Spectral Learning of Hidden Markov Models from Dynamic and Static Data

We develop spectral learning algorithms for Hidden Markov Models that learn not only from time series, or dynamic data but also static data drawn independently from the HMM’s stationary distribution. This is motivated by the fact that static, orderless snapshots are usually easier to obtain than time series in quite a few dynamic modeling tasks. Building on existing spectral learning algorithms, our methods solve convex optimization problems minimizing squared loss on the dynamic data plus a regularization term on the static data. Experiments on synthetic and real human activities data demonstrate better prediction by the proposed method than existing spectral algorithms.