We introduce the Variational Hölder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational parameters, the VH bound involves minimization of a convex upper bound to the intractable integral with respect to the variational parameters. Minimization of the...

The study of nonpositively curved spaces goes back to the discovery of hyperbolic space, the work of Hadamard around 1900, and Car-tan's work in the 20's. These spaces play a signiicant role in many areas: Lie group theory, combinatorial and geometric group theory, dynamical systems, harmonic maps and vanishing theorems, geometric topology, Kleinian group theory, and Teichm uller theory. In som...

The most prominent feature of sheet material forming process is an elastic recovery phenomenon during unloading which leads to springback and side wall curl. Therefore evaluation of springback and side wall curl is mandatory for production of precise products. In this paper, the effects of some parameters such as friction coefficient, sheet thickness, yield strength of sheet and blank-holder fo...