def naivebayesPY$($X$,$ Y$)$:

$"""$

naivebayesPY$($X$,$ Y$)$ returns $[$pos$,$neg$]$

Computation of P$($Y$)$

Input:

X : n input vectors of d dimensions $($nxd$)$

Y : n labels $(-1$ or $+1)($nx$1)$

Output:

pos: probability p$($y$=1)$

neg: probability p$($y$=-1)$

$"""$

# add one positive and negative example to avoid division by zero $("$plus$-$one smoothing"$)$

Y $=$ np$.$concatenate$([$Y$,[-1,1]])$

n $=$ len$($Y$)$

# YOUR CODE HERE

raise NotImplementedError$()$