bayeisan kdey
This commit is contained in:
parent
bd9f8e2cb4
commit
3e7a431d26
|
|
@ -0,0 +1,99 @@
|
|||
from sklearn.linear_model import LogisticRegression
|
||||
import quapy as qp
|
||||
from BayesianKDEy.plot_simplex import plot_prev_points, plot_prev_points_matplot
|
||||
from quapy.functional import strprev
|
||||
from quapy.method.aggregative import KDEyML
|
||||
from quapy.protocol import UPP
|
||||
import quapy.functional as F
|
||||
import numpy as np
|
||||
from tqdm import tqdm
|
||||
|
||||
|
||||
def bayesian(kdes, data, prob_classifier, init=None, MAX_ITER=100_000, warmup=3_000):
|
||||
"""
|
||||
Bayes:
|
||||
P(prev|data) = P(data|prev) P(prev) / P(data)
|
||||
i.e.,
|
||||
posterior = likelihood * prior / evidence
|
||||
we assume the likelihood be:
|
||||
prev @ [kde_i_likelihood(data) 1..i..n]
|
||||
prior be uniform in simplex
|
||||
"""
|
||||
def pdf(kde, X):
|
||||
# todo: remove exp, since we are then doing the log every time? (not sure)
|
||||
return np.exp(kde.score_samples(X))
|
||||
|
||||
X = prob_classifier.predict_proba(data)
|
||||
test_densities = [pdf(kde_i, X) for kde_i in kdes]
|
||||
|
||||
def log_likelihood(prev, epsilon=1e-8):
|
||||
# test_likelihoods = sum(prev_i*dens_i for prev_i, dens_i in zip (prev, test_densities))
|
||||
test_likelihoods = prev @ test_densities
|
||||
test_loglikelihood = np.log(test_likelihoods + epsilon)
|
||||
return np.sum(test_loglikelihood)
|
||||
|
||||
def log_prior(prev):
|
||||
# todo: adapt to arbitrary prior knowledge (e.g., something around training prevalence)
|
||||
return 1 # it is not 1 but we assume uniform, son anyway is an useless constant
|
||||
|
||||
def sample_neighbour(prev):
|
||||
rand_prev = F.uniform_prevalence_sampling(n_classes=len(prev), size=1)
|
||||
rand_direction = rand_prev - prev
|
||||
neighbour = F.normalize_prevalence(prev + rand_direction*0.05)
|
||||
return neighbour
|
||||
|
||||
n_classes = len(prob_classifier.classes_)
|
||||
current_prev = F.uniform_prevalence(n_classes) if init is None else init
|
||||
current_likelihood = log_likelihood(current_prev) + log_prior(current_prev)
|
||||
|
||||
# Metropolis-Hastings
|
||||
samples = []
|
||||
for _ in tqdm(range(MAX_ITER), total=MAX_ITER):
|
||||
proposed_prev = sample_neighbour(current_prev)
|
||||
|
||||
# probability of acceptance
|
||||
proposed_likelihood = log_likelihood(proposed_prev) + log_prior(proposed_prev)
|
||||
acceptance = proposed_likelihood - current_likelihood
|
||||
|
||||
# decide acceptance
|
||||
if np.log(np.random.rand()) < acceptance:
|
||||
# accept
|
||||
current_prev = proposed_prev
|
||||
current_likelihood = proposed_likelihood
|
||||
|
||||
samples.append(current_prev)
|
||||
|
||||
# remove "warmup" initial iterations
|
||||
samples = np.asarray(samples[warmup:])
|
||||
return samples
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
qp.environ["SAMPLE_SIZE"] = 500
|
||||
cls = LogisticRegression()
|
||||
kdey = KDEyML(cls)
|
||||
|
||||
train, test = qp.datasets.fetch_UCIMulticlassDataset('waveform-v1', standardize=True).train_test
|
||||
|
||||
with qp.util.temp_seed(0):
|
||||
print('fitting KDEy')
|
||||
kdey.fit(*train.Xy)
|
||||
|
||||
shifted = test.sampling(500, *[0.1, 0.1, 0.8])
|
||||
prev_hat = kdey.predict(shifted.X)
|
||||
mae = qp.error.mae(shifted.prevalence(), prev_hat)
|
||||
print(f'true_prev={strprev(shifted.prevalence())}, prev_hat={strprev(prev_hat)}, {mae=:.4f}')
|
||||
|
||||
kdes = kdey.mix_densities
|
||||
h = kdey.classifier
|
||||
samples = bayesian(kdes, shifted.X, h, init=prev_hat, MAX_ITER=100_000, warmup=0)
|
||||
|
||||
print(f'mean posterior {strprev(samples.mean(axis=0))}')
|
||||
|
||||
plot_prev_points(samples, true_prev=shifted.prevalence())
|
||||
|
||||
|
||||
# report = qp.evaluation.evaluation_report(kdey, protocol=UPP(test), verbose=True)
|
||||
# print(report.mean(numeric_only=True))
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,94 @@
|
|||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
from scipy.stats import gaussian_kde
|
||||
|
||||
|
||||
def plot_prev_points(prevs, true_prev):
|
||||
|
||||
def cartesian(p):
|
||||
dim = p.shape[-1]
|
||||
p = p.reshape(-1,dim)
|
||||
x = p[:, 1] + p[:, 2] * 0.5
|
||||
y = p[:, 2] * np.sqrt(3) / 2
|
||||
return x, y
|
||||
|
||||
# simplex coordinates
|
||||
v1 = np.array([0, 0])
|
||||
v2 = np.array([1, 0])
|
||||
v3 = np.array([0.5, np.sqrt(3)/2])
|
||||
|
||||
# transform (a,b,c) -> Cartesian coordinates
|
||||
x, y = cartesian(prevs)
|
||||
|
||||
# Plot
|
||||
fig, ax = plt.subplots(figsize=(6, 6))
|
||||
ax.scatter(x, y, s=50, alpha=0.05, edgecolors='none')
|
||||
ax.scatter(*cartesian(true_prev), s=5, alpha=1)
|
||||
|
||||
# edges
|
||||
triangle = np.array([v1, v2, v3, v1])
|
||||
ax.plot(triangle[:, 0], triangle[:, 1], color='black')
|
||||
|
||||
# vertex labels
|
||||
ax.text(-0.05, -0.05, "y=0", ha='right', va='top')
|
||||
ax.text(1.05, -0.05, "y=1", ha='left', va='top')
|
||||
ax.text(0.5, np.sqrt(3)/2 + 0.05, "y=2", ha='center', va='bottom')
|
||||
|
||||
ax.set_aspect('equal')
|
||||
ax.axis('off')
|
||||
plt.show()
|
||||
|
||||
|
||||
def plot_prev_points_matplot(points):
|
||||
|
||||
# project 2D
|
||||
v1 = np.array([0, 0])
|
||||
v2 = np.array([1, 0])
|
||||
v3 = np.array([0.5, np.sqrt(3) / 2])
|
||||
x = points[:, 1] + points[:, 2] * 0.5
|
||||
y = points[:, 2] * np.sqrt(3) / 2
|
||||
|
||||
# kde
|
||||
xy = np.vstack([x, y])
|
||||
kde = gaussian_kde(xy)
|
||||
xmin, xmax = 0, 1
|
||||
ymin, ymax = 0, np.sqrt(3) / 2
|
||||
|
||||
# grid
|
||||
xx, yy = np.mgrid[xmin:xmax:200j, ymin:ymax:200j]
|
||||
positions = np.vstack([xx.ravel(), yy.ravel()])
|
||||
zz = np.reshape(kde(positions).T, xx.shape)
|
||||
|
||||
# mask points in simplex
|
||||
def in_triangle(x, y):
|
||||
return (y >= 0) & (y <= np.sqrt(3) * np.minimum(x, 1 - x))
|
||||
|
||||
mask = in_triangle(xx, yy)
|
||||
zz_masked = np.ma.array(zz, mask=~mask)
|
||||
|
||||
# plot
|
||||
fig, ax = plt.subplots(figsize=(6, 6))
|
||||
ax.imshow(
|
||||
np.rot90(zz_masked),
|
||||
cmap=plt.cm.viridis,
|
||||
extent=[xmin, xmax, ymin, ymax],
|
||||
alpha=0.8,
|
||||
)
|
||||
|
||||
# Bordes del triángulo
|
||||
triangle = np.array([v1, v2, v3, v1])
|
||||
ax.plot(triangle[:, 0], triangle[:, 1], color='black', lw=2)
|
||||
|
||||
# Puntos (opcional)
|
||||
ax.scatter(x, y, s=5, c='white', alpha=0.3)
|
||||
|
||||
# Etiquetas
|
||||
ax.text(-0.05, -0.05, "A (1,0,0)", ha='right', va='top')
|
||||
ax.text(1.05, -0.05, "B (0,1,0)", ha='left', va='top')
|
||||
ax.text(0.5, np.sqrt(3) / 2 + 0.05, "C (0,0,1)", ha='center', va='bottom')
|
||||
|
||||
ax.set_aspect('equal')
|
||||
ax.axis('off')
|
||||
plt.show()
|
||||
|
||||
|
||||
Loading…
Reference in New Issue