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// Copyright ©2016 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package stat_test
import (
"fmt"
"math"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/integrate"
"gonum.org/v1/gonum/stat"
)
func ExampleROC_weighted() {
y := []float64{0, 3, 5, 6, 7.5, 8}
classes := []bool{false, true, false, true, true, true}
weights := []float64{4, 1, 6, 3, 2, 2}
tpr, fpr, _ := stat.ROC(nil, y, classes, weights)
fmt.Printf("true positive rate: %v\n", tpr)
fmt.Printf("false positive rate: %v\n", fpr)
// Output:
// true positive rate: [0 0.25 0.5 0.875 0.875 1 1]
// false positive rate: [0 0 0 0 0.6 0.6 1]
}
func ExampleROC_unweighted() {
y := []float64{0, 3, 5, 6, 7.5, 8}
classes := []bool{false, true, false, true, true, true}
tpr, fpr, _ := stat.ROC(nil, y, classes, nil)
fmt.Printf("true positive rate: %v\n", tpr)
fmt.Printf("false positive rate: %v\n", fpr)
// Output:
// true positive rate: [0 0.25 0.5 0.75 0.75 1 1]
// false positive rate: [0 0 0 0 0.5 0.5 1]
}
func ExampleROC_threshold() {
y := []float64{0.1, 0.4, 0.35, 0.8}
classes := []bool{false, false, true, true}
stat.SortWeightedLabeled(y, classes, nil)
tpr, fpr, thresh := stat.ROC(nil, y, classes, nil)
fmt.Printf("true positive rate: %v\n", tpr)
fmt.Printf("false positive rate: %v\n", fpr)
fmt.Printf("cutoff thresholds: %v\n", thresh)
// Output:
// true positive rate: [0 0.5 0.5 1 1]
// false positive rate: [0 0 0.5 0.5 1]
// cutoff thresholds: [+Inf 0.8 0.4 0.35 0.1]
}
func ExampleROC_unsorted() {
y := []float64{8, 7.5, 6, 5, 3, 0}
classes := []bool{true, true, true, false, true, false}
weights := []float64{2, 2, 3, 6, 1, 4}
stat.SortWeightedLabeled(y, classes, weights)
tpr, fpr, _ := stat.ROC(nil, y, classes, weights)
fmt.Printf("true positive rate: %v\n", tpr)
fmt.Printf("false positive rate: %v\n", fpr)
// Output:
// true positive rate: [0 0.25 0.5 0.875 0.875 1 1]
// false positive rate: [0 0 0 0 0.6 0.6 1]
}
func ExampleROC_knownCutoffs() {
y := []float64{8, 7.5, 6, 5, 3, 0}
classes := []bool{true, true, true, false, true, false}
weights := []float64{2, 2, 3, 6, 1, 4}
cutoffs := []float64{-1, 3, 4}
stat.SortWeightedLabeled(y, classes, weights)
tpr, fpr, _ := stat.ROC(cutoffs, y, classes, weights)
fmt.Printf("true positive rate: %v\n", tpr)
fmt.Printf("false positive rate: %v\n", fpr)
// Output:
// true positive rate: [0.875 1 1]
// false positive rate: [0.6 0.6 1]
}
func ExampleROC_equallySpacedCutoffs() {
y := []float64{8, 7.5, 6, 5, 3, 0}
classes := []bool{true, true, true, false, true, true}
weights := []float64{2, 2, 3, 6, 1, 4}
n := 9
stat.SortWeightedLabeled(y, classes, weights)
cutoffs := make([]float64, n)
floats.Span(cutoffs, math.Nextafter(y[0], y[0]-1), y[len(y)-1])
tpr, fpr, _ := stat.ROC(cutoffs, y, classes, weights)
fmt.Printf("true positive rate: %.3v\n", tpr)
fmt.Printf("false positive rate: %.3v\n", fpr)
// Output:
// true positive rate: [0.167 0.333 0.583 0.583 0.583 0.667 0.667 0.667 1]
// false positive rate: [0 0 0 1 1 1 1 1 1]
}
func ExampleROC_aUC_unweighted() {
y := []float64{0.1, 0.35, 0.4, 0.8}
classes := []bool{true, false, true, false}
tpr, fpr, _ := stat.ROC(nil, y, classes, nil)
// Compute Area Under Curve.
auc := integrate.Trapezoidal(fpr, tpr)
fmt.Printf("true positive rate: %v\n", tpr)
fmt.Printf("false positive rate: %v\n", fpr)
fmt.Printf("auc: %v\n", auc)
// Output:
// true positive rate: [0 0 0.5 0.5 1]
// false positive rate: [0 0.5 0.5 1 1]
// auc: 0.25
}
func ExampleROC_aUC_weighted() {
y := []float64{0.1, 0.35, 0.4, 0.8}
classes := []bool{true, false, true, false}
weights := []float64{1, 2, 2, 1}
tpr, fpr, _ := stat.ROC(nil, y, classes, weights)
// Compute Area Under Curve.
auc := integrate.Trapezoidal(fpr, tpr)
fmt.Printf("auc: %f\n", auc)
// Output:
// auc: 0.444444
}
func ExampleTOC() {
classes := []bool{
false, false, false, false, false, false,
false, false, false, false, false, false,
false, false, true, true, true, true,
true, true, true, false, false, true,
false, true, false, false, true, false,
}
min, ntp, max := stat.TOC(classes, nil)
fmt.Printf("minimum bound: %v\n", min)
fmt.Printf("TOC: %v\n", ntp)
fmt.Printf("maximum bound: %v\n", max)
// Output:
// minimum bound: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10]
// TOC: [0 0 1 1 1 2 2 3 3 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10]
// maximum bound: [0 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10]
}
func ExampleTOC_unsorted() {
y := []float64{8, 7.5, 6, 5, 3, 0}
classes := []bool{true, false, true, false, false, false}
weights := []float64{4, 1, 6, 3, 2, 2}
stat.SortWeightedLabeled(y, classes, weights)
min, ntp, max := stat.TOC(classes, weights)
fmt.Printf("minimum bound: %v\n", min)
fmt.Printf("TOC: %v\n", ntp)
fmt.Printf("maximum bound: %v\n", max)
// Output:
// minimum bound: [0 0 0 3 6 8 10]
// TOC: [0 4 4 10 10 10 10]
// maximum bound: [0 4 5 10 10 10 10]
}
func ExampleTOC_aUC_unweighted() {
classes := []bool{true, false, true, false}
_, ntp, _ := stat.TOC(classes, nil)
pos := ntp[len(ntp)-1]
base := float64(len(classes)) - pos
// Compute the area under ntp and under the
// minimum bound.
x := floats.Span(make([]float64, len(classes)+1), 0, float64(len(classes)))
aucNTP := integrate.Trapezoidal(x, ntp)
aucMin := pos * pos / 2
// Calculate the area under the curve
// within the bounding parallelogram.
auc := aucNTP - aucMin
// Calculate the area within the bounding
// parallelogram.
par := pos * base
// The AUC is the ratio of the area under
// the curve within the bounding parallelogram
// and the total parallelogram bound.
auc /= par
fmt.Printf("number of true positives: %v\n", ntp)
fmt.Printf("auc: %v\n", auc)
// Output:
// number of true positives: [0 0 1 1 2]
// auc: 0.25
}
func ExampleTOC_aUC_weighted() {
classes := []bool{true, false, true, false}
weights := []float64{1, 2, 2, 1}
min, ntp, max := stat.TOC(classes, weights)
// Compute the area under ntp and under the
// minimum and maximum bounds.
x := make([]float64, len(classes)+1)
floats.CumSum(x[1:], weights)
aucNTP := integrate.Trapezoidal(x, ntp)
aucMin := integrate.Trapezoidal(x, min)
aucMax := integrate.Trapezoidal(x, max)
// Calculate the area under the curve
// within the bounding parallelogram.
auc := aucNTP - aucMin
// Calculate the area within the bounding
// parallelogram.
par := aucMax - aucMin
// The AUC is the ratio of the area under
// the curve within the bounding parallelogram
// and the total parallelogram bound.
auc /= par
fmt.Printf("number of true positives: %v\n", ntp)
fmt.Printf("auc: %f\n", auc)
// Output:
// number of true positives: [0 0 2 2 3]
// auc: 0.444444
}
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