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

Geometric

Trials until the first success; the discrete memoryless law.
Type discreteSupport {1, 2, …}Family Waiting time
Probability massP(X=k) = p(1−p)ᵏ⁻¹
discrete

Geometric in motion

0.55.5111621
Support{1, 2, …}
Mean3.333
Variance7.778
Connections

Where the geometric
comes from — and leads.

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

Exponentialtime step→0

Scaled geometric waiting times converge to exponential waiting time.

Limiting result

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