  In this paper, we apply machine learning to distributed private data owned by
multiple data owners, entities with access to non-overlapping training
datasets. We use noisy, differentially-private gradients to minimize the
fitness cost of the machine learning model using stochastic gradient descent.
We quantify the quality of the trained model, using the fitness cost, as a
function of privacy budget and size of the distributed datasets to capture the
trade-off between privacy and utility in machine learning. This way, we can
predict the outcome of collaboration among privacy-aware data owners prior to
executing potentially computationally-expensive machine learning algorithms.
Particularly, we show that the difference between the fitness of the trained
machine learning model using differentially-private gradient queries and the
fitness of the trained machine model in the absence of any privacy concerns is
inversely proportional to the size of the training datasets squared and the
privacy budget squared. We successfully validate the performance prediction
with the actual performance of the proposed privacy-aware learning algorithms,
applied to: financial datasets for determining interest rates of loans using
regression; and detecting credit card frauds using support vector machines.
