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Combinatorial Characterizations of the Learnability of Conditional Distributions — arXiv:2610.31890

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.31890
License (as archived): CC0-1.0
Archived: 2026-10-26T20:13:55.672Z
SHA-256 of the archived text: 9d620bf5aa04ab4a2fa7d0b6c21c8fa6b3a89ec96ade214d1100d23cbaeb9cb9
Stable URL of this page: https://metraipolis.com/documento/dc_e439d7130540

How to cite

Combinatorial Characterizations of the Learnability of Conditional Distributions — arXiv:2610.31890 — arXiv (en), https://arxiv.org/abs/2610.31890 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e439d7130540 (Metraipolis archive dc_e439d7130540, sha256 9d620bf5aa04ab4a2fa7d0b6c21c8fa6b3a89ec96ade214d1100d23cbaeb9cb9)

BibTeX

@misc{dce439d7130540,
  title = {Combinatorial Characterizations of the Learnability of Conditional Distributions — arXiv:2610.31890},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.31890},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e439d7130540; sha256 9d620bf5aa04ab4a2fa7d0b6c21c8fa6b3a89ec96ade214d1100d23cbaeb9cb9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.31890. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the PAC-learnability of function classes that map inputs to probability distributions over a finite space. The learner observes i.i.d. input-label pairs, with each label sampled from the conditional distribution of an unknown target hypothesis in the class. We measure learning through excess risk under a bounded proper loss that satisfies two mild assumptions. We introduce the \textbf{fat$_\gamma$Natarajan dimension}, which generalizes both fat$_\gamma$ and Natarajan dimension, and prove that its finiteness at every positive scale is necessary and sufficient for learnability. We also introduce a \textbf{fat$_\gamma$Graph} dimension extending the classical \gra dimension and establish inequalities comparing the two dimensions at different scales, leading to an equivalent characterization of learnability. Finally, we show that a distribution-valued function class is learnable if and only if each of its coordinate classes is learnable in the probabilistic concept model.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.31890 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-26T19:49:03.453Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).