If you want to own as Yi, build him hybrid, all I have to say. You got slightly less burst than pure AP Yi, but you last longer, deal more attack damage and of course the items opens for awesome plays.

I won't bother going through every minor detail(You all know how Yi works), but this is the most important hints you need:
Use the passive in lane: Stack it up, Alpha leap enemy champion and use Wuju style on him.
Try to use meditate mid-combat: Meditate reduces damage done to you, thus wasting enemy champions mana as well as healing you(beware of cc)
Use Zhonyas Hourglass while waiting for Alpha Leap CD.
Deathfire Grasp can be cast while in the "Q" animation, use it then!'
Ult resets all CD's!

You'll beat ANY pure AP Yi mid early with this build! Auto-attack him or loose lane!

Lich-Bane: Self explanatory, part of your burst.
Boots: Magic penetration is your friend.
Gunblade, wtf? Lifesteal and AD, gives you an upper hand while spells are on CD. Also got slow and minor damage active.
Deathfire-Grasp: CD is back on DFG, build it and improve your burst.
Zonyas Hourglass: Used to make plays and wait for CD's, also brings some armor, so you can actually challenge bruisers 1v1.
Nashor's Tooth: Attack speed and CDR. More alpha leaps and more damage while spells are on CD.

Try build before you vote. This is the only AP Yi i'm using, and i have yet to be defeated by those pure AP Yi's.
Have fun!