README.md

ROC

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Questions to David Rotermund

The following code is for the case where the amount of data for both classes is the same.

Test data

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(1)

a_x = rng.normal(1.5, 1.0, size=(5000))
b_x = rng.normal(0.0, 1.0, size=(5000))


ab_x = np.concatenate([a_x, b_x])
edges = np.histogram_bin_edges(ab_x, bins=100, range=None, weights=None)

h_a, _ = np.histogram(a_x, bins=edges)
h_b, _ = np.histogram(b_x, bins=edges)

h_a = h_a.astype(np.float32)
h_b = h_b.astype(np.float32)

h_a /= h_a.sum()
h_b /= h_b.sum()

edges = (edges[1:] + edges[:-1]) / 2.0

plt.plot(edges, h_a, "c.", label="Class -1")
plt.plot(edges, h_b, "m.", label="Class +1")
plt.ylabel("Probability of a value")
plt.ylabel("Edge center")
plt.legend()
plt.show()

Find the cumsum maximum

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(1)

a_x = rng.normal(1.5, 1.0, size=(5000))
b_x = rng.normal(0.0, 1.0, size=(5000))

data_data = np.concatenate([a_x, b_x])
data_class = np.concatenate(
    [np.full_like(a_x, -1 / a_x.shape[0]), np.full_like(b_x, +1 / b_x.shape[0])]
)
idx = np.argsort(data_data)

data_data = data_data[idx]
data_class = data_class[idx]

data_cumsum = np.cumsum(data_class)

plt.plot(data_cumsum)
plt.plot(
    [np.argmax(data_cumsum), np.argmax(data_cumsum)], [0, np.max(data_cumsum)], "k--"
)
plt.ylabel("Cumsum of the classes")
plt.xlabel("Sorted sample id")
plt.show()

How to create an estimate from the ROC cumsum maximum

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(1)

a_x = rng.normal(1.5, 1.0, size=(5000))
b_x = rng.normal(0.0, 1.0, size=(5000))

data_data = np.concatenate([a_x, b_x])
data_class = np.concatenate(
    [np.full_like(a_x, -1 / a_x.shape[0]), np.full_like(b_x, +1 / b_x.shape[0])]
)
data_class_id = np.concatenate([np.full_like(a_x, -1), np.full_like(b_x, +1)])
idx = np.argsort(data_data)

data_data = data_data[idx]
data_class = data_class[idx]
data_class_id = data_class_id[idx]

data_cumsum = np.cumsum(data_class)
border = np.argmax(np.abs(data_cumsum))

if data_cumsum[border] < 0:
    estimate = np.concatenate(
        (
            np.full_like(data_class[: border + 1], -1),
            np.full_like(data_class[border + 1 :], +1),
        )
    )

else:
    estimate = np.concatenate(
        (
            np.full_like(data_class[: border + 1], +1),
            np.full_like(data_class[border + 1 :], -1),
        )
    )


performance = 100.0 * (data_class_id == estimate).sum() / data_class_id.shape[0]
print(f"Performance: {performance}% correct")

plt.subplot(2, 1, 1)
idx_a = np.where(data_class < 0)[0]
idx_b = np.where(data_class > 0)[0]
idx = np.arange(0, data_class.shape[0])

plt.plot(data_data[idx_a], np.zeros_like(idx_a), "c*")
plt.plot(data_data[idx_b], np.zeros_like(idx_b), "m.")
plt.yticks([])
plt.title("Data")

plt.subplot(2, 1, 2)
idx_a = np.where(estimate < 0)[0]
idx_b = np.where(estimate > 0)[0]
idx = np.arange(0, estimate.shape[0])

plt.plot(data_data[idx_a], np.zeros_like(idx_a), "c*")
plt.plot(data_data[idx_b], np.zeros_like(idx_b), "m.")
plt.yticks([])
plt.title("Estimate")
plt.xlabel("Data Value")
plt.show()

Output:

Performance: 77.31% correct