# Calibrated Multivariate Regression with Application to Neural Semantic Basis Discovery

arXiv: https://arxiv.org/abs/1305.2238 · HTML: https://mlsanity.com/paper/1305.2238/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2013.

## Built on by (most cited first, 2 of 2)

- [Deep Learning Assisted End-to-End Synthesis of mm-Wave Passive Networks with 3D EM Structures: A Study on A Transformer-Based Matching Network](https://mlsanity.com/paper/2201.02141/) (2022)
- [Pivotal Estimation of Linear Discriminant Analysis in High Dimensions](https://mlsanity.com/paper/2309.09831/) (2023)

## Abstract (arXiv)

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/ε), where ε 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 textttcamel implementing the proposed method is available on the Comprehensive R Archive Network urlhttp://cran.r-project.org/web/packages/camel/.