arXiv：cs.LG（机器学习，全量分类）· Kyle Ritscher, Carlos Llosa-Vite·· 13 小时前AI 评分26
异方差 CP 张量分解 HCP：用低秩精度张量建模逐元素噪声
Heteroskedastic Canonical Polyadic Tensor Decomposition
AI 导读
研究者提出异方差-CP（HCP），在 CP 分解中用非恒定、低秩的精度张量建模张量各元素的噪声方差，并给出交替块坐标上升法，从含噪观测中同时恢复低秩均值张量与精度张量。该方法计算开销与 CP-ALS 同阶，在合成实验和一项 EEG 应用中做了验证。
正文
Abstract:When minimizing the squared-error loss, the popular CP decomposition can be interpreted as parameter inference in a Gaussian model with a low-rank mean tensor and constant variance across the tensor entries. We introduce heteroskedastic-CP (HCP), which models entrywise variability with a non-constant, low-rank precision tensor, and develop an alternating block-coordinate ascent method to recover both the low-rank mean and precision tensors from noisy observations. Our procedure is computationally competitive, with the same leading-order factor-update complexity as CP-ALS. We demonstrate HCP on synthetic experiments and an EEG application.
| Comments: | 35 pages, 16 figures |
| Subjects: | Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML) |
| Report number: | SAND2026-27105O |
| Cite as: | arXiv:2610.00498 [stat.ME] |
| (or arXiv:2610.00498v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2610.00498 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Kyle Ritscher [view email]
[v1]
Wed, 30 Sep 2026 18:01:09 UTC (3,572 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org