Learning Conditional Expectation Operators via Functional Newton Updates
We introduce the Functional Spectral-Newton Method (FSNM) for learning the leading singular structure of a conditional expectation operator without fixing a basis or reproducing kernel Hilbert space. FSNM fits a low-rank representation of the centered joint-to-product density ratio kernel by alternating functional Newton updates. Each update reduces to a preconditioned regression, which we approximate with vector-valued regression trees in a stagewise boosting procedure. At the population level, we establish descent and an $O(1/T)$ best-iterate block-stationarity rate under a relative weak-learner accuracy condition, and show that every nondegenerate local minimum over the full centered $...
| Authors | Thiago Ramos, Alek Fröhlich, Daniel Perazzo et al. |
|---|---|
| Primary category | stat.ML |
| Published | 28 September 2026 |
| Last updated at source | 28 September 2026 |
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