GATE 2026 DA – Question 55
Consider that Linear Ridge Regression is being used to learn a prediction function $y_{pred} = w^Tx$, where $w, x \in \mathbb{R}^2$ and Mean Absolute Error (MAE) is used to measure the prediction error. A weight of 0.20 is associated with the regularizer.
At an intermediate step of the training process, assume that the parameter $w = [-3.00, 4.00]^T$. In the next step, for the input $x = [1.00, 2.00]^T$, the predicted value of $y$ is noted. Let the relation between $x = [x_1, x_2]^T$ and the true value of $y$ be $y_{true} = x_1 + x_2$.
The value of the overall regularized loss function for this instance is _______ . (*Rounded off to two decimal places*)
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Correct answer: 6.96 to 7.04
Explanation
The prediction is $w^Tx = -3(1) + 4(2) = 5$ and the true value is $1 + 2 = 3$, so the absolute error is $|5 - 3| = 2$. The ridge penalty is the weight 0.20 times the squared norm of $w$: $0.20(9 + 16) = 5$. The regularized loss is $2 + 5 = 7.00$.