Michal Matuszak

Solving ramified optimal transport problem in the bayesian influence diagram framework

The goal of the ramified optimal transport is to find an optimal transport path between two given probability measures. One measure can be identified with a source while the other one with a target. The problem is well known to be NP---hard. We develop an algorithm for solving a ramified optimal transport problem within the framework of Bayesian networks. It is based on the decision strategy optimisation technique that utilises self---annealing ideas of Chen---style stochastic optimisation. Resulting transport paths are represented in the form of tree---shaped structures. The effectiveness of the algorithm has been tested on computer---generated examples.

Locally Specified Polygonal Markov Fields for Image Segmentation

We introduce a class of polygonal Markov fields driven by local activity functions. Whereas the local rather than global nature of the field specification ensures substantial additional flexibility for statistical applications in comparison to classical polygonal fields, we show that a number of simulation algorithms and graphical constructions, as developed in our previous joint work with M.N.M. van Lieshout and R. Kluszczynski, carry over to this more general framework. Moreover, we provide explicit formulae for the partition function of the model, which directly implies the availability of closed form expressions for the corresponding likelihood functions. Within the framework of this theory we develop an image segmentation algorithm based on Markovian optimization dynamics combining the simulated annealing ideas with those of Chen-style stochastic optimization, in which successive segmentation updates are carried out simultaneously with adaptive optimization of the local activity functions.

A new stochastic algorithm for strategy optimisation in Bayesian influence diagrams

The problem of solving general Bayesian influence diagrams is well known to be NP-complete, whence looking for efficient approximate stochastic techniques yielding suboptimal solutions in reasonable time is well justified. The purpose of this paper is to propose a new stochastic algorithm for strategy optimisation in Bayesian influence diagrams. The underlying idea is an extension of that presented in [2] by Chen who developed a self-annealing algorithm for optimal tour generation in traveling salesman problems (TSP). Our algorithm generates optimal decision strategies by iterative self-annealing reinforced search procedure, gradually acquiring new information while driven by information already acquired. The effectiveness of our method has been tested on computer-generated examples.

Stochastic techniques in influence diagrams for learning bayesian network structure

The problem of learning Bayesian network structure is well known to be NP---hard. It is therefore very important to develop efficient approximation techniques. We introduce an algorithm that within the framework of influence diagrams translates the structure learning problem into the strategy optimisation problem, for which we apply the Chens self---annealing stochastic optimisation algorithm. The effectiveness of our method has been tested on computer---generated examples.

Smooth conditional transition paths in dynamical gaussian networks

We propose an algorithm for determining optimal transition paths between given configurations of systems consisting of many objects. It is based on the Principle of Least Action and variational equations for Freidlin-Wentzell action functionals in Gaussian networks set-up.We use our method to construct a system controlling motion and redeployment between units formations. Another application of the algorithm allows a realistic transformation between two sequences of character animations in a virtual environment. The efficiency of the algorithm has been evaluated in a simple sandbox environment implemented with the use of the NVIDIA CUDA technology.