Poisson distribution

As explained in Machine Learning System Design

A probability distribution for the count of events occurring independently at a constant average rate in a fixed interval or exposure.

The Poisson distribution appears here as a practical shortcut for bootstrap validation. When the dataset is much larger than 100, Poisson(1) closely approximates binomial(n, 1/n), allowing observations to be sampled independently without tying the procedure to dataset size. section 7.4

Faster bootstrap validation

Replacing multinomial sampling with independent Poisson(1) sampling made bootstrap validation easy to parallelize and reportedly increased speed by roughly 100–1,000 times with additional techniques. section 7.4

Distribution recall with every point being a bootstrapped original dataset; the red line is a 99% lower confidence bound.

Use the recall distribution and its 99% lower confidence bound to see how bootstrap samples support metric-confidence estimates. section 7.4

How Machine Learning System Design covers it

How deep it goes

Approximates binomial(n, 1/n) with Poisson(1) for large datasets but does not derive the distribution generally.

Examples

Uses Poisson(1) bootstrap samples to estimate distributions and a 99% lower confidence bound for recall.

What it assumes

Assumes familiarity with bootstrap, multinomial and binomial sampling, validation metrics, and confidence bounds.

What you can do after

Apply it via independent Poisson(1) sampling to parallelize large-scale bootstrap validation.

How it connects

Connects Poisson sampling with bootstrap, binomial distribution, multinomial sampling, confidence bounds, precision, and recall.

liveBookmanning.com

Read Machine Learning System Design on liveBook Get the book at manning.com

Also explained in

• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  Natural Language Processing in Action, Second EditionA Poisson distribution is a probability distribution for counting events in a fixed interval given a specified average rate.
• 

  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.
• 

  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.

Compare how 7 books explain Poisson distribution →

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 Machine Learning System Design. The section links point to the parts of the book it draws on.