Derive censoring logprob from minimum, maximum, rounding and casting operations#8363
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Derive censoring logprob from minimum, maximum, rounding and casting operations#8363ricardoV94 wants to merge 4 commits into
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- Infer logprob of maximum/minimum censoring
- Infer logprob of trunc and round_half_away_from_zero rounding
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## main #8363 +/- ##
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- Coverage 91.79% 87.42% -4.38%
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Files 128 128
Lines 21007 21068 +61
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- Hits 19283 18418 -865
- Misses 1724 2650 +926
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The rewrite claimed any measurable base and derived the mass of the interval a continuous variable would round into. That interval is only the right one for a continuous base, and the dtype does not settle the question in either direction. A base that already sits on the integers is left untouched by every rounding, save for the upcast the Ops apply to a discrete input. Deriving the mass of the resulting degenerate cell shifted it by one: floor of a poisson(3) at 3 returned the mass of 4. Reducing the rounding to that cast instead leaves the base's own logprob to apply, and also covers a rounding of a rounding, which used to be declined. A float dtype, on the other hand, does not establish continuity, as an intermediate MeasurableVariable can be supported on the integers while carrying one. Rounding a clipped variable pooled the mass at its upper bound into the neighbouring cell and left the bound with a probability of zero: floor(clip(normal(0.5, 1), 0, 3)) at 3 returned -inf instead of log(P(x >= 3)) = -5.08. Only a RandomVariable states its own support, so other bases are now declined rather than assumed continuous.
maximum(x, c) and minimum(x, c) with a single measurable operand are rewritten to one-sided clips (both-measurable graphs are order statistics and are not claimed), reusing the existing clip machinery for the discrete and continuous cases alike. The unbounded side uses the measurable variable itself as its bound, which find_measurable_clips already understood as one-sided clipping and which, unlike +-inf constants, does not upcast discrete variables (previously one-sided clips of discrete variables failed to be claimed for this reason). Whether each side is bounded is decided once at claim time and stored on the MeasurableClip op. Clips of clips are fused eagerly into a single clip by combining the bounds with maximum/minimum (constant bounds fold), so two-sided censoring like maximum(minimum(x, ub), lb) becomes one node. logcdf/icdf are also implemented for clipped variables (the point masses at the bounds absorb the tail quantiles).
Truncation towards zero is the interval [x, x+1) for positive values, (x-1, x] for negative ones, and (-1, 1) pooled at zero. Rounding half away from zero shares the intervals of round half to even, since the tie-breaking rule only differs on a measure-zero set of the continuous base variable.
A float -> int cast rounds towards zero, so it is the `trunc` a user could have written themselves composed with a cast that only relabels the dtype. Rewriting it to that form leaves the judgement of whether the base may be truncated to `find_measurable_roundings`, and the relabelling cast is then claimed as measure-preserving. The other narrowing casts are not truncations and stay unclaimed: casting to an unsigned int wraps around for negative values (-2.7 -> 254 for uint8), and casting to bool tests `x != 0`, which collapses the support onto two points rather than partitioning it. `round_logprob` snaps the value onto the cell whose mass it asks for, and the Op it uses to do so rejects the integer value that a cast to int hands it. The snapping is an identity on such a value, so only its dtype needs adjusting.
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