Pith. Sign in

RECORD

Unnormalized Measures in Information Theory

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Peter Harremoës

Information Theory · Submitted 6 Feb 2022

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

The authors' main claim We claim that the main reason to normalize measures is that probability measures are related to codes via Kraft's inequality.

how it is stated · asserted 0.96 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2202.02668 (version 1)
Pith IDFLJTM2VM, Pith's permanent record of this paper and its review
CitationPeter Harremo\"es. "Unnormalized Measures in Information Theory." arXiv:2202.02668 (2022). https://pith.science/paper/FLJTM2VM
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,384 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.13 · human participants 0.03 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.20 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that the main reason to normalize measures is that probability measures are related to codes via Kraft's inequality. Using a minimum description length approach to statistics we will demonstrate with that measures that are not normalized require a new interpretation that we will call the Poisson interpretation. With the Poisson interpretation many problems can be simplified. The focus will shift from from probabilities to mean values. We give examples of improvements of test procedures, improved inequalities, simplified algorithms, new projection results, and improvements in our description of quantum systems.

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 Information theory is built on probability measures and by definition a probability measure has total mass 1. background 1.00 0.04 0.03 asserted 1.00
s1 Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. background 0.97 0.06 0.03 hedged possibility 0.75
s2 We claim that the main reason to normalize measures is that probability measures are related to codes via Kraft's inequality. interpretation 0.43 0.22 0.38 asserted 0.96
s3 Using a minimum description length approach to statistics we will demonstrate with that measures that are not normalized require a new interpretation that we will call the Poisson interpretation. contribution 0.58 0.85 0.21 asserted 1.00
s4 With the Poisson interpretation many problems can be simplified. result 0.55 0.40 0.17 asserted 0.54
s5 The focus will shift from from probabilities to mean values. interpretation 0.92 0.52 0.14 asserted 0.96
s6 We give examples of improvements of test procedures, improved inequalities, simplified algorithms, new projection results, and improvements in our description of quantum systems. contribution 0.59 0.90 0.15 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.47 · evidence from proof or derivation 0.61.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • 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

Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that the main reason to normalize measures is that probability measures are related to codes via Kraft's inequality. Using a minimum description length approach to statistics we will demonstrate with that measures that are not normalized require a new interpretation that we will call the Poisson interpretation. With the Poisson interpretation many problems can be simplified. The focus will shift from from probabilities to mean values. We give examples of improvements of test procedures, improved inequalities, simplified algorithms, new projection results, and improvements in our description of quantum systems.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 5 sentences without a confident label

Builds on 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.