20 research outputs found
Multiple imputation for continuous variables using a Bayesian principal component analysis
We propose a multiple imputation method based on principal component analysis
(PCA) to deal with incomplete continuous data. To reflect the uncertainty of
the parameters from one imputation to the next, we use a Bayesian treatment of
the PCA model. Using a simulation study and real data sets, the method is
compared to two classical approaches: multiple imputation based on joint
modelling and on fully conditional modelling. Contrary to the others, the
proposed method can be easily used on data sets where the number of individuals
is less than the number of variables and when the variables are highly
correlated. In addition, it provides unbiased point estimates of quantities of
interest, such as an expectation, a regression coefficient or a correlation
coefficient, with a smaller mean squared error. Furthermore, the widths of the
confidence intervals built for the quantities of interest are often smaller
whilst ensuring a valid coverage.Comment: 16 page
Adaptive Higher-order Spectral Estimators
Many applications involve estimation of a signal matrix from a noisy data
matrix. In such cases, it has been observed that estimators that shrink or
truncate the singular values of the data matrix perform well when the signal
matrix has approximately low rank. In this article, we generalize this approach
to the estimation of a tensor of parameters from noisy tensor data. We develop
new classes of estimators that shrink or threshold the mode-specific singular
values from the higher-order singular value decomposition. These classes of
estimators are indexed by tuning parameters, which we adaptively choose from
the data by minimizing Stein's unbiased risk estimate. In particular, this
procedure provides a way to estimate the multilinear rank of the underlying
signal tensor. Using simulation studies under a variety of conditions, we show
that our estimators perform well when the mean tensor has approximately low
multilinear rank, and perform competitively when the signal tensor does not
have approximately low multilinear rank. We illustrate the use of these methods
in an application to multivariate relational data.Comment: 29 pages, 3 figure
Image denoising based on nonlocal Bayesian singular value thresholding and Stein's unbiased risk estimator
© 1992-2012 IEEE. Singular value thresholding (SVT)- or nuclear norm minimization (NNM)-based nonlocal image denoising methods often rely on the precise estimation of the noise variance. However, most existing methods either assume that the noise variance is known or require an extra step to estimate it. Under the iterative regularization framework, the error in the noise variance estimate propagates and accumulates with each iteration, ultimately degrading the overall denoising performance. In addition, the essence of these methods is still least squares estimation, which can cause a very high mean-squared error (MSE) and is inadequate for handling missing data or outliers. In order to address these deficiencies, we present a hybrid denoising model based on variational Bayesian inference and Stein's unbiased risk estimator (SURE), which consists of two complementary steps. In the first step, the variational Bayesian SVT performs a low-rank approximation of the nonlocal image patch matrix to simultaneously remove the noise and estimate the noise variance. In the second step, we modify the conventional SURE full-rank SVT and its divergence formulas for rank-reduced eigen-triplets to remove the residual artifacts. The proposed hybrid BSSVT method achieves better performance in recovering the true image compared with state-of-the-art methods