2,870 research outputs found
Tensor-on-tensor regression
We propose a framework for the linear prediction of a multi-way array (i.e.,
a tensor) from another multi-way array of arbitrary dimension, using the
contracted tensor product. This framework generalizes several existing
approaches, including methods to predict a scalar outcome from a tensor, a
matrix from a matrix, or a tensor from a scalar. We describe an approach that
exploits the multiway structure of both the predictors and the outcomes by
restricting the coefficients to have reduced CP-rank. We propose a general and
efficient algorithm for penalized least-squares estimation, which allows for a
ridge (L_2) penalty on the coefficients. The objective is shown to give the
mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for
inference. We illustrate the approach with an application to facial image data.
An R package is available at https://github.com/lockEF/MultiwayRegression .Comment: 33 pages, 3 figure
Prediction with Dimension Reduction of Multiple Molecular Data Sources for Patient Survival
Predictive modeling from high-dimensional genomic data is often preceded by a
dimension reduction step, such as principal components analysis (PCA). However,
the application of PCA is not straightforward for multi-source data, wherein
multiple sources of 'omics data measure different but related biological
components. In this article we utilize recent advances in the dimension
reduction of multi-source data for predictive modeling. In particular, we apply
exploratory results from Joint and Individual Variation Explained (JIVE), an
extension of PCA for multi-source data, for prediction of differing response
types. We conduct illustrative simulations to illustrate the practical
advantages and interpretability of our approach. As an application example we
consider predicting survival for Glioblastoma Multiforme (GBM) patients from
three data sources measuring mRNA expression, miRNA expression, and DNA
methylation. We also introduce a method to estimate JIVE scores for new samples
that were not used in the initial dimension reduction, and study its
theoretical properties; this method is implemented in the R package R.JIVE on
CRAN, in the function 'jive.predict'.Comment: 11 pages, 9 figure
A methodology for small scale rural land use mapping in semi-arid developing countries using orbital imagery. 2: Capabilities of remote sensing techniques for land use surveys
There are no author-identified significant results in this report
A methodology for small scale rural land use mapping in semi-arid developing countries using orbital imagery. Part 6: A low-cost method for land use mapping using simple visual techniques of interpretation
The author has identified the following significant results. It was found that color composite transparencies and monocular magnification provided the best base for land use interpretation. New methods for determining optimum sample sizes and analyzing interpretation accuracy levels were developed. All stages of the methodology were assessed, in the operational sense, during the production of a 1:250,000 rural land use map of Murcia Province, Southeast Spain
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