An architecture able to model temporal sequences of input--output data is presented. The architecture, called Markov Mixture of Experts (MME), combines a set of static models (called experts) by means of a Markov chain. To each state of the Markov chain, a unique distinct expert is assigned. Each output is produced by the expert corresponding to the current state of the Markov chain. The transitions between states, which correspond to switching between the various experts, depend probabilistically on both the current state and on the input variables. The architecture is an extension of both the Mixture of Experts architecture and the Hidden Markov Models.
It is shown that the parameters of the experts and the transition probabilities can be simultaneously estimated from input--output data only. The algorithm presented is an iterative algorithm based on the Estimation--Maximisation procedure; as a consequence, the unobserved states are estimated as well.
The algorithm is used in a fine motion task for a robot arm. Such a task is performed in stages; during each stage, the arm is required to move maintaining contact with a given surface of the surrounding objects. Due to multiple sources of uncertainty, the state of contact (i.e. which are the surfaces in contact with the arm) must be estimated from measurements and previous state information. This is achieved by a MME with the state of contact as hidden state variable.