Transfer learning for sparse variable selection in high-dimensional regression from quadratic measurement

Abstract

In signal processing, the functional relationship between the unknown parameters and response variables extends to the nonlinear forms. A representative model is the quadratic measurement regression. In high-dimensional scenarios, model complexity poses challenges for estimation and variable selection. In this study, we propose a generic transfer learning algorithm and an automatic transferable source detection algorithm to identify helpful sources for the quadratic measurement regression model. The core idea of the general algorithm is based on pre-training and fine-tuning techniques. To our knowledge, this is the first study that introduces transfer learning into this model. Numerous simulation experiments demonstrated the effectiveness of the proposed transfer learning algorithm. In simulation experiments, the proposed transfer algorithm reduced the square-sum error of the results to approximately 1. On a real-world speech dataset, the proposed algorithm significantly improved the accuracy of the reconstructed signals. In the best-case scenario, the minimum mean square error was reduced to 1/4th of that without transfer. The code is available at https://github.com/Sarkovqx/Transfer-QMR.