Poisson distribution

As explained in Natural Language Processing in Action, Second Edition

A Poisson distribution is a probability distribution for counting events in a fixed interval given a specified average rate.

How Natural Language Processing in Action, Second Edition covers it

How deep it goes

Explains its single average-length parameter and generative role, but does not develop probability formulas or inference details.

Examples

Uses document generation and a comments corpus whose mean tokenized length is approximately 54.21.

What you can do after

Apply it by estimating an average document length and using that value to parameterize document-length generation.

How it connects

Connects document length with Dirichlet distribution, topic mixtures, bag-of-words generation, and term-topic probabilities.

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Also explained in

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  Statistics Every Programmer NeedsThe Poisson distribution gives the probabilities of observing specified counts of events in a fixed interval when events occur independently at a constant average rate.
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  Ensemble Methods for Machine LearningA Poisson distribution is a discrete probability distribution for the number of events occurring in a fixed interval under a constant-rate event process.
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  Machine Learning System DesignA probability distribution for the count of events occurring independently at a constant average rate in a fixed interval or exposure.
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  Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIThe Poisson distribution models the number of events occurring in a fixed interval when events occur independently at a constant average rate.
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  liveBookmanning.com
  Causal AIThe Poisson distribution gives the probabilities of the number of events occurring in a fixed interval under a constant-rate event process.
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  liveBookmanning.com
  Grokking StatisticsThe Poisson distribution is a discrete probability distribution for the number of events occurring in a fixed interval under a constant-rate independent-event assumption.

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Related concepts

• probability distributionkind of · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
• Poisson regressionused by · Poisson regression is a generalized linear model for count or rate outcomes using a Poisson response distribution and typically a log link.
• rate parameterhas part · A rate parameter is a parameter that controls the frequency or rate of events or outcomes in a probability distribution.
• exponential distributioncontrasts with · The exponential distribution is a continuous probability distribution over nonnegative values with an exponentially decreasing density, commonly modeling waiting times between events in a constant-rate Poisson process.
• discrete distributionkind of · A discrete probability distribution assigns probability mass to outcomes in a finite or countably infinite set of distinct values.
• binomial distributionalternative to · A binomial distribution is the probability distribution of the number of successes in a fixed number of independent trials, each with the same probability of success.

This explainer was generated by Manning's knowledge graph from the text of Natural Language Processing in Action, Second Edition. The section links point to the parts of the book it draws on.