25,120 research outputs found
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
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
Deep Exponential Families
We describe \textit{deep exponential families} (DEFs), a class of latent
variable models that are inspired by the hidden structures used in deep neural
networks. DEFs capture a hierarchy of dependencies between latent variables,
and are easily generalized to many settings through exponential families. We
perform inference using recent "black box" variational inference techniques. We
then evaluate various DEFs on text and combine multiple DEFs into a model for
pairwise recommendation data. In an extensive study, we show that going beyond
one layer improves predictions for DEFs. We demonstrate that DEFs find
interesting exploratory structure in large data sets, and give better
predictive performance than state-of-the-art models
Bayesian variable selection using cost-adjusted BIC, with application to cost-effective measurement of quality of health care
In the field of quality of health care measurement, one approach to assessing
patient sickness at admission involves a logistic regression of mortality
within 30 days of admission on a fairly large number of sickness indicators (on
the order of 100) to construct a sickness scale, employing classical variable
selection methods to find an ``optimal'' subset of 10--20 indicators. Such
``benefit-only'' methods ignore the considerable differences among the sickness
indicators in cost of data collection, an issue that is crucial when admission
sickness is used to drive programs (now implemented or under consideration in
several countries, including the U.S. and U.K.) that attempt to identify
substandard hospitals by comparing observed and expected mortality rates (given
admission sickness). When both data-collection cost and accuracy of prediction
of 30-day mortality are considered, a large variable-selection problem arises
in which costly variables that do not predict well enough should be omitted
from the final scale. In this paper (a) we develop a method for solving this
problem based on posterior model odds, arising from a prior distribution that
(1) accounts for the cost of each variable and (2) results in a set of
posterior model probabilities that corresponds to a generalized cost-adjusted
version of the Bayesian information criterion (BIC), and (b) we compare this
method with a decision-theoretic cost-benefit approach based on maximizing
expected utility. We use reversible-jump Markov chain Monte Carlo (RJMCMC)
methods to search the model space, and we check the stability of our findings
with two variants of the MCMC model composition () algorithm.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS207 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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