FRM Part I · FRM Exam Part I · Machine-Learning Methods
In a KNN classifier, an analyst moves from K = 1 to K = 25 on a noisy credit dataset. Which is the expected effect?
Increasing K from 1 to 25 lowers variance and raises bias, producing a smoother decision boundary. K = 1 is the most flexible and overfits noise, while averaging over many neighbors stabilizes predictions but may blur real structure.
- ALower variance and higher bias, with a smoother decision boundaryCorrect
- BHigher variance and lower bias, with a more jagged boundary
- CZero training error is guaranteed at K = 25
- DBoth bias and variance fall because more neighbors are used
Explanation
Small K gives a flexible, jagged boundary with low bias and high variance, and K = 1 gives zero training error. Increasing K averages over more neighbors, smoothing the boundary, reducing variance and raising bias.
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