jblas
jblas is a fast linear algebra library for Java. jblas is based on BLAS and LAPACK, the de-facto industry standard for matrix computations, and uses state-of-the-art implementations like ATLAS for all its computational routines, making jBLAS very fast. jblas can is essentially a light-wight wrapper around the BLAS and LAPACK routines. These packages have originated in the Fortran community which explains their often archaic API. On the other hand modern implementations are hard to beat performance wise. jblas aims to make this functionality available to Java programmers such that they do not have to worry about writing JNI interfaces and calling conventions of Fortran code. jblas depends on an implementation of the LAPACK and BLAS routines. Currently it is tested with ATLAS (http://math-atlas.sourceforge.net ) and BLAS/LAPACK (http://…/lapack)

Sobolev Integral Probability Metric (IPM)
We propose a new Integral Probability Metric (IPM) between distributions: the Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions for functions (critic) restricted to a Sobolev ball defined with respect to a dominant measure $\mu$. We show that the Sobolev IPM compares two distributions in high dimensions based on weighted conditional Cumulative Distribution Functions (CDF) of each coordinate on a leave one out basis. The Dominant measure $\mu$ plays a crucial role as it defines the support on which conditional CDFs are compared. Sobolev IPM can be seen as an extension of the one dimensional Von-Mises Cram\’er statistics to high dimensional distributions. We show how Sobolev IPM can be used to train Generative Adversarial Networks (GANs). We then exploit the intrinsic conditioning implied by Sobolev IPM in text generation. Finally we show that a variant of Sobolev GAN achieves competitive results in semi-supervised learning on CIFAR-10, thanks to the smoothness enforced on the critic by Sobolev GAN which relates to Laplacian regularization. …

Statistical Inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation. Initial requirements of such a system of procedures for inference and induction are that the system should produce reasonable answers when applied to well-defined situations and that it should be general enough to be applied across a range of situations. Inferential statistics are used to test hypotheses and make estimations using sample data. …