spread_normals.py

'''
Code releated for stack exchange question:
https://math.stackexchange.com/questions/4519928/how-do-i-stop-my-normals-from-spreading-out-under-perturbation
'''

import numpy as np
from tqdm import tqdm
import pylab as plt
import pandas as pd
import seaborn as sns
from scipy.stats import skew, kurtosis

N = 500
dx = 0.01
n_iters = 100_000

X = np.random.normal(size=N)

data = []
for i in tqdm(range(n_iters)):
    X += dx * np.random.normal(size=N)
    data.append(
        {
            "m1": X.mean(),
            "m2": X.std(),
            "m3": skew(X),
            "m4": kurtosis(X),
        }
    )

df = pd.DataFrame(data)

plt.title(f"{N}-dim indep. norm. vectors perturbated by {dx:0.2f}*N(0,1)")
plt.plot(df.m1, label="mu")
plt.plot(df.m2, label="std")
plt.plot(df.m3, label="skew")
plt.plot(df.m4, label="kurtosis")

plt.xlabel(f"# of perturbations")
plt.legend()
sns.despine()
plt.savefig("drift_example.png")

plt.show()