Abstract Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets the data. Unfortunately, such fine-grained analysis can easily reveal individual information. We study regression algorithms that satisfy differential privacy , a constraint which guarantees an algorithm’s output reveals little a...

We study random design linear regression with no assumptions on the distribution of covariates and a heavy-tailed response variable. In this distribution-free setting, we show that boundedness conditional second moment given is necessary sufficient condition for achieving nontrivial guarantees. As starting point, prove an optimal version classical in-expectation bound truncated least squares es...

Real life data often includes information from different channels. For example, in computer vision, we can describe an image using different image features, such as pixel intensity, color, HOG, GIST feature, SIFT features, etc.. These different aspects of the same objects are often called multi-view (or multi-modal) data. Lowrank regression model has been proved to be an effective learning mech...