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where is the instance, [] the expectation value, is a class into which an instance is classified, (|) is the conditional probability of label for instance , and () is the 0–1 loss function: L ( x , y ) = 1 − δ x , y = { 0 if x = y 1 if x ≠ y {\displaystyle L(x,y)=1-\delta _{x,y}={\begin{cases}0&{\text{if }}x=y\\1&{\text{if }}x\neq y\end ...
x erf x 1 − erf x; 0: 0: 1: 0.02: 0.022 564 575: 0.977 435 425: 0.04: 0.045 111 106: 0.954 888 894: 0.06: 0.067 621 594: 0.932 378 406: 0.08: 0.090 078 126: 0.909 ...
Fano's inequality can be interpreted as a way of dividing the uncertainty of a conditional distribution into two questions given an arbitrary predictor. The first question, corresponding to the term (), relates to the uncertainty of the predictor.
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Assume that the conditional distribution of X, given that the label Y takes the value r is given by (=) =,, …, where "" means "is distributed as", and where denotes a probability distribution. A classifier is a rule that assigns to an observation X = x a guess or estimate of what the unobserved label Y = r actually was.
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