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Binomial distribution

As explained in Machine Learning System Design

A probability distribution for the number of successes in a fixed number of independent Bernoulli trials with a common success probability.

The binomial distribution models independent success-or-failure observations with a shared probability. In validation workflows, binomial(n, 1/n) lets each observation be sampled independently during bootstrap instead of drawing a full multinomial sample. section 7.4

For datasets much larger than 100, binomial(n, 1/n) closely approximates Poisson(1). Because Poisson(1) does not depend on dataset size, the sampling can be parallelized, reportedly accelerating computation by roughly 100–1,000 times. section 7.4

Bootstrap recall bounds

Independent bootstrap samples produce a recall distribution from which a 99% lower confidence bound can be selected; the reported example places recall above 0.071 on average in 99 of 100 cases. section 7.4

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

Use the recall-distribution figure to connect repeated sampling with confidence-bound selection. section 7.4

How Machine Learning System Design covers it

How deep it goes
Explains the binomial-to-Poisson approximation and its computational rationale, but does not derive the distribution mathematically.
Examples
Demonstrates binomial(n,1/n) sampling for bootstrap datasets and evaluates resulting recall distributions.
What it assumes
Assumes familiarity with bootstrap and multinomial sampling while treating the binomial approximation operationally.
What you can do after
Apply it to replace multinomial bootstrap sampling with independently parallelizable draws in large validation datasets.
How it connects
Connects binomial sampling with bootstrap, multinomial distribution, Poisson distribution, and confidence bounds.

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