67 research outputs found
Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery
We propose a calibrated multivariate regression method named CMR for fitting
high dimensional multivariate regression models. Compared with existing
methods, CMR calibrates regularization for each regression task with respect to
its noise level so that it simultaneously attains improved finite-sample
performance and tuning insensitiveness. Theoretically, we provide sufficient
conditions under which CMR achieves the optimal rate of convergence in
parameter estimation. Computationally, we propose an efficient smoothed
proximal gradient algorithm with a worst-case numerical rate of convergence
\cO(1/\epsilon), where is a pre-specified accuracy of the
objective function value. We conduct thorough numerical simulations to
illustrate that CMR consistently outperforms other high dimensional
multivariate regression methods. We also apply CMR to solve a brain activity
prediction problem and find that it is as competitive as a handcrafted model
created by human experts. The R package \texttt{camel} implementing the
proposed method is available on the Comprehensive R Archive Network
\url{http://cran.r-project.org/web/packages/camel/}.Comment: Journal of Machine Learning Research, 201
Learning to rank from medical imaging data
Medical images can be used to predict a clinical score coding for the
severity of a disease, a pain level or the complexity of a cognitive task. In
all these cases, the predicted variable has a natural order. While a standard
classifier discards this information, we would like to take it into account in
order to improve prediction performance. A standard linear regression does
model such information, however the linearity assumption is likely not be
satisfied when predicting from pixel intensities in an image. In this paper we
address these modeling challenges with a supervised learning procedure where
the model aims to order or rank images. We use a linear model for its
robustness in high dimension and its possible interpretation. We show on
simulations and two fMRI datasets that this approach is able to predict the
correct ordering on pairs of images, yielding higher prediction accuracy than
standard regression and multiclass classification techniques
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