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LinearPFN: Amortized Variable Selection for Linear Models with Interactions — arXiv:2610.06580

Source: arXiv
Original: https://arxiv.org/abs/2610.06580
License (as archived): CC0-1.0
Archived: 2026-10-06T05:31:41.917Z
SHA-256 of the archived text: 92143c0a206483512dcd8d22812bf81dd0bad8c43031c31067cd76daab7d2b47
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How to cite

LinearPFN: Amortized Variable Selection for Linear Models with Interactions — arXiv:2610.06580 — arXiv, https://arxiv.org/abs/2610.06580 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_048ff16cce2e (Metraipolis archive dc_048ff16cce2e, sha256 92143c0a206483512dcd8d22812bf81dd0bad8c43031c31067cd76daab7d2b47)

BibTeX

@misc{dc048ff16cce2e,
  title = {LinearPFN: Amortized Variable Selection for Linear Models with Interactions — arXiv:2610.06580},
  howpublished = {arXiv},
  url = {https://arxiv.org/abs/2610.06580},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_048ff16cce2e; sha256 92143c0a206483512dcd8d22812bf81dd0bad8c43031c31067cd76daab7d2b47},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv, https://arxiv.org/abs/2610.06580. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Spike-and-slab regression is a standard Bayesian formulation of variable selection: it returns a posterior distribution over which candidate effects are active rather than a single selected subset, so that every candidate effect carries an inclusion probability. Its cost grows exponentially with the number of candidate effects, so the posterior can be enumerated exactly only when the number of predictors is small. Beyond that reach, the posterior has to be approximated, typically by Markov chain Monte Carlo over the model space, which requires a fresh run for every dataset and, within a fixed budget of steps, may fail to converge. We present LinearPFN, a prior-data fitted transformer network that amortizes spike-and-slab inference for linear models with main effects and pairwise interactions. The network is pretrained once on synthetic datasets, drawn from an explicitly specified prior, and a single forward pass over a new dataset returns posterior inclusion probabilities, posterior-mean coefficients and posterior predictive distributions with no per-dataset fitting. The prior is conjugate by design, so that the posterior for each fixed set of active effects has a closed form, and wherever the exact posterior is still computable by enumeration we verify the network's outputs against it. On real predictor matrices from published social-science datasets, with outcomes drawn from the prior so that the true active set is known, LinearPFN attains a higher per-dataset selection AUC and a higher F1 under the median probability model rule than five classical baselines. The lead holds when the coefficients, the interactions or the noise depart from the prior. Code: this https URL . Trained model: this https URL .

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2610.06580 — 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 2026-10-06T05:27:05.897Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).