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I've been using Hidden Markov Models (HMM) for some time. Now I would like to know about any other statistical model that can prove to be as useful as HMM. For example I was exploiting HMM for gesture recognition. Can other statistical concepts work like HMM, i.e. statistical inference for finding the different parameters such as transition probabilities?
I have heard of Neural Networks and Bayesian statistical inference. Are these concept similar to HMM?
There are some good answers here already, but I thought I'd chime in with one more, which has been used in areas related to gesture recognition.
This paper by Taylor, Hinton, and Roweis is similar to an HMM in the sense that it's a time series model with latent states, but:
1) the structure of the hidden states can be much more complex (many many more possible states) and
2) many of the connections are undirected (as in a conditional random field or a Markov random field) rather than directed.
Figure 2 shows a diagram of the basic model, and the authors have some great videos of what the model can learn on their websites.
HMMs are a special case of probabilistic graphical models (PGM), which include very broad range of more or less related (in terms of particular application) models.
There are at least to generic models that you could give a try:
CRF)It is also worth noting, that on the coursera platform one can find a good introductionary course regarding PGMs: https://www.coursera.org/course/pgm
Neural Networks on the other hand are quite generic term, which includes dozens of actual models. The most common understanding of this term ie. Multi Layer Perceptron (also refered as Artificial Neural Network, Feedforward Neural Network) is a different concept, which is rather a regression method then actual probabilistic model. On the other hand there are some probabilistic versions of neural networks which can be used in the similar tasks.
Recurrent neural networks are a discriminative model which can be used to solve many tasks that you'd typically use an HMM for. They are now (at least if the TIMIT benchmark is correct) the state of the art in speech recognition. They are successfully used in language modelling and many more areas. A good introductory text is Ilya Sutskever's phd thesis.
I'm not sure if it qualifies under your criteria, but Kalman Filters are much like HMM's with continuous (Gaussian) latent state space.
You might be interested in looking into Echo State Networks though they do not explicitly model transition probabilities between states. They are easy to implement and fast to train.
Here is an introductory article that you may find useful: http://www.scholarpedia.org/article/Echo_state_network
