Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the v...

Recently proposed distance dependent Chinese Restaurant Process (ddCRP) generalizes extensively used Chinese Restaurant Process (CRP) by accounting for dependencies between data points. Its posterior is intractable and so far only MCMC methods were used for inference. Because of very different nature of ddCRP no prior developments in variational methods for Bayesian nonparametrics are appliable...

The relationship between mathematical programming and classical calculus of variation was explored and extended by Hanson [6]. Thereafter variational programming problems have attracted some attention in literature. Duality for multiobjective variational problems has been of much interest in the recent years, and several contributions have been made to its development (see, e.g., Bector and Hus...

We introduce new and interesting model of system of generalized set-valued equilibrium problems which generalizes and unifies the system of set-valued equilibrium problems, the system of generalized implicit vector variational inequalities, the system of generalized vector and vector-like variational inequalities introduced by Ansari et al. (2002), the system of generalized vector variational i...

Amortized variational inference (AVI) replaces instance-specific local inference with a global inference network. While AVI has enabled efficient training of deep generative models such as variational autoencoders (VAE), recent empirical work suggests that inference networks can produce suboptimal variational parameters. We propose a hybrid approach, to use AVI to initialize the variational par...

we introduce and discuss the homotopy perturbation method, the adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. then, we give an example of the stefan problem with  kinetics and solve it by these methods.

we describe a variational problem on a surface under a constraintof geometrical character. necessary and sufficient conditions for the existence ofbifurcation points are provided. in local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. the problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.

we prove a strong convergence result for a sequence generated by halpern's type iteration for approximating a common fixed point of a countable family of quasi-lipschitzian mappings in a real hilbert space. consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...

Variational methods provide a computationally scalable alternative to Monte Carlo methods for large-scale, Bayesian nonparametric learning. In practice, however, conventional batch and online variational methods quickly become trapped in local optima. In this paper, we consider a nonparametric topic model based on the hierarchical Dirichlet process (HDP), and develop a novel online variational ...