No description available.

Zugl.: Karlsruhe, Univ., Diss., 2005

Universiẗat, Diss., 2005--Karlsruhe.

In Natural Language Processing (NLP), speech and text are parsed and generated with language models and parser models, and translated with translation models. Each model contains a set of numerical parameters which are found by applying a suitable training algorithm to a set of training data. Many such training algorithms are instances of the Expectation-Maximization (EM) algorithm. In [BSV15], a generic EM algorithm for NLP is described. This work presents a particular speech model, the Hidden Markov model, and its standard training algorithm, the Baum-Welch algorithm. It is then shown that the Baum-Welch algorithm is an instance of the generic EM algorithm introduced by [BSV15], from which follows that all statements about the generic EM algorithm also apply to the Baum-Welch algorithm, especially its correctness and convergence properties.

No description available.

No description available.

Many complexity measures are defined as the size of a minimal representation in a specific model class. One such complexity measure, which is important because it is widely applied, is statistical complexity. It is defined for discrete-time, stationary stochastic processes within a theory called computational mechanics. Here, a mathematically rigorous, more general version of this theory is presented, and abstract properties of statistical complexity as a function on the space of processes are investigated. In particular, weak-* lower semi-continuity and concavity are shown, and it is argued that these properties should be shared by all sensible complexity measures. Furthermore, a formula for the ergodic decomposition is obtained. The same results are also proven for two other complexity measures that are defined by different model classes, namely process dimension and generative complexity. These two quantities, and also the information theoretic complexity measure called excess entropy, are related to statistical complexity, and this relation is discussed here. It is also shown that computational mechanics can be reformulated in terms of Frank Knight's prediction process, which is of both conceptual and technical interest. In particular, it allows for a unified treatment of different processes and facilitates topological considerations. Continuity of the Markov transition kernel of a discrete version of the prediction process is obtained as a new result.

Univ., Diss.--Kiel, 2001.

Univ, Diss--Köln, 2003.

Time-delayed actions appear as an essential component of numerous systems especially in evolution processes, natural phenomena, and particular technical applications and are associated with the existence of a memory. Under common conditions, external forces or state dependent parameters modify the length of the delay with time. Consequently, an altered dynamical behavior emerges, whose characterization is compulsory for a deeper understanding of these processes. In this thesis, the well-investigated class of time-homogeneous finite-state Markov processes is utilized to establish a variation of memory length by combining a first-order Markov chain with a memoryless Markov chain of order zero. The fluctuations induce a non-stationary process, which is accomplished for two special cases: a periodic and a random selection of the available Markov chains. For both cases, the Kolmogorov-Sinai entropy as a characteristic property is deduced analytically and compared to numerical approximations to the entropy rate of related symbolic dynamics. The convergences of per-symbol and conditional entropies are examined in order to recognize their behavior when identifying unknown processes. Additionally, the connection from Markov processes with varying memory length to hidden Markov models is illustrated enabling further analysis. Hence, the Kolmogorov-Sinai entropy of hidden Markov chains is calculated by means of Blackwell’s entropy rate involving Blackwell’s measure. These results are used to verify the previous computations.