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弹性核岭回归及其语音学应用AI 解读

Predicting the shapes of entire curves requires accounting for nonlinear geometry and unknown alignments between curves. We develop elastic kernel ridge regression, a nonparametric method for planar curve responses with scalar, multivariate, or functional covariates. Using square-root velocity representations, we formulate penalized conditional Fréchet mean estimation in a shape space invariant to translation, rotation, scaling, and reparametrization. A vector-valued…

无穷维球面核岭回归AI 解读

We introduce a novel regression framework designed to model non-linear responses situated on a sphere $\mathbb{S}$ of finite or infinite dimension. Unlike traditional tangent-space regressions, which lift responses to a tangent space $T_o \mathbb{S}$ and thereby violate intrinsic spherical distances, our proposed method employs an intrinsic approach. We model the conditional mean through an intercept $o \in \mathbb{S}$ and a linear predictor function $f: \mathfrak{X} \to T_o \mathbb{S}$…