ML Models From Scratch · Medium

Linear Regression Trainer

Train linear regression end to end with explicit gradients and parameter updates.

Task

Implement class LinearRegression(initial_weights: np.ndarray, initial_bias: float, learning_rate: float). Implement an end-to-end linear regression trainer with explicit forward, loss, backward, step, fit, and predict methods.

Requirements

Copy the initial weights so training does not mutate the caller's array.
forward(x) and predict(x) return x @ weights + bias for a batch of rows.
loss(predictions, targets) returns mean squared error.
backward(x, predictions, targets) stores weight_grad and bias_grad for mean squared error.
step() applies one gradient-descent update using learning_rate.
fit(x, y, epochs) records the loss before each update in loss_history.
Do not call an autograd backward API in the core implementation.

Example

model = LinearRegression(
    np.array([0.0]),
    initial_bias=0.0,
    learning_rate=0.1,
)
model.fit(
    np.array([[1.0], [2.0]]),
    np.array([3.0, 5.0]),
    epochs=2,
)
model.predict(np.array([[1.0], [2.0]]))
# array([2.76, 4.47])