Introduction k-fold Cross Validation

import numpy as np
import matplotlib.pyplot as plt
plt.rcParams.update({'font.size': 16})
import pandas as pd
from sklearn.model_selection import KFold

df = pd.read_csv("https://raw.githubusercontent.com/roualdes/data/master/hospital.csv")
df.head()

	stay	age	infection_risk	xray	beds	region	nurses
0	7.13	55.7	4.1	39.6	279	4	241
1	8.82	58.2	1.6	51.7	80	2	52
2	8.34	56.9	2.7	74.0	107	3	54
3	8.95	53.7	5.6	122.8	147	4	148
4	11.20	56.5	5.7	88.9	180	1	151

The loss function for the mean is

\[loss(\mu | y) = \sum_{n=1}^N (y_n - \mu)^2\]

plt.hist(df["infection_risk"], bins = "fd", histtype = "step");

np.mean(df["infection_risk"])

4.354867256637168

dfh = df.head(20)
np.mean(dfh["infection_risk"])

4.745

dft = df.tail(20)
np.mean(dft["infection_risk"])

4.11

def mse(y, yhat):
    return np.mean( (y - yhat) ** 2 )

m = np.mean(dft["infection_risk"])
mse(dfh["infection_risk"], m)

2.0907

kf = KFold(n_splits = 5, shuffle = True, random_state = 204)
mses = []
means = []
for train_idx, test_idx in kf.split(df):
    train_df = df.iloc[train_idx]
    test_df = df.iloc[test_idx]
    m = np.mean(train_df["infection_risk"])
    means.append(m)
    err = mse(test_df["infection_risk"], m)
    mses.append(err)

mdx = np.argmin(mses)
means[mdx]

4.334444444444444