Nonuniform Markov models

A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model must decide that each symbol in a string depends on at most a small, finite number of other symbols in the string. In this report we propose a new way to model conditional independence in Markov models. The central feature of our nonuniform Markov model is that it makes predictions of varying lengths using contexts of varying lengths. Experiments on the Wall Street Journal reveal that the nonuniform model performs slightly better than the classic interpolated Markov model. This result is somewhat remarkable because both models contain identical numbers of parameters whose values are estimated in a similar manner. The only difference between the two models is how they combine the statistics of longer and shorter strings. Keywords: nonuniform Markov model, interpolated Markov model, conditional independence, statistical language model, discrete time series.Comment: 17 page

Graphical Markov models: overview

We describe how graphical Markov models started to emerge in the last 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression graphs are singled out as being best suited for analyzing longitudinal data and for tracing developmental pathways. Interpretations are illustrated using two sets of data and some of the more recent, important results for sequences of regressions are summarized.Comment: 22 pages, 9 figure

Markov-switching generalized additive models

We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation and further illustrated by modelling how energy price in Spain depends on the Euro/Dollar exchange rate

Unsupervised Neural Hidden Markov Models

In this work, we present the first results for neuralizing an Unsupervised Hidden Markov Model. We evaluate our approach on tag in- duction. Our approach outperforms existing generative models and is competitive with the state-of-the-art though with a simpler model easily extended to include additional context.Comment: accepted at EMNLP 2016, Workshop on Structured Prediction for NLP. Oral presentatio