Random Vector

import matplotlib.pyplot as plt
import numpy as np
print(np.__version__)
import torch 
import torch.nn as nn

import pandas as pd
# Retina mode
%matplotlib inline
%config InlineBackend.figure_format = 'retina'

1.26.4

df = pd.read_html("http://socr.ucla.edu/docs/resources/SOCR_Data/SOCR_Data_Dinov_020108_HeightsWeights.html")

store_df = df[0]
store_df.columns = store_df.iloc[0]
store_df = store_df.iloc[1:]
store_df = store_df.astype(float)
store_df = store_df.drop(columns=["Index"])
store_df = store_df.dropna()

store_df.head()

	Height(Inches)	Weight(Pounds)
1	65.78331	112.9925
2	71.51521	136.4873
3	69.39874	153.0269
4	68.21660	142.3354
5	67.78781	144.2971

mu_vec = store_df.mean()
print(mu_vec)

0
Height(Inches)     67.993114
Weight(Pounds)    127.079421
dtype: float64

cov_matrix = store_df.cov()
print(cov_matrix)

0               Height(Inches)  Weight(Pounds)
0                                             
Height(Inches)        3.616382       11.151029
Weight(Pounds)       11.151029      135.976532

store_df - mu_vec

	Height(Inches)	Weight(Pounds)
1	-2.209804	-14.086921
2	3.522096	9.407879
3	1.405626	25.947479
4	0.223486	15.255979
5	-0.205304	17.217679
...	...	...
24996	1.509036	-9.048221
24997	-3.444854	-6.886221
24998	-3.294564	-8.813921
24999	-0.463934	5.188779
25000	0.884496	-2.205221

25000 rows × 2 columns

(store_df - mu_vec).shape

(25000, 2)

((store_df - mu_vec).values.T@(store_df - mu_vec).values)/(store_df - mu_vec).shape[0]

array([[  3.61623749,  11.15058313],
       [ 11.15058313, 135.97109293]])

store_df.cov()

	Height(Inches)	Weight(Pounds)
0
Height(Inches)	3.616382	11.151029
Weight(Pounds)	11.151029	135.976532

# Plot the data

plt.scatter(store_df["Height(Inches)"], store_df["Weight(Pounds)"], alpha=0.1, color='k')
plt.xlabel("Height")
plt.ylabel("Weight")

Text(0, 0.5, 'Weight')

# Diagonal covariance matrix

X = torch.distributions.multivariate_normal.MultivariateNormal(
    loc = torch.tensor([0.0, 0.0]),
    covariance_matrix = torch.tensor([[1.0, 0.0], [0.0, 1.0]])
)

X_samples = X.sample((5000,))
plt.scatter(X_samples[:, 0], X_samples[:, 1], alpha=0.1, color='k')

torch.round(torch.cov(X_samples.T))

tensor([[1., 0.],
        [0., 1.]])