Polynomial features in ML Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What are polynomial features in machine learning?

Polynomial features are new features created by raising existing features to a power and combining them. They help models learn more complex patterns by adding curved relationships.

beginner

Why do we use polynomial features in a model?

We use polynomial features to allow simple models like linear regression to fit curves and capture non-linear relationships in data.

intermediate

How does degree affect polynomial features?

The degree controls the highest power of features included. Higher degree means more complex features but can cause overfitting if too high.

beginner

What is an example of polynomial features for two variables x and y with degree 2?

For x and y, degree 2 polynomial features include: 1 (bias), x, y, x², xy, y².

intermediate

What is a potential downside of using polynomial features?

Using too many polynomial features can make the model complex, slow to train, and prone to overfitting, especially with small data.

What does adding polynomial features to a dataset help a model do?

A Reduce the number of features

B Make the model linear only

C Capture non-linear relationships

D Remove noise from data

Polynomial features help models learn curved or non-linear patterns by adding powers and combinations of original features.

Which of these is NOT a polynomial feature of degree 2 for variables x and y?

A y³

B xy

C x²

D y²

y³ is degree 3, which is higher than degree 2, so it is not included in degree 2 polynomial features.

What happens if you use a very high degree for polynomial features?

A Model becomes simpler

B Model may overfit

C Model ignores features

D Model always improves

High degree polynomial features can cause the model to fit noise, leading to overfitting.

Polynomial features are mainly used with which type of model?

A Linear models

B Decision trees

C Neural networks only

D Clustering algorithms

Polynomial features transform data so linear models can fit non-linear patterns.

Which term is usually included automatically when generating polynomial features?

A Only squared features

B Only original features

C Only interaction terms

D Bias term (constant 1)

The bias term (constant 1) is included to allow the model to fit an intercept.

Explain what polynomial features are and why they are useful in simple terms.

Think about how adding powers of features changes what the model can learn.

Describe the risks of using very high degree polynomial features in a model.

Consider what happens when a model tries to fit too many details.

Practice

1. What is the main purpose of using PolynomialFeatures in machine learning?

easy

A. To create new features by adding powers and combinations of existing features

B. To reduce the number of features in the dataset

C. To normalize the data between 0 and 1

D. To split the dataset into training and testing sets

Solution

1. Step 1: Understand the role of PolynomialFeatures

   PolynomialFeatures generates new features by raising existing features to powers and combining them, helping models learn curves.

2. Step 2: Compare with other options

   Feature reduction, normalization between 0 and 1, and splitting into training/testing sets describe different preprocessing steps, not feature creation with powers.

3. Final Answer:

   To create new features by adding powers and combinations of existing features -> Option A

4. Quick Check:

   PolynomialFeatures = create new polynomial features [OK]

Hint: PolynomialFeatures adds powers and combos of features [OK]

Common Mistakes:

• Confusing feature creation with normalization
• Thinking it reduces features instead of expanding
• Mixing it up with data splitting

2. Which of the following is the correct way to import and create polynomial features of degree 2 using scikit-learn?

easy

A. from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(degree=2)

B. from sklearn.linear_model import PolynomialFeatures
poly = PolynomialFeatures(2)

C. import PolynomialFeatures from sklearn.preprocessing
poly = PolynomialFeatures(degree=2)

D. from sklearn.preprocessing import PolynomialFeatures
poly = PolynomialFeatures(3)

Solution

1. Step 1: Check the correct import statement

   PolynomialFeatures is in sklearn.preprocessing, so 'from sklearn.preprocessing import PolynomialFeatures' is correct.

2. Step 2: Verify the degree parameter

   To create degree 2 features, use degree=2 in the constructor.

3. Final Answer:

   from sklearn.preprocessing import PolynomialFeatures poly = PolynomialFeatures(degree=2) -> Option A

4. Quick Check:

   Import from preprocessing and set degree=2 [OK]

Hint: Import from preprocessing and set degree=2 [OK]

Common Mistakes:

• Importing from wrong module
• Forgetting 'degree=' keyword
• Setting wrong degree value

3. Given the code below, what is the output of X_poly?

from sklearn.preprocessing import PolynomialFeatures
import numpy as np
X = np.array([[2, 3]])
poly = PolynomialFeatures(degree=2, include_bias=False)
X_poly = poly.fit_transform(X)
print(X_poly)

medium

A. [[2 3 5 6 9]]

B. [[1 2 3 4 6 9]]

C. [[2 3 4 6 9]]

D. [[2 3 4 5 6 9]]

Solution

1. Step 1: Understand PolynomialFeatures output with degree=2 and include_bias=False

   Features include original features, their squares, and pairwise products: [x1, x2, x1^2, x1*x2, x2^2].

2. Step 2: Calculate values for X = [2, 3]

   x1=2, x2=3; x1^2=4, x1*x2=6, x2^2=9; so output is [[2, 3, 4, 6, 9]].

3. Final Answer:

   [[2 3 4 6 9]] -> Option C

4. Quick Check:

   Polynomial features = original + squares + products [OK]

Hint: Output includes original, squares, and cross-products [OK]

Common Mistakes:

• Including bias term when include_bias=False
• Miscomputing squares or products
• Adding extra features not in degree 2

4. Identify the error in the following code snippet that uses PolynomialFeatures:

from sklearn.preprocessing import PolynomialFeatures
X = [[1, 2], [3, 4]]
poly = PolynomialFeatures(degree=3)
X_poly = poly.fit_transform(X)
print(X_poly)

medium

A. X should be a NumPy array, not a list of lists

B. No error; code runs correctly

C. Missing import for NumPy

D. Degree 3 is not supported by PolynomialFeatures

Solution

1. Step 1: Check input type compatibility

   PolynomialFeatures accepts lists or arrays, so X as list of lists is valid.

2. Step 2: Verify degree parameter and imports

   Degree 3 is supported; no NumPy import needed if not used explicitly.

3. Final Answer:

   No error; code runs correctly -> Option B

4. Quick Check:

   PolynomialFeatures accepts lists and degree 3 [OK]

Hint: PolynomialFeatures accepts lists; degree 3 is valid [OK]

Common Mistakes:

• Assuming input must be NumPy array
• Thinking degree 3 is invalid
• Expecting import errors without NumPy usage

5. You have a dataset with 3 features and want to add polynomial features up to degree 3. How many features will the transformed dataset have if include_bias=False?

hard

A. 10

B. 20

C. 16

D. 19

Solution

1. Step 1: Use formula for number of polynomial features

   Number of features = C(n + d, d) - 1 if include_bias=False, where n=3, d=3.

2. Step 2: Calculate combinations

   C(3+3, 3) = C(6, 3) = 20; subtract 1 for no bias gives 19 features.

3. Final Answer:

   19 -> Option D

4. Quick Check:

   Features = combinations(6,3)-1 = 19 [OK]

Hint: Use combinations(n+d, d) minus bias if excluded [OK]

Common Mistakes:

• Forgetting to subtract bias feature
• Using wrong combination formula
• Confusing degree with number of features