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review/17-mutual_genes/mpschr-mutex-b1898f6/plot_upset.ipynb
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| import pandas as pd | ||
| import numpy as np | ||
| import scipy.stats | ||
| ''' | ||
| MIT License | ||
| Copyright (c) 2021 Nikita Kazeev | ||
| Permission is hereby granted, free of charge, to any person obtaining a copy | ||
| of this software and associated documentation files (the "Software"), to deal | ||
| in the Software without restriction, including without limitation the rights | ||
| to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | ||
| copies of the Software, and to permit persons to whom the Software is | ||
| furnished to do so, subject to the following conditions: | ||
| The above copyright notice and this permission notice shall be included in all | ||
| copies or substantial portions of the Software. | ||
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | ||
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | ||
| FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | ||
| AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | ||
| LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | ||
| OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | ||
| SOFTWARE. | ||
| ''' | ||
| # AUC comparison adapted from | ||
| # https://github.com/Netflix/vmaf/ | ||
| def compute_midrank(x): | ||
| """Computes midranks. | ||
| Args: | ||
| x - a 1D numpy array | ||
| Returns: | ||
| array of midranks | ||
| """ | ||
| J = np.argsort(x) | ||
| Z = x[J] | ||
| N = len(x) | ||
| T = np.zeros(N, dtype=np.float) | ||
| i = 0 | ||
| while i < N: | ||
| j = i | ||
| while j < N and Z[j] == Z[i]: | ||
| j += 1 | ||
| T[i:j] = 0.5*(i + j - 1) | ||
| i = j | ||
| T2 = np.empty(N, dtype=np.float) | ||
| # Note(kazeevn) +1 is due to Python using 0-based indexing | ||
| # instead of 1-based in the AUC formula in the paper | ||
| T2[J] = T + 1 | ||
| return T2 | ||
|
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||
| def fastDeLong(predictions_sorted_transposed, label_1_count): | ||
| """ | ||
| The fast version of DeLong's method for computing the covariance of | ||
| unadjusted AUC. | ||
| Args: | ||
| predictions_sorted_transposed: a 2D numpy.array[n_classifiers, n_examples] | ||
| sorted such as the examples with label "1" are first | ||
| Returns: | ||
| (AUC value, DeLong covariance) | ||
| Reference: | ||
| @article{sun2014fast, | ||
| title={Fast Implementation of DeLong's Algorithm for | ||
| Comparing the Areas Under Correlated Receiver Operating Characteristic Curves}, | ||
| author={Xu Sun and Weichao Xu}, | ||
| journal={IEEE Signal Processing Letters}, | ||
| volume={21}, | ||
| number={11}, | ||
| pages={1389--1393}, | ||
| year={2014}, | ||
| publisher={IEEE} | ||
| } | ||
| """ | ||
| # Short variables are named as they are in the paper | ||
| m = label_1_count | ||
| n = predictions_sorted_transposed.shape[1] - m | ||
| positive_examples = predictions_sorted_transposed[:, :m] | ||
| negative_examples = predictions_sorted_transposed[:, m:] | ||
| k = predictions_sorted_transposed.shape[0] | ||
|
|
||
| tx = np.empty([k, m], dtype=np.float) | ||
| ty = np.empty([k, n], dtype=np.float) | ||
| tz = np.empty([k, m + n], dtype=np.float) | ||
| for r in range(k): | ||
| tx[r, :] = compute_midrank(positive_examples[r, :]) | ||
| ty[r, :] = compute_midrank(negative_examples[r, :]) | ||
| tz[r, :] = compute_midrank(predictions_sorted_transposed[r, :]) | ||
| aucs = tz[:, :m].sum(axis=1) / m / n - float(m + 1.0) / 2.0 / n | ||
| v01 = (tz[:, :m] - tx[:, :]) / n | ||
| v10 = 1.0 - (tz[:, m:] - ty[:, :]) / m | ||
| sx = np.cov(v01) | ||
| sy = np.cov(v10) | ||
| delongcov = sx / m + sy / n | ||
| return aucs, delongcov | ||
|
|
||
|
|
||
| def calc_pvalue(aucs, sigma): | ||
| """Computes log(10) of p-values. | ||
| Args: | ||
| aucs: 1D array of AUCs | ||
| sigma: AUC DeLong covariances | ||
| Returns: | ||
| log10(pvalue) | ||
| """ | ||
| l = np.array([[1, -1]]) | ||
| z = np.abs(np.diff(aucs)) / np.sqrt(np.dot(np.dot(l, sigma), l.T)) | ||
| return np.log10(2) + scipy.stats.norm.logsf(z, loc=0, scale=1) / np.log(10) | ||
|
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|
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||
| def compute_ground_truth_statistics(ground_truth): | ||
| assert np.array_equal(np.unique(ground_truth), [0, 1]) | ||
| order = (-ground_truth).argsort() | ||
| label_1_count = int(ground_truth.sum()) | ||
| return order, label_1_count | ||
|
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|
|
||
| def delong_roc_variance(ground_truth, predictions): | ||
| """ | ||
| Computes ROC AUC variance for a single set of predictions | ||
| Args: | ||
| ground_truth: np.array of 0 and 1 | ||
| predictions: np.array of floats of the probability of being class 1 | ||
| """ | ||
| order, label_1_count = compute_ground_truth_statistics(ground_truth) | ||
| predictions_sorted_transposed = predictions[np.newaxis, order] | ||
| aucs, delongcov = fastDeLong(predictions_sorted_transposed, label_1_count) | ||
| assert len(aucs) == 1, "There is a bug in the code, please forward this to the developers" | ||
| return aucs[0], delongcov | ||
|
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||
| def delong_roc_test(ground_truth, predictions_one, predictions_two): | ||
| """ | ||
| Computes log(p-value) for hypothesis that two ROC AUCs are different | ||
| Args: | ||
| ground_truth: np.array of 0 and 1 | ||
| predictions_one: predictions of the first model, | ||
| np.array of floats of the probability of being class 1 | ||
| predictions_two: predictions of the second model, | ||
| np.array of floats of the probability of being class 1 | ||
| """ | ||
| order, label_1_count = compute_ground_truth_statistics(ground_truth) | ||
| predictions_sorted_transposed = np.vstack((predictions_one, predictions_two))[:, order] | ||
| aucs, delongcov = fastDeLong(predictions_sorted_transposed, label_1_count) | ||
| return calc_pvalue(aucs, delongcov) |