Linear regression under log-concave and Gaussian scale mixture errors: comparative study

Gaussian Scale Mixture Models for Robust Linear Multivariate Regression with Missing Data

Functional Inequalities for Gaussian and Log-Concave Probability Measures

We give three proofs of a functional inequality for the standard Gaussian measure originally due to William Beckner. The first uses the central limit theorem and a tensorial property of the inequality. The second uses the Ornstein-Uhlenbeck semigroup, and the third uses the heat semigroup. These latter two proofs yield a more general inequality than the one Beckner originally proved. We then ge...

A recurrent log-linearized Gaussian mixture network

Context in time series is one of the most useful and interesting characteristics for machine learning. In some cases, the dynamic characteristic would be the only basis for achieving a possible classification. A novel neural network, which is named "a recurrent log-linearized Gaussian mixture network (R-LLGMN)," is proposed in this paper for classification of time series. The structure of this ...

Active and passive learning of linear separators under log-concave distributions

We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear separators under nearly log-concave distributions. Building on this, we provide a computationally efficient PAC algorithm with optimal (up to a constant factor) sa...

Diagnostic Measures in Ridge Regression Model with AR(1) Errors under the Stochastic Linear Restrictions

Outliers and influential observations have important effects on the regression analysis. The goal of this paper is to extend the mean-shift model for detecting outliers in case of ridge regression model in the presence of stochastic linear restrictions when the error terms follow by an autoregressive AR(1) process. Furthermore, extensions of measures for diagnosing influential observations are ...