A shared-parameter continuous-time hidden Markov and survival model for longitudinal data with informative dropout

A shared-parameter approach for jointly modeling longitudinal and survival data is proposed. With respect to available approaches, it allows for time-varying random effects that affect both the longitudinal and the survival processes. The distribution of these random effects is modeled according to a continuous-time hidden Markov chain so that transitions may occur at any time point. For maximum likelihood estimation, we propose an algorithm based on a discretization of time until censoring in an arbitrary number of time windows. The observed information matrix is used to obtain standard errors. We illustrate the approach by simulation, even with respect to the effect of the number of time windows on the precision of the estimates, and by an application to data about patients suffering from mildly dilated cardiomyopathy

The Matrix Ridge Approximation: Algorithms and Applications

We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge approximation}. In particular, we define the matrix ridge approximation as an incomplete matrix factorization plus a ridge term. Moreover, we present probabilistic interpretations using a normal latent variable model and a Wishart model for this approximation approach. The idea behind the latent variable model in turn leads us to an efficient EM iterative method for handling the matrix ridge approximation problem. Finally, we illustrate the applications of the approximation approach in multivariate data analysis. Empirical studies in spectral clustering and Gaussian process regression show that the matrix ridge approximation with the EM iteration is potentially useful

Bayesian adaptive learning of the parameters of hidden Markov model for speech recognition

A theoretical framework for Bayesian adaptive training of the parameters of a discrete hidden Markov model (DHMM) and of a semi-continuous HMM (SCHMM) with Gaussian mixture state observation densities is presented. In addition to formulating the forward-backward MAP (maximum a posteriori) and the segmental MAP algorithms for estimating the above HMM parameters, a computationally efficient segmental quasi-Bayes algorithm for estimating the state-specific mixture coefficients in SCHMM is developed. For estimating the parameters of the prior densities, a new empirical Bayes method based on the moment estimates is also proposed. The MAP algorithms and the prior parameter specification are directly applicable to training speaker adaptive HMMs. Practical issues related to the use of the proposed techniques for HMM-based speaker adaptation are studied. The proposed MAP algorithms are shown to be effective especially in the cases in which the training or adaptation data are limited.published_or_final_versio

Additive, Dynamic and Multiplicative Regression

We survey and compare model-based approaches to regression for cross-sectional and longitudinal data which extend the classical parametric linear model for Gaussian responses in several aspects and for a variety of settings. Additive models replace the sum of linear functions of regressors by a sum of smooth functions. In dynamic or state space models, still linear in the regressors, coefficients are allowed to vary smoothly with time according to a Bayesian smoothness prior. We show that this is equivalent to imposing a roughness penalty on time-varying coefficients. Admitting the coefficients to vary with the values of other covariates, one obtains a class of varying-coefficient models (Hastie and Tibshirani, 1993), or in another interpretation, multiplicative models. The roughness penalty approach to non- and semiparametric modelling, together with Bayesian justifications, is used as a unifying and general framework for estimation. The methodological discussion is illustrated by some real data applications