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...

klinkenberg permeability is an important parameter in tight gas reservoirs. there are conventional methods for determining it, but these methods depend on core permeability. cores are few in number, but well logs are usually accessible for all wells and provide continuous information. in this regard, regression methods have been used to achieve reliable relations between log readings and klinke...

The mode of a distribution provides an important summary of data and is often estimated based on some non-parametric kernel density estimator. This article develops a new data analysis tool called modal linear regression in order to explore highdimensional data. Modal linear regression models the conditional mode of a response Y given a set of predictors x as a linear function of x. Modal linea...

The advantage of using linear regression in the leaves of a regression tree is analysed in the paper. It is carried out how this modiication aaects the construction, pruning and interpretation of a regression tree. The modiication is tested on artiicial and real-life domains. The results show that the mod-iication is beneecial as it leads to smaller classiica-tion errors of induced regression t...