Hidden Markov Model Identifiability via Tensors

The prevalence of hidden Markov models (HMMs) in various applications of statistical signal processing and communications is a testament to the power and flexibility of the model. In this paper, we link the identifiability problem with tensor decomposition, in particular, the Canonical Polyadic decomposition. Using recent results in deriving uniqueness conditions for tensor decomposition, we are able to provide a necessary and sufficient condition for the identification of the parameters of discrete time finite alphabet HMMs. This result resolves a long standing open problem regarding the derivation of a necessary and sufficient condition for uniquely identifying an HMM. We then further extend recent preliminary work on the identification of HMMs with multiple observers by deriving necessary and sufficient conditions for identifiability in this setting.Comment: Accepted to ISIT 2013. 5 pages, no figure

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

Extending dynamic segmentation with lead generation: A latent class Markov analysis of financial product portfolios

A recent development in marketing research concerns the incorporation of dynamics in consumer segmentation.This paper extends the latent class Markov model, a suitable technique for conducting dynamic segmentation, in order to facilitate lead generation.We demonstrate the application of the latent Markov model for these purposes using a database containing information on the ownership of twelve financial products and demographics for explaining (changes in) consumer product portfolios.Data were collected in four bi-yearly measurement waves in which a total of 7676 households participated.The proposed latent class Markov model defines dynamic segments on the basis of consumer product portfolios and shows the relationship between the dynamic segments and demographics.The paper demonstrates that the dynamic segmentation resulting from the latent class Markov model is applicable for lead generation.market segmentation;Markov chains;marketing;demography;measurement

A semi-Markov model for price returns

We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday return are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorreletion function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from first of January 2007 until end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis