We introduce a framework for modeling parameter symmetries in variational inference by explicitly mixing a base approximating density over a symmetry group. We show that this can be done tractably for the case of a Gaussian mixture over the orthogonal group under an isotropic variance assumption. Initial results show that inference with a symmetrized posterior avoids component collapse and lead...

Selecting N random points in a unit square corresponds to selecting a random permutation. Placing symmetry restrictions on the points, we obtain special kinds of permutations : involutions, signed permutations and signed involutions. We are interested in the statistics of the length (in numbers of points) of the longest up/right path in each symmetry type as the number of points increases to in...

Supersymmetry between bosons and fermions is modeled within PT −symmetric quantum mechanics. A non-Hermitian alternative to the Witten’s supersymmetric quantum mechanics is obtained. Work supported by the grant Nr. A 1048004 of GA AS CR. e-mail: [email protected]

The junction tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present a novel stochastic algorithm which we call the Christmas tree algorithm for building of junction trees sequentially by adding one node at a time to the underlying decomposable graph. The algorithm has two important theoretical properties. Firstly, every junc...

We define the decomposition property for partial actions of discrete groups on C⁎-algebras. Decomposable systems appear naturally in practice, and many commonly occurring can be decomposed into with property. For instance, any action a finite group is an iterated extension decomposable systems. Partial are always globalizable amenable, regardless acting group, their globalization explicitly des...