In this paper, we propose a DRO framework that relies on a new distance inspired by Unbalanced Optimal Transport (UOT).

We consider logistic regression, and more generally, linear classification, in the streaming model. In our setting, we are given a dataset consisting ofT examples (xt,yt), where t [T], xt Rd, yt { 1,1}. The examples arrive one by one, and moreover, the nonzero coordinates of each examplext arrive one by one.

A specific focus is on the on the trade-off between bit depth and the number of projections given a fixed budget of bits for storage or transmission.

In this paper, we propose a DRO framework that relies on a new distance inspired by Unbalanced Optimal Transport (UOT).

Differential privacy is a cryptographically motivated definition of privacy which has gained considerable attention in the algorithms, machine-learning and data-mining communities. While there has been an explosion of work on differentially private machine learning algorithms, a major barrier to achieving end-to-end differential privacy in practical machine learning applications is the lack of an effective procedure for differentially private parameter tuning, or, determining the parameter value, such as a bin size in a histogram, or a regularization parameter, that is suitable for a particular application. In this paper, we introduce a generic validation procedure for differentially private machine learning algorithms that apply when a certain stability condition holds on the training algorithm and the validation performance metric. The training data size and the privacy budget used for training in our procedure is independent of the number of parameter values searched over. We apply our generic procedure to two fundamental tasks in statistics and machine-learning - training a regularized linear classifier and building a histogram density estimator that result in end-to-end differentially private solutions for these problems.

This establishes a clear and provable separation of the minimax rates between the active setting and the no-interaction setting.