Neyman-Pearson (NP) Classification Algorithms and NP Receiver Operating Characteristic (NP-ROC) Curves

## Project description

# nproc: Neyman-Pearson (NP) Classification Algorithms and NP Receiver Operating Characteristic (NP-ROC) Curves

In many binary classification applications, such as disease diagnosis and spam detection, practitioners commonly face the need to limit type I error (i.e., the conditional probability of misclassifying a class 0 observation as class 1) so that it remains below a desired threshold. To address this need, the Neyman-Pearson (NP) classification paradigm is a natural choice; it minimizes type II error (i.e., the conditional probability of misclassifying a class 1 observation as class 0) while enforcing an upper bound, alpha, on the type I error. Although the NP paradigm has a century-long history in hypothesis testing, it has not been well recognized and implemented in classification schemes. Common practices that directly limit the empirical type I error to no more than alpha do not satisfy the type I error control objective because the resulting classifiers are still likely to have type I errors much larger than alpha. As a result, the NP paradigm has not been properly implemented for many classification scenarios in practice. In this work, we develop the first umbrella algorithm that implements the NP paradigm for all scoring-type classification methods, including popular methods such as logistic regression, support vector machines and random forests. Powered by this umbrella algorithm, we propose a novel graphical tool for NP classification methods: NP receiver operating characteristic (NP-ROC) bands, motivated by the popular receiver operating characteristic (ROC) curves. NP-ROC bands will help choose in a data adaptive way and compare different NP classifiers.

Details

```
See details in: http://advances.sciencemag.org/content/4/2/eaao1659.full
```

Usage

```
npc(x, y, method = ("logistic", "svm", "nb"), alpha = 0.05, delta = 0.05, split = 1, split_ratio = 0.5, n_cores = 1, band = False, randSeed = 0)
```

Arguments

```
x n * p observation matrix. n observations, p covariates.
y n 0/1 observatons.
method logistic: Logistic regression.
svm: Support Vector Machines.
nb: Naive Bayes.
alpha the desirable upper bound on type I error. Default = 0.05.
delta the violation rate of the type I error. Default = 0.05.
split the number of splits for the class 0 sample. Default = 1. For ensemble version, choose split > 1.
split_ratio the ratio of splits used for the class 0 sample to train the classifier. Default = 0.5.
n_cores number of cores used for parallel computing. Default = 1.
band whether to generate both lower and upper bounds of type II error. Default = False.
randSeed the random seed used in the algorithm.
```

Example

```
import numpy as np
import os
from nproc import npc
test = npc()
np.random.seed(1)
n = 10000
x = np.random.normal(0, 1, (n,2))
c = 1+3*x[:,0]
y = np.random.binomial(1, 1/(1+np.exp(-c)), n)
fit = test.npc(x, y, 'logistic', n_cores=os.cpu_count())
x_test = np.random.normal(0, 1, (n,2))
c_test = 1+3*x_test[:,0]
y_test = np.random.binomial(1, 1/(1+np.exp(-c_test)), n)
pred_score = test.predict(fit,x_test)
fitted_score = test.predict(fit,x)
print(np.mean(pred_score[0]==y_test))
print(np.mean(fitted_score[0]==y))
```

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