Relational topic models have shown promise on analyzing document network structures and discovering latent topic representations. This paper presents three extensions: 1) unlike the common link likelihood with a diagonal weight matrix that allows the-same-topic interactions only, we generalize it to use a full weight matrix that captures all pairwise topic interactions and is applicable to asym...

In this paper, we use the auxiliary principle technique coupled with the principle of iterative regularization to suggest and analyze some new iterative algorithms for solving mixed quasi variational inequalities. We also study the convergence criteria of these algorithms under some suitable and mild conditions. Several special cases are also considered. Results obtained in this paper continue ...

It was recently shown that the alternating direction method with logarithmicquadratic proximal regularization can yield an efficient algorithm for a class of variational inequalities with separable structures. This paper further shows the O(1/t) convergence rate for this kind of algorithms. Both the cases with a simple or general Glowinski’s relaxation factor are discussed.

, Abstract. This paper is concerned with the derivation of open-loop 8tackelberg (OL8) solutions of a class of continuoustime two-player nonzero-sum differential games characterized by quadratic cost functionals and linear singular systems. By applying the calculus of variations, necessary conditions are derived under which the op~n-Ioop 8tackelberg solution of the leader exists. Under the tran...

These four lectures are for the “Workshop on QuantumMarginals and Density Matrices” at the Fields Institute in Toronto, July 27-31, 2009.

We present a variational approximation to the information bottleneck of Tishby et al. (1999). This variational approach allows us to parameterize the information bottleneck model using a neural network and leverage the reparameterization trick for efficient training. We call this method “Deep Variational Information Bottleneck”, or Deep VIB. We show that models trained with the VIB objective ou...

A simultaneous space-time variational formulation of a parabolic evolution problem is solved with an adaptive wavelet method. This method is shown to converge with the best possible rate in linear complexity. Thanks to the use of tensor product bases, there is no penalty in complexity due to the additional time dimension. Special wavelets are designed such that the bi-infinite system matrix is ...

This paper presents a novel variational model for inverse consistent deformable image registration. This model deforms the source and target image simultaneously, and aligns the deformed source and deformed target images in the way that the both transformations are inverse consistent. The model does not computes the inverse transforms explicitly, alternatively it finds two more deformation fiel...

Two absolute energy minimum principles are developed for first-principle linear-scaling electronic structure calculations. One is with a normalization constraint and the other without any constraint. The density matrix is represented by a set of nonorthogonal localized orbitals and an auxiliary matrix which at the minimum becomes a generalized inverse of the overlap matrix of the localized orbi...

Recently, the variational Bayesian approximation was applied to probabilistic matrix factorization and shown to perform very well in experiments. However, its good performance was not completely understood beyond its experimental success. The purpose of this paper is to theoretically elucidate properties of a variational Bayesian matrix factorization method. In particular, its mechanism of avoi...