Can Metadata Fix the Gauge? Calibration Turns Sparse Multi-Source Learning from Sparse PCA into Sparse Mean Recovery
Source labels tell us where a sample came from, but not how that source oriented its coordinates. In a sparse Gaussian multi-source model with source-specific sign gauges, that distinction changes the learning problem. Without calibration, pooling across sources erases the mean signal, and the source-labelled experiment reduces to sparse PCA. With task-independent relative-gauge metadata, synchronization aligns sources and the same observations become a sparse mean problem. We formalize the value of metadata through AlignedMass, which quantifies how much first-order signal a metadata-induced alignment restores. Source labels create only limited AlignedMass, whereas valid calibration can c...
| Authors | Yirong Xiang, Yibo Zhou |
|---|---|
| Primary category | cs.LG |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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