Differentially private density plots
Techniques are described for responding to queries of a private database system. A request is received from a client device to perform a query of the private database system. A level of differential privacy corresponding to the request is identified comprising privacy parameters ε and δ. A set of data stored in the private database system and a set of operations corresponding to the query are identified. The set of operations comprises generating a density plot visualization for one or more subsets of the set of data. The set of data is segmented into disjoint regions. For each disjoint region, a density is identified, and the density is plotted in a differentially private density plot visualization using one or more graphical elements.
1. A method, comprising:
receiving a request from a client device to perform a query of a private database system;
identifying a level of differential privacy corresponding to the request, the identified level of differential privacy comprising privacy parameters ε and δ;
identifying a set of data stored in the private database system and a set of operations to be performed on the set of data corresponding to the requested query;
modifying the set of operations based on the identified level of differential privacy such that a performance of the modified set of operations produces a result set that is (ε,δ)-differentially private;
performing the modified set of operations based on the identified level of differential privacy such that a performance of the set of operations produces a result set that is (ε,δ)-differentially private, where performing the modified set of operations comprises segmenting the result set into disjoint regions and for each disjoint region:
determining a density of the disjoint region; and
plotting the density for the disjoint region in a differentially private density plot visualization, the visualization using a graphical element determined responsive to the determined density; and
providing the differentially private density plot visualization to the client device for display on a hardware display of the client device.
2. The method of claim 1 , wherein segmenting the result set into disjoint regions comprises:
identifying loci corresponding to the request, the loci specifying boundaries of the disjoint regions; and
segmenting the set of data into the disjoint regions responsive to the identified loci.
3. The method of claim 1 , wherein determining the density of the disjoint region comprises:
performing a differentially private count for the disjoint region based on the identified level of differential privacy; and
determining the density of the disjoint region based on the differentially private count.
4. The method of claim 1 , wherein determining the density of the disjoint region comprises:
performing a two-dimensional private wavelet transform for the disjoint region; and
determining the density of the disjoint region based on the two-dimensional private wavelet transform.
5. The method of claim 1 , wherein the visualization distinguishes different densities using different variations of the graphical element.
6. The method of claim 1 , wherein determining the density of the disjoint region comprises:
comparing a differentially private count for the disjoint region to a threshold value; and
determining the density of the disjoint region responsive to the comparison.
7. The method of claim 6 , wherein the threshold value is based on confidence intervals on Laplace noise within the differentially private count performed upon each disjoint region.
8. A system comprising:
a processor for executing computer program instructions; and
a non-transitory computer-readable storage medium storing computer program instructions executable by the processor to perform operations comprising:
receiving a request from a client device to perform a query of a private database system;
identifying a level of differential privacy corresponding to the request, the identified level of differential privacy comprising privacy parameters ε and δ;
identifying a set of data stored in the private database system and a set of operations to be performed on the set of data corresponding to the requested query;
modifying the set of operations based on the identified level of differential privacy such that a performance of the modified set of operations produces a result set that is (ε,δ)-differentially private;
performing the modified set of operations based on the identified level of differential privacy such that a performance of the set of operations produces a result set that is (ε,δ)-differentially private, where performing the modified set of operations comprises segmenting the result set into disjoint regions and for each disjoint region:
determining a density of the disjoint region; and
plotting the density for the disjoint region in a differentially private density plot visualization, the visualization using a graphical element determined responsive to the determined density; and
providing the differentially private density plot visualization to the client device for display on a hardware display of the client device.
9. The system of claim 8 , wherein segmenting the result set into disjoint regions comprises:
identifying loci corresponding to the request, the loci specifying boundaries of the disjoint regions; and
segmenting the set of data into the disjoint regions responsive to the identified loci.
10. The system of claim 8 , wherein determining the density of the disjoint region comprises:
performing a differentially private count for the disjoint region based on the identified level of differential privacy; and
determining the density of the disjoint region based on the differentially private count.
11. The system of claim 8 , wherein determining the density of the disjoint region comprises:
performing a two-dimensional private wavelet transform for the disjoint region; and
determining the density of the disjoint region based on the two-dimensional private wavelet transform.
12. The system of claim 8 , wherein the visualization distinguishes different densities using different variations of the graphical element.
13. The system of claim 8 , wherein determining the density of the disjoint region comprises:
comparing a differentially private count for the disjoint region to a threshold value; and
determining the density of the disjoint region responsive to the comparison.
14. The system of claim 13 , wherein the threshold value is based on confidence intervals on Laplace noise within the differentially private count performed upon each disjoint region.
15. A non-transitory computer-readable storage medium storing computer program instructions executable by a processor to perform operations including:
receiving a request from a client device to perform a query of a private database system;
identifying a level of differential privacy corresponding to the request, the identified level of differential privacy comprising privacy parameters ε and δ;
identifying a set of data stored in the private database system and a set of operations to be performed on the set of data corresponding to the requested query;
modifying the set of operations based on the identified level of differential privacy such that a performance of the modified set of operations produces a result set that is (ε,δ)-differentially private;
performing the modified set of operations based on the identified level of differential privacy such that a performance of the set of operations produces a result set that is (ε,δ)-differentially private, where performing the modified set of operations comprises segmenting the result set into disjoint regions and for each disjoint region:
determining a density of the disjoint region; and
plotting the density for the disjoint region in a differentially private density plot visualization, the visualization using a graphical element determined responsive to the determined density; and
providing the differentially private density plot visualization to the client device for display on a hardware display of the client device.
16. The non-transitory computer-readable storage medium of claim 15 , wherein segmenting the result set into disjoint regions comprises:
identifying loci corresponding to the request, the loci specifying boundaries of the disjoint regions; and
segmenting the set of data into the disjoint regions responsive to the identified loci.
17. The non-transitory computer-readable storage medium of claim 15 , wherein determining the density of the disjoint region comprises:
performing a differentially private count for the disjoint region based on the identified level of differential privacy; and
determining the density of the disjoint region based on the differentially private count.
18. The non-transitory computer-readable storage medium of claim 15 , wherein determining the density of the disjoint region comprises:
performing a two-dimensional private wavelet transform for the disjoint region; and
determining the density of the disjoint region based on the two-dimensional private wavelet transform.
19. The non-transitory computer-readable storage medium of claim 15 , wherein the visualization distinguishes different densities using different variations of the graphical element.
20. The non-transitory computer-readable storage medium of claim 15 , wherein determining the density of the disjoint region comprises:
comparing a differentially private count for the disjoint region to a threshold value; and
determining the density of the disjoint region responsive to the comparison.