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2 International Journal of Applied Mathematics and Computer Science

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On Naive Bayes in Speech Recognition

Toth L., Kocsor A., Csirik J.

International Journal of Applied Mathematics and Computer Science

2005

Vol. 15, no 2

287-294

The currently dominant speech recognition technology, hidden Markov modeling, has long been criticized for its simplistic assumptions about speech, and especially for the naive Bayes combination rule inherent in it. Many sophisticated alternative models have been suggested over the last decade. These, however, have demonstrated only modest improvements and brought no paradigm shift in technology. The goal of this paper is to examine why HMM performs so well in spite of its incorrect bias due to the naive Bayes assumption. To do this we create an algorithmic framework that allows us to experiment with alternative combination schemes and helps us understand the factors that influence recognition performance. From the findings we argue that the bias peculiar to the naive Bayes rule is not really detrimental to phoneme classification performance. Furthermore, it ensures consistent behavior in outlier modeling, allowing efficient management of insertion and deletion errors.

Inequality-Based Approximation of Matrix Eigenvectors

Kocsor A., Dombi J., Balint I.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 4

533-538

A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally different nature of their approximations.