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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 ...
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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.
The probability of type I errors is called the "false reject rate" (FRR) or false non-match rate (FNMR), while the probability of type II errors is called the "false accept rate" (FAR) or false match rate (FMR). If the system is designed to rarely match suspects then the probability of type II errors can be called the "false alarm rate". On the ...
Neyman–Pearson lemma [5] — Existence:. If a hypothesis test satisfies condition, then it is a uniformly most powerful (UMP) test in the set of level tests.. Uniqueness: If there exists a hypothesis test that satisfies condition, with >, then every UMP test in the set of level tests satisfies condition with the same .
As CDFs are defined by integrating a probability density function, the failure probability density is defined such that: Exponential probability functions, often used as the failure probability density f ( t ) {\displaystyle f(t)} .