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

Pick the loss by asking


how the data can be wrong.

The objective is an assumption about residuals and outcomes. Probe each curve to see how that assumption changes penalties and gradients.

Fundamentals

Objectivescalar score optimized in training

Output constraintreal, positive, or probability-valued prediction

Gradientdirection and scale of parameter updates

data type → likelihood → link/output → loss
Negative log-likelihood

Mean squared error

ℒ = ½(ŷ − y)²
-1prediction →
The distribution atlas comes back

A neural network often predicts distribution parameters, not the final answer directly. Its output head supplies μ, p, λ, or scale; negative log-likelihood scores how well those predicted distributions explain the observations.

Continue the path

Semi-supervised learning

A few labels plus many unlabeled examples: see when pseudo-labels and consistency actually help — and when they quietly hurt.

Propagate a label