Highly Adaptive Ridge
In this paper we propose the Highly Adaptive Ridge (HAR): a regression method that achieves a $n^{-1/3}$ dimension-free L2 convergence rate in the class of right-continuous functions with square-integrable sectional derivatives. This is a large nonparametric function class that is particularly appropriate for tabular data. HAR is exactly kernel ridge regression with a specific data-adaptive kernel based on a saturated zero-order tensor-product spline basis expansion. We use simulation and real data to confirm our theory. We demonstrate empirical performance better than state-of-the-art algorithms for small datasets in particular.
Code (0)
등록된 구현이 없습니다.
Tasks
regressionSimilar Papers 제목 키워드 기반
Highly Adaptive Principal Component Regression
The Highly Adaptive Lasso (HAL) is a nonparametric regression method that achieves almost dimension-free convergence rates under minimal smoothness assumptions, but its implementation can be computationally prohibitive i…
Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges
Long-span roadway bridges exhibit highly localized structural responses under vehicular loading, making repeated FE analysis computationally expensive for applications such as influence surface generation and structural …
Heterogeneity-Adaptive Diffusion Schrodinger Bridge for PET-Guided Whole-Body MRI Translation
While whole-body multimodal medical imaging scanners have been increasingly recognized for more effective medical applications, the excessive long acquisition time in PET-MR scanning is a major obstacle in more efficient…
Oversampling Divide-and-conquer for Response-skewed Kernel Ridge Regression
The divide-and-conquer method has been widely used for estimating large-scale kernel ridge regression estimates. Unfortunately, when the response variable is highly skewed, the divide-and-conquer kernel ridge regression …
regressionRuyi2 Technical Report
Large Language Models (LLMs) face significant challenges regarding deployment costs and latency, necessitating adaptive computing strategies. Building upon the AI Flow framework, we introduce Ruyi2 as an evolution of our…