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Model Criticism via Stochastic Optimization — arXiv:2610.37837

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.37837
License (as archived): CC0-1.0
Archived: 2026-11-01T02:31:04.928Z
SHA-256 of the archived text: b595dafa44bb8b98d7491fc674691e2782034e9e7924b8bbd34283b8520d6eca
Stable URL of this page: https://metraipolis.com/documento/dc_7ccd160bd46d

How to cite

Model Criticism via Stochastic Optimization — arXiv:2610.37837 — arXiv (en), https://arxiv.org/abs/2610.37837 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7ccd160bd46d (Metraipolis archive dc_7ccd160bd46d, sha256 b595dafa44bb8b98d7491fc674691e2782034e9e7924b8bbd34283b8520d6eca)

BibTeX

@misc{dc7ccd160bd46d,
  title = {Model Criticism via Stochastic Optimization — arXiv:2610.37837},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.37837},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7ccd160bd46d; sha256 b595dafa44bb8b98d7491fc674691e2782034e9e7924b8bbd34283b8520d6eca},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.37837. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Many generative models are specified by how data are simulated. An observation is a deterministic transform $Y=G(\theta,X)$ of a draw $X$ from an assumed noise law, indexed by a structural parameter $\theta$. Such models cover discrete, continuous and functional data, as well as i.i.d. replicates of stochastic processes, but their likelihoods are often unavailable. We propose a simulation-based procedure that tests whether such a model fits the data and, when it does not, locates where it fails, without choosing a test statistic. The procedure splits the data in two and is formulated as a two-stage stochastic program. In the estimation stage, $\theta$ is fitted on the first block by minimizing a Wasserstein distance between the data and simulations from the model. In the recourse stage, $\theta$ is frozen at the fitted $\tilde{\theta}$, and a finite set of representative noise values $\{\bar x_j\}$ is pushed through the fitted mechanism to give model atoms $G(\tilde{\theta},\bar x_j)$. The held-out block optimizes weights $\textbf{w}$ on the model atoms to best match its own distribution. The optimized weights are then compared with theoretical weights under correct specification. Since each model atom is the image of known noise values, the disagreement between optimal and theoretical weights points to the part of the noise law that is wrong. The split makes the scaled weights conditionally multinomial, yielding a calibrated Pearson test. We prove strong consistency of both stages under checkable assumptions and illustrate the procedure on a Gaussian location--scale family, the number of segregating sites under Kingman's coalescent, a Yule process, and an Ornstein--Uhlenbeck diffusion.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ME, nuovi lavori del giorno).
Categorie arXiv: Methodology (stat.ME) ; Computation (stat.CO).
Pagina del lavoro: https://arxiv.org/abs/2610.37837 — 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 2026-11-01T02:13:43.966Z dalla pagina https://arxiv.org/list/stat.ME/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).