| title: | Hidden random structures |
|---|---|
| reg no: | ETF5694 |
| project type: | Estonian Science Foundation research grant |
| subject: |
1.2. Applied Mathematics |
| status: | accepted |
| institution: | TU Faculty of Mathematics |
| head of project: | Jüri Lember |
| duration: | 01.01.2004 - 31.12.2007 |
| description: | We investigate the processes generated by observing a stochastic scenery along a path of a stochastic process. This is a broad class of processes including also the observations of a random scenery as well as hidden Markov models. These processes constitute the main directions of the research. The first direction is focused on scenerey reconstruction and related areas, the second direction concentrates on the training algorithms for emission parameter estimation in hidden Markov models. The problem of scenery reconstruction can be described as follows. A realization of a stochastic process (the scenery) is observed along a path of a random walk. Is it possible to reconstruct the underlying scenery? After H. Matzinger five years ago proposed the first scenery reconstruction algorithm, the scenery reconstruction has been a vivid field of discrete probability. However, there are still several open problems: How to reconstruct a random 2 color scenery if the random walk is allowed to jump? When a periodic scenery can be reconstructed? Is it possible to reconstruct a scenery when the random walk can jump unboundedly? Solving these problems is a task of the project. Hidden Markov models have become important in number of applications. These include speech recognition, genetics and physics. Often the main focus is the estimation of the emission parameters. The standard method - EM training - is often slow and computationally involved, so that some cheap alternatives are needed. One of them is the so-called Viterbi training used in Philips speech recognition systems. It is fast and cheap, but the output of the training is often far from MLE. A task of the project is to adjust the Viterbi training so that the adjusted algorithm has the good properties of the Viterbi training but gives the more accurate estimators. Such compromize-trainings are of theoretical and practical interest. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Jüri Lember | TU Faculty of Mathematics | lecturer | |