Differentially private machine learning using a random forest classifier
A request from a client is received to generate a differentially private random forest classifier trained using a set of restricted data. The differentially private random forest classifier is generated in response to the request. Generating the differentially private random forest classifier includes determining a number of decision trees and generating the determined number of decision trees. Generating a decision tree includes generating a set of splits based on the restricted data, determining an information gain for each split, selecting a split from the set using an exponential mechanism, and adding the split to the decision tree. The differentially private random forest classifier is provided to the client.
1. A method, comprising:
receiving a request from a client to generate a differentially private random forest classifier trained using a set of restricted data stored by a private database system, the request identifying a level of differential privacy corresponding to the request, the identified level of differential privacy comprising privacy parameters ε and δ, wherein ε describes a degree of information released about the set of restricted data due to the request and δ describes an improbability of the request satisfying (ε)-differential privacy;
generating the differentially private random forest classifier in response to the request, generating the classifier comprising:
determining a number of decision trees comprising the differentially private random forest classifier;
generating the determined number of decision trees, wherein a decision tree comprises a plurality of leaf nodes representing classification categories, and generating the decision tree comprises:
generating a set of splits based on features of the set of restricted data;
determining an information gain for each split of the set of splits;
selecting a split from the set of splits using an exponential mechanism based at least in part on the determined information gains of the splits in the set and at least one of the privacy parameters;
adding the selected split to the decision tree at a node; and
determining, for a certain leaf node of the plurality of leaf nodes representing a certain classification category of the classification categories, a differentially private count of entities in the set of restricted data in the certain classification category; and
providing the differentially private random forest classifier to the client, the provided differentially private random forest classifier comprising the differentially private count of entities in the certain classification category represented by the certain leaf node.
2. The method of claim 1 , wherein determining the information gain for a split of the set of splits comprises evaluating:
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log
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wherein n o is determined by:
Σ i t io ,
wherein n i is determined by:
Σ o t io ,
wherein n t is determined by either:
Σ i n i or Σ o n o ,
wherein o is a numeric representation of a classification category, i is a numeric representation of a feature of data in the set of restricted data, and t io is a number of data tuples in the set of restricted data having both the classification category represented by o and the feature represented by i.
3. The method of claim 2 , wherein selecting a split from the set of splits using the exponential mechanism is further based on a sensitivity, wherein the sensitivity of the exponential mechanism is determined by:
log
2
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1
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+
1
log
2
.
4. The method of claim 1 , wherein generating the random forest classifier in response to the request is based on one or more model parameters, including at least one of a number of decision trees to be used in the classifier, a number of splits to include in the decision trees, a maximum tree height, and a utility gain threshold, and wherein each of the one or more model parameters is at least one of a default value and a value included in the request.
5. The method of claim 1 ,
wherein the restricted data stores records comprising rows and columns;
wherein the rows are associated with patients having a medical condition;
wherein the columns contain values describing health data for the patients; and
wherein providing the differentially private random forest classifier to the client comprises estimating whether a new patient has the medical condition.
6. The method of claim 1 ,
wherein the set of data stores records comprising rows and columns;
wherein the rows are associated with customers having a financial account;
wherein the columns contain values describing financial data for the customers; and
wherein providing the differentially private random forest classifier to the client comprises estimating whether a new customer can perform a financial transaction.
7. A non-transitory computer-readable storage medium storing computer program instructions executable by a processor to perform operations, the operations comprising:
receiving a request from a client to generate a differentially private random forest classifier trained using a set of restricted data stored by a private database system, the request identifying a level of differential privacy corresponding to the request, the identified level of differential privacy comprising privacy parameters ε and δ, wherein ε describes a degree of information released about the set of restricted data due to the request and δ describes an improbability of the request satisfying (ε)-differential privacy;
generating the differentially private random forest classifier in response to the request, generating the classifier comprising:
determining a number of decision trees comprising the differentially private random forest classifier;
generating the determined number of decision trees, wherein a decision tree comprises a plurality of leaf nodes representing classification categories, and generating the decision tree comprises:
generating a set of splits based on features of the set of restricted data;
determining an information gain for each split of the set of splits;
selecting a split from the set of splits using an exponential mechanism based at least in part on the determined information gains of the splits in the set and at least one of the privacy parameters;
adding the selected split to the decision tree at a node; and
determining, for a certain leaf node of the plurality of leaf nodes representing a certain classification category of the classification categories, a differentially private count of entities in the set of restricted data in the certain classification category; and
providing the differentially private random forest classifier to the client, the provided differentially private random forest classifier comprising the differentially private count of entities in the certain classification category represented by the certain leaf node.
8. The non-transitory computer-readable storage medium of claim 7 , wherein determining the information gain for a split of the set of splits comprises evaluating:
-
∑
i
n
i
∑
o
t
io
n
i
log
2
t
io
n
i
,
wherein n o is determined by:
Σ i t io ,
wherein n i is determined by:
Σ o t io ,
wherein n t is determined by either:
Σ i n i or Σ o n o ,
wherein o is a numeric representation of a classification category, i is a numeric representation of a feature of data in the set of restricted data, and t io is a number of data tuples in the set of restricted data having both the classification category represented by o and the feature represented by i.
9. The non-transitory computer-readable storage medium of claim 8 , wherein selecting a split from the set of splits using the exponential mechanism is further based on a sensitivity, wherein the sensitivity of the exponential mechanism is determined by:
log
2
(
n
t
+
1
)
+
1
log
2
.
10. The non-transitory computer-readable storage medium of claim 7 , wherein generating the random forest classifier in response to the request is based on one or more model parameters, including at least one of a number of decision trees to be used in the classifier, a number of splits to include in the decision trees, a maximum tree height, and a utility gain threshold, and wherein each of the one or more model parameters is at least one of a default value and a value included in the request.
11. The non-transitory computer-readable storage medium of claim 7 ,
wherein the restricted data stores records comprising rows and columns;
wherein the rows are associated with patients having a medical condition;
wherein the columns contain values describing health data for the patients; and
wherein providing the differentially private random forest classifier to the client comprises estimating whether a new patient has the medical condition.
12. The non-transitory computer-readable storage medium of claim 7 ,
wherein the set of data stores records comprising rows and columns;
wherein the rows are associated with customers having a financial account;
wherein the columns contain values describing financial data for the customers; and
wherein providing the differentially private random forest classifier to the client comprises estimating whether a new customer can perform a financial transaction.
13. 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 to generate a differentially private random forest classifier trained using a set of restricted data stored by a private database system, the request identifying a level of differential privacy corresponding to the request, the identified level of differential privacy comprising privacy parameters ε and δ, wherein ε describes a degree of information released about the set of restricted data due to the request and δ describes an improbability of the request satisfying (ε)-differential privacy;
generating the differentially private random forest classifier in response to the request, generating the classifier comprising:
determining a number of decision trees comprising the differentially private random forest classifier;
generating the determined number of decision trees, wherein a decision tree comprises a plurality of leaf nodes representing classification categories, and generating the decision tree comprises:
generating a set of splits based on features of the set of restricted data;
determining an information gain for each split of the set of splits;
selecting a split from the set of splits using an exponential mechanism based at least in part on the determined information gains of the splits in the set and at least one of the privacy parameters;
adding the selected split to the decision tree at a node; and
determining, for a certain leaf node of the plurality of leaf nodes representing a certain classification category of the classification categories, a differentially private count of entities in the set of restricted data in the certain classification category; and
providing the differentially private random forest classifier to the client the provided differentially private random forest classifier comprising the differentially private count of entities in the certain classification category represented by the certain leaf node.
14. The system of claim 13 , wherein determining the information gain for a split of the set of splits comprises evaluating:
-
∑
i
n
i
∑
o
t
io
n
i
log
2
t
io
n
i
,
wherein n o is determined by:
Σ i t io ,
wherein n i is determined by:
Σ o t io ,
wherein n t is determined by either:
Σ i n i or Σ o n o ,
wherein o is a numeric representation of a classification category, i is a numeric representation of a feature of data in the set of restricted data, and t io is a number of data tuples in the set of restricted data having both the classification category represented by o and the feature represented by i.
15. The system of claim 14 , wherein selecting a split from the set of splits using the exponential mechanism is further based on a sensitivity, wherein the sensitivity of the exponential mechanism is determined by:
log
2
(
n
t
+
1
)
+
1
log
2
.
16. The system of claim 13 ,
wherein the restricted data stores records comprising rows and columns;
wherein the rows are associated with patients having a medical condition;
wherein the columns contain values describing health data for the patients; and
wherein providing the differentially private random forest classifier to the client comprises estimating whether a new patient has the medical condition.
17. The system of claim 13 ,
wherein the set of data stores records comprising rows and columns;
wherein the rows are associated with customers having a financial account;
wherein the columns contain values describing financial data for the customers; and
wherein providing the differentially private random forest classifier to the client comprises estimating whether a new customer can perform a financial transaction.