Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Hidden Markov models (HMM) are stochastic models capable of statistical learning and classification. They have been applied in speech recognition and handwriting recognition because of their great adaptability and versatility in handling sequential signals. On the other hand, as these models have a complex structure and also because the involved data sets usually contain uncertainty, it is difficult to analyze the multiple observation training problem without certain assumptions. For many years researchers have used the training equations of Levinson (1983) in speech and handwriting applications, simply assuming that all observations are independent of each other.  presents a formal treatment of HMM multiple observation training without imposing the above assumption. In this treatment, the multiple observation probability is expressed as a combination of individual observation probabilities without losing generality. This combinatorial method gives one more freedom in making different dependence-independence assumptions. By generalizing Baum's auxiliary function into this framework and building up an associated objective function using the Lagrange multiplier method, it is proven that the derived training equations guarantee the maximization of the objective function. Furthermore,  show that Levinson's training equations can be easily derived as a special case in this treatment.
['Xiaolin Li', 'Marc Parizeau', 'Réjean Plamondon']
I am writing a research paper on a idea Training hidden Markov models with multiple observations-a combinatorial method
[{"from": "human", "value": "I am writing a research paper on a idea Training hidden Markov models with multiple observations-a combinatorial method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Hidden Markov models (HMM) are stochastic models capable of statistical learning and classification. They have been applied in speech recognition and handwriting recognition because of their great adaptability and versatility in handling sequential signals. On the other hand, as these models have a complex structure and also because the involved data sets usually contain uncertainty, it is difficult to analyze the multiple observation training problem without certain assumptions. For many years researchers have used the training equations of Levinson (1983) in speech and handwriting applications, simply assuming that all observations are independent of each other.  presents a formal treatment of HMM multiple observation training without imposing the above assumption. In this treatment, the multiple observation probability is expressed as a combination of individual observation probabilities without losing generality. This combinatorial method gives one more freedom in making different dependence-independence assumptions. By generalizing Baum's auxiliary function into this framework and building up an associated objective function using the Lagrange multiplier method, it is proven that the derived training equations guarantee the maximization of the objective function. Furthermore,  show that Levinson's training equations can be easily derived as a special case in this treatment."}]