Modeling
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LearnProbabilityMechanisms, distributions, transformations, and limits.Bayesian learningPosterior updates, Thompson sampling, and Bayesian optimization.Deep learningActivations, likelihood-derived objectives, and the architectures built from them.01Activations02Likelihood to loss03ObjectivesSemi-supervisedUse a few labels and many unlabeled examples without hiding the assumptions.ReferenceDistributionsRelationship mapSource & method

Uniform

Equal density over an interval and the source of inverse-transform simulation.
Type continuousSupport a ≤ x ≤ bFamily Bounded
Probability densityf(x) = 1/(b−a)
continuous

Uniform in motion

-0.20.10.50.81.2
Supporta ≤ x ≤ b
Mean0.5
Variance0.08333
Connections

Where the uniform
comes from — and leads.

Every link is one of the four moves from the relationship map: special cases, transformations, limits, and Bayesian conjugacy.

Exponential−log U / λ

Inverse-transform sampling turns U(0,1) into Exp(λ).

TransformationCauchytan π(U−½)

The Cauchy quantile transforms a standard uniform variate.

Transformation

Zoom out

See every connection at once.

The relationship map draws the whole backbone — special cases, transformations, limits, and conjugacies — in one guided view.

Open the map