Correlate an array of categorical features to binary outcome
How large is N?
Can you reshape your data into something like:

target   i1  i2  i3  i4  i5 ... i9 ... iN
     1    1   0   1   0   0 ...  0 ...  0        
     1    0   0   0   1   1 ...  1 ...  0
     0    1   0   0   0   0 ...  0 ...  0


Once you have fit everything into a data frame, you can use any two-class supervised classification algorithm to build your model. There is no "best" model in general, but try a few to see which one works the best with your data.

Sorry for posting as an answer; comment doesn't allow preformatted text.