Bayesian Feature Weighting for Unsupervised ... - Semantic Scholar

Report 4 Downloads 143 Views
       !"$#% &(') * &+-,./0 ( 1 32 4 5 -67'('(8 9  :&=@?A9B>C$9 ( D  EFHG1FHI(J"KLINMPORQ&FHGG1OTS U(KLQ&VWOXV&FZY[I\F^]_GNKL` ab1ced!fhghijb1klgmon0pPmliceqrghb1fsrt uvbketb wkLuyxlbfDz{uyg}|@m!n~Bfhuyghuzh€(pPmlyqLi‚Lud ƒ0doket mlqLxob1f1„r~p…„†pBdokedo‡Ld E…KLˆW‰Šˆ&`GNKL‹Œ`1O†Q U(KrG1KL‰]ŽF( &O†‘X’&`NO†Q a…bcedof{g“ib1kHgm!n s^g“d\g“uvz{ghutz wkLuyxlbfDz{uyg}|@m!n~Bfhuyghuzh€(pPmlyqLi‚Lud ƒ0doket mlqLxob1f1„r~p…„†pBdokedo‡Ld ”–•—o˜r™Lš›†˜ d!kem!gh€ebfuykez{g“doket b¤€Lbf“bn_b1d\g“qLf“b"¤Bbuv¥o€HghuvkL¥ªcevd¡|rzdªzhuy¥o¢ kLuy¯RtdokHgPf“movbo­s^uykRt bg“€Lbk^qLi‚Rb1fPmonTced\g“uyb1klgDz0g“bke‡ez0g“m"‚†b zhijdoyÑ„ñ¬^kLm\¤uyke¥¶¤€LutD€Z¥ob1kLb1z…cLf“m\xHu‡rb ijmlfhb‡ruvz“t f“uviuvked!¢ œ)bcLf“b1zhbkHgžd>ibgh€Lmr‡Ÿn_mlf x¡dofhud!‚eybzhbvb1t5¢ h g mlfh|´uykLn_mof“ijd!ghuvmokX¤BmoqL‡)‚Rb3m!n¥of“b1d!g ‚Rb1kLb ¯eg1­(ÚÛkÐgh€eb1zhb g“uymlk†£¡¤Bbuv¥o€HghuvkL¥¦uyk§d!k¨qLkezhqLc†bf“xHuzhb1‡¨ybNd!f“kLuyke¥ ! d cecLyutd!ghuvmokez1„Ax\dofhud!‚Lvb¶zhbvb1t5g“uymlkÐuvz d!g/gh€Lb3‡ruvz“t f“b g“uymlkÐm!n tmokHghb©Hg…qez{uvkL¥ª~«d¡|lb1zhuvdokzh€Lf“uykL¬\do¥obo­«®«€Lb‚edozhuvz h g e € b¶uyk^xlb1z{ghuv¥ld\g“mof/d!kR‡´i@d¡|Z‚†b¶‚edlz{bN‡)mokÐcLf“uymlf/uykrn_mlfhi@d!¢ n_mlf0gh€ebijmr‡rbRuvzBd°¯ekLuyghb…iju±©^ghqefhbmon[i"qLyghuvx\d!f“u±¢ h g v u o m kA­ ÚÛk´¥lbkLb1f“do„ñ€Lm\¤BbxlbfN„Ri@do¬HuvkL¥uykLn_mof“ibN‡Ê‡rbNt uz{uvmokRz d!ghb²°doqez“z{ud!kZ‡ruz{ghf“uy‚LqLghuvmokez1­œ)b‡rb1ijmokez{ghfDd\g“b o m . k gh€Lb3qrghuvyuyg}|Ðm!nx\d!f“ud!‚Lvb1z"ijd¡|)kLmog‚†b¶n_b1dlz{uv‚Lvb3zhmZ¤Bb €Lm\¤)g“€Lb0ijmr‡rbHced!fDd!ijbghbfDz[doke‡/t vqez{ghbf&doz“z{uv¥okL¢ B ¤ o m L q ‡ªvuv¬obghmjf“bv|@mokzhtD€Lb1ijb1zBghm@zhbvb1t g«x\dofhud!‚Lvb1z«doqrghmo¢ ijbkHgDzªtdok³‚Rb´t moijcLqLghb1‡³zhuvi"qLyg“dokLbmlqez{v|µqRz}¢ @ i \ d “ g v u t1d!vy|l­ uvkL¥¶d!kb·@tuyb1kHg…¸º¹%d!v¥omlfhuygh€ei­P»cLcLv|^uyke¥¶moqLf ƒ0d!f“ud!‚Lvb(z{b1ybNt5ghuvmok¦g“b1tD€LkLuòHqLb1z¶n_mof¶zhqLc†bf“xHuzhb1‡¦ybNd!f“kLuvkL¥ ~«d¡|obNz{ud!kz{€Lf“uvkL¬\d!¥obBijmr‡rb^g“m°dt mlijcLyb©"cLf“mo‚r¢ €ed¡xlb ‚Rb1bk´¤uv‡rb1y|Zz{ghqR‡ruybN‡T­/¾Lmlf…b©rdoijcLybNz„Tzhbb½²bmlfh¥lb vbi uvkml‚r¼}b1t gWf“b1tmo¥okeu±g“uymlkª½Ža…qL|^¥oqLvq[„o~«dofhkedof“‡[„ d!kR‡ ¾LmHz}g“bfºÕNÖoÖ^ó^„ Ò¥d!ke‡/ÓlmofD‡Ldok"À!ÂoÂeÕo„1sriuygh€d!ke‡ ô°ml€Lk ‡rb³¾efhb1u±gDdozXd!kR‡¿¾emofDz{|Hgh€ÁÀ!ÂlÂlÀoà „mlqLfXb ©rc†bf“u±¢ Õ1ÖlÖoõHÃ5­Ws^qefhcLf“uz{uvkL¥ov|o„1gh€ebBz“d!ijbºt1d!kLkLmogW‚†bPz“d!u‡ d!‚†moqLgWqLkr¢ ijbkHgDz|^uyb1v‡3¥om^mr‡ªf“b1zhqLyg“z1­ zhqLcRb1fhx^uz{bN‡ vb1dofhkLuvkL¥R­W»zhu‡rbBn_fhmli ked!uvxob«z{bNd!fDtD€ ijb g“€Lmr‡Lz„ gh€ebB¤Bmof“¬m!nW½ö[uvq[„H÷†€edokL¥e„!Ødoyqei"‚†m…d!kR‡"öAd¡¤f“bkRt bBÀoÂoÂHÀoà zhbbi@z0ghm ‚†bg“€LbmlkLy|cLf“uykRt uvcLybN‡@d!cLcefhmHdotD€ghm/g“€LuzºcLf“mo‚L¢ Ä ÅlÆÈÇÊɖ˵ÌÎͧÏ)ÇÊÅL赮 vbi­öAuyq³ø ùú\ûºcefhmo¼}b1t5ggh€ebj‡ed\g“dªghm(d3ym\¤Bbf°‡ruvijbkezhuymlk ®«€Lb§uvic†mofhg“doket b§mon´qLkezhqLc†bf“x^uvzhb1‡ybNd!f“kLuyke¥¿uz–¥of“m\¤«¢ ¤ijuyu±gh©^€Ôg“qLØ«fhb"pBi» „ mr‡rd!b1kev‡µzm!d!n cLghcL€Lv|Xb‡L¹Zd\d!gDdLf“¬o­«m\~Px)|tD€ed!d!kRuvd!kµv|l¹(g“uvt1mld!kHvghy|ªbuypBkHdoghb1fh¥ovm(fDd\g“ghm ¢ uvkL¥(uykÐi@d!k^|Zf“b1zhb1dof“tD€)d!f“b1dlz„[uvketyqe‡LuykL¥(‚euymluykrn_mlfhi@d!ghutz1„ uvkL¥Xmoqrgªgh€LbZmogh€Lb1f@ced!fDd!ijbghbfDz1„ºg“€Lb|–zhdoijcLyb(mlkLv|.gh€eb ‡Ld!g“d(ijuvkLuyke¥e„ mo‚r¼}bNt5g"f“b1tmo¥lkLu±g“uymlk[„ ‡Ld\gDd!‚edlz{b¶tyqez{ghb1fhuvkL¥R„ ‚Lf“m\¤z{uvkL¥Xg“m^mozªn_mlf‡Luy¥lu±gDd!°yuv‚LfDd!f“uybNz„…t movd!‚†mofDd\ghuvxobZ¯e±¢ ijt mlu±ij©^g“cRqLmlfhkLb@bdokHyg“vz1mr­td\®«g“€Luymlbk´cLx\fhmodo¼}fhb1ud!t ‚Lghuvvmob1k@z°m!donAke‡Zgh€Lg“b°€L‡Lb@d\k^gDd/qLi"g“m‚†bd"f/ym\mo¤BnBbØ«fBpB‡r» u±¢ ghb1fhuvkL¥¶doke‡uykrn_mlfhi@d!ghuvmokfhbghf“uyb1x¡doº½Ž~BvbuфeÒ¥¶doke‡(ÓlmofD‡Ld!k ijbkezhuvmok/uzAkLb1b1‡rbN‡ghmt mokRz}g“fhqet gAb ·¶tuyb1klg&¹Zd!f“¬om\xtD€ed!uvkez1­ À!ÂlÂlÀL„ ~«dofhkedof“‡Ôd!ke‡–¾emofDz{|Hgh€³À!ÂlÂLÕl„ ~«dofhkedof“‡[„Pa…qL|^¥oqLvq d!kR‡¶¾Lmlf“zh|Hgh€ªÀ!ÂlÂLÕl„oaqe|H¥lqLvq¶b gd!Ñ­HÀoÂoÂlÀL„l²movqL‚[„Ls^vmokeuyi gh×fDm\d!¤BW‡rbxlmobi@fN„\d!x\uvk(d!f“d!uvdoke‚L‡[y„eb€Lzhb1bkevb1t t blgh„euvmomokjkeb €edoymHz&z{g“bNm/zB‚Rgh€Lb…b‡rmouykHkLg“bqLu±uvg“kuyxlghb/€LbkLm!zhc†g“uyb1mlt5k ¢ d!kR‡Ô®&d!i@d¡|om¦Õ1ÖlÖoÖe„ ×m!n_i@d!kek–doke‡¦Ø0qLÙ1uvtD€ed¦ÕNÖoÖoÖHÃ5­¦ÚÛk ijmlz{gm!nAg“€Lb1zhb°z{bg{ghuvkL¥Hz„rmlkLbg}|Hceuvt1d!vy|@‚†b¥luykez‡ed\g“dd!kRd!y¢ m!n ¤€ed!gdlt5g“qed!Tx\d!f“ud!‚Lvb1z«d!f“b°‚Rb1uyke¥¶z{b1ybNt5ghbN‡T­ |rz{uz‚^|(¤Pb1uy¥l€lg“uyke¥3mlfzhbvb1t ghuvkL¥dzhqL‚ezhb g/m!nºuvkrn_mlfhi@d\g“uyxlb n_b1d!ghqLf“b1z1­ÚÛk.t moijcLqLghbf"xHuzhuymlk[„An_mlf b ©Ldoiceybl„Wuvk^xob1z{ghuv¥ld!¢ n_ÚÛmokfghi€euvuyz…©^ghceqLd!f“c†b bijfN„emr¤B‡rb bcLzf“dob1kezhb‡kHg…b ©rdªcL~Bd!d¡uvk(|lb1€Lzhm\uvdo¤Èku±zhg€L|^f“uyuvkeb¬¡‡Ldoz¥ob/dijg“f“mrdoke‡rbz{¢ ghmlf“zjmonÜghb1kÎdoz“z{uv¥ok¦¤Pb1uy¥l€Hg“zghmÐn_bNd\g“qLfhbNz¶zhqetD€³doz@t mlymlqLfN„ cedofhb1klgibgh€Lmr‡Ðn_mlf"x\d!f“ud!‚Lvb¶z{b1ybNt5g“uymlk†£¡¤Bbuv¥o€HghuvkL¥R­®«€eb z{ghbf“bmR„ºijm!g“uymlk[„0g“b ©^ghqefhb(d!kR‡Ôzh€ed!c†bo­³²bkeb(b ©rcLf“b1z“z{uvmok f“bvbx\d!kHgWx\dofhud!‚Lvb1z&d!kR‡ ijmr‡rb^cedof“doibghb1f“zWd!f“bPt mlijcLqrghbN‡ d!kRd!v|^zhuz¤uygh€ÎaÒ»Ýijut f“m!¢Ûd!f“f“d¡|rz1„¤€Lbf“bmokLbZtyqRz}g“bfDz xobNt5g“mofDz½_ced!ghuvbkHg“zDäuygh€¶gh€Lmlqezhdoke‡Lzºm!nTbkHghf“uvb1z½Ž¥ob1kLb1zDÃ5„Huvz ¤uygh€(d!kb ·¶t uvbkHg¸P¹7doy¥lmof“u±g“€Li­ Þߺàlá}âHãä}åÛâHæèçæèéê1ëèçHâHê1ìrí“á}æèî5êë†ã1ä{ïoí“ä5ð

ý    ü ”þý ˵ǴÅ!ÿ ” ÇÊÅHÆ ”³ )œ b ‚Rb1¥ouvk¤u±g“€d@zhuviceyb/b©rdoijcLyb/¤€euvtD€uvyvqez{ghfDd\ghbNz«gh€eb qrg“uyvu±g}|3uykx\d!f“ud!‚Lvbzhbvb1t ghuvmokn_mofqekez{qecRb1fhx^uz{bN‡ªvb1dofhkLuvkL¥R­ ö[bg°gh€Lb@‡Ld!g“ d )‚†b@‡ruz}g“fhuv‚Lqrg“b1‡Zm\xlbf°dªijuy©^ghqLf“bjm!nºiqL±¢ ghuvx\d!f“uvd!ghb¥ldoqez“z{ud!kez1 „  

  $½ # ä€Lbf“b *ij+ u±©^uvg“z/qLghfh€Lb/b@tmo‡rijuvijcRbmlkekLzhbuykHmlgDkÐz,„ m!# nºg“€Ldob¶ke‡ ‡L d!g“dL„ d!!*f“b ghu€ez" b/gh€Li&b@bN%(d!k^')kqL id!ke‚R‡b1f/t mom!¢n x\d!f“uvdoket b…n_mofiuy©^ghqLf“b/t mlic†mokeb' kH.g -\„Ld!kR‡ªg“€Lb t vqez{ghb1fdoz{¢ zhuy¥lkLijbkHgcLfhml‚ed!‚euyvu±g“uybNz z{qei ghm(Õl­¾Lmof«g“€Luzb ©Ld!ijcLvbo„ ¤Bb°dlzhzhqLijb°d g“m!g“doTm!nWgh€L f“bb°iju±©^g“qLfhb/tmoijcRmlkLbkHgDz„r‡rud!¥o¢ mokRd!t m\x\d!f“ud!ketb¶i@d\ghf“ut b1zjdoke‡Ô‡LuyijbkRz{uvmok * +0/ õL­ÔÚÛk do‡e‡ru±g“uymlk[„L¤Bb/z{bgBg“€Lb/ijb1dokezBghm 122 Õ 4 À 9;:: 122 7 4  9;:: 122 8Ö 4 7 9;:: 22 5À 4 6 :: 22 >4 Ö :: 22 7 4 õ :: 2 : 2 : 4 6  > 4 ó 7 #  / 2 8 4  : #= / 2 ? 4 À : #@ / 22 688 44 A :: 3 8Â8 4v4 ÂÕ < 3 ?Â? 44 6À < 3 8Â8 44 Â7 < d!kR‡/doz“z{uv¥okgh€ebºx\d!f“uvdoket b BC Õ/ÕÕÀ°À/GÀ FHld!ke‡°g“€Lb0ijuy©H¢ ghqefhb/cLf“mo‚Rd!‚Lvu±g“uybNz  /D 8 4 6oõ°/E? 4 ÀoD õ? 4 6IAGFJH_­ ²uvxobk¨d.g“f“douykLuvkL¥¦z{bg3m!n‡Ld\gDd.c†mouvklgDLz K© 8© = 4M44 8© =ONONP z“d!ijcLvb1‡)n_f“moi7gh€Lbªghf“qLb¶iju±©^g“qLfhb‡ruz}g“fhuv‚Lqrg“ uy% mlk[„ % ¤Pb¶% bNz}g“u±¢ i@d\g“bgh€Lb(ijmr‡rbced!fDd!ijb g“bfDz  d!keQ‡ #ÈqezhuykL¥X¸P¹X­0œ)b doz“zhqLijbg“€LRb B zdofhb¬^kLm\¤k[„^‚Lqrgg“€Lb/d!f“¥oqLijb1klg«b ©^g“bke‡Lz ked!ghqLfDd!vy|"ghm"d" OS zhtbkedofhuvm°¤u±g“€¶qLkL¬^kLm\¤kjx\d!f“uvdoket bNz­ ¾Lf“moi d!‚†m\xobl„ºuyg¶uvz@docLcedofhb1klggh€Rd\g@gh€eb¯ef“z{gjgh€Lf“bbn_bNd\ghqefhbNzjm!n ‡Ld!g“Td d!f“bÔqezhb n_qe¶uyk x\d!f“|^uykL¥§‡rb1¥of“bb1z´n_mlf.t doz“z{uy¯Rtd!¢ ghuvmokA­)pPmok^xob1f“zhbv|o„Agh€Lb3vdlz}g"gh€Lf“bb@n_bNd\g“qLfhbNz €ed¡xlb@mokLv|Ðd i@d!f“¥ouvked!eVb Uñb1t5gPmok¶‡rbghbf“ijuykeuykL¥ ghm ¤€LutD€¶t mlijcRmlkLbkHgºuvk gh€eb°ghf“qLb/‡ruvz{ghf“uv‚Lqrghuvmok(dj‡Ld!g“dcRmluykHg‚†bvmokL¥Hz­ »z3uvyvqez{ghfDd\ghbN‡Î‚^|¦gh€Lb)t mlklg“moqLf3cLvm!g“zuvk ¾&uy¥lqLf“bµÕo„uykr¢ t vqe‡ruvkL¥Xg“€Lbʁdoz{g¶g“€Lfhb1bZuvfhf“bvbx\d!kHg@n_bNd\ghqefhbNz¶uvk³ghfDd!uvkLuvkL¥ b ©Ldlt bf“‚ed!ghb1zt doz“zhu±¯Rt1d\g“uymlkZmokÊgh€Lbjiju±©^g“qLfhb@tmoijcRmlkLbkHgDz ‚†b1tdoqezhbʤBbÊi@d¡|³‡rb g“b1t5gu‡ruymHz{|^ketf“dlt uvb1z@uvk¨z“d!ijcLvb1Wz A­ Ø0f“qLkLuvkL¥°g“€Lbuvfhf“bvbx\d!kHg n_b1d!ghqLf“b1z0€Lmo‡Lzijmof“bcLf“moijuz{b«n_mlf dZ¥lbkLb1f“doyuvÙbN‡Ðb1z{ghuvi@d\ghb‚†b1tdoqezhbª¤Bbª¤uvy«‚†b3vb1z“z"cefhmlkLb ghm¶ghfDd!uvkLuyke¥¶mokZdof{g“u±nŽdlt5g“zuyk(g“€Lb"z“d!ijcLvb"‡Ld!g“dL­œ³€ebk(¤Bb xob1fhuy¯ebN‡µg“€Luz¶b ©rc†bf“uyijb1klgDd!vy|l„t doz“z{uy¯Rt1d\ghuvmok¦m!n°g“€Lb´À!Âl ghfDd!uvkLuvkL¥(b ©LdoiceybNz°¤Bdlz/t mof“f“b1t5g/mlkÐÖlÖL­ 7 cRb1f“tbkHg m!n«gh€eb uvkez}gDd!ketb1zn_mof…x¡dofhud!‚eyb"zhbvb1t ghuvmok[„†‚Lqrg°mokeyX| 6Hór­ 7 c†bfDt b1kHg m!n&gh€eb°ghuvib/¤€ebk3ghfDd!uvkLb1‡mokd!vñgh€eb/x¡dofhud!‚eybNz­ ®«€Luz@b ©LdoiceybZzhqL¥o¥lb1z{g“zg“€ed\g¶uyn d!k^|Hgh€LuvkL¥e„Bx\d!f“uvdo‚LvbZz{b¢ vb1t5g“uymlk–€edoz¶d)¥lfhbNd\g@cRmoghb1klg“uvdo‚†bkLb¯Lgªuvk–tvdlzhzhuy¯Rtd!ghuvmok d!kR‡¶t vqez{ghbf“uvkL¥ cLf“mo‚Lvbi@z1„Hdoke‡jbxlbk¶ijmlfhbzhm ¤€Lb1kª‡rbNd!y¢ uvkL¥µ¤uygh€¨€Luy¥l€r¢Û‡ruyijb1kez{uvmokRd!…‡ed\g“de­ ¾efhmli z{mlib)z{uvijcLvb b ©rc†bf“uyijb1klgDz¤Pb´cRb1f{n_mlfhijb1‡[„uygi@d¡|³d!z{mԂRb)g“€Lb)t1dozhb gh€Rd\gºx\d!f“ud!‚Lvbz{b1ybNt5g“uymlk@uvzmonT¥of“b1d\g“bf€Lb1ycjg“€ed!k@uvkªzhqLc†bfh¢ x^uvzhb1‡)vb1dofhkLuvkL¥R­ªs^qLf“cLfhuzhuykL¥ly|l„Ad!vijmlz{g"d!v gh€Lbªyuyghb1f“d!ghqLf“b mok@x\dofhud!‚Lvbzhbvb1t ghuvmokªdoke‡@z{€efhuvkL¬\d!¥lbuvzºuyk¶gh€Lb…fhb1¥of“b1z“z{uvmok t mlkHghb ©^gN­

True mixture distribution 4

0.06

2

True mixture distribution

0.04

x2

4 0.06

0.02

0

0.02

10

0

0 5

20

−10

0.04

−5

−4

5

x1

10

−5

0

5

10

x1

4

44

0.06 0.06 22

2

0.04 0.04 0.02 0.02 0 0 5 5

0 5

−5 −5

20

−2 −2

−2

0 0

10

00

0

−10 −10

0 0

10 10

20 20

−4 −4 −5 −5

−4

0

−10

−5

0

00

55

x1

10 10

EM estimate using relevant variable

5

10

x1

4

0.06 2 0.04

x2

−5

010

−10

EM estimate using all variables EM estimate using all variables

0.02

0

0

20

x2

0.06

−5

0

0 −2

−4

x2

−5

2

−2

x2

0 5

0

0.04

0.02

0 −2

0 5 20 0

10 −5

−4

0 −10

−5

0

5

x1

10

¾&uy¥lqLf“bÕYZ[løV\^]G_?`5ùbahú!ùbc$]d_ ]fePùhgLøúI[Gi\úG_RùŒúkjløl]femi¡úda(cŽúnûyø `ø ûvpø oqù c$]G_rcJ_.qù st]u[dcJ\j&ø _8`(c$]G_?`&vxwygLWø \zc;{lqù |5ah}ø o~]G\.?]G_†&ø _eù \@ø“dú _8`€cJ_µhù gLø¶bù a(|e ø [Gc`5bù a(c$n&|rqù c$]G_ e~ap]G\sg,c$o~g‚sº}ø `Gú \.†ûyø hù gL€ø [oú!ùŒ^ú gLdú i¡^ø [dc ƒ&ø ahVø _R)ù i¡ú!„û |e(ø `€]Gi\Vø aJù geø/©T Õ o~]G\.?]G_†&ø _e…ù v †(_}o~]G_?`5bù ahGú `5$ù ‡Thù gLmø \@ø“dú _8`Gú ahø«hù gLø~ú yaO]&{IcJ\@ú\ùÛø „û ˆ/hù gL)ø ` dú \jø cJ_ÐJù geø"©L‰À op]d\Š?]G_ñVø _R$ù ‡msg,c$o~gL`(|jkjHVø `Dbù ` hù gLú\ù ya(|5_?cJ_‹jhù gLø `~ø op]d_Œ[i\Gú a(cŽIú n ûvWø st]d|rû [‰nD}ø nD&ø _†bø 0qù cŽú\û…ù ]uo„û |,`5ùŒ&ø a(cJ_‹j‹v0wygLø [Gc`5qù a(c$nV|rqù c$]G_ sŽcÜJù g^i¡dú a(cŽú nûy.ø `ø ûy~ø obù c$]d_nDøùùÛVø apú IŒaO]k{IcJ\jú!ùŒVø ` hù gLøjqù a(|e^ø [Gc`5qù a(c$nV|rqù c$]G_yv‚`~cJ_,j( ú `Gú \.†ûyø¶ùŒVø `5‘ù `ø$ù ‡’sºRø j‹]\ù &ø a(aO]Ga~`“]fe•”vJ”d–3Gú _Œ[^”IvM—I–ŠeV]da…hù gLøqù ahdú cJ_?cJ_‹j^sŽcÜJù gdú _Œ[˜sŽcÜhù g,™ ]G|r˜ù i\Gú a(cŽú nûyLø `øûy~ø o qù c$]G_yv›šœ]!ùŒøÊJù ge€ø yaO]nDIú nVc܄û cÜqù ˆ[Gc`5bù a(c$n&|5™ qù c$]G_8`•`Og8]dsŽ_‰cJ_´Jù g5c`Ž!jd|5a“ø"Gú a“Rø |5__Œ]Ga(\@ú\;û cž1~ø [Iv Ÿ ý ˵Ì  ¡ m ´Ï´‹Å ¢jÅrÏ ” ÇÊÅLË.Æ ®«€Lb…imr‡rb1Ruzºd"z}gDd!ke‡Ldof“‡¯RkLu±g“bijuy©Hg“qLf“bm!n[iqLyghuvx¡dofhud\g“b ²°d!qRzhzhuvdok‡Luvz{ghf“uy‚eqrghuvmokezkY

£…¤ M M ¥ I Œ h½ O¦ # k%(') à ½}Õ¡Ã   ¤€Lb1fh‰b Kk ˜§T¨ I" ¦˜© / Õ 4&4k4«ª¬P‡rbkLmoghbNz g“€Lb3ml‚ezhbf“x¡d!¢ ghuvmokRz„ ¤z­ ½ ®% # %(' ÃBbketmoijcedlzhzhb1zdoyñg“€Lb/ijm^‡Lb[cedof“doi¢ b g“bfDz„ ‡rb1kLm!g“b1zgh€eb@iuy©ruyke¥(¤Pb1uy¥l€lgDz®„ #¦doke‡ ‡rb1kLm!g“b gh€ebZijb1 d!k³doke‡³t m\x\d!f“ud!ketb3mong“€LbZijuy©Hg“qLf“bZt mo' ijc†mokLb1kHg ‡rb1kez{uyghuvb1z1„[d!kR‡ *  ‡rbkem!ghbNz…gh€Lbk^qLi"‚†bf°m!nBt moijc†mokLb1kHg“z1­

®«€Lb ijuy©^ghqLf“b ijmr‡rbWuvz…‡rb ¯ekeb1‡mokg“€Lbz{g“doke‡Ldof“‡cLf“mo‚ed!¢ ‚Luvyuyg}|3zhuviceyb©uK  Y .¯ Ân_mlfd!v-doke‡    °Œ / ÕdPH­ œ)b"t mlket b1klg“f“d!ghb°mokg“€Luvz…z{uvijcLvb ijm^‡LbTn_mlfcLf“b1zhbkHg“d!ghuvmok cLqLf“c†mlzhb1z1­ ×m\¤BbxlbfN„b©Hg“bkezhuvmokez3ghm–€LuvbfDd!fDtD€Lutdo…ijuy©H¢ ghqefhbNz…½~BdofhkRd!fD‡doke‡¶¾emofDz{|Hgh€ªÀoÂoÂeÕo„o×m!n_i@d!kLkÊÕ1ÖoÖlÖlà doke‡ x\d!f“uvd!ghuvmokedoTiju±©^ghqefhbNz ½Ž~BvbuAbg…d!Ñ­†ÀoÂoÂHÀoÃBd!f“b/z}g“f“douy¥l€lghn_mofh¢ ¤«d!fD‡T­…öWd\ghb1f1„†uvk)s^bNt5ghuvmok 7 ­vÕo„†¤PbcLfhbNz{b1kHg…dªzhyuv¥o€Hgimr‡^¢ uy¯Rtd!ghuvmok)m!nBgh€Luz°ijm^‡Lbn_mlf/moqLf/ml‚r¼}b1t g°f“b1tmo¥lkLu±g“uymlk´doke‡ i"qe±g“uyijb1‡Luvdg“f“dokez{d\g“uymlk3docLcLvuvt1d\ghuvmokRz­ œ)bÈuvkHghf“mr‡rqet bÈg“€Lb vd!ghb1klgÎdoyvmrtd\g“uymlkx\d!f“ud!‚Lvb1z²± § KlÕ 4k4&4 PghmÐuvke‡rutd\g“bªg“€ed\g¶d)cedof{g“uvtqLvdofzhb1òHqLb1ket b

‚†bv% mokL¥H%z/* gh m)dÊzhcRbNt uy¯RtªtyqRz}g“bzf -!­´®«€LbNz{b3uyke‡Luvt1d\ghmlf"x\d!f“uy¢ d!‚eybN³z K´± Õ 4k4&4 ª¬P t mof“f“b1zhcRmlke‡@g“mjdok3uÑ­ u­ ‡T­0z“d!ijcLvb n_f“moig“€Lb

f¦O‡r© u/z}g“fhuv‚L% qrg“uyml% ˜k µ&$½ ± / -à / Œ ­ ¶®·$¸ “E ¹ ºk»^¹½¼A“E ¾°zJ º ’Y ºNœJ ¿°R º´»@U œ)bn_mlyvm\¤žd3€LuvbfDd!fDtD€Luvt1d! ~«d¡|ob1zhud!kZz{ghfDd\ghb1¥o|(¤€Lb1fhbgh€eb qLkL¬^kLm\¤k´ced!fDd!ijbghbfDz ¤ d!ke‡Zgh€Lb@doyvmrtd\g“uymlkZx\d!f“uvdo‚Lvb1z³± d!f“bfhb1¥ldof“‡rbN‡µdlzj‚Rb1uykL¥.‡Lf“d¡¤kÔn_fhmli docLcLf“mocLf“uvd!ghbcLf“uymlf ‡ruz}g“fhuv‚Lqrg“uymlkez1­œ´bdotD¬^kLm\¤vb1‡r¥lb/moqLf…qLket b1f{gDd!uvkHg}|3d!‚†moqLg gh€ebªb ©Ldlt5g/n_mof“iŸm!n«gh€Lb3cLf“uymlf ‚^|)zhcRbNt uyn_|^uykL¥Êu±guykÐg“bf“ijz m!nºzhmoijb qekL¬^kLm\¤k(ced!fDd!ijbghbfDz ½Ž€H|^c†bf“ced!fDd!ijbghbfDzDÃ5­œ)b cLdotb€^|^cRb1fhcefhuvmofDzmlk´zhmoijbmon0gh€eb€^|^c†bf“ced!fDd!ijb g“bfDzzhm gh€Rd\g0uvfhf“bvbx\d!kHg n_b1d!ghqLf“b1zdofhbzh€Lf“qLkL¬ g“m/d/t moijijmokx\d!vqLbo­ ®«€ed!gªuvz1„«gh€ebÊb1z{ghuvi@d\g“uymlk³m!n°gh€Lb´€^|Hc†bf“cedof“doibghb1f“zj¤uvy d!vvm\¤µqez g“m/bvuyijuvked\g“bgh€ebVb Uñb1t5gPm!nñuyf“fhb1yb1x\d!kHg n_b1d\g“qLf“b1zuvk gh€eb/iuy©^ghqLf“b/ijmr‡rbÑ­ À qLf΀euyb1f“dof“tD€Lutdo(~Bd¡|lb1zhuvdokijmr‡rb´uvz ‡rbcLut5g“b1‡$dlz³d ¥ofDd!ce€Luvt1d![ijmr‡rb1Auvkʾ&uy¥lqLfhb"ÀL­®«€Lb"doyvmrtd\g“uymlkx¡dofhud!‚eybNz ± dofhbdlzhzhqLijb1‡g“m"‚†b‡rfDd¡¤kjn_fhmli d/iqLyghuvkLmoijud!ñ‡ruvz{ghf“uy¢ ‚L qrg“uymlk[?„ ± Á  ½}Õ ¦  Ã5„L¤€LutD€(do‡rijuyg“zBg“€Lb ‡rbkRz{uyg}| µWb½ ± ~£  à /   ?à bÄÅ«Æ$Ç %   ¤€Lb1fh‘b È  $½ ± à / ÕBuyn ‚†bvmokL¥HzWghm°¥of“moqLzc -Pdoke“‡ È  b½ ± à /  m!g“€Lbf“¤uz{bl­Wœ)bcLdotbd/t mok!¼}qL¥ld!ghba…uyf“uvtD€eybgºcLf“uymlfmokjgh€eb iju±©ruvkL¥´tm^b ·¶t uvbkHg“z  ÊÉ   q½ ËLÃ5„€Rd¡xHuvkL¥(g“€Lb¶n_mlyvm\¤uvkL¥ ‡rb1kez{uyg}| µW½  £ ËLà / ½bË ÃyÌ Íkb½ Í&Ë Í N à ½bË Ã Â  ŒÎ ~Ï  % ½ÀlÃ Ì  Ì     ¤€Lb1fhb Ì «½ Í ÃZ‡rbkLmoghbNzgh€LbÔ²°doijijdÔn_qLkRt5ghuvmok doke‡ Ë N /  Ë­ œ)b¶doz“z{uv¥ok)d²°doqezhzhud!k)cLfhuvmofg“m3g“€Lb¶t mlijcRmlkLbkHg/ijb1d!kRz # =   = h½ #WS %OÐ Ã5„…¤€Lbf“b Ð uvz‡rud!¥lmokedo¤uygh€ÈbvbijbkHg“z Ñzhb f“% xo4&b14k‡34 % ‡LÑ d\gD" dL­­0œ)®«b°€Lb°g“dou¬o‡r•b b1d#WuSz«ghghm@mj‚†bNb z}g“zhuyi@doijd\g“cLb°yb°gh€Lijb b1dok3zmozhnWqetDg“€L€3b/gh€emod!‚Lg¢ gh€eb/uyf“fhb1yb1x\d!kHg«n_b1d\g“qLf“b1z«€ed¡xlb Ñ S zkLbNd!fÙ1bf“mjÑ doS ke‡ªgh€Lb tmofh¢ f“b1zhcRmlke‡ruvkL¥/t moijc†mokLb1kHg“z m!Œn # dotfhmHzhz&¥lfhmlqLcez d!f“bz{€Lf“qLkL¬ ghm\¤«d!fD‡Lz«zhbkezhuy‚eyb/t mlijimlk3x\do yqLbNz­

œ)b…cLdotbdt mlk\¼}qL¥ld!ghb…uyk^xob1f“zhb ¢Œœ³uz{€edof{gPcLfhuvmofPmokªgh€Lb°t mo¢ x\d!f“uvdoket bNz ') Ò‹Ó " b½ Ô % Ô ' SNÃ5„Rdo‡rijuyg{ghuvkL¥jg“€Lb ‡rbkRz{uyg}| µ&½ ' £ Ô %(' S tÃ Õ £ ' £ Ï®ÄÖ× " ×  Ç$Ø = b©^yc K‹Ù ½}GÕ Ú!Àofà ۅÜr$½ Ô ' S ' Ï  ~à P ®«€Luz¶cLf“uvmof@uz¶t b1klg“bf“b1‡–d\gªgh€LbÊtm\x\d!f“uvdoket bm!n°gh€ebʇLd\gDd 'Ñ Ý = S!­ºߜ)Þáb/à cL$½ vâ dlt b à „«dokn_mouvf k^xoä b1f“/ zhb°²°Õ do4&ij4k4 ij* d@+ ‡L­¿uvz{gh®«f“€Luy‚euvzqrgh‡ruvmouz}kg“fhmouv‚LkqrbNg“douymltDk€ % % do‡Liuyg“zgh€Lb %p‡rã b1kezhu±g}| µ&½ Ñ Ý = £ â %~ã Ã Õæå Ñ Ý?= ç ÏyèéÏ  b©^uc êÙ Ñ ã = 4 Ýáë ®«€Lb Ñ Ý = dofhb/doz“zhqLijb1‡ªghmj‚Rb/uvke‡rb1cRb1ke‡rb1kl´g Y µW½ Ð £ â %~ã à /  " µ&½ Ñ Ý = £ â %pã Ã Ý s^uvket b@doyg“€LbjcLf“uymlf“z°d!f“bjt mok!¼}qL ¥ld!ghbo„Amo‚rgDd!uvkLuyke¥3g“€Lb@c†mlz{¢ ghb1fhuvmof…‡ruvz{ghf“uv‚LqrghuvmokRzm!n&gh€eb"cedof“doibghb1f“z«‚^|t mokR‡ru±g“uymlkLuvkL¥ mok3gh€eb d!vymrtd!ghuvmokx\d!f“uvdo‚LybNzBuvzz{ghfDd!uv¥o€Hghn_mof“¤Bdof“‡T­ a α

Σ∗ Σ

b υ

µ∗

τ

λ

µ z x

¾&uy¥lqLf“bªÀ5Y˜ìlZzí²eV]da¶ùhgLø^îúdˆoø(`(cŽúd_\zc;{lùq|5ahø^\^]k[lø û‘sŽcÜùJg `Og,a(cJ_5ïokú jllø ya(c$]Ga~`&vwŒge)ø {^~ø [˜g5ˆpL&ø a(™MeGú ahdú \jøùŒ&ø a~`jdú ahzø ah…ø Œ™ ahVø `Vø _RùŒ~ø [‚sŽcÜhù gTn~]&{^(ø `~‡@hù gL‰ø i¡dú a(cŽú nûy(ø `‚[oøùŒ&ø a(\˜cJ_†~ø [²nVˆ.hù gLø [oú!ùŒú3éú `œ[]d|?n ûv˜ø o&cJaOoûyVø `p‡«Gú _Œ[¶Jù geRø |5_5ïG_y]GsŽ_ua“Gú _Œ[I]G\ði¡dú a(cJ™ ú nûyVø `RsŽcÜJù gÊVø \.†qù ˆWo&cJaOo ûv(ø `&v ý  ÍÎÇ ” Ç´År赮 ñ Ï.Ë  ®«€Lb°cedof“doibghb1f“zPm!nWgh€Lb°iju±©^g“qLfhbijmr‡rb[t1d!kLkLmog‚Rb/t mli¢ cLqrg“b1‡d!kRd!v|lg“uvt1d!vy|ªqLkLvb1z“z«mokLb°¬^kLm\¤zBgh€ebijuy©^ghqLf“b/uykR‡ru±¢ td!ghmlfBx\dofhud!‚Lvb1z1­&œ´b°€ed¡xlbg“mf“b1zhmofhgºg“mjkHqeib1fhutdoñibgh€r¢ mr‡Lz1­ À kLb/td!kuvijcLyb1ijbkHgd@²uy‚L‚Rzz“d!ijcLvbfBghm¶tmoijcLqrg“b gh€eb"cedof“doibghb1f“zdoke‡(d!vymrt1d\ghuvmokx\d!f“ud!‚Lvb1z1­®«€Luvzuvz…‡rmokeb ‚^|.zhdoijcLyuvkL¥´gh€Lbcedof“doibghb1f“zd!ke‡Ôd!vymrt1d\ghuvmokµx¡dofhud!‚eybNz n_f“moiŸgh€Lb1uyffhbNz{c†b1t ghuvxob3cRmHz}g“bf“uymlf“z1­Z×m\¤BbxlbfN„Ag“€Luvzd!v¥omo¢ f“u±g“€Li$td!kʂRbt moijcLqLg“d\g“uymlked!vv|3uvkHghbkRz{uvxob"n_mofg“€LbdocLcLvu±¢ td!ghuvmokezº¤Pb…€ed¡xobuyk¶ijuvke‡T­ÚÛkez{ghbNdo‡@¤Bbmlcrgºn_mlfBdok@b ©rc†b1t5¢ g“d!ghuvmok)i@d\©ruyijuvÙ1d!ghuvmok–½Ž¸º¹´Ã°d!v¥omof“uygh€Li$g“m(t moijcLqLghbjgh€eb \@&ú {IcJ\z|5\%˜ú ?]é`5ùÛVø a(c$]da(c½¹Z»ØBÃcRmluykHg b1z{ghuvi@d\g“b1z°m!nBgh€eb iju±©^g“qLfhb/ijmr‡rb1­

ò·$¸ ¾³óô¿WõBŠX»}¹Wº œöXó

»nÜg“bfuykLuyghud!vuvÙ1d\g“uymlk[„[g“€Lbª¸P¹ doy¥lmof“u±g“€Li$n_mlf"¹Z»اbNz}g“u±¢ i@d\g“uymlk3uyghb1f“d!ghb1z«‚†b g}¤Bbb1kgh€Lb°n_mlyvm\¤uyke¥"g}¤Bm@z}g“bcezkY ¸Œ· ¾Á`1G1FHm’ ÷/pPmliceqrghbžgh€Lb¿b ©rcRbNt5gDd\ghuvmok m!nXgh€eb¿t mli¢ cLvb g“b vmo¥o¢Ñc†mlz{ghb1fhuvmofݤuygh€d!vymrt1d\ghuvmok%x\d!f“ud!‚Lvb1ùz ø½ ¤ à / úŒû +ý þ~ÿ D yml¥ µWb½ ± % % ¤ à FŒ„T¤€Lbf“b ¤ Ä Ç f“bcefhbNz{b1klgDz g“€LbÄÅéx\ü doyqLbm!Ç n0g“€Lb"cRd!fDd!ijb g“bfDzd\g…gh€LbcLf“bx^uvmoqezghuvijb z{ghb1c[­ · ó `GNFH‘’ ÷°¹Zd\©ruvijuyÙ1b"m\xob1fg“€LbcRd!fDd!ijb g“bfD&z Y ¤ Ä ‹Ç / dofh¥0þi@d!© ø½ ¤ à ¾Lmlfg“€Lbj¸ z{ghbcA„†¤BbtmoijcLqrg“b"g“€LbcRmHz}g“bf“uymlfm!ng“€Lbjd!vymo¢ td!ghuvmokx\d!f“uvdo‚LybN&z Y µWb½ ± / -

Ã

 ­ µW½b± / - £ % ¤ Ä Ç Ã / µ&h½ ~£% ¤ Ä % ¤ Ç ÄÃ Ç % ¤€LutD€[„Luvk3mlqLftdlz{bl„ruvz¥ouvxobk3‚^Œ| Y $½ 6Hà /   Œ h½ h½ O ¦ # k# %(') à à p

¦  %(')  Œ ¾Lmlfgh€Lb(¹ z{ghb1c[„º¤BbkLm!g“b3g“€ed\ggh€eb3n_qeket5g“uymlk ø½ ¤ Ãb©^¢ cedoke‡LzBghm ¥ ¥ Ù ÀÕ à £ £ Ù ÀÕ ½h Ù # à H Ï  ½h Ù # à  ' 

  Õ ' Õ ¥ Ù À yml¥ £ £ Ù À ½h# ÙL# S à H Ï  ½h# ÙL# S à РР   Õ ¥ Ù À ½bÔ *+ Õ¡Ã^yml¥ £ £ Ù ÀÕ Û…Ü^½bÔ S Ï  à ') ' '  ¥ «½ يâœÙ¦ÕNÃ^vmo¥ å Ñ Ý= ç Ù ã = 4 ÑÝ Ý ®&d!¬^uyke¥¨‡rb1fhuvx\d\ghuvxobNz„"¤PbÔmo‚rgDd!uvk gh€LbÔn_movvm\¤uykL¥¨qLcñ‡Ld\g“b b1òHqed!ghuvmokezBn_mlf«gh€Lb/ijmr‡rb1[ced!fDd!ijbghbfDzkY  

 







 

 



 

















 



















ª  !  Ë Ë  Ù ÙÔÕ Œ    * #  ½ V' Ï  Ð Ï  Ã Ï  ' Ï  ½ ¥  Ã Ð Ï  # S D   ½$ ÙL#  à ½$ ÙL#  ÃfH;F Ô ' S Ô ½ *+ ÕNà '  Ñ Ý = â  ã=  Õ Àdâ *Õ À ¥  ½h#  Ý Ù # ÝS à =    ¤€Lb1fhb  ­  M  ­)®«€eb1zhb¶qLcñ‡Ld\g“b1z1„ ghmo¥lb g“€Lbf¤u±g“€ b1òHqed!ghuvmokн$H6 Ã5„etmokez{ghuyghqrg“b/moqLf¸P¹7doy¥lmof“u±g“€Li­ 



















































"



#









!

wzhuvkL¥"g“€Lb°i@d\ghf“uy©ªuyk^xlbfDz{uvmok¶vbiji@dL„^¤Bb/td!k3fhb1¤fhuyghb…gh€eb qLcñ‡Ld\g“b z}g“bcn_mof’#  doz #  Ð ½ ') OÐ Ã Ï  ½ ¥  à ') ½ ') OÐ Ã Ï  # S

ÚÛk g“€Luz b ©rcLf“b1z“z{uvmok[„¡¤BbB‡Lmok S g&€Rd¡xob0g“m°uyk^xob1f{gWgh€Lb‡rud!¥lmokedo i@d\g“fhuy© Ð ­@®«€Luz/c†bf“iuyg“z bvbijbkHg“z m!n Ð ghm(¥lmghmÙb1fhmR„ d!vvm\¤uykL¥n_mof«n_bNd\g“qLfhb zhbvb1t ghuvmok[­ ¾Lf“moi7gh€eb¸P¹ qLc†‡ed\ghbb1òHqed!ghuvmokez1„ mokLb3td!kµfhbNdo‡ruvy|)mo‚L¢ zhbf“xob g“€Lbjz{€Lf“uvkL¬\d!¥obuyk´moc†bfDd\g“uymlk[­/»z ÂL„†g“€LbbNz}g“u±¢ i@d\g“bBmoneg“€Lbijb1d!kRzz{€Lf“uvkL¬rzAg“mgh€Lbz“d!ijcLÑ vb«ibNd!kjd!ke‡"gh€eb t m\x\dofhud!ketbPzh€Lf“uykL¬rzWghm…gh€ebzhdoiceyb«t m\x\d!f“ud!ketbo­A®P|^cLuvt1d!vy| ¤BbkLmlfhi@doyuz{bgh€ebj‡ed\g“dzhmªg“€ed\“g #WS / Âd!kR‡ ' S / Ò " ­ ×b1ket bl„^gh€Lb°g“bf“Ê i Ô Suyk3gh€eb/qLc†‡ed\ghb/monAg“€Lb/t m\x\d!f“uvdoket bNz z{g“d!‚euyvuvzhb1z gh€Lbd!v¥omlfh' uygh€ei­´®«€ed\guvz1„u±gjcLf“bxlbkHg“z gh€Lb3uyv±¢ t mlke‡ruyghuvmokLuvkL¥cL€Lb1kLmoijbkemok´dofhuzhuykL¥ªn_fhmli$€ed¡x^uyke¥dokÊqLkr¢ ‚†moqLke‡Lb1‡yuv¬ob1yuv€Lm^mr‡T­ Ë m´Ï)Ç ²É ´Ï.²Ë ³Æ¨ÅlÇ´År赮 ²” ‰L ÅrÏ ” ÇÊÅLË.Æ À xob1f)gh€Lb–doz{gX‡Lb1tdl‡rbo„@¤Bb–€ed¡xob¦b ©rc†bf“uyb1ket bN‡¿dok¿b©^¢ cLvmlzhuymlkÝm!n.i"qe±g“uyijb1‡Luvduvk ‡ruv¥ouyg“doÊvuy‚ef“dofhuvb1zÎdoke‡>gh€eb ¤Bmof“v‡^¢Œ¤u‡rb ¢Œ¤Pb1‚[­:ÚÛkced!fhghut qLd!fN„¶¤Bb΀ed¡xlb³¤u±g“kLb1z“z{bN‡ gh€eb)b1ijbf“¥obkRt b)m!nd!f“¥ob)t mlyvb1t ghuvmokezm!njd!kLkem!g“d!ghbN‡Îuvi¢ d!¥lb1z1­ ¸©Ld!ijcLvb1zÔm!nÊgh€LbNz{bÈuykRt vqe‡rbÈgh€LbžpPmlfhb1‡Ld!g“d!¢ zhb g¦½z{b1bµ¾&uy¥lqLf“xb 6là „"ijmlz{gÊiqez{b1qLi uyi@do¥obµtmovybNt5ghuvmokRz ½ lÃ5„«gh€eb ¤Bb‚¨dof“tD€euyxlbÔ½ rà „ºkLb1¤zcL€Lmo¢ ghml¥ofDd!cL€Rz„rcLf“uvx¡d!ghb°cL€Lmoghm¶doy‚Lqeijzd!ke‡x^uv‡Lbmlz1­º¹(qe±g“uyijb ¢ ‡rud f“mo‚†m!g“uvt1z„H¤€Lbf“bf“mo‚†m!gDzPdltòHqLuvfhbuvi@d!¥lb1z1„HzhmoqLkR‡Lzºdoke‡ ghb©^gWdoz[gh€Lb1|…ked¡x^uv¥ld!ghb&gh€Lf“moqe¥o€ d«cedof{g“uvtqLvdof[bk^x^uvfhmlkLijbkHg d!zhm3f“b1zhqLyg“zuyk´gh€euvzg}|^c†bmonB‡Ld!g“de­®P|Hceuvt1d!vy|l„ñgh€LbNz{b@d!kL¢ kLmog“d\g“uymlkezPfhbn_bfBghmgh€Lb/tmokHghb1klgBm!nWgh€Lb°d!kLkem!g“d!ghbN‡¶uvijdo¥obl„ ‚Lqrg i@d¡|Zx\dofh|(uvk)gh€Lb1uyf"dlttqLf“dlt |(d!kR‡)tmoketuvzhbkeb1z“z­j¾Lmlf uvkez}gDd!ketbo„¡g“€LbpPmof“brd!kLkem!g“d!ghuvmokez&‡rbNzhtfhuv‚Rb«zhcRbNt uy¯RtBuyi@d!¥lb t mlkHghbkHgN„†‚eqrg/kLm!g/d!vWmonºuyg1­ ¹(qezhbqei t mlyvb1t ghuvmokezd!f“b m!nÜ¢ ghb1k(d!kLkLmog“d!ghb1‡ª¤u±g“€(z{mlib/zhcRbNt uy¯Rti@d\ghb1fhud!TzhqetD€dozBgh€eb d!fhghuz{gd!ke‡X‡ed\ghbªm!ndot1òlqeuvzhu±g“uymlk[„d!ke‡ÐmonÜghb1kXgh€Lb3d!kLkLmog“d!¢ ghuvmokRz‡rb1do[¤u±g“€(z{mlib°fDd\g“€Lbfd!‚Rz}g“f“dlt5gi@d\ghb1fhud!Ñ­ ®«€Lb"dokLkLmog“d\g“b1‡uvi@d!¥ob‡Ld\gDd¶d!vym\¤zqezg“m@n_mof“i"qLd\g“b mo‚L¢ ¼}b1t gÊf“b1t ml¥okLuyghuvmokÈdozZd³z{g“d!ghuz}g“uvt1d! i@dltD€Luykeb´g“f“dokezhvd!ghuvmok cLf“mo‚Lvbi ½aqe|H¥lqLvqµb g¶do­0À!ÂlÂlÀlÃ5­Ðœ´bzhb¥oijb1klgjuvijdo¥obNz uvklg“m´f“b¥luymlkezª½Ž‚Lvmo‚ezDÃ"doke‡Xg“€LbkԁybNd!f“kXghm)cLf“b1‡rut5g¤Pmlf“‡ez qezhuyke¥´f“b¥luymlkez­X¸PdotD€.f“b¥luymlk.uvzj‡rbNzhtfhuv‚†b1‡.‚^|.zhmoijbz{bg m!n"n_b1d\g“qLf“b1z1­¿ÚÛk¨ijdltD€LuvkLbÊg“f“dokezhvd!ghuvmok[„dµyb©ruvtmok΁vuyke¬^z ¤BmofD‡Lz)uykmlkLb–vdokL¥oqedo¥obÔghm ¤BmofD‡Lz)uyk g“€Lb³m!g“€Lbf.d!kL¢ ¥oqRd!¥obl­Ô½~Pf“m\¤k[„a…bvvd´Ø0uvb ghfDdL„a…bvvd)Ø0uvb g“f“dÊd!ke‡.¹Zbfh¢ t b1fÊÕNÖoÖ 6e„º¹(b1vdoibN‡ À!ÂlÂLÕ¡Ã5­ ÚÛkÎg“€Lb´‡Lmoi@d!uvk³m!n ml‚r¼}b1t g f“b1t ml¥okLuyghuvmokA„ºg“€Lbn_b1d!ghqLf“bZ¤BbZdoz“z{mrt ud\g“b3¤uygh€³uvi@d!¥lb(fhb¢ ¥ouvmokRz ‡rmZkLmog"ked!ghqLfDd!vy|)mrttqLc^|´dZ‡ruz“t f“b ghb3z{cedlt bl­®«€eb zhuyijcLvb1z{gBzhmovqrghuvmok¶ghm g“€LuzºcLf“mo‚eyb1i uzºghm qezhb…ô¢Œijb1dokezg“m xobNt5g“mofòHqed!kHg“uvzhbgh€Lb uvi@d!¥lbf“b¥luymlk3f“bcefhbNz{b1klgDd\g“uymlk[­®«€Luvz d!cecLfhmHdotD€[„†do‡rmlcrghbN‡(uvkµ½Ža…qL|^¥oqLvqÊbg°do­TÀ!ÂlÂlÀlÃ5„e¤«doz¤Pb1y 













$

'

&%

$(*)

,+.-/-103254/4"6/6/687-1+:9A@87BC@/D.4CE/FGH4"-1+I9A@J7+1-"G:K ,+.-/-103254/4"6/6/6875FC@IL+H9M.>N7BC@1D

bn1

y uvmoki@d!keb¥lf“dlzhz«zh¬^| ¼}bgcLd!kLb/zh¬H| ¾&uy¥lqLf“bœ68Y Ž{^úG\.†ûyøV`‘e~aO]d\$ùJgeø ]Gahøû [oú\ùÛúW`ø ù hìR|5ˆ&j|rû„| øùú\û v³—,””d— v (ø geúGi\ø´úG`~`V]´o&cŽú\ùÛøp[ ïoø&ˆGst]Gap[é`ÊúG_y[ `øqj™ \@Vø _R$ù `)eV]Ga¶øDú o~g cJ\jkú jlVø ‡³n&|rŠù sºWø [I]G_ mù ïd_Œ]dsTsg5c$opg‚st]GaO[ o~]Ga(ahVø `q8]d_Œ[G`¶ù ]‰sg,c$o~gr` ø j\j&ø _e…ù v wygL ø _?|5\^nDVø aW]«e^st]Gap[é` Gú _y[€`ø jd\@&ø _ebù `“oDGú _ n“˜ø [Gc ƒ…Vø ah&ø _eù P&ø i¡&ø _‰sgeVø _´Jù geVø ˆªdú ahø hù gLø `Gú \@(ø ‡sº)ø \jdú ˆlgLdú i¡Šø \€]dahøhù gLdú _W]G_†’ø `qø j\@Vø _Rù eV]Ga³ú `(cJ_‹joûyø st]Gap[é‡m]da“\€]dahø hù gLdú _ ]d_†œø st]GaO[.eV]Ga^ú `~cJ_,j!ûv˜ø nû ]Inkv PO

XW

p(wn1|bn2)

:Y

[Z

f“b1t b1uyxlb1‡Ô‚^|.gh€ebÊt mliceqrghb1f@xHuzhuymlk–tmoiji"qekLu±g}|Ƚ_uygª¤Bmok ‚†b1z{g&cedocRb1fAcLf“uvÙbºuvktmo¥lkLu±g“uyxlbºt mlijcLqrghb1fWx^uz{uvmok d!g&¸«ppPƒ À!ÂlÂlÀlÃ5­Aœ)b¤BmoqL‡yuv¬ob«g“m z{qLf“ijmoqLkHgg“€LbcLf“mo‚Lvbi¿m!nñ€ed¡xH¢ uvkL¥@ghmªuykHghf“mr‡rqetb/kLmouz{b"‚H|3xobNt5ghmlfòHqed!kHg“uvzhuyke¥jgh€Lb ‚eyml‚ez„ zhmµuvkez}g“b1dl‡Î¤Bb)dl‡rmocrgdԇLuvz“t f“b g“b ¢}²°d!qez“z{ud!k–g“f“dokezhvd!ghuvmok ijmr‡rb^g“€ed\gºdoyvm\¤zAqRz&ghmghfDd!kezhd\ghb²°d!qRzhzhuvdok"n_bNd\g“qLfhbNz ‡ru±¢ f“b1t5g“y|g“m‡Luvz“t f“b g“b"n_bNd\ghqefhbNz­"®«€ebjzh€Lf“uyke¬¡do¥obt moijc†mokLb1kHg m!nmlqLf/ijm^‡LbPdoyvm\¤z/qez/ghmÊt1d!f“fh|Zmlqrg/n_b1d!ghqLf“bªzhbvb1t ghuvmok ¤uygh€Luvkgh€Luz«ghfDd!kRz{d\g“uymlk3cLf“mrt bN‡rqLf“bo­ ·$¸ œ ¹W¿ª‰U ¼®õt¿°R º´»@U ó » ¾lõ)¼ À qLf°d!cLcefhmHdotD€(g“m3f“b1tmo¥okeu±g“uymlkZuvz°doked!vmo¥lmoqez«g“mijdltD€LuvkLb ghfDd!kRz{d\g“uymlk[„Rdlzmof“uv¥ouvked!vy|3cLf“moc†mlzhb1‡‚^|)½aqL|^¥lqLyq´b g…do­ À!ÂlÂlÀlÃ5­°œ´bg“f“dokez{d\g“b"uvi@d!¥obfhb1¥ouvmokez½Ž¾efhb1ketD€RÃghm¤Pmlf“‡ez ½Ž¸ºkL¥ovuz{€Rà ­$ÚÛk§ced!fhghut qLd!fN„°moqLf(ijmr‡rb1"dot g“z(doz(d§ûvOø {IcJ™ o~]G_R„ld°‡rbx^ut bNz gh€ed!g0cLf“b1‡rut5gDzmokLb«f“bcLf“b1zhbkHgDd\ghuvmok½_¤BmofD‡Lz ¸0ke¥ovuvzh€Rë¥luyxlbk(d!kLmogh€Lb1ff“bcLf“b1zhbkHg“d!ghuvmokн_uvi@d!¥ob"fhb1¥ouvmokez ¦¦ ¾Lf“bkRtD€RÃ5­ö[bNd!f“kLuyke¥Zdyb©^ut mlk)n_fhmliŸ‡Ld!g“duz"d(z{g“doke‡Ld!fD‡ cLf“mo‚Lvbi¨uyk/i@dltD€LuykebghfDd!kezhd\ghuvmokvu±g“bfDd\ghqefhb½~Pf“m\¤k°b gWdo­ Õ1ÖlÖ 6e„†¹(b1vdoijb1‡ÐÀ!ÂoÂeÕNà ­"®º|^cLutdoyv|o„[dvb ©rut mok´uvz°vb1dofhkeb1‡ n_f“moi dn_mlfhi m!n‡Ld\gDd@z{bg¬^kLm\¤kdozdokXú!„û c;j_†~ø [nVcÜùÛOø {lù dªghb ©^g°uyk´g}¤Bmªd!kL¥lqed!¥lb1z¤€ebf“bf“moqL¥l€Êt mlfhf“b1zhc†moke‡rb1ket bl„ c†bf“€ed!cezd\gg“€Lb cedof“do¥ofDd!cL€mofzhbkHg“bketb/yb1xobÑ„euz¬^kLm\¤kA­ ®«€Lb/cLf“mo‚eyb1i m!n yb©ruvtmok(dot1òlqeuvzhu±g“uymlk3uvk^xomlyxlb1z«‡rb g“bf“ijuykr¢ uvkL¥/cLf“b1t uzhb«tmof“fhbNz{c†mokR‡rbketb1z&‚†b g}¤Bbbkj¤BmofD‡Lz m!nT‡ru U†b1fhb1kHg d!kL¥lqed!¥lb1z1­¦»ked!vmo¥lmoqezhy|l„º¤Bb(td!k³tmokezhuv‡Lbf¶dЇLd\gDdÐz{bg t mlkezhuvz{ghuvkL¥µmon"d!kLkem!g“d!ghbN‡³uyi@do¥ob1z3dozd!k doyuv¥okeb1‡³‚Luyghb©^g zhuyketb¤Bb€ed¡xobd!k@uvi@d!¥lbt mokRz{uz}g“uyke¥/m!nñfhb1¥ouvmokez1„od!kR‡@d/z{bg m!nBghb©^g1­œ´b¶¬^kLm\¤¿gh€eb@ghb©Hg¥om^b1z°¤uygh€Ðg“€Lb¶uvijdo¥obl„A‚Lqrg ¤Bb°‡Lmok S g¬^kLm\¤ ¤€LutD€¤Pmlf“‡3¥om^b1zB¤uygh€(¤€LutD€fhb1¥ouvmok[­ pPmoijcLqLghuvkL¥ gh€Lb g“f“dokez{d\g“uymlk cLf“mo‚Rd!‚Luvyuyghuvb1z uz kLmog z{ghfDd!uv¥o€Hg{n_mlfh¤«d!fD‡‚RbNtd!qRz{b¤Pb€ed¡xob"d htD€LutD¬ob1kZd!ke‡Êb¥l¥ zhu±g“qed\g“uymlk Y§ghm¨‚LqLuvv‡ gh€LbÔghfDd!kezhd\ghuvmok cefhml‚ed!‚Luvvu±g“uybNzZ¤Bb kLb1b1‡ghm°¬^kLm\¤.g“€Lbt mlfhf“b1t g tmof“fhbNz{c†mokR‡rbketb1z&‚†b g}¤Bbbkuvi¢ d!¥lb1zBd!ke‡¶¤Pmlf“‡Lz1„H‚Lqrg«ghm¯e¥oqefhb…moqrgBgh€Lb°t mlfhf“b1zhc†moke‡rb1ket bNz ¤Bb kLbbN‡ghm@¬^kLm\¤Ègh€eb/ghfDd!kezhd\ghuvmokcLf“mo‚Rd!‚Luvyuyghuvb1z1­«»zb©^¢ cLd!uvkLb1‡uvk(½Ža…qL|^¥oqLvq@b gºdo­lÀoÂoÂHÀoÃ5„o¤Pbtdokjm\xobfDt mlijbºg“€Luvz \

bn3

TS

]

H^

`_

Ca

b n2) 2| p(w n

VU

RQ

bn2

wn1

p(wn3|bn2)

wn3

wn2

horse

Gandalf

trees

¾&uy¥lqLf“bX>?Y wygeø)úG`~`V]´o&cŽú\ùqc$]G_xŒaO]InDún&cÜû„cÜùbcŽøV`}yaO]Gi´c$[oø)ùhgLø o~]Ga(ahVø `q8]d_Œ[løV_yo“øV` ÛúG`~`~c;j_?\@ø&_eùb` €n“øùqsºø“ø&_ÊøDúo~gst]Gap[@úG_Œ[ hù gLœø i¡dú a(c$]G|,`RcJ\@ú&jHøR`ø j\jø&_eùb` fnû]nV` v cLf“mo‚Lvbi ‚^|Îi@dofh¥luykedoyuzhuykL¥Ôm\xob1fªg“€LbÐcRmHzhzhuy‚eybXdoz“zhm^tuvd!¢ ghuvmokRzqRz{uvkL¥Ðd´ijuy©^ghqLf“b3ijmr‡rb1„Bd!kµu‡rbNdZg“€ed\g@¤«dozmof“uy¥o¢ uvked!vy|(cefhmlcRmHz{bN‡(n_mof…ghb©^g°uvk–½Ž~Bfhm\¤kÊb g d!Ñ­ Õ1ÖoIÖ 6là ­ ®«€Luvz ijmr‡rbrdoz“zhqLijb1zWmokLb¢g“m!¢ŒmokLbPcLfhml‚ed!‚euyvuvz{ghutºdlzhzhuv¥okLijbkHgDzWdlz zh€Lm\¤k uvk¾&uv¥oqLf“tb >R­W¾Lmlf b1dotD€"‚Lyml‚ uvkgh€Lb ¢g“€ uvijdo¥obl„1g“€Lbf“bBuvz dcefhml‚ed!‚Luvvu±g}|°m!nLuyg ‚Rã b1uykL§¥°do¨ z“zh" m^tuvd!ghbN‡/¤* u±g“€ b1dltD€ m!nrg“€LbB¤Pmlf“‡Lz uvk g“€Lbºuvi@d!¥lbo­W¹Zmof“bºcLf“b1tuvzhbv|o„Ngh€eb ghfDd!kRz{d\g“uymlkªijmr‡rb[uz ¥luyxlbkª‚^y| Y µW½ ã £ …à /   ¥ µWb½ â  / © fÃ Û ½ ã / ã  £ /  à    M ¤€Lb1fh•b µWb½ â  / © Çrbkem!ghbNzgh€Lb¶doyuv¥okeib1kHg°cefhml‚ed!‚Luvvu±g“uybNz zhqetD€gh€ed!‘g â uyn ghfDd!kezhd\ghbNz ghm ­®«€Lbk^qLi"‚†bf m!n&‚Lvmo‚ezdoke‡ª ¤B/ mofD© ‡LzBuvã k3 g“€Lb * ¢Ñgh€uyi@d!¥lb/d! f“ b  d!ke‡  „ f“b1zhcRbNt5ghuvxob1y|l­sruyketb@gh€eb¶¤Pmlf“‡ez/uykÐg“€LbªdokLkLmokRd\ghuvmokRz d!f“b qLkLmlf“‡Lbf“b1‡T„g“€Lbf“bÊuzkLmµf“b1dlz{mlk–n_mofcLf“b n_b1fhf“uyke¥µz{c†b1tu±¯†t d!vuv¥okLijbkHgDz­®«€Lb1fhbn_mof“bo„r¤Bb°zhb Žg µ&$½ â  / © à / éÕ Ú  ­ ÚÛk¿½aqe|H¥lqLvq¨bgdo­À!ÂlÂlÀlÃ5’„ Û ½ ã / ã  £ /  êuzd ‡ruzhtfhbghbg“f“dokezhvd!ghuvmokjg“do‚Lvbo­ ÚÛk@gh€euvzBd!cLcefhmHdotD€[„\g“€Lbg“f“dokez{¢ d\ghuvmokjcLf“mo‚Rd!‚Luvyuyghuvb1áz Û «½ Í £ Í Ã0d!f“b²°d!qez“zhuvdok[­W¹(mlfhbcefhbNt uz{b1y|l„ gh€ebf“bZuvzªmokLbʲ°doqez“z{ud!k¦n_mof3b1dltD€¦¤BmofD‡¦uyk–g“€LbZxlm^t1d!‚LqL¢ d!f“|o­ ¸ºdotD€@¤BmofD‡j¥ob1kLbfDd\g“b1zuvi@d!¥lb…zhb¥oijb1klgDzn_f“moid tmofh¢ f“b1zhcRmlke‡ruvkL¥ª²°d!qez“zhuvdoktyqez{ghb1f1­B~B|tyqez{ghb1fhuvkL¥jg“€Lb/¤Pmlf“‡ez ½Žz“d¡|ª¤uygh€Zô¢Œijb1dokez«mofs^ƒažijbgh€Lmr‡LzDÃ5„Ru±guzdovzhm@cRmHzhzhuy¢ ‚Lvb"g“m3€Rd¡xob"d²°d!qez“zhuvdokÊt vqez{ghbf…n_mof°bNdotD€ÊtmoketbcrgN­°®«€eb ‡ruzhtfhbghb¢Û²°doqezhzhud!k¶g“f“dokezhvd!ghuvmokªijmr‡rb1[uvz«kem\¤ µ&½ ã £ …à / Â Ï Â ¥ Û ½ ã  £  à  bS

cU

dS

U

e

gf



f

f

e

ghji lk e

f

<e

i

<e

mf

<e

<e

Tn

Ro

o

<e

f

f

f

<e



o

f

 !   / Â Ï Â ¥ ½ ã  ¦ #  %('  Ã  ½  Ã   !   

<e

h

i

e

hpi

k?i

o

5qsrt

h

<e

i

e

h

i

k?i

uf

¤€Lb1fhb˜-/uvzuykÊgh€Lbf“dokL¥ob3½$- / Õ % 4&4k4 % WÃ5„  ‡rb1kLm!g“b1z…d cedof{g“uvtqLvdof¤Pmlf“‡"ghml¬ob1k[„od!kR‡  ½  à / Õuyn  d!cecRbNd!fDz uvk gh€eb ¢Ñgh€d!kLkLmog“d!ghuvmok[„\mogh€Lb1fh¤uz{bPu±g uz&Âe­W®«€LbBuvke‡rb ©œ-ºuvz gh€ebuvke‡r* b©ªn_mlfPg“€Lb ¤BmofD‡@ghml¬ob1kezd!ke‡dot1t mlf“‡ruvkL¥ly|gh€eb t vqez}g“bfDz­3ÚÛkÐgh€Lbªbke‡T„Wgh€eb¶mo‚r¼}bNt5g“uyxlb@uvz ghm(¥ob1kLbfDd\g“b ¤BmofD‡Lzn_fhmli ‚Lvmo‚Rz­®«€Luz/uvz"dZz}g“f“douy¥l€Hg{n_mof“¤«d!fD‡Zd!cLceyutd!¢ ghuvmokªm!n[~«d¡|ob1z0fhqLvbo´„ µW½ £ ã tà լµ&½ ã £ …hà µW½ ‘à ÕrµW½ ã £ …úz{uvketb ¤Bb°tqLf“fhb1klg“y|3doz“z{qLijb/dqLkLuyn_mof“i cLf“uymlf«n_moŽf µ&½ …à ­ ®«€LuzAijmr‡rb1Huz&dx\d!f“uvd!ghuvmok monrgh€LbPiuy©^ghqLf“bºijmr‡rb1HmonLb1òHqed!¢ ghuvmokÐÕl­ w…z{uvkL¥jg“€Lb°kLm!gDd\ghuvmok Û ½ Ã

 !­ µ&½$â  / ©V£  %~ã  % ¤ Ä Ç Ã /  Ý  ã  Û ½ ã £  £ Ý 5à %   gh€eb/qLc†‡ed\ghbNz«n_mof«g“€Lb/cedof“doibghb1f“z«d!f“b oJv

dq rt

xo

o

HfPw

uf

Ifpw

v

v

f

f

uf

f

2



e

f

 

f

<e

RMS error for µ

uf

e

f

<e

<e

1.5 MAP α=50

ML all

1

MAP α=11

kyi

Š

z {y|~}€/P‚IƒI„†…J|‰ ‚‡ƒ ˆVŠŒˆ ‹  Ž

Þ

z …œ|~}C

…



ˆ

 Ž „œž

 ž

ž

 Ž ‹

Š ž

Ž

ƒ



ž

‘

Š

• ,’”“ 

0.5

Rš Š 

Ž Š i ƒ   š i Šƒ

 ƒ

‚Iƒ

ŠlÖZ‡Lu;Uñbf“bkHg"¤BmofD‡Lz1­ œ)bt mlkez{u‡rb1f n_moqLf0ijmr‡rb1vz1­&®«€eb¯efDz}g0uz0d°i@d\©ruvi"qLi¿yuv¬ob¢ vuy€Lm^mr‡ijm^‡Lb[g“€ed\ggDd!¬lb1zdo‡Lx¡dokHg“d!¥lb°m!nd!vTgh€Lb n_b1d\g“qLf“b1z1­ ®«€Lb(zhb1t mlke‡.uzjz{uvijuyd!fN„ºb©Lt bcLgg“€ed\g@uyg¶uvzghfDd!uvkLbN‡.mokey| mokmoqef«tD€emout bm!nWf“bvbx\doklgBn_b1d!ghqLf“b1z1„rijb1dok3d!kR‡3z{g“doke‡Ld!fD‡ ‡rb1xHud\g“uymlk–m!n t mlymlqLf1­Èœ)bʇrud!¥omlked!vuvÙbgh€Lb´t m\x\d!f“uvdoket bNz uvkZ‚Rmogh€)¹Zö.ijb g“€Lmr‡Lz…ghm3ijdouykHgDd!uvkÊz}gDd!‚Luvvu±g}|m!ng“€Lb¸P¹ d!v¥omlfhuygh€ei„do±g“€LmoqL¥l€–gh€Luz3im\xlbÊt mlijb1zªd!g¶gh€eb´t mHz}g3m!n vmlz“zm!nx\d!vqed!‚eyb uvkrn_mlfhi@d\g“uymlk[­®«€Lb doz{gg}¤Bm@imr‡rb1vz…d!f“b x\d!f“uvdokHg“z0mon[gh€eb¹Z»…Ø „^¤€Lbf“b¤Bb‡Luvdo¥omokRd!vuyÙ1bgh€Lb°t m\x\dofhuy¢ d!kRt b1zuykmokeb ijm^‡LbAdoke‡¬ob1bcgh€Lb/qec†‡Ld!ghbN‡(t m\x\d!f“uvdoket bNz qLkHghmlqetD€LbN‡´uvkÐgh€eb¶m!g“€LbfN­~Bmogh€.~«d¡|obNz{ud!k´ibgh€Lmr‡Lz"qezhb cedof“doibghb1fºx\d!vqLb1zºm!®n Ô / kÕ 6e‹„ â / Ù/Յd!ke‡ ã / éÕ Ú^ÕNÂoÂlÂoÂo doz«‚†b n_mlfhbl­ ®WmijbNdozhqLfhbgh€eb@cRb1f{n_mlfhi@d!kRt bm!nºg“€Lb@ijmr‡rbz„W¤Pbji@d!kL¢ qedoyv|Xd!kLkLmog“d!ghb1‡.gh€Lbuvijdo¥obNz uvk.gh€ebªg“b1z{gjzhb gN­XÚÛkÔzhmoijb tdlz{bNz„.gh€Lb1fhb ijuy¥l€lg ‚†b¿ijmlfhb¿gh€edok7mlkLbÁd!kLkLmog“d!ghuvmok ‡rb1bijb1‡Xtmof“fhbNt5g/‚RbNtdoqez{bjg“€Lb¶‚Lvmo‚.tmokezhuz}g“b1‡)m!nzhbxob1f“do zhqL‚r¼}b1t g“z1­œ´b°qezhb1‡ªg}¤Bmjzhuviceyb°‚Lqrg&b U†bNt5g“uyxlbb1fhf“mofBijb1d!¢ zhqLfhbN&z Y “E ¹ “‘Q Y&®«€LuzPibNdozhqLf“bfhb1cRmlf{gDz0d!kªbf“fhmlfm!n0Õuyn[kLmokeb monPg“€Lb@k´ijmHz}g vuy¬lbv|ZcLf“b1‡rut5g“b1‡´¤Pmlf“‡ez°fhbNz{qLyg“z°uvkÐd tmof“fhbNt5g«‚Lyml‚(d!kLkLmog“d!ghuvmok[­ “E ¹ “`NKL‘X’ ‰ŽF^tV Y.®«€euvzijb1dlz{qLf“bÊf“bc†mofhg“zªgh€eb´cLf“mo‚L¢ do‚Luyvuyg}|Xm!n…dok.uykRt mof“f“b1t5gjd!kLkem!g“d!ghuvmok.¥luyxlbkXg“€ed\gj¤Bb z“d!ijcLvb/n_f“moi g“€Lb"bNz}g“uyi@d!ghb1‡¤BmofD‡3cLfhml‚ed!‚euyvu±g“uybNzn_mlf dcedof{g“uvtqLvdof‚Lvmo‚[­ ~Bm!g“€(bf“fhmlfibNdozhqLf“b1zdofhb d¡xlbfDd!¥obN‡¶m\xlbf«gh€eb k^qLi"‚†bf…m!n ‚Lvmo‚ezºuyk@bNdotD€juvijdo¥obl„ld!kR‡"g“€Lbkªm\xobf g“€Lbk^qLi‚Rb1fºm!nT‡rmrt5¢ qLijbkHgDzuvkgh€Lb"‡ed\g“d@zhb gN­ºœ)b"d!zhm¶t moijcedofhbg“€Lb ijmr‡rbz S cLf“b1‡rut5g“uymlkezghm¶g“€LbcLfhbN‡rut5ghuvmokRzml‚rg“douykLbN‡(qezhuyke¥¶gh€ebb1i¢ cLuvfhutdoº¤BmofD‡´n_fhbNòlqebket|Êm!ng“€Lb@g“f“douykLuvkL¥Êzhb gN­Z¹Zd\gDtD€LuvkL¥ gh€ebcRb1f{n_mlfhi@doket b«m!n†gh€ebbijcLuvfhutdoe‡rbkRz{uyg}|"uzf“b1òHqLuvfhbN‡ g“m ‡rb1imlkez{ghfDd\ghb/kemokr¢Ñghf“uyx^ud![vb1dofhkeuykL¥R­amluykL¥3z{qL‚Rz}gDd!kHghud!vy| ‚†b g{g“bfPgh€edok@gh€euvzPmokjg“€Lb°pPmlfhb1R‡Ld!g“d/uzº‡ruy·¶t qLyg1­0®«€eb…d!kL¢ kLmog“d\g“mofDzg}|^cLutdoyv|cefhm\x^u‡rbzhbxob1f“doet mlijimlk¶¤BmofD‡Lz½hø´v j‹v `OïGˆé‡!sºú\ùÛVø a~‡8L~ø ]pñûyø¡Ã5„rd!kR‡ n_b1¤Pb1fybNzhztmoijijmok"¤BmofD‡Lz«½h´ø v j‹v qù c;jl&ø a!Ã5­X®«€Luz"ijb1dokez/g“€ed\g@d!kekLm!gDd\ghuvkL¥ÊdoyBuvijdo¥obNz"¤uygh€[„ z“d¡|o„ `«ïdˆé‡’sºú\ùÛVø a5„[doke‡ e~ø ]pñûyøjuz…d3ijm^‡LbfDd\ghb1y|zhqettb1z“z}n_qL z{ghfDd\ghb1¥o|l­µØ bfhn_mof“i@d!ketbªqezhuyke¥Êg“€Lb(bijcLuvfhutdo«¤Pmlf“‡.n_fhb¢ òHqLbkRt |ª¤Bmoqev‡‚†b fhbN‡rqetb1‡u±n g“€Lb bijcLuvf“uvt1d!A‡rb1kezhu±g}|3¤Bdlz ijmof“b Rd!g1­µ®«€^qez1„0g“€Lbuyketfhb1ijbkHgmon…c†bfhn_mof“i@d!ketbªm\xob1f gh€eb/bijcLuvfhutdo[‡rbkezhuyg}|¶uvzdzhbkRz{uv‚Lvbuvke‡rutd!ghmlf1­ ¾&uy¥lqLf“b1zõ¶gh€Lf“moqe¥o€)ó¶z{€Lm\¤Èg“€Lbb1fhf“mofibNdozhqLf“b cLvm!g“z…n_mlf Ø ¢“Õl„oØ «…¢ 6°d!ke‡jØ «¢Œz“d!ijcLvb1‡mokj‚†m!g“€jgh€Lbg“f“douykeuykL¥/doke‡ ghbNz}g«z{bg“zºn_mof…ÕNÀ°uvke‡rb1cRb1ke‡rbkHgBghf“uvdovzºqezhuykL¥ gh€Lbzhdoib‡Ld\gDd zhb g1­&®«€LbBx¡dofhud!kRt b0uvk/gh€ebP‚†m¡©ceymog“zWuvz&‡rqLbPghm…f“doke‡rmoiÈuvkLu±¢ ghud!vuvÙ1d\g“uymlk[­®«€Lb/¹Z»ØÔg“bke‡LzBg“m@z{€Lm\¤ ybNzhz«x\d!f“ud!ketb‡rqeb ghm°g“€Lbz{g“d!‚euyvu±g}|"gh€LbcefhuvmofDz&cLvdlt bmlk"g“€Lbijm^‡LbÑ­ ®«€euvzb©^¢ ghfDd@z{g“d!‚euyvu±g}|3d!vym\¤z«qezghm¶do‡Lmocrgn_qLvy¢Œtm\x¡dofhud!kRt bimr‡rb1vz d!kR‡ª€Lb1ket b/ml‚rg“douyk‚†b g{g“bff“b1zhqLyg“z1­

0.1

0

Method

¾&uy¥lqLf“bó,Y ø~o~]pjd_cÜùbc$]d_)ø&a(aO]Ga~`R|,`(cJ_‹jªùhgLø •™f–W\jøDúé`(|5ahø´v wygLWø g?]Ga(cž´]G_RùŒú!û„û cJ_†Xø o~]da(ah(ø `q?]G_y[é`3…ù ]´Jù geø(øV\.ŒcJa(c$oDú!û.[Gc`(™ qù a(c$nV|rqù c$]G_}Œah~ø [Gc$oqù c$]G_8`&v ¸0kRt moqef“do¥ouvkL¥ov|o„Tg“€Lbª~«d¡|obNz/ijb g“€Lmr‡Lz/g“bke‡)g“mZcLdot bªym\¤ uvic†mofhg“doket bmokÊgh€Lbn_b1d!ghqLf“b1z…¤Pbz{qRz{c†b1t g€ed¡x^uvkL¥¶kLmf“by¢ bx\doket bghmg“€Lb@t mokRt bcLg“zgh€eb|´‡Lb1z“t f“uy‚†bo­j®«€Lbjb1z{ghuvi@d\ghbN‡ ‡rud!¥lmokedo†b1yb1ijbkHg“zmon Ð ¤Pb1fhIb Y Ñ /D 8 4 >¨? 4yՖ8 4  ? 4 ֞Õ 4 A >4 ÖÈ5À 4 >§8À 4 À 684 À 684 >dF ÚÛk¿gh€Luz.zhu±g“qed\g“uymlk[„gh€Lb–¯efDz{g)n_mlqLfXt mlic†mokebkHg“zÐmonªgh€eb ijb1dokezf“b n_b1fg“mªg“€Lbjd!f“b1dL„R©T„ñ|Zd!ke‡Ê‚RmlqLke‡Ldofh|e£\dofhbNdn_b1d!¢ ghqefhbNzAd!kR‡°gh€LbPvdlz}g z{uy©/t mof“f“b1zhcRmlke‡ghmg“€LbºijbNd!k"doke‡ z{g“d!kL¢ ‡Ldof“‡‡rbx^ud\g“uymlk)½Žvdo‚Rët mlymlqLf1­ s^mlibjz“d!ijcLvbf“b1tmo¥okeu±g“uymlkZfhbNz{qe±gDzmlk´d!f“‚LuyghfDd!f“|ghb1z{g/z{bg uvijdo¥obNzd!f“bzh€Lm\¤ uvk(¾&uy¥lqLfhbN)z A@d!ke‡ÖL­ 



m¶·«

ML

Original cat

flowers

cat

mane

cat

~¿

lion

cat

mane

cat cat

®«€Lb…pPmlfhb1^‡ed\g“d°doke‡u±gDz0z{b1¥oijbkHgDd\ghuvmokRzW¤Bbf“bB¬Huvke‡rv|"cefhmo¢ x^uv‡Lb1‡§‚^| ô°mo‚LqezÊ~BdofhkRd!fD‡Èdoke‡ Ø vkedofÊaqe|H¥lqLvq[­œ)b ¤BmoqL‡–yuv¬obZghm.g“€ed!ke¬¦¸ºfhutZ~BfhmrtD€^q³d!ke‡ ô°b}¼}uvbÊ~«d!mXn_mlf cLf“m^m!nÜ¢ŒfhbNdo‡ruvkL¥ g“€Lb/cedocRb1f1­ É ™ › — ê ä}é^á}êæèä{îDï åã °ðH ê1ã1éHä{ï ïoåHã1êä}é^å ï!á}çlâ æ±îhá}àlð ä}íDå ð RíDêä}éHæèé °á}âHíåÛí êé Wã1ë_ð HçHçeð ð ê ä}é^á}êí“ä{ä}ï æèé °ê ð äÛá Bà Nàlë±à ñð[êé^ï Hãä}å !á}â ð ð &ëèàHå AãNëÜð HçlçRð !ð ëèíDæ ïlæ ä}ð æèî{3âHëèð í“á&ê1ëèëèTã\î5ßêðá}æèãNé ðRê1éHï BNð ã…ä{ïHð ê1«é æèí“áÛ3á}í“ð ä}æèhî{ð â Lð íDð î ¡Rí“äWêá}ê1íDéHé\ï á ð Bâ^êâlä{ê  ê éHæ í5ïlå   Tä}íDåÛå  ê ìoä}æ±ï Ní jßð ä}ã 0é í“ä}ñîDðíhä « íDëèð ë±ê Að Aæèí“áÛä{ê ð r ð0âHßí ð «êá}íDâHëèë±í ê [êá}æèí“æèîDáÛä{å0ê ã A…åŒá{ð êá}oæèð0åŒá}ê1æèî5éHêï ë

ê1î{âHæèél í áÛä{ê1élåÛëyê á}æèãNé  Têä{ê /í“á}í“äíDåŒð á}æ êá}æèãNé  «à 1àHëèð à ñð ð êä}BéHêì ä{Œïí“î“á@°ä}íDð îDã ïlNí éHæ lá} æèä}ãNí“馿èá{êê1å å êð«îhêâlé^æ±élï íªláÛã1ä{êä}å éH!åÛá}ë±êâ á}! æèãNé RRð í5ê ä}éHæèé …êë±ílæèîDã1é vã1ä0êoí5ï°æ ê Ní Nã\î5ê1ìlàHë±êä BíDãä NçHí æ ä}æè"î5êð ë hð1ê1ê éH\ïíD%å HNã1ê åŒä}á}æyí“êä ìHëèí0åÛð íDñëèíDð î“á}æèãN$é # &Bð éHçlê1àHëèæèìlìlë±ä{æèêåÛá}âlæèí5ã1ïeé ð ê1«é^íDïçHíêäÛá á}/í /íDé\å á"&Bã élj'æ ¡í“êä}é^åÛêæ á 1"í /ã íDRé\á í loê1îDåDæèð íDélîDíªê1é^ï Ñé vã1ä ê á}æ±ã1é oå BãNëèàlìãNëèBíDî“(ð àH ë±êðäAîDoë±ê1ëèåÛãNåÛél)æ Hæ î5êá}æè…ãNé/ð ã °^ð…î5êêéHé^îDï íh*ä †&ê ë±ê1åÛê åA\ãïoæ±åÛî“ñã ð Ní“ä ê1éHï ð îDë±ê1åÛå/,.ço-.ä}/í5ïl æèî“á}æèã1éÊ0ì #\ð NíDélíí oçlä}í“åÛåÛæ±ã1é /ãNéHæ á}ãä}æ±é  + ð Tä}ãN3 ì^êìHæèëèæèåŒá}æ±î&ëyê á}íDé\áTåÛhíð êé!á}æèîAê1éHê1ë oåÛæèå 1 ã êéHé Bð + 2 1 ã êéHé BðAêé^ï [à 4Dæèî{â^ê lð íDëèå vã1äîDã1ëèëyêìrã1ä{ê á}5æ Ní 3 ^ë á}í“ä}æèé 607 98 ð †Hê á}çlíDçRé\ð á°îDë±ê1åÛå /:!ð ã!ï Ræèà Plð ð;r"ð ð â^ê1é ð lð ê A\íDð åÛæ±Tê1éZêëèà îDëèàlìråŒá}ã í“ä}æè3é ð 0[ðAæ á}ê1â ã ? l=ð …ð  Wã1ëÜð@# @A ãä{ïB&Bélæ'¡í“ä}åÛæ á Tä}íDåÛåDð íDë±ê /íDï hð GF ð D ð ! [ä}íDåÛåDð C 98 !ED ßã "ð á}âHðAí ê1éHAï ã1á}æèNé ãä{ïHBêé æèìHìl3åð îD{ë±êð åÛåÛæ'Hí“ä ð 0æ&á}âÈãNé ¡êí“çHä çl1ë±íDæèî5éHê îDá}íæèãNä{éÎêá}á}íDã å ê \íDåÛæ±êé íDêá}àlä}í@åÛí“ë±1í“î“ð á}æèãNé HC I8 A oâlæ låÛí ð†ê1/éHïíDé\já{êá}êæèë±ãNæ é o!Eð !%! 0# ð Bãä ê1ëè'æ 4Dí5ï3î“àlá}åê1éHï3æ ê 1í ^çHçeð# # 0#!ð /æ á}â àHåÛæè3é ð!êé^ê ï \íDåÛãNæ±ê1âlé