In this paper, we propose several dictionary learning algorithms for sparse representations that also impose specific structures on the learned dictionaries such they have low coding complexity and are numerically efficient to use: reduced number of addition/multiplications even avoid multiplications altogether. We base our work factorizations in highly structured basic building blocks (binary ...

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...