Differentially private iteratively reweighted least squares

1. A method, comprising:

receiving a dataset, at a data requestor, comprising a plurality of input-output pairs;

perturbing, at the data requestor, a first moment of the dataset by adding noise;

perturbing, at the data requestor, a second moment of the dataset by adding noise;

obtaining, at the data requestor, a differential private (DP) iteratively reweighted least squares (IRLS) function based on the perturbed first moment and the perturbed second moment; and

generating, at the data requestor, a differentially private output by applying the DP IRLS function to the dataset.

2. The method of claim 1 , in which the first moment is a mean of the dataset and the second moment is a covariance of the dataset.

3. The method of claim 1 , further comprising:

perturbing the first moment via a Laplace mechanism; and

perturbing the second moment by adding Wishart noise.

4. The method of claim 1 , further comprising determining an amount of noise to add to the first moment via a Laplace mechanism based on an amount of change that can occur to a data point of the dataset.

5. The method of claim 1 , in which the DP IRLS function is a concentrated differential private (CDP) iteratively reweighted least squares function.

6. The method of claim 1 , in which the differentially private output comprises an L1 minimization solution.

7. An apparatus, comprising:

a memory; and

at least one processor coupled to the memory, the at least one processor configured:

to receive a dataset, at a data requestor, comprising a plurality of input-output pairs;

to perturb, at the data requestor, a first moment of the dataset by adding noise;

to perturb, at the data requestor, a second moment of the dataset by adding noise;

to obtain, at the data requestor, a differential private (DP) iteratively reweighted least squares (IRLS) function based on the perturbed first moment and the perturbed second moment; and

to generate, at the data requestor, a differentially private output by applying the DP IRLS function to the dataset.

8. The apparatus of claim 7 , in which the first moment is a mean of the dataset and the second moment is a covariance of the dataset.

9. The apparatus of claim 7 , in which the at least one processor is further configured:

to perturb the first moment via a Laplace mechanism; and

to perturb the second moment by adding Wishart noise.

10. The apparatus of claim 7 , in which the at least one processor is further configured to determine an amount of noise to add to the first moment via a Laplace mechanism based on an amount of change that can occur to a data point of the dataset.

11. The apparatus of claim 7 , in which the DP IRLS function is a concentrated differential private (CDP) iteratively reweighted least squares function.

12. The apparatus of claim 7 , in which the differentially private output comprises an L1 minimization solution.

13. An apparatus, comprising:

means for receiving a dataset, at a data requestor, comprising a plurality of input-output pairs;

means for perturbing, at the data requestor, a first moment of the dataset by adding noise;

means for perturbing, at the data requestor, a second moment of the dataset by adding noise;

means for obtaining, at the data requestor, a differential private (DP) iteratively reweighted least squares (IRLS) function based on the perturbed first moment and the perturbed second moment; and

means for generating, at the data requestor, a differentially private output by applying the DP IRLS function to the dataset.

14. The apparatus of claim 13 , in which the first moment is a mean of the dataset and the second moment is a covariance of the dataset.

15. The apparatus of claim 13 , further comprising:

means for perturbing the first moment via a Laplace mechanism; and

means for perturbing the second moment by adding Wishart noise.

16. The apparatus of claim 13 , further comprising means for determining an amount of noise to add to the first moment via a Laplace mechanism based on an amount of change that can occur to a data point of the dataset.

17. The apparatus of claim 13 , in which the DP IRLS function solution is a concentrated differential private (CDP) iteratively reweighted least squares function.

18. The apparatus of claim 13 , in which the differentially private output comprises an L1 minimization solution.

19. A non-transitory computer-readable medium having program code recorded thereon, the program code executed by a processor and comprising:

program code to receive a dataset, at a data requestor, comprising a plurality of input-output pairs;

program code to perturb, at the data requestor, a first moment of the dataset by adding noise;

program code to perturb, at the data requestor, a second moment of the dataset by adding noise;

program code to obtain, at the data requestor, a differential private (DP) iteratively reweighted least squares (IRLS) function based on the perturbed first moment and the perturbed second moment; and

program code to generate, at the data requestor, a differentially private output by applying the DP IRLS function to the dataset.

20. The non-transitory computer-readable medium of claim 19 , in which the first moment is a mean of the dataset and the second moment is a covariance of the dataset.

21. The non-transitory computer-readable medium of claim 19 , further comprising:

program code to perturb the first moment via a Laplace mechanism; and

program code to perturb the second moment by adding Wishart noise.

22. The non-transitory computer-readable medium of claim 19 , in which the program code to perturb the first moment further comprises program code to determine an amount of noise to add to the first moment via a Laplace mechanism based on an amount of change that can occur to a data point of the dataset.

23. The non-transitory computer-readable medium of claim 19 , in which the DP IRLS function is a concentrated differential private (CDP) iteratively reweighted least squares function.