Suppose you have trained an SVM classifier with a RBF kernel, and You suspect that the SVM is underfitting your dataset. What should you do to C?

Question

BlackTom AI · Accepted Answer

Increase C because C is the SVM penalty parameter that controls the trade-off between margin width and misclassification on the training set.

1) Relevant knowledge points and concepts
- C in SVM: a larger C places a higher penalty on misclassification, forcing the optimizer to fit training points more closely (smaller margin, lower bias, higher variance). A smaller C relaxes penalties, yielding a wider margin and more regularization (higher bias, lower variance).
- Underfitting: model exhibits high bias (poor training performance or too-simple decision boundary). To reduce underfitting you must increase model complexity (reduce regularization).
- RBF kernel gamma: gamma controls the kernel width. Higher gamma => more localized/complex decision boundaries; lower gamma => smoother/simpler boundaries.

2) Step-by-step reasoning
- Observed problem: underfitting (high bias) with RBF SVM.
- Goal: increase model flexibility so it can capture more complex patterns.
- Action on C: increase C to reduce regularization and allow the decision boundary to fit training data more tightly.
- Alternative knobs: gamma can also be increased to make the RBF kernel more flexible, but the question specifically asks what to do to C.

3) Calculations/intermediate steps
- No numeric calculation required. Conceptually: increasing C shifts optimization toward minimizing classification errors over maximizing margin, which reduces bias.

4) Why the correct answer is correct
- Increasing C directly reduces regularization, permitting a more complex decision boundary and hence addressing underfitting.

5) Why other options are incorrect
- Decrease C: increases regularization and makes underfitting worse.
- Keep C unchanged but decrease gamma: makes the kernel smoother and less flexible, worsening underfitting.
- Keep C unchanged but increase gamma: can reduce underfitting by making the kernel more complex, but it does not change C; the question specifically asks what to do to C.

6) Conclusion
- Therefore, you should Increase C. This matches the provided correct answer.

Suppose you have trained an SVM classifier with a RBF kernel, and You suspect that the SVM is underfitting your dataset. What should you do to C? 单项选择题

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