Multinomial distribution
A multinomial distribution is a probability distribution for counts of outcomes in multiple mutually exclusive categories across a fixed number of independent trials.
Machine Learning System Design
A probability distribution for counts across multiple categories in a fixed number of independent trials.
- How it is used
- Supports bootstrap resampling for estimating uncertainty in validation metrics such as precision and recall.
- How deep it goes
- Explains multinomial sampling operationally, then contrasts it with binomial and Poisson approximations without deriving the distribution.
- Examples
- Uses repeated bootstrap datasets, precision and recall distributions, and a 99% lower recall confidence bound.
- What you can do after
- Evaluate validation uncertainty and recognize when direct multinomial bootstrap sampling is too computationally expensive.
Read how Machine Learning System Design explains multinomial distribution →
Math and Architectures of Deep Learning
A probability distribution over counts of outcomes from repeated independent trials with multiple mutually exclusive categories.
- How it is used
- Models category counts across repeated trials for probabilistic analysis in machine learning.
- How deep it goes
- Defines the probability function, relates counts to binomial distributions, derives moments, and verifies them computationally.
- Examples
- Uses four photo classes, ten trials, count vector (1, 2, 1, 6), and PyTorch sampling and log-probability checks.
- What you can do after
- Apply via PyTorch to calculate log probabilities, sample count vectors, and compare empirical and theoretical moments.
Read how Math and Architectures of Deep Learning explains multinomial distribution →
Related concepts
- binomial distributionequivalent 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.
- categorical distributionincludes · A categorical distribution is a discrete probability distribution over a finite set of mutually exclusive categories or outcomes.
- random vectorproduces · A random vector is a vector-valued random variable whose components are jointly modeled random variables.
- multinomialused by · Multinomial is a sampling operation that draws one or more categorical outcomes according to specified probabilities or nonnegative weights.
- samplingused by · Sampling is a procedure for selecting or generating observations, values, or outcomes from a larger population, signal, or probability distribution according to a specified method.
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