Localizing the Latent Structure Canonical Uncertainty: Entropy Profiles for Hidden Markov Models

This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state uncertainty. The entropy of the state sequence that explains an observed sequence for a given hidden Markov chain model can be considered as the canonical measure of state sequence uncertainty. This canonical measure of state sequence uncertainty is not reflected by the classic multivariate state profiles computed by the smoothing algorithm, which summarizes the possible state sequences. Here, we introduce a new type of profiles which have the following properties: (i) these profiles of conditional entropies are a decomposition of the canonical measure of state sequence uncertainty along the sequence and makes it possible to localize this uncertainty, (ii) these profiles are univariate and thus remain easily interpretable on tree structures. We show how to extend the smoothing algorithms for hidden Markov chain and tree models to compute these entropy profiles efficiently.Comment: Submitted to Journal of Machine Learning Research; No RR-7896 (2012

Prevalence, Patterns, and Outcomes of Opioid Use by Injured Workers in Tennessee.

Ph.D. Thesis. University of Hawaiʻi at Mānoa 2018

Relativistic Coulomb Problem: Analytic Upper Bounds on Energy Levels

The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic Schr\"odinger formalism towards incorporation of relativistic effects) with the Coulomb interaction potential (the static limit of the exchange of some massless bosons, as present in unbroken gauge theories). The nonlocal nature of the Hamiltonian encountered here, however, renders extremely difficult to obtain rigorous analytic statements on the corresponding solutions. In view of this rather unsatisfactory state of affairs, we derive (sets of) analytic upper bounds on the involved energy eigenvalues.Comment: 12 pages, LaTe