Sesión 14 B

Sesión 14 B#

Modelos de Mezcla Gaussiana (GMM)#

from sklearn.mixture import GaussianMixture
from matplotlib import pyplot as plt
import numpy as np
import pandas as pd

import os
ruta = os.path.join('..', 'data', 'bank_customer_data.csv')
df = pd.read_csv(ruta)
df.head()
income debt labels
0 2.985433 1.467052 0.0
1 1.661632 6.248713 1.0
2 2.131999 6.693823 1.0
3 5.851889 4.742888 2.0
4 3.404236 2.991008 0.0 
df.shape

(400, 3)

df.labels.value_counts()

labels
0.0    200
1.0    150
2.0     50
Name: count, dtype: int64

1. Gaussian Mixture Model (GMM) básico#

GaussianMixture?

  • También puedes checar la documentación oficial de sklearn sobre GMM aquí.

# Modelo de mezclas Gaussianas
gmm = GaussianMixture(
    n_components=3
)

# Entrenamos
gmm.fit(df[['income', 'debt']])

GaussianMixture(n_components=3)
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# Parámetros óptimos: means_
gmm.means_[0]

array([2.96040004, 2.57742868])

# Parámetros óptimos: covariances_
gmm.covariances_

array([[[ 1.09095334, -0.21668949],
        [-0.21668949,  1.08251907]],

       [[ 0.53573118, -0.10747755],
        [-0.10747755,  0.76187159]],

       [[ 0.948484  ,  0.90614216],
        [ 0.90614216,  1.00900976]]])

# Parámetros óptimos: weights_
gmm.weights_

array([0.49736151, 0.37979719, 0.1228413 ])

from scipy.stats import multivariate_normal

# Gaussianas ajustadas
X1 = multivariate_normal(
    mean=gmm.means_[0],
    cov=gmm.covariances_[0]
)
X2 = multivariate_normal(
    mean=gmm.means_[1],
    cov=gmm.covariances_[1]
)
X3 = multivariate_normal(
    mean=gmm.means_[2],
    cov=gmm.covariances_[2]
)
#X4 = multivariate_normal(
#    mean=gmm.means_[3],
#    cov=gmm.covariances_[3]
#)

# Predicción de probabilidades
probas = gmm.predict_proba(df[['income', 'debt']])
probas

array([[9.97898701e-01, 3.63395861e-06, 2.09766539e-03],
       [1.59470132e-03, 9.98405299e-01, 1.28157116e-49],
       [4.45537550e-04, 9.99554462e-01, 1.41247255e-48],
       ...,
       [9.96186473e-01, 3.81352745e-03, 4.36364940e-11],
       [9.99985299e-01, 2.23920789e-06, 1.24613957e-05],
       [2.87390800e-01, 7.12609200e-01, 4.97269931e-23]], shape=(400, 3))

# Convertir a DataFrame
df_probas = pd.DataFrame(
    probas,
    columns=[f"componente_{i}" for i in range(3)]
)

df_probas
componente_0 componente_1 componente_2
0 0.997899 0.000004 2.097665e-03
1 0.001595 0.998405 1.281571e-49
2 0.000446 0.999554 1.412473e-48
3 0.000871 0.000003 9.991260e-01
4 0.988526 0.002157 9.317247e-03
... ... ... ...
395 0.977300 0.000057 2.264287e-02
396 0.051108 0.948892 5.911349e-29
397 0.996186 0.003814 4.363649e-11
398 0.999985 0.000002 1.246140e-05
399 0.287391 0.712609 4.972699e-23

400 rows × 3 columns

# Datos
plt.scatter(
    x=df['income'],
    y=df['debt'], 
    c=gmm.predict_proba(df[['income', 'debt']]),
    cmap='Accent',
    alpha=0.5
)
# Añadimos etiquetas a los ejes
plt.xlabel('Ingresos mensuales (x100k MXN)')
plt.ylabel('Deuda (x100k MXN)')

# Gaussiana 1
x = np.linspace(0, 8, 100)
y = np.linspace(0, 8, 100)
X, Y = np.meshgrid(x, y)
z = X1.pdf(np.dstack((X, Y)))
# Graficamos la función de densidad
plt.contour(X, Y, z, levels=10, cmap='rainbow')

# Gaussiana 2
x = np.linspace(0, 8, 100)
y = np.linspace(0, 8, 100)
X, Y = np.meshgrid(x, y)
z = X2.pdf(np.dstack((X, Y)))
# Graficamos la función de densidad
plt.contour(X, Y, z, levels=10, cmap='rainbow')

# Gaussiana 3
x = np.linspace(0, 8, 100)
y = np.linspace(0, 8, 100)
X, Y = np.meshgrid(x, y)
z = X3.pdf(np.dstack((X, Y)))
# Graficamos la función de densidad
plt.contour(X, Y, z, levels=10, cmap='rainbow')

# Gaussiana 4
#x = np.linspace(0, 8, 100)
#y = np.linspace(0, 8, 100)
#X, Y = np.meshgrid(x, y)
#z = X4.pdf(np.dstack((X, Y)))
# Graficamos la función de densidad
#plt.contour(X, Y, z, levels=10, cmap='rainbow')

/tmp/ipykernel_1189/1720985629.py:2: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored
  plt.scatter(

<matplotlib.contour.QuadContourSet at 0x79696c4edbd0>
../_images/9479a7ec64cbfab332d79184dc980e423fef0b9407a000e0d970f1a428d022af.png

2. Probar varios números de componentes y comparar BIC#

import warnings
warnings.filterwarnings('ignore')

#BIC
ks = range(1, 10)
bics = []

for k in ks:
    gmm = GaussianMixture(n_components=k)
    gmm.fit(df[['income', 'debt']])
    bics.append(gmm.bic(df[['income', 'debt']]))

list1 = list(zip(ks, bics))
list1

[(1, 3139.7023248527153),
 (2, 3047.3837113363734),
 (3, 2848.5387889567273),
 (4, 2878.8971484807275),
 (5, 2916.0991099907646),
 (6, 2946.246983381312),
 (7, 2977.954275497212),
 (8, 3006.681357865192),
 (9, 3035.3456323761566)]

min(list1, key=lambda x: x[1])

(3, 2848.5387889567273)

#AIC
aics = []
for k in ks:
    gmm = GaussianMixture(n_components=k)
    gmm.fit(df[['income', 'debt']])
    aics.append(gmm.aic(df[['income', 'debt']]))

list2 = list(zip(ks, aics))
list2

[(1, 3119.7450021171753),
 (2, 3003.4776013181854),
 (3, 2780.788837891324),
 (4, 2786.7990912971527),
 (5, 2799.482076627995),
 (6, 2809.136688817821),
 (7, 2810.809417537192),
 (8, 2819.294055008664),
 (9, 2832.147419284117)]

min(list2, key=lambda x: x[1])

(3, 2780.788837891324)

# Mostrar resultados
plt.plot(ks, bics, marker='o', label="BIC", color='purple')
plt.plot(ks, aics, marker='o', label="AIC", color='green')
plt.xlabel("Número de componentes (k)")
plt.ylabel("Valor del criterio")
plt.legend()
plt.show()
../_images/4c4ecba12e30bb601e087d8b7715bc5d7dca820894b61fa4f501ab6ac2aa5ba8.png