Conociendo nuestros datos de pingüinos. 🗺🧭🐧
Instalar librerías necesarias
Importar librerías
import empiricaldist
import janitor
import matplotlib.pyplot as plt
import numpy as np
import palmerpenguins
import pandas as pd
import scipy.stats
import seaborn as sns
import sklearn.metrics
import statsmodels.api as sm
import statsmodels.formula.api as smf
import statsmodels.stats as ss
import session_info
Run to view results
Establecer apariencia general de los gráficos
%matplotlib inline
sns.set_style(style='whitegrid')
sns.set_context(context='notebook')
plt.rcParams['figure.figsize'] = (11, 9.4)
penguin_color = {
'Adelie': '#ff6602ff',
'Gentoo': '#0f7175ff',
'Chinstrap': '#c65dc9ff'
}
Run to view results
Cargar los datos
Utilizando el paquete palmerpenguins
Datos crudos
raw_penguins_df = palmerpenguins.load_penguins_raw()
raw_penguins_df
Run to view results
Run to view results
Datos previamente procesados
preprocessed_penguins_df = palmerpenguins.load_penguins()
preprocessed_penguins_df
Run to view results
Utilizando los conjuntos de datos de seaborn
preprocessed_penguins_df = sns.load_dataset("penguins")
Run to view results
Utilizando la interfaz de Deepnote
Links de importación de datos:
raw_penguins_df2 = pd.read_csv('penguins_raw.csv')
raw_penguins_df2
Run to view results
preprocessed_penguins_df2 = pd.read_csv('penguins.csv')
preprocessed_penguins_df2
Run to view results
Colecta y validación de datos
¿Qué tipo de dato son las variables del conjunto de datos?
preprocessed_penguins_df.dtypes
Run to view results
¿Cuántas variables de cada tipo de dato tenemos en el conjunto de datos?
(
preprocessed_penguins_df
.dtypes
.value_counts()
)
Run to view results
¿Cuántas variables y observaciones tenemos en el conjunto de datos?
preprocessed_penguins_df.shape
Run to view results
¿Existen valores nulos explicitos en el conjunto de datos?
(
preprocessed_penguins_df
.isnull()
.any()
)
Run to view results
De tener observaciones con valores nulos, ¿cuántas tenemos por cada variable?
(
preprocessed_penguins_df
.isnull()
.sum()
.sort_values(ascending=False)
)
Run to view results
¿Cuántos valores nulos tenemos en total en el conjunto de datos?
(
preprocessed_penguins_df
.isnull()
.sum()
.sum()
)
Run to view results
¿Cuál es la proporción de valores nulos por cada variable?
(
preprocessed_penguins_df
.isnull()
.melt(value_name='missing')
.pipe(
lambda df: (
sns.displot(
data=df,
y='variable',
hue='missing',
multiple='fill',
aspect=2
)
)
)
)
Run to view results
¿Cómo podemos visualizar los valores nulos en todo el conjunto de datos?
(
preprocessed_penguins_df
.isnull()
.transpose()
.pipe(
lambda df: sns.heatmap(data=df)
)
)
Run to view results
¿Cuántas observaciones perdemos si eliminamos los datos faltantes?
processed_penguins_df = (
preprocessed_penguins_df
.dropna()
)
processed_penguins_df
Run to view results
Conteos y proporciones
Preludio: ¿Qué estadísticos describen el conjunto de datos?
Todas las variables
processed_penguins_df.describe(include='all')
Run to view results
Solo las numéricas
processed_penguins_df.describe(include=[np.number])
Run to view results
Solo categóricas - 1
processed_penguins_df.describe(include=object)
Run to view results
Solo categóricas - 2
(
processed_penguins_df
.astype(
{
'species': 'category',
'island': 'category',
'sex': 'category'
}
)
.describe(include=['category', object])
)
Run to view results
¿Cómo visualizar los conteos?
Pandas
(
processed_penguins_df
.species
.value_counts()
.plot(
kind='bar',
# color=penguin_color.values()
)
)
Run to view results
Seaborn
sns.catplot(
data=processed_penguins_df,
x='species',
kind='count',
palette=penguin_color,
# order=processed_penguins_df.value_counts('species', sort=True).index
)
Run to view results
(
processed_penguins_df
.value_counts('species', sort=True)
.reset_index(name='count')
.pipe(
lambda df: (
sns.barplot(
data=df,
x='species',
y='count',
palette=penguin_color
)
)
)
)
Run to view results
¿Cómo visualizar las proporciones?
(
processed_penguins_df
.add_column('variable', '')
.pipe(
lambda df: (
sns.displot(
data=df,
x='variable',
hue='species',
multiple='fill',
palette=penguin_color
)
)
)
)
Run to view results
Medidas de tendencia central
Media o promedio
processed_penguins_df.bill_depth_mm.mean()
np.mean(processed_penguins_df.bill_depth_mm)
processed_penguins_df.mean()
processed_penguins_df.median()
processed_penguins_df.mode()
processed_penguins_df.describe(include=object)
Run to view results
np.mean(processed_penguins_df.bill_depth_mm)
Run to view results
processed_penguins_df.mean()
Run to view results
Mediana
processed_penguins_df.median()
Run to view results
Moda
processed_penguins_df.mode()
Run to view results
processed_penguins_df.describe(include=object)
Run to view results
Medidas de dispersión
¿Cuál es el valor máximo de las variables?
processed_penguins_df.max()
Run to view results
¿Cuál es el valor mínimo de las variables?
processed_penguins_df.min()
Run to view results
¿Cuál es el rango de las variables?
processed_penguins_df.max(numeric_only=True) - processed_penguins_df.min(numeric_only=True)
Run to view results
¿Cuál es la desviación estándar de las variables?
processed_penguins_df.std()
Run to view results
¿Cuál es el rango intercuartílico?
processed_penguins_df.quantile(0.25)
Run to view results
processed_penguins_df.quantile(0.75) - processed_penguins_df.quantile(0.25)
Run to view results
(
processed_penguins_df
.quantile(q=[0.75, 0.50, 0.25])
.transpose()
.rename_axis('metric')
.reset_index()
.assign(
iqr = lambda df: df[0.75] - df[0.25]
)
)
Run to view results
¿Cómo puedo visualizar la distribución de una variable?
Histograma
sns.histplot(
data=processed_penguins_df,
x='flipper_length_mm',
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.mean(),
color='red',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.median(),
color='blue',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.mode().values[0],
color='black',
linestyle='dashed',
linewidth=4
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.quantile(0.25),
color='yellow',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.quantile(0.75),
color='yellow',
linestyle='dashed',
linewidth=2
)
Run to view results
Diagrama de caja / boxplot
sns.boxplot(
x=processed_penguins_df.flipper_length_mm,
)
Run to view results
Limitaciones
def freedman_diaconis_bindwidth(x: pd.Series) -> float:
"""Find optimal bindwidth using Freedman-Diaconis rule."""
IQR = x.quantile(0.75) - x.quantile(0.25)
N = x.size
return 2 * IQR / N ** (1 / 3)
Run to view results
sns.histplot(
data=processed_penguins_df,
x='flipper_length_mm',
binwidth=6.3
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.mean(),
color='red',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.median(),
color='blue',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.mode().values[0],
color='black',
linestyle='dashed',
linewidth=4
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.quantile(0.25),
color='yellow',
linestyle='dashed',
linewidth=2
)
plt.axvline(
x=processed_penguins_df.flipper_length_mm.quantile(0.75),
color='yellow',
linestyle='dashed',
linewidth=2
)
Run to view results
Distribuciones: PMFs, CDFs y PDFs
Funciones de probabilidad de masas (PMFs)
Utilizando seaborn
sns.histplot(
data=processed_penguins_df,
x='flipper_length_mm',
binwidth=1,
stat='probability'
)
Run to view results
Utilizando empiricaldist
pmf_flipper_length_mm = empiricaldist.Pmf.from_seq(
processed_penguins_df.flipper_length_mm,
normalize=True
)
Run to view results
pmf_flipper_length_mm.bar()
Run to view results
pmf_flipper_length_mm(231)
Run to view results
processed_penguins_df.flipper_length_mm.max()
Run to view results
Funciones empirícas de probabilidad acumulada (ECDFs)
Utilizando seaborn
sns.ecdfplot(
data=processed_penguins_df,
x="flipper_length_mm"
)
Run to view results
Utilizando empiricaldist
cdf_flipper_length_mm = empiricaldist.Cdf.from_seq(
processed_penguins_df.flipper_length_mm,
normalize=True
)
Run to view results
cdf_flipper_length_mm.plot()
q = 200 # Specify quantity
p = cdf_flipper_length_mm.forward(q)
plt.vlines(
x=q,
ymin=0,
ymax=p,
color = 'black',
linestyle='dashed'
)
plt.hlines(
y=p,
xmin=pmf_flipper_length_mm.qs[0],
xmax=q,
color='black',
linestyle='dashed'
)
plt.plot(q, p, 'ro')
Run to view results
cdf_flipper_length_mm.step()
p_1 = 0.25 # Specify probability
p_2 = 0.75
ps = (0.25, 0.75) # IQR
qs = cdf_flipper_length_mm.inverse(ps)
plt.vlines(
x=qs,
ymin=0,
ymax=ps,
color = 'black',
linestyle='dashed'
)
plt.hlines(
y=ps,
xmin=pmf_flipper_length_mm.qs[0],
xmax=qs,
color='black',
linestyle='dashed'
)
plt.scatter(
x=qs,
y=ps,
color='red',
zorder=2
)
Run to view results
Comparando distribuciones
sns.ecdfplot(
data=processed_penguins_df,
x='flipper_length_mm',
hue='species',
palette=penguin_color
)
Run to view results
Funciones de densidad de probabilidad
sns.kdeplot(
data=processed_penguins_df,
x='flipper_length_mm',
bw_method=0.1
)
Run to view results
stats = processed_penguins_df.body_mass_g.describe()
stats
Run to view results
np.random.seed(42)
xs = np.linspace(stats['min'], stats['max'])
ys = scipy.stats.norm(stats['mean'], stats['std']).cdf(xs)
plt.plot(xs, ys, color='black', linestyle='dashed')
empiricaldist.Cdf.from_seq(
processed_penguins_df.body_mass_g,
normalize=True
).plot()
Run to view results
xs = np.linspace(stats['min']-1000, stats['max'] + 1000)
ys = scipy.stats.norm(stats['mean'], stats['std']).pdf(xs)
plt.plot(xs, ys, color='black', linestyle='dashed')
sns.kdeplot(
data=processed_penguins_df,
x='body_mass_g'
)
Run to view results
Ley de los Grandes Números y Teorema del Límite Central
Ley de los Grandes Números
dice = empiricaldist.Pmf.from_seq([1, 2, 3, 4, 5, 6])
dice.bar()
Run to view results
for sample_size in (1e2, 1e3, 1e4):
sample_size = int(sample_size)
values = dice.sample(sample_size)
sample_pmf = empiricaldist.Pmf.from_seq(values)
plt.figure(figsize=(5,5))
sample_pmf.bar()
plt.axhline(y=1/6, color = 'red', linestyle='dashed')
plt.ylim([0, 0.50])
plt.title(f"Sample size: {sample_size}")
Run to view results
Teorema del límite central
processed_penguins_df.sex.value_counts(normalize=True)
Run to view results
sex_numeric = processed_penguins_df.sex.replace(['Male', 'Female'], [1, 0])
Run to view results
number_samples = 1000
sample_size=35
samples_df = pd.DataFrame()
np.random.seed(42)
for i in range(1, number_samples + 1):
sex_numeric_sample = sex_numeric.sample(sample_size, replace=True).to_numpy()
sample_name = f"sample_{i}"
samples_df[sample_name] = sex_numeric_sample
male_population_mean = samples_df.mean().mean()
print(f"Estimated percentage of male penguins in population is: {male_population_mean * 100:.4f}%")
Run to view results
sample_means_binomial = pd.DataFrame(samples_df.mean(), columns=['sample_mean'])
sns.kdeplot(data=sample_means_binomial)
plt.axvline(x=sex_numeric.mean(), color='red', linestyle='dashed')
Run to view results
sample_size_experiment = pd.DataFrame(
[[i, samples_df.iloc[:, 0:i].mean().mean().mean()] for i in range(1, number_samples + 1)],
columns=['sample_size', 'estimated_mean']
)
Run to view results
sns.scatterplot(
data=sample_size_experiment,
x='sample_size',
y='estimated_mean'
)
plt.axhline(
y=sex_numeric.mean(),
color='red',
linestyle='dashed'
)
plt.ylim([sex_numeric.mean() - 0.20, sex_numeric.mean() + 0.20])
Run to view results
Estableciendo relaciones: Gráfica de puntos
sns.scatterplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
alpha=1/2,
s=100
)
Run to view results
sns.displot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
rug=True
)
Run to view results
sns.displot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
kind='kde',
rug=True
)
Run to view results
sns.jointplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
marginal_kws=dict(bins=25, fill=False)
)
Run to view results
Estableciendo relaciones: Gráficos de violín y boxplots
sns.scatterplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
hue='species',
palette=penguin_color
)
Run to view results
sns.stripplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
palette=penguin_color
)
Run to view results
ax = sns.boxplot(
data=processed_penguins_df,
x='flipper_length_mm',
y='species',
palette=penguin_color,
whis=np.inf
)
ax = sns.stripplot(
data=processed_penguins_df,
x='flipper_length_mm',
y='species',
color='.3'
)
Run to view results
ax = sns.violinplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
color='.8'
)
ax = sns.stripplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
palette=penguin_color
)
Run to view results
sns.swarmplot(
data=processed_penguins_df,
x='species',
y='flipper_length_mm',
hue='species',
palette=penguin_color
)
Run to view results
Estableciendo relaciones: Matrices de correlación
¿Existe una correlación lineal entre alguna de nuestras variables?
processed_penguins_df.corr()
Run to view results
¿Como puedo visualizar los coeficientes de correlación?
sns.heatmap(
data=processed_penguins_df.corr(),
cmap=sns.diverging_palette(20, 230, as_cmap=True),
center=0,
vmin=-1,
vmax=1,
linewidths=0.5,
cbar_kws={"shrink": 0.5},
annot=True
)
Run to view results
sns.clustermap(
data=processed_penguins_df.corr(),
cmap= sns.diverging_palette(20, 230, as_cmap=True), # 'BrBG'
center=0,
vmin=-1,
vmax=1,
linewidths=0.5,
cbar_kws={"shrink": 0.5},
annot=True
)
Run to view results
¿Cómo podría representar una variable categórica como numérica discreta?
processed_penguins_df = (
processed_penguins_df
.assign(
numeric_sex=lambda df: df.sex.replace(['Female', 'Male'], [0, 1])
)
)
Run to view results
sns.clustermap(
data=processed_penguins_df.corr(),
cmap= sns.diverging_palette(20, 230, as_cmap=True), # 'BrBG'
center=0,
vmin=-1,
vmax=1,
linewidths=0.5,
cbar_kws={"shrink": 0.5},
annot=True
)
Run to view results
¿Cuál es una límitante de los coeficientes de correlación lineal?
Sólo nos ayuda a determinar la posible existencia de una correlación lineal, sin embargo, su ausencia no significa que no exista otro tipo de correlación
x = np.linspace(-100, 100, 100)
y = x ** 2
y += np.random.normal(0, 1000, x.size)
sns.scatterplot(x=x, y=y)
np.corrcoef(x, y)
Run to view results
x = np.linspace(-100, 100, 100)
y = x ** 3
y += np.random.normal(0, 1000, x.size)
sns.scatterplot(x=x, y=y)
np.corrcoef(x, y)
Run to view results
sns.scatterplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm'
)
Run to view results
El coeficiente de correlación no nos habla del impacto de la relación
np.random.seed(42)
x_1 = np.linspace(0, 100, 100)
y_1 = 0.1 * x_1 + 3 + np.random.uniform(-2, 2, size=x_1.size)
sns.scatterplot(
x=x_1,
y=y_1
)
x_2 = np.linspace(0, 100, 100)
y_2 = 0.5 * x_2 + 1 + np.random.uniform(0, 60, size=x_2.size)
sns.scatterplot(
x=x_2,
y=y_2
)
plt.legend(labels=['1', '2'])
print(np.corrcoef(x_1, y_1))
print(np.corrcoef(x_2, y_2))
Run to view results
Estableciendo relaciones: Análisis de regresión simple
res_1 = scipy.stats.linregress(x=x_1, y=y_1)
res_2 = scipy.stats.linregress(x=x_2, y=y_2)
print(res_1, res_2, sep="\n")
Run to view results
sns.scatterplot(
x=x_1,
y=y_1
)
fx_1 = np.array([x_1.min(), x_1.max()])
fy_1 = res_1.intercept + res_1.slope * fx_1
plt.plot(fx_1, fy_1)
sns.scatterplot(
x=x_2,
y=y_2
)
fx_2 = np.array([x_2.min(), x_2.max()])
fy_2 = res_2.intercept + res_2.slope * fx_2
plt.plot(fx_2, fy_2)
plt.legend(labels=['1', '1', '2', '2'])
Run to view results
sns.scatterplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm'
)
res_penguins = scipy.stats.linregress(x=processed_penguins_df.bill_length_mm, y=processed_penguins_df.bill_depth_mm)
print(res_penguins)
fx_1 = np.array([processed_penguins_df.bill_length_mm.min(), processed_penguins_df.bill_length_mm.max()])
fy_1 = res_penguins.intercept + res_penguins.slope * fx_1
plt.plot(fx_1, fy_1)
Run to view results
sns.lmplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
height=10
)
Run to view results
Limitaciones del análisis de regresión simple
La regresión lineal simple no es simétrica
x = processed_penguins_df.bill_length_mm
y = processed_penguins_df.bill_depth_mm
res_x_y = scipy.stats.linregress(x=x, y=y)
res_y_x = scipy.stats.linregress(y=x, x=y)
print(res_x_y, res_y_x, sep="\n")
Run to view results
sns.scatterplot(
x=x,
y=y
)
fx_1 = np.array([x.min(), x.max()])
fy_1 = res_x_y.intercept + res_x_y.slope * fx_1
plt.plot(fx_1, fy_1)
Run to view results
sns.scatterplot(
x=y,
y=x
)
fx_1 = np.array([y.min(), y.max()])
fy_1 = res_y_x.intercept + res_y_x.slope * fx_1
plt.plot(fx_1, fy_1)
Run to view results
La regresión no nos dice nada sobre la causalidad, pero existen herramientas para separar las relaciones entre varias variables
La pendiente es -0.634905, lo que significa que cada milímetro adicional de profundidad del pico es asociado a un decremento de -0.634905 milímetros de la longitud del pico de un pingüino.
(
smf.ols(
formula="bill_length_mm ~ bill_depth_mm",
data=processed_penguins_df
)
.fit()
.params
)
Run to view results
(
smf.ols(
formula="bill_depth_mm ~ bill_length_mm",
data=processed_penguins_df
)
.fit()
.summary()
)
Run to view results
Análisis de regresión múltiple
Olvidé mi báscula para pesar a los pingüinos, ¿Cuál sería la mejor forma de capturar ese dato?
Creando modelos
model_1 = (
smf.ols(
formula="body_mass_g ~ bill_length_mm",
data=processed_penguins_df
)
.fit()
)
model_1.summary()
Run to view results
model_2 = (
smf.ols(
formula="body_mass_g ~ bill_length_mm + bill_depth_mm ",
data=processed_penguins_df
)
.fit()
)
model_2.summary()
Run to view results
model_3 = (
smf.ols(
formula="body_mass_g ~ bill_length_mm + bill_depth_mm + flipper_length_mm",
data=processed_penguins_df
)
.fit()
)
model_3.summary()
Run to view results
model_4 = (
smf.ols(
formula="body_mass_g ~ bill_length_mm + bill_depth_mm + flipper_length_mm + C(sex)",
data=processed_penguins_df
)
.fit()
)
model_4.summary()
Run to view results
model_5 = (
smf.ols(
formula="body_mass_g ~ flipper_length_mm + C(sex)",
data=processed_penguins_df
)
.fit()
)
model_5.summary()
Run to view results
Visualizando resultados
models_results = pd.DataFrame(
dict(
actual_value=processed_penguins_df.body_mass_g,
prediction_model_1 = model_1.predict(),
prediction_model_2 = model_2.predict(),
prediction_model_3 = model_3.predict(),
prediction_model_4 = model_4.predict(),
prediction_model_5 = model_5.predict(),
species=processed_penguins_df.species,
sex=processed_penguins_df.sex
)
)
models_results
Run to view results
sns.ecdfplot(
data=models_results#.select_columns(['actual_value', 'prediction_model_5'])
)
Run to view results
sns.kdeplot(
data=models_results,
cumulative=False
)
Run to view results
sns.lmplot(
data=processed_penguins_df,
x='flipper_length_mm',
y='body_mass_g',
height=10,
hue='sex'
)
Run to view results
Análisis de regresión logística
smf.logit(
formula='sex_numeric ~ flipper_length_mm + bill_length_mm + bill_depth_mm + C(island)',
data=processed_penguins_df
).fit().summary()
Run to view results
(
processed_penguins_df
.value_counts(['island', 'sex', 'species'])
.reset_index(name='count')
)
Run to view results
processed_penguins_df.species.unique()
Run to view results
processed_penguins_df = (
processed_penguins_df
.assign(is_adelie=lambda df: df.species.replace(['Adelie', 'Chinstrap', 'Gentoo'], [1, 0, 0]))
)
Run to view results
model_is_adelie = smf.logit(
formula='is_adelie ~ flipper_length_mm + C(sex)',
data=processed_penguins_df
).fit(maxiter=100)
model_is_adelie.params
Run to view results
is_adelie_df_predictions = pd.DataFrame(
dict(
actual_adelie = processed_penguins_df.species.replace(['Adelie', 'Chinstrap', 'Gentoo'], [1, 0, 0]),
predicted_values = model_is_adelie.predict().round()
)
)
is_adelie_df_predictions
Run to view results
(
is_adelie_df_predictions
.value_counts(['actual_adelie', 'predicted_values'])
.reset_index(name='count')
.pivot_wider(
index='actual_adelie',
names_from='predicted_values',
values_from='count'
)
.rename_column('actual_adelie', 'actual / predicted')
)
Run to view results
print(
sklearn.metrics.confusion_matrix(
is_adelie_df_predictions.actual_adelie,
is_adelie_df_predictions.predicted_values
)
)
sklearn.metrics.accuracy_score(
is_adelie_df_predictions.actual_adelie,
is_adelie_df_predictions.predicted_values
)
Run to view results
Paradoja de Simpson
sns.scatterplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm'
)
Run to view results
sns.regplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm'
)
Run to view results
sns.lmplot(
data=processed_penguins_df,
x='bill_length_mm',
y='bill_depth_mm',
hue='species',
height=10,
palette=penguin_color
)
Run to view results
sns.pairplot(data=processed_penguins_df, hue='species', palette=penguin_color)
Run to view results
Información de sesión
session_info.show()
Run to view results