Question

regression classifier. Consider a classifier of the form 14.2 Interpreting the parameters in a ý = sign(x7B+v), where ý is the prediction, the n-vector x is the feature vector, and the n-vector B and scalar v are the classifier parameters. We will assume here that v 0 and B0. Evidently = sign(v) is the prediction when the feature vector x is zero. Show that when |rl < \u|/||8||, are small (i.e., near zero), the classifier makes the prediction = sign(v). Hint. If two numbers a and b satisfy |al < b|, then sign(a + b) = sign(b) This means that we can interpret sign(v) as the classifier prediction when the features are small. The ratio |v|/||B|| tells us how big the feature vector must be before the classifier changes its mind' and predicts - sign(v) we have sign(v). This shows that when all the features

Answer 1

By Cauchy Schwartz inequality, we have -:

2

Also,

sign(v B) by definition. Now sign(v) only when sign(v ) sign(v), which according to the hint is possible only when T v (by Cauchy Schwartz inequality) l|2||8||2 /119

Hence proved the given statement