We consider variational inequalities with different trial and test spaces and a possibly noncoercive bilinear form. Well-posedness has been shown under general conditions that are e.g. valid for the space-time formulation of parabolic variational inequalities. Fine discretizations for such problems resolve in large scale problems and thus in long computing times. To reduce the size of these pro...

Some investigations into energy-based models Tijmen Tieleman Master of Science Graduate Department of Computer Science University of Toronto 2007 Three questions about various energy-based probability models are asked and answered. The first is whether the Contrastive Divergence algorithm computes the gradient of any function at all the answer is no. The second is whether there is a tractable M...

We propose a multi-wing harmonium model for mining multimedia data that extends and improves on earlier models based on two-layer random fields, which capture bidirectional dependencies between hidden topic aspects and observed inputs. This model can be viewed as an undirected counterpart of the two-layer directed models such as LDA for similar tasks, but bears significant difference in inferen...

We consider Maxwell’s equations with impedance boundary conditions on a polyhedron with polyhedral holes. Well-posedness of the variational formulation is proven and a discontinuous Galerkin (dG) approximation is introduced. We prove well-posedness of the dG problem as well as a priori error estimates. Next, we use the frequency ω as a parameter in a multi-query context. For this purpose, we de...

We present a formulation of the Hartree-Fock-Bogoliubov (HFB) equations which solves the problem directly in the basis of natural orbitals. This provides a very efficient scheme which is particularly suited for large scale calculations on coordinate-space grids. The production of new nuclei towards the drip lines and in the super-heavy region (for a review see [1]) has raised a growing interest...

A deep Boltzmann machine (DBM) is a recently introduced Markov random field model that has multiple layers of hidden units. It has been shown empirically that it is difficult to train a DBMwith approximate maximum-likelihood learning using the stochastic gradient unlike its simpler special case, restricted Boltzmann machine (RBM). In this paper, we propose a novel pretraining algorithm that con...