Optimal Distributed Quantizer Design for Binary Classification of Conditionally Independent Vector Sources
Bibliographic record
Abstract
This work addresses the scenario where two dis-tributed sensor nodes encode the input vectors and send their messages to a server node where a joint decoder outputs one of two possible class labels. We assume that the vector sources are discrete and conditionally independent given the class label. The problem is to design the two encoders and the joint decoder such that the probability of classification error is minimized. Up to our knowledge, the only known globally optimal solution to this prob-lem is an exhaustive search, which requires$N^{K_{1}+K_{2}}(N+K_{1}K_{2})$operations, where$N$is the size of the largest alphabet of the input vectors and$K_{k}$is the number of quantizer regions of the encoder at node$k$, for$k=1,2$. We propose a considerably faster globally optimal solution with time complexity$O(K_{1}K_{2}N^{3})$. To achieve this, we first convert the problem to a distributed scalar quantizer design problem in a transformed domain related to the likelihood ratio domain. Next, we prove that the problem is equivalent to a constrained minimum weight path problem in a certain weighted directed acyclic graph with$O(N^{3})$vertices and$O(N^{4})$edges. Further, we show that the dynamic programming solution algorithm to the latter problem can be accelerated by leveraging a fast matrix search technique in matrices with the Monge property.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".