The Probabilistic Convolution Tree: Efficient Exact Bayesian Inference for Faster LC-MS/MS Protein Inference
Bibliographic record
Abstract
Exact Bayesian inference can sometimes be performed efficiently for special cases where a function has commutative and associative symmetry of its inputs (called "causal independence"). For this reason, it is desirable to exploit such symmetry on big data sets. Here we present a method to exploit a general form of this symmetry on probabilistic adder nodes by transforming those probabilistic adder nodes into a probabilistic convolution tree with which dynamic programming computes exact probabilities. A substantial speedup is demonstrated using an illustration example that can arise when identifying splice forms with bottom-up mass spectrometry-based proteomics. On this example, even state-of-the-art exact inference algorithms require a runtime more than exponential in the number of splice forms considered. By using the probabilistic convolution tree, we reduce the runtime to O(k log(k)2) and the space to O(k log(k)) where k is the number of variables joined by an additive or cardinal operator. This approach, which can also be used with junction tree inference, is applicable to graphs with arbitrary dependency on counting variables or cardinalities and can be used on diverse problems and fields like forward error correcting codes, elemental decomposition, and spectral demixing. The approach also trivially generalizes to multiple dimensions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.003 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".