Momentum methods have been shown to accelerate the convergence of standard gradient descent algorithm in practice and theory. In particular, minibatch-based with momentum (MGDM) are widely used solve large-scale optimization problems massive datasets. Despite success MGDM practice, their theoretical properties still underexplored. To this end, we investigate based on linear regression models. W...

BACKGROUND When study data are clustered, standard regression analysis is considered inappropriate and analytical techniques for clustered data need to be used. For prediction research in which the interest of predictor effects is on the patient level, random effect regression models are probably preferred over standard regression analysis. It is well known that the random effect parameter esti...

Department of Statistical Science, Duke University March 24, 2008 We show the posterior consistency of certain nonparametric regression models using Lévy Random field priors. An easily verifiable sufficient condition is derived for the posterior consistency to hold in popular models which use Lévy random fields for regression and function estimation. We apply our results to a Poisson regression...

We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters ?n and suitable regularity conditions. The view concern repeated optimization a randomized objective function, motivated by the need for computationally efficient uncertainty quantification contemporary estimation settings. In context regression, we repeatedly assign ana...