why is SSE cost function convex?

Question

In regards to Machine Learning, in the Adaline rule we say that

$$ J(w)=\frac{1}{2} \sum_{i} (\mbox{target}^{(i)} - \mbox{output}^{(i)})^2, \quad \mbox{output}^{(i)} \in \mathbb{R} $$

is convex. I´d like to know how can we say that? Some proof that it is always convex.

Thank you in advance

@VHarisop thank you for the edit – killezio Mar 04 '17 at 22:59 — killezio, Mar 04 '17 at 22:59

score 1 · Answer 1 · answered Mar 01 '17 at 11:38

1

Please check that the Hessian matrix is positively semidefinite.

For a more concrete answer please write precisely what do you understand by $w$.

answered Mar 01 '17 at 11:38

szw1710

w is the weight of each feature in the rule (an object can have several weights). It represents a value that will decide in a future experiment if a certain object belongs to a class or another class based on that feature. – killezio Mar 04 '17 at 23:01

1 Answers1