157 lines
3.4 KiB
Markdown
157 lines
3.4 KiB
Markdown
# ROC
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{:.no_toc}
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<nav markdown="1" class="toc-class">
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* TOC
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{:toc}
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</nav>
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## Top
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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The following code is for the case where the amount of data for both classes is the same.
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## Test data
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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rng = np.random.default_rng(1)
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a_x = rng.normal(1.5, 1.0, size=(5000))
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b_x = rng.normal(0.0, 1.0, size=(5000))
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ab_x = np.concatenate([a_x, b_x])
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edges = np.histogram_bin_edges(ab_x, bins=100, range=None, weights=None)
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h_a, _ = np.histogram(a_x, bins=edges)
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h_b, _ = np.histogram(b_x, bins=edges)
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h_a = h_a.astype(np.float32)
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h_b = h_b.astype(np.float32)
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h_a /= h_a.sum()
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h_b /= h_b.sum()
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edges = (edges[1:] + edges[:-1]) / 2.0
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plt.plot(edges, h_a, "c.", label="Class -1")
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plt.plot(edges, h_b, "m.", label="Class +1")
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plt.ylabel("Probability of a value")
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plt.ylabel("Edge center")
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plt.legend()
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plt.show()
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```
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## Find the cumsum maximum
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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rng = np.random.default_rng(1)
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a_x = rng.normal(1.5, 1.0, size=(5000))
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b_x = rng.normal(0.0, 1.0, size=(5000))
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data_data = np.concatenate([a_x, b_x])
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data_class = np.concatenate(
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[np.full_like(a_x, -1 / a_x.shape[0]), np.full_like(b_x, +1 / b_x.shape[0])]
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)
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idx = np.argsort(data_data)
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data_data = data_data[idx]
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data_class = data_class[idx]
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data_cumsum = np.cumsum(data_class)
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plt.plot(data_cumsum)
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plt.plot(
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[np.argmax(data_cumsum), np.argmax(data_cumsum)], [0, np.max(data_cumsum)], "k--"
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)
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plt.ylabel("Cumsum of the classes")
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plt.xlabel("Sorted sample id")
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plt.show()
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```
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## How to create an estimate from the ROC cumsum maximum
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```python
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import numpy as np
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import matplotlib.pyplot as plt
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rng = np.random.default_rng(1)
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a_x = rng.normal(1.5, 1.0, size=(5000))
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b_x = rng.normal(0.0, 1.0, size=(5000))
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data_data = np.concatenate([a_x, b_x])
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data_class = np.concatenate(
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[np.full_like(a_x, -1 / a_x.shape[0]), np.full_like(b_x, +1 / b_x.shape[0])]
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)
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data_class_id = np.concatenate([np.full_like(a_x, -1), np.full_like(b_x, +1)])
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idx = np.argsort(data_data)
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data_data = data_data[idx]
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data_class = data_class[idx]
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data_class_id = data_class_id[idx]
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data_cumsum = np.cumsum(data_class)
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border = np.argmax(np.abs(data_cumsum))
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if data_cumsum[border] < 0:
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estimate = np.concatenate(
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(
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np.full_like(data_class[: border + 1], -1),
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np.full_like(data_class[border + 1 :], +1),
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)
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)
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else:
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estimate = np.concatenate(
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(
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np.full_like(data_class[: border + 1], +1),
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np.full_like(data_class[border + 1 :], -1),
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)
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)
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performance = 100.0 * (data_class_id == estimate).sum() / data_class_id.shape[0]
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print(f"Performance: {performance}% correct")
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plt.subplot(2, 1, 1)
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idx_a = np.where(data_class < 0)[0]
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idx_b = np.where(data_class > 0)[0]
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idx = np.arange(0, data_class.shape[0])
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plt.plot(data_data[idx_a], np.zeros_like(idx_a), "c*")
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plt.plot(data_data[idx_b], np.zeros_like(idx_b), "m.")
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plt.yticks([])
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plt.title("Data")
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plt.subplot(2, 1, 2)
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idx_a = np.where(estimate < 0)[0]
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idx_b = np.where(estimate > 0)[0]
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idx = np.arange(0, estimate.shape[0])
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plt.plot(data_data[idx_a], np.zeros_like(idx_a), "c*")
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plt.plot(data_data[idx_b], np.zeros_like(idx_b), "m.")
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plt.yticks([])
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plt.title("Estimate")
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plt.xlabel("Data Value")
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plt.show()
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```
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Output:
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```python
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Performance: 77.31% correct
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```
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