Problem 1 - Group B

Presentation

a)

  • The main intuition is that if we have a large margin, we are far away from the decision boundary, hence we make more confident predictions.

  • Another intuition, based on bias-variance tradeoff.

b)

  • Bound should get tighter as we increase the margin (and the number of data points \(n\)).

c)

  • The term \[\frac{\gamma}{B}\] makes sense because the margin depends directly on how large the weights can be in \[\min_{i} y_i w^T x_i.\] If gamma is not zero, we can multiply \(w\) by any \(\alpha > 1\) and get a larger margin.

  • Similar argument for \(D\)

  • For tighter bounds on input and weights, we can get a tighter bound on generalization error.

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