Compiling Probabilistic Programs for Variable Elimination with Information Flow
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Bibliographic record
Abstract
A key promise of probabilistic programming is the ability to specify rich models using an expressive programming language. However, the expressive power that makes probabilistic programming languages enticing also poses challenges to inference, so much so that specialized approaches to inference ban language features such as recursion. We present an approach to variable elimination and marginal inference for probabilistic programs featuring bounded recursion, discrete distributions, and sometimes continuous distributions. A compiler eliminates probabilistic side effects, using a novel information-flow type system to factorize probabilistic computations and hoist independent subcomputations out of sums or integrals. For a broad class of recursive programs with dynamically recurring substructure, the compiler effectively decomposes a global marginal-inference problem, which may otherwise be intractable, into tractable subproblems. We prove the compilation correct by showing that it preserves denotational semantics. Experiments show that the compiled programs subsume widely used PTIME algorithms for recursive models and that the compilation time scales with the size of the inference problems. As a separate contribution, we develop a denotational, logical-relations model of information-flow types in the novel measure-theoretic setting of probabilistic programming; we use it to prove noninterference and consequently the correctness of variable elimination. CCS Concepts: • Theory of computation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>→</mml:mo> </mml:math> Probabilistic computation; Program semantics; Program reasoning; Type theory; • Mathematics of computing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>→</mml:mo> </mml:math> Bayesian computation; Statistical software; • Computing methodologies <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>→</mml:mo> </mml:math> Machine learning; • Software and its engineering <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mo>→</mml:mo> </mml:math> Compilers; Functional languages; Language features; Formal language definitions .
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it