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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N^{K_{1}+K_{2}}(N+K_{1}K_{2})$</tex> operations, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> is the size of the largest alphabet of the input vectors and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$K_{k}$</tex> is the number of quantizer regions of the encoder at node <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex>, for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k=1,2$</tex>. We propose a considerably faster globally optimal solution with time complexity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(K_{1}K_{2}N^{3})$</tex>. 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(N^{3})$</tex> vertices and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(N^{4})$</tex> 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 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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".