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Basics of Multivariate Analysis in Neuroimaging Data
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Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery.

Han Liu1, Lie Wang2, Tuo Zhao

  • 1Department of Operations Research and Financial Engineering, Princeton University, NJ 08544, USA, hanliu@princeton.edu.

Journal of Machine Learning Research : JMLR
|March 21, 2017
PubMed
Summary

We introduce Calibrated Multivariate Regression (CMR), a new method for high-dimensional data. CMR improves performance and reduces tuning sensitivity, outperforming existing techniques in simulations and real-world applications.

Keywords:
brain activity predictioncalibrationhigh dimensionlow Rankmultivariate regressionsparsity

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Area of Science:

  • Statistics
  • Machine Learning
  • Computational Neuroscience

Background:

  • High-dimensional multivariate regression models are crucial in various scientific fields.
  • Existing methods often struggle with performance and sensitivity to tuning parameters.
  • Accurate parameter estimation is essential for reliable data analysis.

Purpose of the Study:

  • To introduce Calibrated Multivariate Regression (CMR), a novel method for fitting high-dimensional multivariate regression models.
  • To enhance both finite-sample performance and tuning insensitiveness compared to existing approaches.
  • To provide theoretical guarantees and efficient computational methods for CMR.

Main Methods:

  • Developed a calibrated regularization strategy that adapts to the noise level of each regression task.
  • Provided theoretical analysis establishing conditions for optimal convergence rates in parameter estimation.
  • Designed an efficient smoothed proximal gradient algorithm with a convergence rate of O(1/ϵ).

Main Results:

  • CMR demonstrates consistent outperformance over other high-dimensional multivariate regression methods in simulations.
  • The method achieves improved finite-sample performance and is less sensitive to tuning parameters.
  • CMR proved competitive with expert-designed models in a brain activity prediction task.

Conclusions:

  • CMR offers a robust and efficient solution for high-dimensional multivariate regression.
  • The method provides theoretical guarantees and practical advantages in performance and usability.
  • The R package 'camel' is available for implementing CMR in diverse applications.