Multivariate semi-markov matrices

Semi-tied Full-covariance Matrices for Hidden Markov Models

There is normally a simple choice made in the form of the covariance matrix to be used with HMMs. Either a diagonal covariance matrix is used, with the underlying assumption that elements of the feature vector are independent, or a full or block-diagonal matrix is used, where all or some of the correlations are explicitly modelled. Unfortunately when using full or block-diagonal covariance matr...

The KTH Visit in Semi-Markov Processes

Institutional Repository Multivariate Markov

Embeddable Markov Matrices

We give an account of some results, both old and new, about any n× n Markov matrix that is embeddable in a one-parameter Markov semigroup. These include the fact that its eigenvalues must lie in a certain region in the unit ball. We prove that a well-known procedure for approximating a non-embeddable Markov matrix by an embeddable one is optimal in a certain sense.

Semi-tied covariance matrices

A standard problem in many classification tasks is how to model feature vectors whose elements are highly correlated. If multi-variate Gaussian distributions are used to model the data then they must have full covariance matrices to accurately do so. This requires a large number of parameters per distribution which restricts the number of distributions that may be robustly estimated, particular...