Categorical distribution
A categorical distribution is a discrete probability distribution over a finite set of mutually exclusive categories or outcomes.
Fabulous Adventures in Data Structures and Algorithms
A categorical distribution assigns probabilities to a finite set of mutually exclusive categories.
- How it is used
- Represents weighted finite random choices and supports sampling and later Bayesian calculations.
- How deep it goes
- Develops projected weights and compares four sampling algorithms, including alias construction and its costs.
- Examples
- Uses a color-labeled die, zero-weight histogram, and cold-and-sneezing joint distribution.
- What you can do after
- Build it from scratch in C# with integer weights, or apply `ToCategorical` and `ToJoint` to weighted values.
Read how Fabulous Adventures in Data Structures and Algorithms explains categorical distribution →
Causal AI
Categorical is a Pyro distribution object representing a categorical probability distribution.
- How it is used
- Represents discrete outcomes and supplies a Pyro object for randomly generating category indices.
- How deep it goes
- Defines categories, probabilities, discrete notation, and Pyro sampling, but does not develop categorical inference or parameter estimation.
- Examples
- Uses food categories, probabilities [.45, .30, .25], Pyro construction, and sampled indices such as tensor(1.).
- What you can do after
- Apply it via Pyro by constructing a Categorical object with probabilities and calling sample() for random category generation.
Math and Architectures of Deep Learning
A discrete probability distribution over exactly one of several mutually exclusive classes in a single trial.
- How it is used
- Frames single-trial class uncertainty for machine-learning problems involving classification and probability distributions.
- How deep it goes
- Defines class probabilities, relates categorical to Bernoulli and multinomial distributions, and represents outcomes with one-hot vectors.
- Examples
- Uses a four-class photo database containing Einstein, Curie, Gauss, and other-photo outcomes.
- What you can do after
- Evaluate/understand single-trial class probabilities and encode outcomes as one-hot vectors.
Read how Math and Architectures of Deep Learning explains categorical distribution →
Related concepts
- maximum likelihood estimationequivalent to · Maximum likelihood estimation is a statistical method that selects parameter values maximizing the likelihood of observed data under a specified probabilistic model.
- Pointer Networkproduced by · A Pointer Network is an attention-based sequence-to-sequence neural architecture that outputs positions or elements selected from its input sequence.
- Bernoulli distributionincludes · A Bernoulli distribution is a discrete probability distribution for one binary outcome, assigning probability p to one outcome and 1−p to the other.
- gumbel-softmaxused by · Gumbel-Softmax is a differentiable approximation that samples from categorical distributions while enabling gradient-based optimization.
- uniform distributionincludes · A uniform distribution assigns equal probability to each outcome in a discrete support or constant probability density across a continuous interval.
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