Vector-Valued Least-Squares Regression under Output Regularity Assumptions. (arXiv:2211.08958v1 [stat.ML])

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 …

arxiv assumptions least regression squares vector