The Lempel-Ziv-Welch (LZW) compression algorithm is widely used because it achieves an excellent compromise between compression performance and speed of execution. A simple way to improve the compression without significantly degrading its speed is proposed, and experimental data shows that it works in practice. Even better results are achieved with an additional optimization of “phasing in” bi...

An algorithm is presented for analyzing the transitive behavior of reversible one-dimensional cellular automata, where reversibility refers to injective cellular automata which have a bijective behavior for spatially periodic configurations. In particular we study reversible automata where the ancestors of finite sequences differ at both ends (technically, with both Welch indices different from...

In this lecture, we will address problems 3 and 4. First, continuing from the previous lecture, we will view BaumWelch Re-estimation as an instance of the Expectation-Maximization (EM) algorithm and prove why the EM algorithm maximizes data likelihood. Then, we will proceed to discuss discriminative training under the maximum mutual information estimation (MMIE) framework. Specifically, we will...

During the past two weeks or so, we discussed HMMs and how we can utilize them for various purposes. We developed di erent formulas and algorithms (e.g. Forward Algorithm, Backward Algorithm). Unfortunately, while doing so, we encountered an essential problem: all of these algorithms and formulas, assume that θ is known. And so, in the last two lessons, our goal was to estimate the parameters θ...

The paper exposes a non-parametric approach to latent and co-latent modeling of bivariate data, based upon alternating minimization of the Kullback-Leibler divergence (EM algorithm) for complete log-linear models. For categorical data, the iterative algorithm generates a soft clustering of both rows and columns of the contingency table. Well-known results are systematically revisited, and some ...

It is the problem of computer science that how we detect the handwritten character and word, so it is also the problem in the field of image processing and pattern recognition of computer science. The meaning of handwritten character and word recognition refers to the identification of the characters or word which is written by a human being. Our approach is this, how this problem solved correc...

Hidden Markov model (HMM) as a sequential classifier has important applications in speech and language processing [Rab89] [JM08] and biological sequence analysis [Kro98]. In this project, we analysis the parallelism in the three algorithms for HMM training and classification, i.e. forward algorithm, Viterbi algorithm, and Baum-Welch algorithm, for graphical processing units (GPU). Based on the ...

Consider a stationary precise hidden Markov model (HMM) with n hidden states Xk, taking values xk in a set {1, . . . ,m} and n observations Ok, taking values ok. Both the marginal model pX1(x1), the emission models pOk|Xk(ok|xk) and the transition models pXk|Xk−1(xk|xk−1) are unknown. We can then use the Baum–Welch algorithm [see, e.g., 4] to get a maximum-likelihood estimate of these models. T...

The EM algorithm, e.g. as Baum-Welch reestimation, is an important tool for parameter estimation in discrete-time Hidden Markov Models. We present a direct reestimation of rate constants for applications in which the underlying Markov process is continuous in time. Previous estimation of discrete-time transition probabilities is not necessary.