Adaptive algorithms and stochastic approximations
Adaptive algorithms and stochastic approximations
System identification (2nd ed.): theory for the user
System identification (2nd ed.): theory for the user
The O.D. E. Method for Convergence of Stochastic Approximation and Reinforcement Learning
SIAM Journal on Control and Optimization
Gradient Convergence in Gradient methods with Errors
SIAM Journal on Optimization
Inference in Hidden Markov Models (Springer Series in Statistics)
Inference in Hidden Markov Models (Springer Series in Statistics)
On analytic properties of entropy rate
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On the optimality of symbol-by-symbol filtering and denoising
IEEE Transactions on Information Theory
Capacity of Finite State Channels Based on Lyapunov Exponents of Random Matrices
IEEE Transactions on Information Theory
Analyticity of Entropy Rate of Hidden Markov Chains
IEEE Transactions on Information Theory
Derivatives of Entropy Rate in Special Families of Hidden Markov Chains
IEEE Transactions on Information Theory
Convergence of a Particle-Based Approximation of the Block Online Expectation Maximization Algorithm
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special Issue on Monte Carlo Methods in Statistics
Multi-appliance recognition system with hybrid SVM/GMM classifier in ubiquitous smart home
Information Sciences: an International Journal
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This paper considers the asymptotic properties of the recursive maximum-likelihood estimator for hidden Markov models. The paper is focused on the analytic properties of the asymptotic log-likelihood and on the point-convergence and convergence rate of the recursive maximum-likelihood estimator. Using the principle of analytic continuation, the analyticity of the asymptotic log-likelihood is shown for analytically parameterized hidden Markov models. Relying on this fact and some results from differential geometry (Lojasiewicz inequality), the almost sure point convergence of the recursive maximum-likelihood algorithm is demonstrated, and relatively tight bounds on the convergence rate are derived. As opposed to the existing result on the asymptotic behavior of maximum-likelihood estimation in hidden Markov models, the results of this paper are obtained without assuming that the log-likelihood function has an isolated maximum at which the Hessian is strictly negative definite.