Differentially private processing and database storage

A non-transitory computer-readable storage medium storing computer program instructions executable by a processor to perform operations for returning differentially private results in response to a query to a database storing restricted health data for a plurality of patients, the database storing records comprising rows and columns, where the rows are associated with patients having a medical condition, and columns of the rows contain values describing health data for the patients, the operations comprising:

• receiving a database query from a client device, the database query requesting a linear model describing correlations among values of columns in a set of records in the database, the database query specifying a degree of privacy to maintain for the restricted data;
• performing the database query on the set of records in the database to produce a differentially private version of the linear model that maintains the specified degree of privacy for the restricted data, performing the query comprising:
• modeling the values of the columns in the set of records in the database to produce a linear model comprising a set of parameters θ that describe correlations among the values describing health data for the patients;
• minimizing a loss function on the linear model over possible values of the set of parameters θ to produce an optimal set of parameters θ;
• and
• perturbing the optimal set of parameters θ to produce the differentially private version of the linear model, the set of parameters θ perturbed by a factor defined by:
• θ
• T
• ⁢
• v
• (
• G
• (
• 4
• ·
• K
• 2
• ·
• R
• 2
• 2
• ·
• (
• log
• ⁢
• 1
• δ
• +
• ϵ
• )
• ϵ
• 2
• )
• )
• where K and R2 are constants, c describes a degree of information released about the restricted data stored in the database due to the query, and δ describes an improbability of the query satisfying (ε)-differential privacy;
• returning the differentially private version of the linear model to the client device in response to the query;
• and
• estimating whether a new patient has the medical condition while maintaining the specified degree of privacy for the restricted data by using the differentially private version of the linear model on health data of the new patient.

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 for returning differentially private results in response to a query to a database storing restricted health data for a plurality of patients, the database storing records comprising rows and columns, where the rows are associated with patients having a medical condition, and columns of the rows contain values describing health data for the patients, the operations comprising:
• receiving a database query from a client device, the database query requesting a linear model describing correlations among values of columns in a set of records in the database, the database query specifying a degree of privacy to maintain for the restricted data;
• performing the database query on the set of records in the database to produce a differentially private version of the linear model that maintains the specified degree of privacy for the restricted data, performing the query comprising:
• modeling the values of the columns in the set of records in the database to produce a linear model comprising a set of parameters θ that describe correlations among the values describing health data for the patients;
• minimizing a loss function on the linear model over possible values of the set of parameters θ to produce an optimal set of parameters θ;
• and
• perturbing the optimal set of parameters θ to produce the differentially private version of the linear model, the set of parameters θ perturbed by a factor defined by:
• θ
• T
• ⁢
• v
• (
• G
• (
• 4
• ·
• K
• 2
• ⁣
• R
• 2
• 2
• ·
• (
• log
• ⁢
• ⁢
• 1
• δ
• +
• ϵ
• )
• ϵ
• 2
• )
• )
• where K and R2 are constants, c describes a degree of information released about the restricted data stored in the database due to the query, and δ describes an improbability of the query satisfying (ε)-differential privacy;
• returning the differentially private version of the linear model to the client device in response to the query;
• and
• estimating whether a new patient has the medical condition while maintaining the specified degree of privacy for the restricted data by using the differentially private version of the linear model on health data of the new patient.