A demonstration of the nproc package
نویسندگان
چکیده
Let (X,Y ) be random variables where X ∈ X is a vector of d features and Y ∈ {0, 1} represents a binary class label. A data set that contains independent observations {(xi, yi)} i=1 sampled from the joint distribution of (X,Y ) are often divided into training data {(xi, yi)}i=1 and test data {(xi, yi)} i=n+1. Based on training data, a classifier φ(·) is a mapping φ : X → {0, 1} that returns the predicted class label given X. Classification error occurs when φ(X) 6= Y , and the binary loss is defined as 1(φ(X) 6= Y ), where 1(·) denotes the indicator function. The risk is defined as R(φ) = E[1(φ(X) 6= Y )] = P (φ(X) 6= Y ), which can be expressed as a weighted sum of type I and II errors: R(φ) = P (Y = 0)R0(φ) + P (Y = 1)R1(φ), where R0(φ) = P (φ(X) 6= Y |Y = 0) denotes the type I error, and R1(φ) = P (φ(X) 6= Y |Y = 1) denotes the type II error. The classical classification paradigm aims to find an oracle classifier φ∗ by minimizing the risk, φ∗ = arg minφR(φ). In contrast, the NP classification paradigm aims to mimic the NP oracle classifier φα with respect to a pre-specified type I error upper bound α, φα = arg minφ: R0(φ)≤αR1(φ), where α reflects users’ conservative attitude (priority) towards the type I error. Back to Top
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