Zero–one loss and risk
Definition taught in Statistical classifiers and discriminant analysis, part of Statistical learning
Zero–one loss and risk
| Type | Definition |
| Taught in | Statistical classifiers and discriminant analysis |
| Part | Statistical learning |
Let (X,Y) be a new point drawn from the target distribution. The zero–one loss of the classifier is
l\bigl(Y,\eta(X)\bigr) = \begin{cases} 0, & \eta(X)=Y,\\ 1, & \eta(X)\ne Y, \end{cases} =\sum_{g=1}^{G} Y_g\, Q\bigl[g,\eta(X)\bigr].
The conditional risk at X=\mathbf{x} is the expected loss over Y drawn from its conditional distribution, which is multinomial with a single trial and probabilities \tau_1(\mathbf{x}),\ldots,\tau_G(\mathbf{x}).
Used in
- Taught in Statistical classifiers and discriminant analysis, where the derivation and examples are.
- Also used in Model selection for stochastic models · Estimating error rates · Nearest neighbours · Classification trees · Ensembles, random forests, and boosting
- All 8 questions on Statistical classifiers and discriminant analysis
See also
Conditional distribution · Bayes-optimal rule · Fixed-rule error · Training data and classifier · Posterior class probability · Fisher’s direction · Classification problem · Bayes classifier