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Two kinds of Hierarchical Markov Models are the Hierarchical hidden Markov model [2] and the Abstract Hidden Markov Model. [3] Both have been used for behavior recognition [4] and certain conditional independence properties between different levels of abstraction in the model allow for faster learning and inference. [3] [5]
Figure 1. Probabilistic parameters of a hidden Markov model (example) X — states y — possible observations a — state transition probabilities b — output probabilities. In its discrete form, a hidden Markov process can be visualized as a generalization of the urn problem with replacement (where each item from the urn is returned to the original urn before the next step). [7]
Reinforcement learning utilizes the MDP framework to model the interaction between a learning agent and its environment. In this framework, the interaction is characterized by states, actions, and rewards. The MDP framework is designed to provide a simplified representation of key elements of artificial intelligence challenges.
Markov random fields find application in a variety of fields, ranging from computer graphics to computer vision, machine learning or computational biology, [13] [14] and information retrieval. [15] MRFs are used in image processing to generate textures as they can be used to generate flexible and stochastic image models.
Structured prediction or structured output learning is an umbrella term for supervised machine learning techniques that ... such as a hidden Markov model or ...
The hierarchical hidden Markov model (HHMM) is a statistical model derived from the hidden Markov model (HMM). In an HHMM, each state is considered to be a self-contained probabilistic model. More precisely, each state of the HHMM is itself an HHMM. HHMMs and HMMs are useful in many fields, including pattern recognition. [1] [2]
The forward–backward algorithm is an inference algorithm for hidden Markov models which computes the posterior marginals of all hidden state variables given a sequence of observations/emissions ::=, …,, i.e. it computes, for all hidden state variables {, …,}, the distribution ( | :).
The Forward algorithm will then tell us about the probability of data with respect to what is expected from our model. One of the applications can be in the domain of Finance, where it can help decide on when to buy or sell tangible assets. It can have applications in all fields where we apply Hidden Markov Models.