Implement Gradient Descent | Dataford Interview Questions

Your question is Implement Gradient Descent. Start with the requirements on the right.

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Problem

Plymouth Rock Assurance is prototyping a simple claim-severity model: prediction = weight * x + bias. Implement batch gradient descent to minimize mean squared error across training examples.

Formal Specification

Implement gradient_descent(x, y, learning_rate, iterations).

x is a list of numeric feature values.
y is a list of numeric target values, where y[i] corresponds to x[i].
Start with weight = 0.0 and bias = 0.0.
For each iteration, compute gradients over the entire dataset before updating either parameter:
- error_i = weight * x[i] + bias - y[i]
- d_weight = (2 / n) * sum(error_i * x[i])
- d_bias = (2 / n) * sum(error_i)
Update both parameters using the learning rate.
Return [weight, bias], rounded to 10 decimal places.

Constraints

1 <= len(x) == len(y) <= 10^4
-10^3 <= x[i], y[i] <= 10^3
0 < learning_rate <= 1
0 <= iterations <= 10^4
Return weight and bias rounded to 10 decimal places

Function Signature

def gradient_descent(x, y, learning_rate, iterations):