Results on user Sample Clauses

Results on user level privacy. In all experiments, we compare our methods with the baseline and fixed-sampling methods, which are denoted by “base- line” and “fixed” in figures. Unless specified, we use LPA by default as the underlying histogram method for the sampling point. We also use “DSAT-true” and “fixed-true” to denote the non-private versions of DSAT and fixed-sampling. Absolute error vs. k. Figure 4.2 investigates how utility changes with various k values, which specify the budget allocation ratio between s1 and s2 for the decision and sampling stages respectively. With the value of C being 10, we compute k to be 0.0532 due to theorem 4.3.4. From Figure 4.2, we can observe that the empirical result matches the theoretical result well and the utility reaches the optimal value with k between 0.01 and 0.1. The error increases as k becomes larger or smaller than 0.1 or or 0.01, respectively. This is reasonable because larger k may lead to more perturbation error while smaller k values result in more update error. 1000 Absolute error 900 DSAT 800 700 600 500 0.0001 0.0005 0.001 0.01 0.05 0.1 0.25 0.5 0.8 k Figure 4.2. Absolute error vs. k DSFT and DSAT. In this experiment, we compare our proposed two methods DSFT and DSAT. From figure 4.3, we can observe that the error of DSFT is very sensitive to the threshold value T. As T initially increases, the error decreases thanks to the decreased perturbation error. As T further increases, the error increases back up due to the increased sampling error which becomes the dominant error. Without prior 46.4 PRIVACY-PRESERVING DYNAMIC HISTOGRAM RELEASE WITH DISTANCE-BASED SAMPLING knowledge, it is difficult to determine the optimal T. However, the average absolute error of DSAT is close to the lowest error of DSFT with the optimal threshold T value being around 0.025. Here the initial value of T for DSAT can be arbitrarily selected. Thus, the DSAT method with the PID control can effectively adjust T to an optimal one. In the remaining experiments, we only use DSAT to compare with other methods. 4000 Absolute error 3000 DSAT DSFT 2000 1000 0 0.01 0.025 0.05 0.1 0.25 0.5 T Figure 4.3. Absolute error vs. threshold value T Absolute error vs. differential privacy. Figure 4.4 compares DSAT with other methods under various privacy budgets. The larger the privacy budget is, the closer the query accuracy is to non-private versions. Since the baseline performs one order of magnitude worse than other methods in most experiments, we do not i...