# High-dimensional nonparametric changepoint detection via low-rank degree-two density projection

arXiv: https://arxiv.org/abs/2608.13922 · HTML: https://mlsanity.com/paper/2608.13922/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 7 of 7)

- [Multiple-change-point detection for high dimensional time series via sparsified binary segmentation](https://mlsanity.com/paper/1611.08639/) (2016)
- [High-dimensional changepoint estimation via sparse projection](https://mlsanity.com/paper/1606.06246/) (2016)
- [Narrowest-Over-Threshold Detection of Multiple Change-points and Change-point-like Features](https://mlsanity.com/paper/1609.00293/) (2016)
- [Optimal nonparametric multivariate change point detection and localization](https://mlsanity.com/paper/1910.13289/) (2019)
- [Seeded Binary Segmentation: A general methodology for fast and optimal change point detection](https://mlsanity.com/paper/2002.06633/) (2020)
- [Change-point Detection for Sparse and Dense Functional Data in General Dimensions](https://mlsanity.com/paper/2205.09252/) (2022)
- [Detecting and dating structural breaks in functional data without dimension reduction](https://mlsanity.com/paper/1511.04020/) (2015)

## Abstract (arXiv)

Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified. We introduce a representation-based approach that retains all degree-at-most-two density information while replacing density estimation by matrix mean estimation. For observations in [-1,1]d, a symmetric feature matrix H2(X)∈R(d+1)×(d+1) is constructed so that M(f)=Ef H2(X) is an isometric encoding of the degree-two orthogonal projection of the density. We scan matrix CUSUMs after rank-r truncation, exploiting the low rank of the projected jump rather than sparsity of individual coordinates. The resulting LRD estimator has a tent-shaped population objective and a nonasymptotic operator-norm analysis whose leading stochastic term scales as √rdlog(nd). For multiple changes, we give a seeded narrowest-over-threshold procedure and prove exact recovery by an induction that preserves an isolating interval for every undetected change. A cross-fitted scalar refinement learns the changing low-rank direction on one fold and localizes on the other, attaining widetilde OPp(kappa-2) error; a matching Le Cam lower bound shows optimality up to logarithms. A geometrically β-mixing extension follows from a dependent matrix Bernstein inequality. Experiments with ambient dimension up to 200, a three-change d=100 sequence, and a 128-feature human-activity benchmark show that the method remains computationally practical and accurately detects pure dependence changes that are invisible to mean CUSUMs.