GATE DA 2026 Set 1 — Question 55
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Machine Learning → Model Evaluation & Validation → Regression Error Metrics
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Question
Consider that Linear Ridge Regression is being used to learn a prediction function , where 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 . In the next step, for the input , the predicted value of is noted. Let the relation between and the true value of be .The value of the overall regularized loss function for this instance is _______ . (Rounded off to two decimal places)
Correct answer
6.9 to 7.1
Solution
Given:
Step 2: Calculate
Step 3: Calculate the Error term (MAE)
Since it is a single instance, MAE is simply the absolute error:Step 4: Calculate the Regularizer term
Ridge regression typically uses the squared norm of the weights:Step 5: Calculate Total LossThe value is 7.00.
- Prediction function:
- Error metric: Mean Absolute Error (MAE)
- Regularizer weight:
- Parameter vector:
- Input vector:
- True value relation:
Step 2: Calculate
Step 3: Calculate the Error term (MAE)
Since it is a single instance, MAE is simply the absolute error:Step 4: Calculate the Regularizer term
Ridge regression typically uses the squared norm of the weights:Step 5: Calculate Total LossThe value is 7.00.
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