Apprendre Challenge: Fitting a Line with Gradient Descent

A student is exploring how to use gradient descent to fit a straight line to a small dataset. The dataset shows years of experience versus salary (in thousands), and the goal is to find the best-fitting line using an iterative update rule.

Your task is to adjust the slope ( $m$ **) and intercept ( $b$ ) so that the line closely follows the data points.

The expression you are trying to minimize is:

\frac{1}{n}\sum^n_{i=1}(y_i - (mx_i + b))^2

The gradient descent update rules for minimizing this function are:

m \larr m - \alpha \frac{\partial J}{\partial m} \\[6 pt] b \larr b - \alpha \frac{\partial J}{\partial b}

Where:

$\alpha$ is the learning rate (step size);
$\frac{\partial J}{\partial m}$ is the partial derivative of the loss function with respect to $m$ ;
$\frac{\partial J}{\partial b}$ is the partial derivative of the loss function with respect to $b$ .

This loss measures how far off your predicted points are from the actual data. (P.S. Smaller values mean the line fits the data better.)

In order to find values $m$ and $b$ , use gradient descent.

Tâche

Swipe to start coding

Complete the Python code below to implement the gradient descent steps.
Fill in the missing expressions using basic Python operations.
Track how the values of m and b change as the algorithm runs.

Solution

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Section 3. Chapitre 11

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Your task is to adjust the slope ( $m$ **) and intercept ( $b$ ) so that the line closely follows the data points.

The expression you are trying to minimize is:

\frac{1}{n}\sum^n_{i=1}(y_i - (mx_i + b))^2

The gradient descent update rules for minimizing this function are:

m \larr m - \alpha \frac{\partial J}{\partial m} \\[6 pt] b \larr b - \alpha \frac{\partial J}{\partial b}

Where:

$\alpha$ is the learning rate (step size);
$\frac{\partial J}{\partial m}$ is the partial derivative of the loss function with respect to $m$ ;
$\frac{\partial J}{\partial b}$ is the partial derivative of the loss function with respect to $b$ .

This loss measures how far off your predicted points are from the actual data. (P.S. Smaller values mean the line fits the data better.)

In order to find values $m$ and $b$ , use gradient descent.

Tâche

Swipe to start coding

Complete the Python code below to implement the gradient descent steps.
Fill in the missing expressions using basic Python operations.
Track how the values of m and b change as the algorithm runs.

Solution

Passez à un bureau pour une pratique réelleContinuez d'où vous êtes en utilisant l'une des options ci-dessous

Tout était clair ?

Merci pour vos commentaires !

Section 3. Chapitre 11

single

Challenge: Fitting a Line with Gradient Descent

Solution

Awesome!

Challenge: Fitting a Line with Gradient Descent

Solution

Awesome!