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Minimum MS. E. Gerber's Lemma

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Or Ordentlich, Ofer Shayevitz

Information Theory · Submitted 31 May 2015

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that in many cases our bound is tighter than the one obtained from Mrs. Gerber's Lemma.

how it is stated · asserted 0.94 read the record →

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arXiv ID1506.00253 (version 1)
Pith IDAM4CZ7XD, Pith's permanent record of this paper and its review
CitationOfer Shayevitz, Or Ordentlich. "Minimum MS. E. Gerber's Lemma." arXiv:1506.00253 (2015). https://pith.science/paper/AM4CZ7XD
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,135 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.19 · human participants 0.02 · controlled comparison 0.32 · randomized assignment 0.01 · states quantitative result 0.48 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Mrs. Gerber's Lemma lower bounds the entropy at the output of a binary symmetric channel in terms of the entropy of the input process. In this paper, we lower bound the output entropy via a different measure of input uncertainty, pertaining to the minimum mean squared error (MMSE) prediction cost of the input process. We show that in many cases our bound is tighter than the one obtained from Mrs. Gerber's Lemma. As an application, we evaluate the bound for binary hidden Markov processes, and obtain new estimates for the entropy rate.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Mrs. background 0.96 0.02 0.01 unclear 1.00
s1 Gerber's Lemma lower bounds the entropy at the output of a binary symmetric channel in terms of the entropy of the input process. background 1.00 0.05 0.11 asserted 1.00
s2 In this paper, we lower bound the output entropy via a different measure of input uncertainty, pertaining to the minimum mean squared error (MMSE) prediction cost of the input process. contribution 0.81 0.93 0.27 asserted 1.00
s3 We show that in many cases our bound is tighter than the one obtained from Mrs. Gerber's Lemma. result 0.97 0.94 0.51 asserted 0.94
s4 As an application, we evaluate the bound for binary hidden Markov processes, and obtain new estimates for the entropy rate. contribution 0.58 0.96 0.10 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • full text
  • figures and tables
  • references and citing sentences
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  • P abstract
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  • S sections
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  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Mrs. Gerber's Lemma lower bounds the entropy at the output of a binary symmetric channel in terms of the entropy of the input process. In this paper, we lower bound the output entropy via a different measure of input uncertainty, pertaining to the minimum mean squared error (MMSE) prediction cost of the input process. We show that in many cases our bound is tighter than the one obtained from Mrs. Gerber's Lemma. As an application, we evaluate the bound for binary hidden Markov processes, and obtain new estimates for the entropy rate.

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