Fix FullSupportBarDistribution tail sampling and quantiles

[ppguo]

Summary

• make FullSupportBarDistribution.cdf() and icdf() use the half-normal outer components already used by forward()
• sample the outer components from their half-normal tails and keep uniform sampling for interior buckets
• preserve batch shape, device, dtype, and temperature behavior with vectorized sampling
• leave bounded BarDistribution unchanged

Fixes #1200

Rationale

The original PFN paper defines both bounded and infinite-support Riemann distributions (arXiv:2112.10510). FullSupportBarDistribution is the infinite-support form used by the regression checkpoints: its existing forward() already evaluates the two outer components as half-normal tails, but inherited cdf(), icdf(), and the old sample() kept all mass within the finite borders.

For a component-conditional probability r, this change uses b_1 - H_L^{-1}(1-r) in the left tail and b_{K-1} + H_R^{-1}(r) in the right tail. Interior buckets retain linear interpolation.

With borders [-2, -1, 1, 2] and component probabilities [0.25, 0.50, 0.25]:

• before: 0/20,000 samples were outside [-2, 2], although the reported density assigns 25% mass there
• after: 4,934/20,000 samples are outside (0.2467); empirical-CDF KS distance is 0.00716 to the documented full-support law versus 0.1266 to the old finite law
• analytic checks now give icdf(0.125) == -2 and icdf(0.875) == 2

Public behavior

This is a public behavior correction: sample(), cdf(), quantiles, median/UCB, and the class's border translation now agree with the existing full-support log density. Samples from the outer components can now lie beyond the finite borders.

There are no function-signature, checkpoint-format, state-dict, border, component-probability, or forward()/log-density changes.

Tests

Validated in an isolated Linux CPU/CUDA environment with Python 3.10.18, PyTorch 2.6.0+cu124, pytest 8.4.2, and Ruff 0.15.12:

• pytest tests/test_architectures/test_bar_distribution.py with CUDA excluded: 19 passed
• pytest tests/test_architectures/test_bar_distribution.py with CPU excluded on CUDA: 19 passed
• ruff check src/tabpfn/architectures/shared/bar_distribution.py tests/test_architectures/test_bar_distribution.py: passed
• ruff format --check src/tabpfn/architectures/shared/bar_distribution.py tests/test_architectures/test_bar_distribution.py: passed
• independent 20,000-sample tail-bucket audit: outside mass 0.2467, full-support KS 0.00716

tests/test_architectures/test_bar_distribution.py is the repository's existing bar-distribution test file; this PR adds the full-support regression cases there. They cover analytic tail checkpoints, CDF/ICDF round trips including probabilities 0 and 1, float32 cumulative-probability roundoff, interior buckets and borders, inherited quantile helpers and border translation, 1D and multidimensional batches, float32/float64, CPU/CUDA, and empirical tail mass/CDF. The repository's full CI suite is separate from these targeted runs.

Follow-up audit

The default regressor also has a standalone finite _cdf() path in utils.translate_probs_across_borders(), and target preprocessing can use the nonlinear safepower transform. Those paths are intentionally unchanged here so this fix stays scoped to FullSupportBarDistribution; maintainers can decide whether they should be addressed in a follow-up PR.

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[Copilot]

Pull request overview

This pull request corrects FullSupportBarDistribution so its cdf(), icdf(), and sample() behavior matches the half-normal tail construction already implemented in forward() (log-density), bringing sampling/quantiles/CDF into agreement for infinite-support regression checkpoints.

Changes:

• Override FullSupportBarDistribution.cdf() and icdf() to use half-normal tails in the two outer buckets while keeping interior buckets as within-bin interpolation.
• Rework FullSupportBarDistribution.sample() to sample outer buckets from half-normal tails and interior buckets uniformly, preserving batch shape/device/dtype without Python loops.
• Add regression tests covering analytic checkpoints, CDF/ICDF round-trips, inherited quantile helpers, border-probability translation, and sampling tail mass; add a changelog entry.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated no comments.

File	Description
tests/test_architectures/test_bar_distribution.py	Adds regression tests ensuring full-support CDF/ICDF/sampling match the half-normal tail law and preserve shape/device/dtype.
src/tabpfn/architectures/shared/bar_distribution.py	Implements full-support CDF/ICDF and vectorized tail-aware sampling for FullSupportBarDistribution.
changelog/1215.fixed.md	Documents the public behavior fix for full-support CDF/quantiles/sampling.

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[oscarkey]

hey @eliott-kalfon, I'm happy to take the review on this one, as I was assigned the original ticket, unless you would like to!

[eliott-kalfon]

hey @eliott-kalfon, I'm happy to take the review on this one, as I was assigned the original ticket, unless you would like to!

Hey Oscar, that would nice thanks. Happy to double check after you too :)

[oscarkey]

hey @ppguo , sorry it's taking so long for me to get to this PR, it has been a busy couple of weeks. But I will review it as soon as possible.