Log-Likelihood
Definition
The log-likelihood is the logarithm of the likelihood of a model for observed data.
For independently modeled observations, the product of probabilities or densities becomes the sum of their logarithms. This facilitates numerical calculation; the maximizing parameters remain the same.
Simply explained
How to convert many small probabilities into an easier-to-compute sum.
Why it matters in practice
Fundamental for statistical estimation and many ML loss functions.
Example from business
A logistic model is estimated via maximum log-likelihood.
Limits and pitfalls
- Misunderstanding likelihood as the probability of the model; directly comparing models with different data bases.
Origin & history
Maximum likelihood estimation was formalized in the early 20th century especially by R. A. Fisher.
Use in mid-sized companies
- Possible application in SMEs: Correctly interpreting statistical models and probabilistic losses.
Frequently asked questions
Is likelihood a probability of the hypothesis?
No. Why log? For numerical stability and additive optimization.
Sources
- Vorlesungsnotizen, Seite 11 · Stanford CS229, Vorlesungsnotizen, Seite 11
Sources checked on 12.10.2026.
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