Summary - Linear algebra
- Machine Learning course
- Beginner
- Lesson 36/112
- 6 min
In this group you learned vectors, matrices, multiplication, and transpose.
Summary: linear algebra
The language of ML is linear algebra:
- Vector: an example or the weights; dot product = linear prediction.
- Matrix: the dataset or layer weights; row operations through broadcasting.
- Matrix multiplication (
@): (m, n) @ (n, p) = (m, p), batch prediction. - Transpose, identity, inverse: the normal equation and Ridge.
tahmin = X @ w + b
w = np.linalg.solve(X.T @ X + 0.1 * np.eye(X.shape[1]), X.T @ y) # RidgeWhen you get a shape error, check the inner dimensions of the matrix multiplication.
Practice Ridge closed form
Find the Ridge weights with alpha = 1.0 using np.linalg.solve(X.T @ X + alpha * np.eye(2), X.T @ y), round them to 3 digits (np.round) and print them.
Starter code
import numpy as np
X = np.array([[1, 0], [0, 1], [1, 1]])
y = np.array([1, 2, 3])
alpha = 1.0
# buraya yazSample solution
import numpy as np
X = np.array([[1, 0], [0, 1], [1, 1]])
y = np.array([1, 2, 3])
alpha = 1.0
w = np.linalg.solve(X.T @ X + alpha * np.eye(2), X.T @ y)
print(np.round(w, 3))Expected output
[0.875 1.375]
Questions and answers
Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.
1 For <code>X</code> (100, 4) and <code>W</code> (4, 8), what does <code>X @ W</code> represent?
- 100 outputs for 8 examples
- The mean of 4 features
- An error
- 8 outputs for each of 100 examples Correct answer
Explanation: The result has shape (100, 8): a layer's output in 8 neurons for 100 examples.
2 Add alpha to the diagonal.
Question
A = X.T @ X + alpha * np.____(X.shape[1])
Answer
A = X.T @ X + alpha * np.eye(X.shape[1])Explanation: With np.eye, the addition only goes onto the diagonal.
3 Match the concepts with their ML counterparts.
| Term | Meaning |
|---|---|
Vector |
A single example |
Matrix |
Dataset |
Dot product |
Linear prediction |
Matrix multiplication |
Batch prediction |