan Yıldırım

The paper was accepted by ACM Transactions on Knowledge Discovery from Data (TKDD) and can be accessed via this link: https://dl.acm.org/doi/10.1145/3706584

In this repository, the main file is "experiments_for_SGLD.m" by which one can run the experiments and obtain the accuracy results (in terms of total variation distance) and the numbers $k$ (average cardinality of the subsets chosen by each algorithm).

Each result in the paper is generated by a different combination of K $\in$ (10, 20), eps1_coeff $\in$ (0.8, 0.9).

After obtaining these results, one can also run the file "plot_results.m" to visualize them as barplots and heatmaps.

Brief information about the other files:

• "AdOBEst_LDP.m" contains the main algorithm.
• "calculate_utility.m" computes the estimation error for 6 different utility functions
• "calculate_FIM.m" computes the Fisher information matrix
• "make_G.m" computes the stochastic matrix G
• "make_p_yx_vec.m" computes the likelihood vector P(Y|X)
• "SGLD_LDP.m" implements the Stochastic Gradient Langevin Dynamics method for approximate MCMC moves.

More information about each of these codes can be found in the comments inside them.