Vector-Valued Least-Squares Regression under Output Regularity Assumptions
This work addresses regression problems with complex outputs for fields like computer vision and bioinformatics, but it is incremental as it extends existing reduced-rank methods to more general assumptions.
The authors tackled least-squares regression with infinite-dimensional output by proposing a reduced-rank method, deriving learning bounds and showing improved statistical performance under output regularity assumptions compared to full-rank methods, with benefits demonstrated on synthetic problems and applications like image reconstruction and multi-label classification.
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in comparison to full-rank method. Our analysis extends the interest of reduced-rank regression beyond the standard low-rank setting to more general output regularity assumptions. We illustrate our theoretical insights on synthetic least-squares problems. Then, we propose a surrogate structured prediction method derived from this reduced-rank method. We assess its benefits on three different problems: image reconstruction, multi-label classification, and metabolite identification.