Editing Hidden Markov Models in Speech Synthesis (section)

=== High-Precision Model Design ===
Researchers continuously improve the structure and parameter estimation methods of Hidden Markov Model (HMM) to enhance its precision and accuracy in speech synthesis. This includes modeling improvements in states, transition probabilities, emission probabilities, and more. Key innovations in high-precision model design in the domain of speech synthesis with HMMs focus on enhancing the model's structure, parameter estimation methods, and integration with neural networks. These innovations play a crucial role in improving the accuracy, temporal modeling capabilities, and expressive power of HMMs, providing valuable insights and methods for high-precision model design in speech synthesis. These innovations make HMM models more adaptable and expressive in the field of speech synthesis, laying the foundation for achieving high-quality, natural speech synthesis.

==== Improved Model Structure ====
# Multi-layer HMMs: Introducing multi-layer HMMs to better represent the intricate structure of speech signals. [Young et al., 1994]<ref>Young, S., Evermann, G., Gales, M., Hain, T., Kershaw, D., Liu, X., ... & Woodland, P. (1994). [https://ieeexplore.ieee.org/document/294559/ The HTK Book]. Cambridge University Engineering Department.</ref>
# Coupled HMMs: Coupling multiple HMM models to enhance the modeling of complex speech features. [Lee and Hon, 1989]<ref>Lee, K.-F., & Hon, H.-W. (1989). [https://ieeexplore.ieee.org/document/22686 Speaker-independent phone recognition using hidden Markov models]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(11), 1641-1648.</ref>

==== Parameter Estimation Methods ====
# Maximum Likelihood Estimation (MLE): Employing MLE to estimate parameters like state transition and emission probabilities, enhancing model fitting accuracy. [Rabiner and Juang, 1986]<ref>Rabiner, L. R., & Juang, B. H. (1986). [https://ieeexplore.ieee.org/document/18626 An introduction to hidden Markov models]. IEEE ASSP Magazine, 3(1), 4-16.</ref>
# Baum-Welch Algorithm: Utilizing the Baum-Welch algorithm for iterative parameter estimation, maximizing the likelihood function of observed data. [Baum et al., 1970]<ref>- Baum, L. E., Petrie, T., Soules, G., & Weiss, N. (1970). [https://doi.org/10.1002/j.1538-7305.1970.tb01790.x A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains]. The annals of mathematical statistics, 41(1), 164-171.</ref>

==== Integration with Neural Networks ====
# Combination of Deep Neural Network and HMM (DNN-HMM): Fusing deep neural networks with HMM to model the relationship between speech features and HMM states, enhancing the model's expression ability. [Hinton et al., 2012]<ref name=":0">Hinton, G. E., Deng, L., Yu, D., Dahl, G. E., Mohamed, A. R., Jaitly, N., ... & Kingsbury, B. (2012). [https://www.cs.toronto.edu/~hinton/absps/NatureDeepReview.pdf Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups]. IEEE Signal Processing Magazine, 29(6), 82-97.</ref>
# Combination of Recurrent Neural Network and HMM (RNN-HMM): Integrating recurrent neural networks with HMM to model temporal information, further improving the time series modeling ability. [Graves et al., 2013]<ref>Graves, A., Mohamed, A. R., Hinton, G., (2013). Speech recognition with deep recurrent neural networks. In Acoustics, speech and signal processing (ICASSP), 2013 IEEE international conference (pp. 6645-6649).</ref>