Sparse Gaussian process methods that use inducing variables require the selection of the inducing inputs and the kernel hyperparameters. We introduce a variational formulation for sparse approximations that jointly infers the inducing inputs and the kernel hyperparameters by maximizing a lower bound of the true log marginal likelihood. The key property of this formulation is that the inducing i...

We discuss intrinsic aspects of Krupka’s approach to finite–order variational sequences. We give intrinsic isomorphisms of the quotient subsheaves of the short finite– order variational sequence with sheaves of forms on jet spaces of suitable order, obtaining a new finite–order (short exact) variational sequence which is made by sheaves of polynomial differential operators. Moreover, we present...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

In this paper, we will use a modified  variational iteration method (MVIM) for solving an inverse heat conduction problem (IHCP). The approximation of the temperature and the heat flux at  are considered. This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional in Euclidian space. Applying this technique, a rapid convergent s...

Abstract In this paper, fixed point arguments and a critical technique are combined leading to hybrid existence results for system of two operator equations where only one the has variational structure. An application periodic solutions semi-variational is given illustrate theory.

Recently, a very attractive logistic regression inference method for exponential family Gibbs spatial point processes was introduced. We combined it with the technique of quadratic tangential variational approximation and derived a new Bayesian technique for analysing spatial point patterns. The technique is described in detail, and demonstrated on numerical examples.

we introduce variational inequality problems on hilbert $c^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. then relation between variational inequalities, $c^*$-valued metric projection and fixed point theory  on  hilbert $c^*$-modules is studied.

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the VlasovPoisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is ver...

In this paper, we use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our method includes the two-step forward-backward splitting and extragradient methods for solving various cl...

We propose a novel variational approach to automatically soft-segment medical images into a fixed number of classes. Our method combines fuzzy classification and active contours in a single variational framework. This approach allows the use of tools from both deformable geometry and clustering in a well-defined setting and provides a useful, unsupervised segmentation technique. The model was t...