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metrics.py
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import numpy as np
import scipy
def nan_r2(y_true, y_hat):
y_true = y_true.reshape(-1)
y_hat = y_hat.reshape(-1)
mask = ~np.isnan(y_true) & ~np.isnan(y_hat)
y_true = y_true[mask]
y_hat = y_hat[mask]
ss_res = np.sum((y_true - y_hat) ** 2)
ss_tot = np.sum((y_true - np.mean(y_true)) ** 2)
r2 = 1 - ss_res / ss_tot
return r2
def two_sample_bootstrap_paired(x, y, func=np.mean, n_boot=1000, rng=np.random.default_rng(0)):
# get rid of nans
x = x.reshape(-1)
y = y.reshape(-1)
nan_loc = np.isnan(x) | np.isnan(y)
x = x[~nan_loc]
y = y[~nan_loc]
n_data = x.shape[0]
stat = np.zeros(n_boot)
for n in range(n_boot):
sample_inds = rng.integers(0, high=n_data, size=n_data)
x_sampled = x[sample_inds]
y_sampled = y[sample_inds]
stat[n] = func(x_sampled) - func(y_sampled)
if np.mean(stat < 0):
stat *= -1
p = np.mean(stat < 0) * 2
return p
def two_sample_boostrap_corr_p(target, data_1, data_2, alpha=0.05, n_boot=1000, rng=np.random.default_rng()):
booted_metric = np.zeros(n_boot)
# get rid of nans
target = target.reshape(-1).astype(float)
data_1 = data_1.reshape(-1).astype(float)
data_2 = data_2.reshape(-1).astype(float)
nan_loc = np.isnan(target) | np.isnan(data_1) | np.isnan(data_2)
target = target[~nan_loc]
data_1 = data_1[~nan_loc]
data_2 = data_2[~nan_loc]
n_data = target.shape[0]
for n in range(n_boot):
sample_inds = rng.integers(0, high=n_data, size=n_data)
target_resampled = target[sample_inds]
data_1_resampled = data_1[sample_inds]
data_2_resampled = data_2[sample_inds]
data_1_corr = nan_corr(target_resampled, data_1_resampled)[0]
data_2_corr = nan_corr(target_resampled, data_2_resampled)[0]
booted_metric[n] = data_1_corr - data_2_corr
data_mean = nan_corr(target, data_1)[0] - nan_corr(target, data_2)[0]
ci = [np.percentile(booted_metric, alpha / 2 * 100),
np.percentile(booted_metric, (1 - alpha / 2) * 100)]
ci = np.abs(np.array(ci) - data_mean)
if np.median(booted_metric) < 0:
booted_metric *= -1
p = 2 * np.mean(booted_metric <= 0)
return p, data_mean, ci
def two_sample_corr_p(target, data_1, data_2, alpha=0.05):
# get rid of nans
target = target.reshape(-1).astype(float).copy()
data_1 = data_1.reshape(-1).astype(float).copy()
data_2 = data_2.reshape(-1).astype(float).copy()
nan_loc = np.isnan(target) | np.isnan(data_1) | np.isnan(data_2)
target = target[~nan_loc]
data_1 = data_1[~nan_loc]
data_2 = data_2[~nan_loc]
n = target.shape[0]
s = np.corrcoef(np.concatenate((target[None, :], data_1[None, :], data_2[None, :]), axis=0))
s_det = np.linalg.det(s)
numerator = (n - 1) * (1 + s[1, 2])
denom_1 = 2 * ((n - 1) / (n - 3)) * s_det
denom_2 = 1/4 * (s[0, 1] + s[0, 2])**2 * (1 - s[1, 2])**3
t = (s[0, 1] - s[0, 2]) * np.sqrt(numerator / (denom_1 + denom_2))
p = scipy.stats.t.cdf(t, n - 3) * 2
return p
def nan_corr(y_true, y_hat, alpha=0.05, mean_sub=True):
y_true = y_true.reshape(-1)
y_hat = y_hat.reshape(-1)
mask = ~np.isnan(y_true) & ~np.isnan(y_hat)
y_true = y_true[mask]
y_hat = y_hat[mask]
if mean_sub:
y_true = y_true - np.mean(y_true)
y_hat = y_hat - np.mean(y_hat)
y_true_std = np.std(y_true, ddof=0)
y_hat_std = np.std(y_hat, ddof=0)
corr = np.mean(y_true * y_hat) / y_true_std / y_hat_std
# now estimate the confidence intervals for the correlation
n = y_true.shape[0]
z_a = scipy.stats.norm.ppf(1 - alpha / 2)
z_r = np.log((1 + corr) / (1 - corr)) / 2
l = z_r - (z_a / np.sqrt(n - 3))
u = z_r + (z_a / np.sqrt(n - 3))
ci_l = (np.exp(2 * l) - 1) / (np.exp(2 * l) + 1)
ci_u = (np.exp(2 * u) - 1) / (np.exp(2 * u) + 1)
ci = [np.abs(ci_l - corr), ci_u - corr]
return corr, ci
def accuracy(y_true, y_hat):
y_true = y_true.reshape(-1)
y_hat = y_hat.reshape(-1)
nan_loc = np.isnan(y_true) | np.isnan(y_hat)
y_true = y_true[~nan_loc]
y_hat = y_hat[~nan_loc]
true_positives = np.sum((y_true == 1) & (y_hat == 1))
true_negatives = np.sum((y_true == 0) & (y_hat == 0))
total = y_true.shape[0]
return (true_positives + true_negatives) / total
def precision(y_true, y_hat):
y_true = y_true.reshape(-1)
y_hat = y_hat.reshape(-1)
nan_loc = np.isnan(y_true) | np.isnan(y_hat)
y_true = y_true[~nan_loc]
y_hat = y_hat[~nan_loc]
true_positives = np.sum((y_true == 1) & (y_hat == 1))
false_positives = np.sum((y_true == 0) & (y_hat == 1))
return true_positives / (true_positives + false_positives)
def recall(y_true, y_hat):
y_true = y_true.reshape(-1)
y_hat = y_hat.reshape(-1)
nan_loc = np.isnan(y_true) | np.isnan(y_hat)
y_true = y_true[~nan_loc]
y_hat = y_hat[~nan_loc]
true_positives = np.sum((y_true == 1) & (y_hat == 1))
false_negatives = np.sum((y_true == 1) & (y_hat == 0))
return true_positives / (true_positives + false_negatives)
def f_measure(y_true, y_hat):
y_true = y_true.reshape(-1)
y_hat = y_hat.reshape(-1)
nan_loc = np.isnan(y_true) | np.isnan(y_hat)
y_true = y_true[~nan_loc]
y_hat = y_hat[~nan_loc]
p = precision(y_true, y_hat)
r = recall(y_true, y_hat)
return (2 * p * r) / (p + r)
def mutual_info(y_true, y_hat):
y_true = y_true.reshape(-1)
y_hat = y_hat.reshape(-1)
nan_loc = np.isnan(y_true) | np.isnan(y_hat)
y_true = y_true[~nan_loc]
y_hat = y_hat[~nan_loc]
p_y_true = np.array([1 - np.mean(y_true), np.mean(y_true)])
p_y_hat = np.array([1 - np.mean(y_hat), np.mean(y_hat)])
p_joint = np.zeros((2, 2))
p_joint[0, 0] = np.mean((y_true == 0) & (y_hat == 0))
p_joint[1, 0] = np.mean((y_true == 1) & (y_hat == 0))
p_joint[0, 1] = np.mean((y_true == 0) & (y_hat == 1))
p_joint[1, 1] = np.mean((y_true == 1) & (y_hat == 1))
p_outer = p_y_true[:, None] * p_y_hat[None, :]
mi = 0
for i in range(2):
for j in range(2):
if p_joint[i, j] != 0:
mi += p_joint[i, j] * np.log2(p_joint[i, j] / p_outer[i, j])
return mi
def metric_ci(metric, y_true, y_hat, alpha=0.05, n_boot=1000, rng=np.random.default_rng()):
y_true = y_true.astype(float)
y_hat = y_hat.astype(float)
y_true = y_true.reshape(-1)
y_hat = y_hat.reshape(-1)
nan_loc = np.isnan(y_true) | np.isnan(y_hat)
y_true = y_true[~nan_loc]
y_hat = y_hat[~nan_loc]
mi = metric(y_true, y_hat)
booted_mi = np.zeros(n_boot)
mi_ci = np.zeros(2)
for n in range(n_boot):
sample_inds = rng.integers(0, high=y_true.shape[0], size=y_true.shape[0])
y_true_resampled = y_true[sample_inds]
y_hat_resampled = y_hat[sample_inds]
booted_mi[n] = metric(y_true_resampled, y_hat_resampled)
mi_ci[0] = np.percentile(booted_mi, alpha / 2 * 100)
mi_ci[1] = np.percentile(booted_mi, (1 - alpha / 2) * 100)
mi_ci = np.abs(mi_ci - mi)
return mi, mi_ci
def metric_null(metric, y_true, n_sample=1000, rng=np.random.default_rng()):
y_true = y_true.reshape(-1)
nan_loc = np.isnan(y_true)
y_true = y_true[~nan_loc]
py = np.mean(y_true)
if py > 0.5:
py = 1
else:
py = 0
sampled_mi = np.zeros(n_sample)
for n in range(n_sample):
random_example = rng.uniform(0, 1, size=y_true.shape) < py
sampled_mi[n] = metric(y_true, random_example)
return np.mean(sampled_mi)