Marginal probability
A marginal probability or distribution describes a variable or event without conditioning on other variables, obtained from a joint distribution by summing or integrating over them.
Outlier Detection in Python
A marginal distribution describes the probability behavior of one variable after accounting for or aggregating over the other variables.
- How it is used
- Detects combinations that are unusual beyond the individual rarity of their feature values.
- How deep it goes
- Explains table margins, expected counts, actual-to-expected ratios, independence assumptions, and detector applications.
- Examples
- Uses contingency tables, missing staff-product combinations, categorical subspaces, and COPOD examples.
- What you can do after
- Evaluate/understand whether a rare combination reflects rare component values or an unexpected relationship among ordinary values.
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Math and Architectures of Deep Learning
The probability distribution for one variable obtained by summing out the other variables from a joint distribution.
- How it is used
- Uses joint distributions to obtain single-variable distributions and support conditional-probability and Bayesian calculations.
- How deep it goes
- Works through discrete table sums, normalization, dependence checks, and Bayes denominators; only briefly extends to continuous variables.
- Examples
- Uses weight-distance tables, weight-height populations, Bayes denominators, and Gaussian mixture component probabilities.
- What you can do after
- Evaluate joint tables, compute marginal distributions, test independence, and identify Bayesian normalization terms.
Read how Math and Architectures of Deep Learning explains marginal probability →
Causal AI
A marginal probability is the probability of a variable or event obtained without conditioning on other variables by summing or integrating them out.
- How it is used
- Uses marginalization to extract distributions for individual variables from joint probabilistic models.
- How deep it goes
- Explains discrete summation, continuous integration, notation, and pgmpy operations, but stops short of broader multivariate inference.
- Examples
- Uses a six-cell X-Y probability table and pgmpy DiscreteFactor marginalize outputs.
- What you can do after
- Apply it via pgmpy to derive marginal tables from discrete joint distributions without altering the original factor.
Related concepts
- marginal likelihoodequivalent to · Marginal likelihood, or Bayesian evidence, is the probability or density of observed data under a model after marginalizing over unknown parameters or latent variables according to their prior distributions.
- message passingproduced by · A communication or computation technique in which entities exchange messages to transmit or propagate information, coordinate work, or update state.
- joint probability distributionused by · A joint probability distribution specifies probabilities or densities for combinations of values taken simultaneously by multiple random variables.
- marginalizationproduced by · Marginalization is the operation of summing or integrating over variables or alternatives that are not retained to obtain a distribution or quantity for the remaining variables.
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