Relate joint, marginal, conditional distributions, entropy, and mutual information.
Core notation for Mutual Information Notation
In information theory, the notation usually represents random variables, alphabets, distributions, code lengths, channels, and logarithm bases. The table below gives a compact starting set for mutual information notation; define any local variation before the first calculation.
| Concept | Notation | How to read it |
|---|---|---|
| Chain rule | H(X,Y)=H(X)+H(Y\mid X) | joint entropy decomposition |
| Entropy | H(X)=-\sum_x p(x)\log p(x) | average uncertainty of X |
| Conditional entropy | H(X\mid Y) | uncertainty remaining after observing Y |
| Mutual information | I(X;Y)=H(X)-H(X\mid Y) | shared information between X and Y |
Practical workflow
Start from H(X,Y)=H(X)+H(Y\mid X) and write one sentence that says it means “joint entropy decomposition.” List the objects and assumptions, evaluate a small example, and then move the verified source into the target document or codebase.
Decisions that must be explicit
- State the logarithm base and resulting unit.
- Distinguish entropy, cross-entropy, and kl divergence.
- Specify discrete sums versus continuous integrals.
Failure checks
- Assuming kl divergence is symmetric.
- Mixing bits and nats in one calculation.
- Using 0 log 0 without the standard limiting convention.
Accessibility and portability
Keep the mutual information notation source selectable and editable. For an isolated character in mutual information notation, Unicode text may be sufficient; for structured expressions, preserve LaTeX, MathML, or a native equation object. When an image of mutual information notation is unavoidable, describe the operation, inputs, conditions, and conclusion rather than listing glyph names.
Verification checklist
- Verify probabilities normalize.
- Test deterministic and uniform distributions.
- Confirm the order of p and q in every divergence.
- Confirm every symbol used in mutual information notation has one defined meaning in the local context.
- Reopen the exported file for Mutual Information Notation and compare it with the editable source.
How this guide was checked
Page purpose: mutual information notation — Understand and apply the topic in mathematical or scientific writing
Automated quality check: Kept noindex until critical findings are resolved.
Verification references
These primary standards and official documentation pages were used to check character identity, syntax, or platform behavior described above.
- The Unicode StandardUnicode Consortium — Character identity, encoding, names, and conformance.
- Unicode Technical Report #25: Unicode Support for MathematicsUnicode Consortium — Mathematical character usage, variants, and notation support.
- LaTeX Project DocumentationThe LaTeX Project — LaTeX syntax, authoring model, and official documentation links.
- MathML CoreW3C — Semantic web mathematics elements and browser behavior.