Introduction to Cross-Validation - Lab

Introduction

In this lab, you'll be able to practice your cross-validation skills!

Objectives

You will be able to:

Compare the results with normal holdout validation
Apply 5-fold cross validation for regression

Let's get started

This time, let's only include the variables that were previously selected using recursive feature elimination. We included the code to preprocess below.

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn.datasets import load_boston

boston = load_boston()

boston_features = pd.DataFrame(boston.data, columns = boston.feature_names)
b = boston_features["B"]
logdis = np.log(boston_features["DIS"])
loglstat = np.log(boston_features["LSTAT"])

# minmax scaling
boston_features["B"] = (b-min(b))/(max(b)-min(b))
boston_features["DIS"] = (logdis-min(logdis))/(max(logdis)-min(logdis))

#standardization
boston_features["LSTAT"] = (loglstat-np.mean(loglstat))/np.sqrt(np.var(loglstat))

X = None
y = None

Train test split

Perform a train-test-split with a test set of 0.20.

from sklearn.model_selection import train_test_split

Fit the model and apply the model to the make test set predictions

Calculate the residuals and the mean squared error

Cross-Validation: let's build it from scratch!

Create a cross-validation function

Write a function k-folds that splits a dataset into k evenly sized pieces. If the full dataset is not divisible by k, make the first few folds one larger then later ones.

We want the folds to be a list of subsets of data!

def kfolds(data, k):
    # Force data as pandas dataframe
    # add 1 to fold size to account for leftovers           
    return None

Apply it to the Boston Housing Data

# Make sure to concatenate the data again

Perform a linear regression for each fold, and calculate the training and test error

Perform linear regression on each and calculate the training and test error.

test_errs = []
train_errs = []
k=5

for n in range(k):
    # Split in train and test for the fold
    train = None
    test = None
    # Fit a linear regression model
    
    #Evaluate Train and Test Errors

# print(train_errs)
# print(test_errs)

Cross-Validation using Scikit-Learn

This was a bit of work! Now, let's perform 5-fold cross-validation to get the mean squared error through scikit-learn. Let's have a look at the five individual MSEs and explain what's going on.

Next, calculate the mean of the MSE over the 5 cross-validations and compare and contrast with the result from the train-test-split case.

Summary

Congratulations! You now practiced your knowledge on k-fold crossvalidation!

whitcrrd/dsc-1-11-17-introduction-to-cross-validation-lab-online-ds-ft-021119