2022/06/16 by Alexander Lambert, Lambert, Alex, Dimitri Bouche +5
Engineering · Mathematics · #Algorithm #Artificial intelligence #Computer science #Context (archaeology) #Control Systems and Identification #Convolution (computer science) #Discrete mathematics #Duality (order theory) #Focus (optics) #Kernel (algebra) #Leverage (statistics) #Mathematical optimization #Mathematics #Numerical methods in inverse problems #Outlier #Regression #Sparse and Compressive Sensing Techniques #Statistics
paper · pdf · doi:10.48550/arxiv.2206.08220
openalex publication_date 2022/06/16 · openalex created_date 2022/06/19 · openalex updated_date 2026/08/05
The focus of the paper is functional output regression (FOR) with convoluted losses. While most existing work consider the square loss setting, we leverage extensions of the Huber and the ε-insensitive loss (induced by infimal convolution) and propose a flexible framework capable of handling various forms of outliers and sparsity in the FOR family. We derive computationally tractable algorithms relying on duality to tackle the resulting tasks in the context of vector-valued reproducing kernel Hilbert spaces. The efficiency of the approach is demonstrated and contrasted with the classical squared loss setting on both synthetic and real-world benchmarks.