6,043 research outputs found
Sparse Probit Linear Mixed Model
Linear Mixed Models (LMMs) are important tools in statistical genetics. When
used for feature selection, they allow to find a sparse set of genetic traits
that best predict a continuous phenotype of interest, while simultaneously
correcting for various confounding factors such as age, ethnicity and
population structure. Formulated as models for linear regression, LMMs have
been restricted to continuous phenotypes. We introduce the Sparse Probit Linear
Mixed Model (Probit-LMM), where we generalize the LMM modeling paradigm to
binary phenotypes. As a technical challenge, the model no longer possesses a
closed-form likelihood function. In this paper, we present a scalable
approximate inference algorithm that lets us fit the model to high-dimensional
data sets. We show on three real-world examples from different domains that in
the setup of binary labels, our algorithm leads to better prediction accuracies
and also selects features which show less correlation with the confounding
factors.Comment: Published version, 21 pages, 6 figure
Differential Privacy Applications to Bayesian and Linear Mixed Model Estimation
We consider a particular maximum likelihood estimator (MLE) and a computationally-intensive Bayesian method for differentially private estimation of the linear mixed-effects model (LMM) with normal random errors. The LMM is important because it is used in small area estimation and detailed industry tabulations that present significant challenges for confidentiality protection of the underlying data. The differentially private MLE performs well compared to the regular MLE, and deteriorates as the protection increases for a problem in which the small-area variation is at the county level. More dimensions of random effects are needed to adequately represent the time- dimension of the data, and for these cases the differentially private MLE cannot be computed. The direct Bayesian approach for the same model uses an informative, but reasonably diffuse, prior to compute the posterior predictive distribution for the random effects. The differential privacy of this approach is estimated by direct computation of the relevant odds ratios after deleting influential observations according to various criteria
Tensor Regression with Applications in Neuroimaging Data Analysis
Classical regression methods treat covariates as a vector and estimate a
corresponding vector of regression coefficients. Modern applications in medical
imaging generate covariates of more complex form such as multidimensional
arrays (tensors). Traditional statistical and computational methods are proving
insufficient for analysis of these high-throughput data due to their ultrahigh
dimensionality as well as complex structure. In this article, we propose a new
family of tensor regression models that efficiently exploit the special
structure of tensor covariates. Under this framework, ultrahigh dimensionality
is reduced to a manageable level, resulting in efficient estimation and
prediction. A fast and highly scalable estimation algorithm is proposed for
maximum likelihood estimation and its associated asymptotic properties are
studied. Effectiveness of the new methods is demonstrated on both synthetic and
real MRI imaging data.Comment: 27 pages, 4 figure
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