According to the Bayes decision rule for a 2 class classification problem:
$d(x) = w_1 : P(w_1 |x) ≥ P(w_2|x) $
And $P(error|x) = min[P(w_1 |x), P(w_2|x)]$
where $P(w_i |x) = p(x|w_i) * P(w_i)$
- By simply following this decision rule $d(x)$, we minimize the probability of error? There is no complicated way or additional formulas for minimizing error?
- In case we want to minimize this error further how do we do it? Increase the number of samples perhaps? Or maybe increase the dimension of feature space i.e., use more features, thereby changing the likelihood $p(x|w_i)$, or combination of both.