45,543 research outputs found
Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States
Motivated by the problem of predicting sleep states, we develop a mixed
effects model for binary time series with a stochastic component represented by
a Gaussian process. The fixed component captures the effects of covariates on
the binary-valued response. The Gaussian process captures the residual
variations in the binary response that are not explained by covariates and past
realizations. We develop a frequentist modeling framework that provides
efficient inference and more accurate predictions. Results demonstrate the
advantages of improved prediction rates over existing approaches such as
logistic regression, generalized additive mixed model, models for ordinal data,
gradient boosting, decision tree and random forest. Using our proposed model,
we show that previous sleep state and heart rates are significant predictors
for future sleep states. Simulation studies also show that our proposed method
is promising and robust. To handle computational complexity, we utilize Laplace
approximation, golden section search and successive parabolic interpolation.
With this paper, we also submit an R-package (HIBITS) that implements the
proposed procedure.Comment: Journal of Classification (2018
Bayesian Deep Net GLM and GLMM
Deep feedforward neural networks (DFNNs) are a powerful tool for functional
approximation. We describe flexible versions of generalized linear and
generalized linear mixed models incorporating basis functions formed by a DFNN.
The consideration of neural networks with random effects is not widely used in
the literature, perhaps because of the computational challenges of
incorporating subject specific parameters into already complex models.
Efficient computational methods for high-dimensional Bayesian inference are
developed using Gaussian variational approximation, with a parsimonious but
flexible factor parametrization of the covariance matrix. We implement natural
gradient methods for the optimization, exploiting the factor structure of the
variational covariance matrix in computation of the natural gradient. Our
flexible DFNN models and Bayesian inference approach lead to a regression and
classification method that has a high prediction accuracy, and is able to
quantify the prediction uncertainty in a principled and convenient way. We also
describe how to perform variable selection in our deep learning method. The
proposed methods are illustrated in a wide range of simulated and real-data
examples, and the results compare favourably to a state of the art flexible
regression and classification method in the statistical literature, the
Bayesian additive regression trees (BART) method. User-friendly software
packages in Matlab, R and Python implementing the proposed methods are
available at https://github.com/VBayesLabComment: 35 pages, 7 figure, 10 table
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