Reducing subspace models for large-scale covariance regression.

@article{Franks2021ReducingSM,
  title={Reducing subspace models for large-scale covariance regression.},
  author={Alexander M. Franks},
  journal={Biometrics},
  year={2021}
}
We develop an envelope model for joint mean and covariance regression in the large p, small n setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we focus on identifying covariance heterogeneity by incorporating information about mean-level differences. We use a Monte Carlo EM algorithm to identify a low-dimensional subspace which explains differences in both means and covariances as a function of covariates… Expand

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References

SHOWING 1-10 OF 73 REFERENCES
Shared Subspace Models for Multi-Group Covariance Estimation
We develop a model-based method for evaluating heterogeneity among several p x p covariance matrices in the large p, small n setting. This is done by assuming a spiked covariance model for each groupExpand
Bayesian nonparametric covariance regression
TLDR
This work proposes to reduce dimensionality and induce a flexible Bayesian nonparametric covariance regression model by relating these location-specific trajectories to a lower-dimensional subspace through a latent factor model with predictor-dependent factor loadings. Expand
Covariance reducing models : An alternative to spectral modelling of covariance matrices
We introduce covariance reducing models for studying the sample covariance matrices of a random vector observed in different populations. The models are based on reducing the sample covarianceExpand
A Bayesian approach for envelope models
The envelope model is a new paradigm to address estimation and prediction in multivariate analysis. Using sufficient dimension reduction techniques, it has the potential to achieve substantialExpand
ESTIMATION OF MULTIVARIATE MEANS WITH HETEROSCEDASTIC ERRORS USING ENVELOPE MODELS
In this article, we propose envelope models that accommodate het- eroscedastic error structure in the framework of estimating multivariate means for di!erent populations. Envelope models wereExpand
ENVELOPE MODELS FOR PARSIMONIOUS AND EFFICIENT MULTIVARIATE LINEAR REGRESSION
We propose a new parsimonious version of the classical multivariate nor- mal linear model, yielding a maximum likelihood estimator (MLE) that is asymp- totically less variable than the MLE based onExpand
Estimation of covariance matrices based on hierarchical inverse-Wishart priors
This paper focuses on Bayesian shrinkage methods for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchicalExpand
A Covariance Regression Model
Classical regression analysis relates the expectation of a response vari- able to a linear combination of explanatory variables. In this article, we propose a covariance regression model thatExpand
Sparse inverse covariance estimation with the graphical lasso.
TLDR
Using a coordinate descent procedure for the lasso, a simple algorithm is developed that solves a 1000-node problem in at most a minute and is 30-4000 times faster than competing methods. Expand
High-dimensional graphs and variable selection with the Lasso
The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims atExpand
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