Logistic Regression, however with yi in $\{0,1\}.$

$($a$)$ Show that with these new labels the objective function can be written as

L$($w$)=\backslash$Sigma $($yi log$($sigm$($w$$xi$))+(1$ yi$)$ log$(1$ sigm$($w$$xi$)))$

where sigm$($a$)=1/(1+$e$^($a$))$ is the sigmoid or logistic function.