Cited By
View all- Das SMishra S(2024)Advances in Differential Privacy and Differentially Private Machine LearningInformation Technology Security10.1007/978-981-97-0407-1_7(147-188)Online publication date: 2-Apr-2024
Features | BUDS | BUDS+ |
---|---|---|
Encoding | One hot | Embedding |
Query Function | Applied | Applied |
Iterative Shuffling | Present | Present |
Noise and Bias Insertion | Absent | Present |
Risk Minimizer | Operates | Operates |
Data Discarding Method | Absent | Present |
Time Bound for Attackers | Not provided | Provided |
Optimal Privacy-utility bound | Good | Better |
Before IS | After IS | ||||
---|---|---|---|---|---|
Name | Age | Height:Weight | Name | Age | Height:Weight |
Shivansh | 22 | 5.1”:48 | Brintika | 71 | 5.1”:48 |
Krishanu | 71 | 4.9”:42 | Shivansh | 22 | 4.9”:42 |
Brintika | 28 | 6.3”:70 | Krishanu | 28 | 6.3”:70 |
Vandita | 30 | 6.00”:80 | Mithila | 15 | 6.00”:80 |
Mithila | 61 | 5.9”:55 | Vandita | 61 | 6.11”:64 |
Aswin | 15 | 6.11”:64 | Aswin | 30 | 5.9”:55 |
n | t, \(n_1\), S, \(\epsilon _\text{BUDS}\) | P | Q | q | \(\delta\) | \(\epsilon _\text{Final}\) | Loss | Utility |
---|---|---|---|---|---|---|---|---|
11,000 | 500, 22, 3, 0.02 | 0.01 | 0.99 | 0.02 | 0.02 | 0.21 | 0.233 \(\hat{V}_\text{Final}\) +0.0004 | Medium |
0.80 | 0.20 | 0.30 | 0.001 | 0.87 | 1.387 \(\hat{V}_\text{Final}\) + 0.0003 | Low | ||
0.99 | 0.99 | 0.01 | 0.02 | 0.16 | 0.173 \(\hat{V}_\text{Final}\) + 0.0002 | High | ||
1,000, 11, 3, 0 | 0.01 | 0.99 | 0.02 | 0.04 | 0.09 | 0.094 \(\hat{V}_\text{Final}\)+ 0.008 | Medium | |
0.20 | 0.20 | 0.50 | 0.00 | 0.38 | 0.462 \(\hat{V}_\text{Final}\) + 0.00 | Low | ||
0.30 | 0.50 | 0.70 | 0.001 | 0.000 | 0.00 \(\hat{V}_\text{Final}\) + 0.007 | High | ||
100,000 | 5,500, 18, 3, 0.11 | 0.01 | 0.99 | 0.02 | 0.02 | 0.20 | 0.221 \(\hat{V}_\text{Final}\)+ 0.0004 | Medium |
0.20 | 0.20 | 0.50 | 0.001 | 0.49 | 0.632 \(\hat{V}_\text{Final}\) + 0.0005 | Low | ||
0.30 | 0.50 | 0.70 | 0.001 | 0.10 | 0.105 \(\hat{V}_\text{Final}\) + 0.0007 | High | ||
2,200, 45, 2, 0.1 | 0.01 | 0.99 | 0.02 | 0.05 | 0.19 | 0.209 \(\hat{V}_\text{Final}\) + 0.001 | Medium | |
0.80 | 0.20 | 0.30 | 0.001 | 0.85 | 1.339 \(\hat{V}_\text{Final}\) + 0.0003 | Low | ||
0.99 | 0.99 | 0.01 | 0.01 | 0.14 | 0.010 \(\hat{V}_\text{Final}\) + 0.0001 | High | ||
1,000,000 | 31,000, 32, 3, 0.03 | 0.01 | 0.99 | 0.02 | 0.02 | 0.12 | 0.127 \(\hat{V}_\text{Final}\) + 0.0004 | Medium |
0.20 | 0.20 | 0.50 | 0.001 | 0.41 | 0.506 \(\hat{V}_\text{Final}\) + 0.0005 | Low | ||
0.30 | 0.50 | 0.70 | 0.001 | 0.03 | 0.030 \(\hat{V}_\text{Final}\) + 0.0007 | High | ||
1,000, 100, 2, 0.2 | 0.01 | 0.99 | 0.02 | 0.02 | 0.11 | 0.116 \(\hat{V}_\text{Final}\) + 0.0004 | Medium | |
0.80 | 0.20 | 0.30 | 0.001 | 0.77 | 1.159 \(\hat{V}_\text{Final}\) + 0.0003 | Low | ||
0.99 | 0.99 | 0.01 | 0.01 | 0.06 | 0.062 \(\hat{V}_\text{Final}\) + 0.0001 | High | ||
100,000,000 | 1,000,000, 99, 3, 0.03 | 0.01 | 0.99 | 0.02 | 0.02 | 0.12 | 0.127 \(\hat{V}_\text{Final}\) + 0.0004 | Medium |
0.20 | 0.20 | 0.50 | 0.001 | 0.41 | 0.506 \(\hat{V}_\text{Final}\) + 0.0005 | Low | ||
0.30 | 0.50 | 0.70 | 0.001 | 0.03 | 0.030 \(\hat{V}_\text{Final}\) + 0.0007 | High | ||
21,800, 458, 2, 0.04 | 0.01 | 0.99 | 0.02 | 0.02 | 0.13 | 0.138 \(\hat{V}_\text{Final}\)+ 0.0004 | Medium | |
0.80 | 0.20 | 0.30 | 0.001 | 0.79 | 1.203 \(\hat{V}_\text{Final}\) + 0.0003 | Low | ||
0.99 | 0.99 | 0.01 | 0.01 | 0.08 | 0.083 \(\hat{V}_\text{Final}\)+ 0.0001 | High |
n | t, \(n_1\), S, \(\epsilon _\text{BUDS}\) | P | Q | q | \(\delta\) | \(\epsilon _\text{Final}\) | Utility |
---|---|---|---|---|---|---|---|
11,000 | 500, 22, 3, 0.02 | 0.99 | 0.99 | 0.01 | 0.02 | 0.16 | High |
1,000, 11, 3, 0 | 0.30 | 0.50 | 0.70 | 0.001 | 0.00 | High | |
100,000 | 5,500, 18, 3, 0.11 | 0.30 | 0.50 | 0.70 | 0.001 | 0.10 | High |
2,200, 45, 2, 0.1 | 0.99 | 0.99 | 0.01 | 0.01 | 0.14 | High | |
1,000,000 | 31,000, 32, 3, 0.03 | 0.30 | 0.50 | 0.70 | 0.001 | 0.03 | High |
1,000, 100, 2, 0.2 | 0.99 | 0.99 | 0.01 | 0.01 | 0.06 | High | |
100,000,000 | 1,000,000, 99, 3, 0.03 | 0.30 | 0.50 | 0.70 | 0.001 | 0.03 | High |
21,800, 458, 2, 0.04 | 0.99 | 0.99 | 0.01 | 0.01 | 0.08 | High |
Gaussian | Laplace | Exponential | |
---|---|---|---|
Differential Privacy | Provides (\(\epsilon , \delta\)) DP | Provides (\(\epsilon , 0\)) DP | Provides (\(\epsilon , 0\)) DP |
Dimension of the dataset | Compatible with all types of database dimensions | Preferable for smaller dimensional datasets | Works well with the smaller dimensional dataset. |
Ease of transformation | Gaussian transformation of other distribution comparatively easy | Laplacian transformation is more complex | Very few distributions can be transformed into exponential. |
Sensitivity | \(l_2\) | \(l_1\) | \(l_1\) |
Symbols | Description |
---|---|
\(X_d\) | The distribution of sample \(d \epsilon \mathbb {N}\) |
\(\mathbb {N}\) | Set of natural numbers |
\(\mathcal {X^*}\) | Set of all distributions on \(X_d\) |
\(\mathcal {M}\) | Randomized algorithm |
X | Input dataset |
Y | Output dataset |
\(\Delta f\) | \(l_1\) Sensitivity |
\(\Delta _2 f\) | \(l_2\) Sensitivity |
\(\mathbb {R}\) | Set of real numbers |
\(Z^*\) | Standard normal random variable |
\(Q^*\) | Query |
S | Number of shufflers and number of group of attributes |
k | Number of attributes in input dataset. |
n | Number of users |
g | Number of reduced attributes after applying query function |
m | Number of attribute names given by the query function |
t | Number of batches |
\(n_i\) | ith batch size, \(i = 1:t\) |
\(\mathcal {X}\) | Attribute subset including related attributes of a particular user for a particular query |
\(S^*\) | User-given clipping parameter and upper bound of the \(l_2\) norm |
\(\sigma ^2_j\) | Variance of Gaussian noise provided by jth user |
\(Z^{\prime }\) | Ratio of noise applied according to \(l_2\)- sensitivity |
l | Stringe of the noise bound for consistency of the noise |
q | Probability for selecting an attribute for the subset \(\mathcal {X}\) |
\(\pi _{S^*}\) | Aggregator function |
\(k^{\prime }\) | Number of attributes in the subset \(\mathcal {X}\) |
\(\epsilon\) | Privacy budget |
\(\delta\) | Probability of information accidentally leaked |
\(\varepsilon\) | Set of all events |
E | An affair |
\(V^*\) | Input dataset vector matrix |
\(v^*i_j\) | ith record of jth user, \(i=1:k^{\prime }; j=1:n\) |
V | Output dataset vector matrix |
\(\hat{V}_\text{Raw}\) | Average aggregate on input dataset before applying any randomized algorithm |
\(\hat{V}_\text{NTR}\) | Average aggregate Noiseless Temporary Report |
\(\hat{V}_\text{New}\) | Average aggregate of noisy distributional report |
\(\hat{V}_\text{cn}\) | Average aggregate report provided by Converger |
\(V_\text{Final}\) | Final report |
\(\epsilon _\text{Final}\) | Total privacy budget for whole mechanism |
\(\varrho\) | Randomized function providing noise and bias |
\(\mathcal {R}(\varrho ())\) | Randomized function for the whole mechanism that is proposed here |
\(\eta _j\) | Gaussian noise for jth user, \(j=1:n\) |
\(\beta\) | Bias |
\(\hat{\beta }\) | Optimal bias |
\(\mathcal {U}\) | Utility function |
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