High-Dimensional Nonparametric Change-Point Detection via Low-Rank Degree-Three Density Projection
Distributional changes can be invisible to means and covariances yet appear in skewness, asymmetric interactions, or other third-order structure. We develop a nonparametric change-point method that retains every degree-at-most-three coefficient of a density while avoiding direct density estimation. For observations in $[-1,1]^d$, we construct a symmetric order-three Legendre feature tensor $H_3(X)\in\Sym^3(\R^{d+1})$ such that $A(f)=\E_fH_3(X)$ is an exact isometric encoding of the degree-three density projection: $\|A(f)-A(g)\|_{\F}=\|P_3(f-g)\|_{L^2}$. Instead, fixed tensor contractions are degree-three polynomial chaoses with $ψ_{2/3}$ tails. The two terms have the characteristic order...
| Authors | Guoqing Zhang, Zhaixin Chen |
|---|---|
| Primary category | cs.LG |
| Published | 16 August 2026 |
| Last updated at source | 16 August 2026 |
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