Vector-Valued Least-Squares Regression under Output Regularity\n Assumptions

2022/11/16 by Luc Brogat-Motte, Alessandro Rudi, Brogat-Motte, Luc +7 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Face and Expression Recognition #Fault Detection and Control Systems #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2211.08958

openalex publication_date 2022/11/16 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28

Abstract

We propose and analyse a reduced-rank method for solving least-squares\nregression problems with infinite dimensional output. We derive learning bounds\nfor our method, and study under which setting statistical performance is\nimproved in comparison to full-rank method. Our analysis extends the interest\nof reduced-rank regression beyond the standard low-rank setting to more general\noutput regularity assumptions. We illustrate our theoretical insights on\nsynthetic least-squares problems. Then, we propose a surrogate structured\nprediction method derived from this reduced-rank method. We assess its benefits\non three different problems: image reconstruction, multi-label classification,\nand metabolite identification.\n

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