CS 331: Artificial Intelligence Bayesian Networks (Inference) Inference

Transcription

1 S 331: rtificil Intllignc ysin Ntworks Infrnc 1 Infrnc Suppos you r givn ysin ntwork with th grph structur n th prmtrs ll figur out Now you woul lik to us it to o infrnc You n infrnc to mk prictions or clssifictions with ys nt 2 1

2 nothr xmpl You r vry sick n you visit your octor. Th octor is l to gt th following informtion from you: HsFvr = Hsough = Hsrthingrolms = tconrcntly = Wht s th proility you hv SwinFlu givn th ov? 3 nothr xmpl N to comput SwinFlu = HsFvr = Hsough = Hsrthingrolms = tconrcntly = Suppos you pss out for you sy wor to th octor. Th octor is only l to trmin you hv fvr. Wht is SwinFlu = HsFvr =? 4 2

3 Qury xmpl SwinFlu = HsFvr = Qury Vril vinc Vril Unosrv vrils: Hsough Hsrthingrolms tconrcntly 5 Quris Formliz W will us th following nottion: X = qury vril = { 1 m } is th st of vinc vrils = osrv vnt Y = {Y 1 Y l r th non-vinc or hin vrils Th complt st of vrils X = {X} Y N to clcult th qury X 6 3

4 Infrnc y numrtion Rcll tht: X X X y n x1... xn xi prnts X i i1 This mns you cn nswr quris y computing sums of proucts of conitionl proilitis from th ntwork y 7 xmpl #1 Qury: = = How o you solv this? 2 stps: 1. xprss it in trms of th joint proility istriution 2. xprss th joint proility istriution in trms of th ntris in th Ts of th ys nt 8 4

5 xmpl #1 Whnvr you s conitionl lik = = us th hin Rul: = / 9 xmpl #1 Whnvr you n to gt sust of th vrils.g. from th full joint istriution us mrginliztion: X X Y y y 10 5

6 6 11 xmpl #1 To xprss th joint proility istriution s th ntris in th Ts us: N i i i N X rnts X X X xmpl #1 Tk th proilitis tht on t pn on th trms in th summtion n mov thm outsi th summtion

7 7 xmpl #1 Tk th proilitis tht on t pn on th trms in th summtion n mov thm outsi th summtion Sums to 1 Sums to 1 xmpl #1 Tk th proilitis tht on t pn on th trms in th summtion n mov thm outsi th summtion Sums to 1 osn t pn on. n mov to th lft

8 8 15 xmpl #2 16 rctic Writ out th qutions for th following proilitis using proilitis you cn otin from th ysin ntwork. You will hv to lv it in symolic form cus th Ts r not shown ut simplify your nswr s much s possil. 1. = = = = =

9 rctic 2. = = 17 rctic 3. = = = = = 18 9

10 omplxity of xct Infrnc urglry rthquk lrm ohnlls rylls Th urglry/rthquk ysin ntwork is n xmpl of polytr Singly connct ntworks k polytrs hv t most on unirct pth twn ny two nos in th ntwork 19 omplxity of xct Infrnc olytrs hv nic proprty: Th tim n spc complxity of xct infrnc in polytrs is linr in th numr of vrils Wht out multiply connct ntworks? louy Sprinklr Rin Wt Grss 10

11 omplxity of xct Infrnc Wht out for multiply connct ntworks? xponntil tim n spc complxity in th numr of vrils in th worst cs nws: Infrnc in ysin ntworks is N-hr vn wors nws: infrnc is #-hr strictly hrr thn N-complt prolms 21 Th Goo Nws lthough xct infrnc is N-hr pproximt infrnc is trctl Lots of promising mthos lik smpling vritionl mthos tc. pproximt infrnc is currnt rsrch topic in chin Lrning 22 11

12 rctic fls fls fls fls fls 0.1 fls fls 0.9 fls fls 0.2 fls 0.8 fls fls 0.3 fls 0.7 fls Wht is =fls=fls? 23 rctic fls fls fls fls fls 0.1 fls fls 0.9 fls fls 0.2 fls 0.8 fls fls 0.3 fls 0.7 fls n you com up with nothr ys nt structur using only th 3 nos ov tht rprsnts th sm joint proility istriution? 24 12

13 Wht You Shoul Know How to o xct infrnc in proilistic quris of ys nts Th complxity of infrnc for polytrs n multiply connct ntworks 25 13