QuaPy/BayesianKDEy/plot_simplex.py

419 lines
14 KiB
Python

import os
import pickle
from pathlib import Path
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from scipy.stats import gaussian_kde
from method.confidence import (ConfidenceIntervals as CI,
ConfidenceEllipseSimplex as CE,
ConfidenceEllipseCLR as CLR,
ConfidenceEllipseILR as ILR)
def get_region_colormap(name="blue", alpha=0.40):
name = name.lower()
if name == "blue":
base = (76/255, 114/255, 176/255)
elif name == "orange":
base = (221/255, 132/255, 82/255)
elif name == "violet":
base = (129/255, 114/255, 178/255)
else:
raise ValueError(f"Unknown palette name: {name}")
cmap = ListedColormap([
(1, 1, 1, 0), # 0: transparent white
(base[0], base[1], base[2], alpha) # 1: color
])
return cmap
def plot_prev_points(samples=None,
show_samples=True,
true_prev=None,
point_estim=None,
train_prev=None,
show_mean=True,
show_legend=True,
region=None,
region_resolution=1000,
confine_region_in_simplex=False,
color='blue',
save_path=None):
plt.rcParams.update({
'font.size': 10, # tamaño base de todo el texto
'axes.titlesize': 12, # título del eje
'axes.labelsize': 10, # etiquetas de ejes
'xtick.labelsize': 8, # etiquetas de ticks
'ytick.labelsize': 8,
'legend.fontsize': 9, # leyenda
})
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
def barycentric_from_xy(x, y):
"""
Given cartesian (x,y) in simplex returns baricentric coordinates (p1,p2,p3).
"""
p3 = 2 * y / np.sqrt(3)
p2 = x - 0.5 * p3
p1 = 1 - p2 - p3
return np.stack([p1, p2, p3], axis=-1)
# simplex coordinates
v1 = np.array([0, 0])
v2 = np.array([1, 0])
v3 = np.array([0.5, np.sqrt(3)/2])
# Plot
fig, ax = plt.subplots(figsize=(6, 6))
if region is not None:
if callable(region):
region_list = [("region", region)]
else:
region_list = region # lista de (name, fn)
if region is not None:
# rectangular mesh
x_min, x_max = -0.2, 1.2
y_min, y_max = -0.2, np.sqrt(3) / 2 + 0.2
xs = np.linspace(x_min, x_max, region_resolution)
ys = np.linspace(y_min, y_max, region_resolution)
grid_x, grid_y = np.meshgrid(xs, ys)
# barycentric
pts_bary = barycentric_from_xy(grid_x, grid_y)
# mask within simplex
if confine_region_in_simplex:
in_simplex = np.all(pts_bary >= 0, axis=-1)
else:
in_simplex = np.full(shape=(region_resolution, region_resolution), fill_value=True, dtype=bool)
# iterate over regions
for (rname, rfun) in region_list:
mask = np.zeros_like(in_simplex, dtype=float)
valid_pts = pts_bary[in_simplex]
mask_vals = np.array([float(rfun(p)) for p in valid_pts])
mask[in_simplex] = mask_vals
ax.pcolormesh(
xs, ys, mask,
shading='auto',
cmap=get_region_colormap(color),
alpha=0.3,
)
if samples is not None:
if show_samples:
ax.scatter(*cartesian(samples), s=15, alpha=0.5, edgecolors='none', label='samples', color='black', linewidth=0.5)
if show_mean is not None:
if isinstance(show_mean, np.ndarray):
ax.scatter(*cartesian(show_mean), s=10, alpha=1, label='sample-mean', edgecolors='black')
elif show_mean==True and samples is not None:
ax.scatter(*cartesian(samples.mean(axis=0)), s=10, alpha=1, label='sample-mean', edgecolors='black')
else:
raise ValueError(f'show_mean should either be a boolean (if True, then samples must be provided) or '
f'the mean point itself')
if true_prev is not None:
ax.scatter(*cartesian(true_prev), s=10, alpha=1, label='true-prev', edgecolors='black')
if point_estim is not None:
ax.scatter(*cartesian(point_estim), s=10, alpha=1, label='KDEy-estim', edgecolors='black')
if train_prev is not None:
ax.scatter(*cartesian(train_prev), s=10, alpha=1, label='train-prev', edgecolors='black')
# 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=1", ha='right', va='top')
ax.text(1.05, -0.05, "Y=2", ha='left', va='top')
ax.text(0.5, np.sqrt(3)/2 + 0.05, "Y=3", ha='center', va='bottom')
ax.set_aspect('equal')
ax.axis('off')
if show_legend:
plt.legend(
loc='center left',
bbox_to_anchor=(1.05, 0.5),
)
plt.tight_layout()
if save_path is None:
plt.show()
else:
os.makedirs(Path(save_path).parent, exist_ok=True)
plt.savefig(save_path)
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, bw_method=0.25)
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()
# -------- new function
def cartesian(p):
dim = p.shape[-1]
p = np.atleast_2d(p)
x = p[:, 1] + p[:, 2] * 0.5
y = p[:, 2] * np.sqrt(3) / 2
return x, y
def barycentric_from_xy(x, y):
"""
Given cartesian (x,y) in simplex returns baricentric coordinates (p1,p2,p3).
"""
p3 = 2 * y / np.sqrt(3)
p2 = x - 0.5 * p3
p1 = 1 - p2 - p3
return np.stack([p1, p2, p3], axis=-1)
def plot_regions(ax, region_layers, resolution, confine):
xs = np.linspace(-0.2, 1.2, resolution)
ys = np.linspace(-0.2, np.sqrt(3)/2 + 0.2, resolution)
grid_x, grid_y = np.meshgrid(xs, ys)
pts_bary = barycentric_from_xy(grid_x, grid_y)
if confine:
mask_simplex = np.all(pts_bary >= 0, axis=-1)
else:
mask_simplex = np.ones(grid_x.shape, dtype=bool)
for region in region_layers:
mask = np.zeros_like(mask_simplex, dtype=float)
valid_pts = pts_bary[mask_simplex]
mask_vals = np.array([float(region["fn"](p)) for p in valid_pts])
mask[mask_simplex] = mask_vals
ax.pcolormesh(
xs, ys, mask,
shading="auto",
cmap=get_region_colormap(region.get("color", "blue")),
alpha=region.get("alpha", 0.3),
label=region.get("label", None),
)
def plot_points(ax, point_layers):
for layer in point_layers:
pts = layer["points"]
style = layer.get("style", {})
ax.scatter(
*cartesian(pts),
label=layer.get("label", None),
**style
)
def plot_simplex(
point_layers=None,
region_layers=None,
region_resolution=1000,
confine_region_in_simplex=False,
show_legend=True,
save_path=None,
):
fig, ax = plt.subplots(figsize=(6, 6))
if region_layers:
plot_regions(ax, region_layers, region_resolution, confine_region_in_simplex)
if point_layers:
plot_points(ax, point_layers)
# simplex edges
triangle = np.array([[0,0],[1,0],[0.5,np.sqrt(3)/2],[0,0]])
ax.plot(triangle[:,0], triangle[:,1], color="black")
# labels
ax.text(-0.05, -0.05, "Y=1", ha="right", va="top")
ax.text(1.05, -0.05, "Y=2", ha="left", va="top")
ax.text(0.5, np.sqrt(3)/2 + 0.05, "Y=3", ha="center", va="bottom")
ax.set_aspect("equal")
ax.axis("off")
if show_legend:
ax.legend(loc="center left", bbox_to_anchor=(1.05, 0.5))
plt.tight_layout()
if save_path:
plt.savefig(save_path)
else:
plt.show()
if __name__ == '__main__':
np.random.seed(1)
# n = 1000
# alpha = [1,1,1]
# prevs = np.random.dirichlet(alpha, size=n)
# def regions():
# confs = [0.99, 0.95, 0.90]
# yield 'CI', [(f'{int(c*100)}%', CI(prevs, confidence_level=c).coverage) for c in confs]
# yield 'CI-b', [(f'{int(c * 100)}%', CI(prevs, confidence_level=c, bonferroni_correction=True).coverage) for c in confs]
# yield 'CE', [(f'{int(c*100)}%', CE(prevs, confidence_level=c).coverage) for c in confs]
# yield 'CLR', [(f'{int(c*100)}%', CLR(prevs, confidence_level=c).coverage) for c in confs]
# yield 'ILR', [(f'{int(c*100)}%', ILR(prevs, confidence_level=c).coverage) for c in confs]
# resolution = 1000
# alpha_str = ','.join([f'{str(i)}' for i in alpha])
# for crname, cr in regions():
# plot_prev_points(prevs, show_mean=True, show_legend=False, region=cr, region_resolution=resolution,
# color='blue',
# save_path=f'./plots/simplex_{crname}_alpha{alpha_str}_res{resolution}.png',
# )
# def regions():
# confs = [0.99, 0.95, 0.90]
# yield 'CI', [(f'{int(c*100)}%', CI(prevs, confidence_level=c).coverage) for c in confs]
# yield 'CI-b', [(f'{int(c * 100)}%', CI(prevs, confidence_level=c, bonferroni_correction=True).coverage) for c in confs]
# yield 'CE', [(f'{int(c*100)}%', CE(prevs, confidence_level=c).coverage) for c in confs]
# yield 'CLR', [(f'{int(c*100)}%', CLR(prevs, confidence_level=c).coverage) for c in confs]
# yield 'ILR', [(f'{int(c*100)}%', ILR(prevs, confidence_level=c).coverage) for c in confs]
# resolution = 100
# alpha_str = ','.join([f'{str(i)}' for i in alpha])
# region = CI(prevs, confidence_level=.95, bonferroni_correction=True)
# p = None # np.asarray([0.1, 0.8, 0.1])
# plot_prev_points(prevs,
# show_samples=True,
# show_mean=None,
# # show_mean=prevs.mean(axis=0),
# show_legend=False,
# # region=[('', region.coverage)],
# # region_resolution=resolution,
# color='blue',
# true_prev=p,
# # train_prev=region.closest_point_in_region(p),
# save_path=f'./plots/prior_test/uniform.png',
# )
plt.rcParams.update({
'font.size': 10,
'axes.titlesize': 12,
'axes.labelsize': 10,
'xtick.labelsize': 8,
'ytick.labelsize': 8,
'legend.fontsize': 9,
})
n = 1000
train_style = {"color": "blue", "alpha": 0.5, "s":15, 'linewidth':0.5, 'edgecolors':None}
test_style = {"color": "red", "alpha": 0.5, "s": 15, 'linewidth': 0.5, 'edgecolors': None}
# train_prevs = np.random.dirichlet(alpha=[1, 1, 1], size=n)
# test_prevs = np.random.dirichlet(alpha=[1, 1, 1], size=n)
# plot_simplex(
# point_layers=[
# {"points": train_prevs, "label": "train", "style": train_style},
# {"points": test_prevs, "label": "test", "style": test_style},
# ],
# save_path=f'./plots/prior_test/uniform.png'
# )
alpha = [40, 10, 10]
train_prevs = np.random.dirichlet(alpha=alpha, size=n)
test_prevs = np.random.dirichlet(alpha=alpha, size=n)
plot_simplex(
point_layers=[
{"points": train_prevs, "label": "train", "style": train_style},
{"points": test_prevs, "label": "test", "style": test_style},
],
save_path=f'./plots/prior_test/informative.png'
)
# train_prevs = np.random.dirichlet(alpha=[8, 1, 1], size=n)
# test_prevs = np.random.dirichlet(alpha=[1, 8, 1], size=n)
# plot_simplex(
# point_layers=[
# {"points": train_prevs, "label": "train", "style": train_style},
# {"points": test_prevs, "label": "test", "style": test_style},
# ],
# save_path=f'./plots/prior_test/wrong.png'
# )
p = 0.6
K = 3
alpha = [p] + [(1. - p) / (K - 1)] * (K - 1)
alpha = np.array(alpha)
for c in [100, 500, 1_000]:
alpha_c = alpha * c
train_prevs = np.random.dirichlet(alpha=alpha_c, size=n)
test_prevs = np.random.dirichlet(alpha=alpha_c[::-1], size=n)
plot_simplex(
point_layers=[
{"points": train_prevs, "label": "train", "style": train_style},
{"points": test_prevs, "label": "test", "style": test_style},
],
save_path=f'./plots/prior_test/concentration_{c}.png'
)