Dirichlet distribution
A Dirichlet distribution is a continuous probability distribution over vectors of nonnegative components that sum to one, parameterized by positive concentration parameters.
Natural Language Processing in Action, Second Edition
A Dirichlet distribution is a probability distribution over categorical probability vectors whose components are nonnegative and sum to one.
- How it is used
- Supports latent Dirichlet allocation by modeling document topic mixtures and topic word distributions.
- How deep it goes
- Explains the distribution's modeling role and generative sequence, but does not derive its mathematics or estimation procedure.
- Examples
- Uses a Dungeons & Dragons dice analogy and a document-generation process involving topic mixtures and word selection.
- What you can do after
- Evaluate how LDiA represents documents as mixtures of topics and assigns probabilistic roles to words.
Read how Natural Language Processing in Action, Second Edition explains Dirichlet distribution →
Causal AI
The Dirichlet distribution is a continuous probability distribution over vectors of nonnegative values that sum to one.
- How it is used
- Uses a conjugate prior to learn categorical conditional-probability parameters in a causal graphical model.
- How deep it goes
- Explains simplex support, categorical conjugacy, count updates, and smoothing, but does not derive the distribution mathematically.
- Examples
- Uses travel-mode probabilities conditioned on employment and region, plus a pgmpy BayesianEstimator listing.
- What you can do after
- Apply it via pgmpy to estimate smoothed categorical conditional probabilities from data.
Related concepts
- conjugacykind of · Conjugacy is the property whereby a prior distribution and a specified likelihood yield a posterior distribution in the same family as the prior.
- beta distributionalternative to · A beta distribution is a continuous probability distribution on the interval [0,1], parameterized by two positive shape parameters.
- latent Dirichlet allocationused by · Latent Dirichlet allocation is a generative probabilistic topic model representing documents as mixtures of latent topics and topics as distributions over words.
- mixture weightuses · A mixture weight is a nonnegative coefficient specifying a component distribution’s relative contribution to a probabilistic mixture, with component weights typically summing to one.
- categorical distributionequivalent to · A categorical distribution is a discrete probability distribution over a finite set of mutually exclusive categories or outcomes.
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