1、 T MY(=)5s“ c1 22= % 23 q f 984L Yf 105dL Yf 166 #E167BKlBKlZE188+ |4 |189K-LZ 7 T+4 |2010dSZE221 T MY(=)5s1 2= % 2.1 T 5 qKlp q= %?5 V U$ !BC B 5 qP(wi)i = 1,.,CbN HKlp q= %?5 Ti = maxiP(wi)5x wib 2.2 q E q T = T / TpP(wi|x) = p(x|wi)P(wi)p(x) . P(wi|x) = P(wi,x)p(x)= p(x|wi)P(wi)p(x) 2.3 f /P(wi|x
2、) + P(w2|x) = 1b P(w1|x) + P(w2|x) = P(w1,x)p(x) + P(w2,x)p(x)= P(w1,x) + P(w2,x)p(x)= p(x)p(x)= 1 2.4sY/ f 1. P(x|w1) = P(x|w2)2. P(w1) = P(w2)/Klp q= %?5bP(x|w1) = P(x|w2) H TP(w1) P(w2)5x w15x w2bP(w1) = P(w2) H TP(x|w1) P(x|w2)5x w15x w2b 2.51.c f w P(wj|x)B Mj = i Hx wib2 T MY(=)5sc f Klp q= %?
3、5TP(wi|x) = maxj=1;:;cP(wj|x)5x wib = V| 5 qHq qM “ TTp(x|wi)P(wi) = maxj=1;:;cp(x|wj)P(wj)5x wib 2.6 5 KlB= %?5 VV U p(x|w1)p(x|w2) (12 22)P(w2)(21 11)P(w1),5x w1Q5 w2b9 HqBR(1|x) =2j=11jP(wj|x)= 11P(w1|x) + 12P(w2|x)R(2|x) =2j=12jP(wj|x)= 21P(w1|x) + 22P(w2|x)TR(1|x) (12 22)P(w2|x)(21 11)P(w1)p(x|
4、w1) (12 22)P(w2)p(x|w2)p(x|w1)p(x|w2) (12 22)P(w2)(21 11)P(w1) Tp(x|w1)p(x|w2) (12 22)P(w2)(21 11)P(w1)5x w1bQ5x w2b 2.7 11 = 22 = 0,12 = 21 N HKlKv % 1 p qMbKlKv % H (11 22) + (21 11)R2p(x|w1)dx(12 22)R1p(x|w2)dx = 0R1p(x|w2)dx =R2p(x|w1)dxN HKlKv % PP1(e) = P2(e) 2.8B %?5 Yf Vl TV7 % Z% u Mb3 T MY
5、(=)5sB %?5Klp q= %?5 Yf V j =maxj=1;:;cP(wj|x)5x wj b 6B Tj = maxj=1;:;cp(x|wj)P(wj)5x wj bI n 5s % P(w1|x) = P(w2|x)p(x|w1)P(w1) = p(x|w2)P(w2)Mb 2.9 f /KlB= % Yf % Zb 2.10 M l(x)ll(x) = p(x|w1)p(x|w2)l(x) 1 k (1) Eln(x)|w1 = Eln+1(x)|w2 (2) El(x)|w2 = 1 (3) El(x)|w1E2l(x)|w2 = var l(x)|w2 5 “5 (1)
6、Eln(x)|w1 =ln(x)p(x|w1)dx = (p(x|w1)n+1(p(x|w2)n dxEln+1(x)|w2 =ln+1p(x|w2)dx = (p(x|w1)n+1(p(x|w2)n dx Eln(x)|w1 = Eln+1(x)|w2(2)El(x)|w2 =l(x)p(x|w2)dx =p(x|w1)dx = 1(3)El(x)|w1E2l(x)|w2 = El2(x)|w2E2l(x)|w2 = var l(x)|w2 2.11 xj(j = 1,2,.,n)n M Exj|wi = ijvar xj|wi = i2j22911 = 22 = 0#12 = 21 = 1
7、 f /= % p qb K 01 /KlB= %Klp q= %Nb 2.12 T= TbP(wi|x) = P(x|wi)P(x)cj=1 P(x|wi)P(wi) 2.13 f Klp q= %w (xu2)T(xu2)5x w1,Q5s w2b|x Kui * b 2.2452.23 1 = 2 1 =1 1212 1 2 = 1 1212 1 1 %?5b6 T MY(=)5sh(x) = lnl(x)= lnp(x|w1) + lnp(x|w2)= 12(x1 u1)T 11 (x1 u1) 12(x2 u2)T 12 (x2 u2) + 12 ln | 1| 2|=12xT( 1
8、1 12 )x( 11 ui 12 uj)Tx+12(uT1 11 u1 uT2 12 u2 + ln| 1| 2|)= 43x1x2 + 43x17lnP(w1)P(w2)= 0b % x1(x2 1) = 0 m1 Uxy1m1:s % 2.2552.24 f / I n f 11 = 22 = 0,12 = 21 1p qW1“b (1) pP(e) = 0.05 HNeyman-Pearson % H9p q P(e)P(e1)P(e2) (2) pKlKv %9p qb 1 f 0-1 f Hq/KlB= %NKlp q= %b 10 f /p qKlbP(e1) = 0.05 H7
9、 T MY(=)5s 2KlKv % H(1122)+(2111)R2p(x|w1)dx(1222)R1p(x|w2)dm =0 VR2p(x|w1)dx =R1p(x|w2)dm R1 = (x1,x2)|x1(x2 1) 0R2 = (x1,x2)|x1(x2 1) f =Qf ( P,P) = ( P P)2#P5 ( sf(P) = 1,0 P 1b“L !Hq/ p3.35= 9PbP(X|P) =Ni=1Pxi(1P)1xi= T pP qP(P|X) = P(X|P)f(P) P(X|P)f(P)dP=Ni=1 Pxi(1P)1xi10Ni=1 Pxi(1P)1xidP 3.7
10、!X = x1,x2,.,xN 1p(x|) “ 0 6 x 6 Hp(x|) = 150b Kv 9 maxkxkbKv 9 “S Kv f f L() = lnp(X|) (1)= N ln (2)9 T MY(=)5s1 PL()Kv H1 xb * N HKv 9 = maxkxk (3) 3.8 T(A1 + B1)1 = A(A + B)1B = B(A + B)1A (A1 + B1)A(A + B)1B = (I + B1A)(A + B)1B= B1(B + A)(A + B)1B= B1B= I(A1 + B1)1 = A(A + B)1B (A1 + B1)1 = B(A
11、 + B)1A 3.15 !p(x) N(u,2)3f (x) N(0,1)Parzen39pN(x) = 1NhNNi=1(xxihN)lhN / (1) E pN(x) N(u,2 + h2N) (2) VarpN(x) = 1NhN2p(x) (1) EpN(x) =pN(x)p(x)dx8.1 SwV U = SbV U W 4L Yf 4.1 1Vx g(x) = wTx + w0 = 0 r = |g(x)|w| g(xq) = 0 Hq/ P|xxq|2rl 2 g xp = x g(x)|w|2w 1 !x g(x) 0xq x g5wTxq + w0 =0b !x r5x x
12、p = r w|w| wTx wTxp = r|w|r =wTx + w0|w| =g(x)|w|b10 T MY(=)5sx Hg(x) 0) 2 uHW b|yi|b 1 !a aTyi b5 B9 aTyi 0 u uaTy 0b 2aTyi b uHaTyi = baTyi 0 uHaTyi = 0aTyi = baTyi = 0 b|yi|b 4.10 + 5f 1$ps “ % b 5f J(a) =yY(aTy)b % ZaTy = 0byps “ HaTy 0 % aTyb ps “ % yY(aTy) 5f b 4.12Widrow-HoffE mb Z5f J(a) = |
13、Yab|2 =Nn=1(aTynbn)2 Kl= IMSEa = (Y TY )1Y Tb0/E pabJ(a)0J(a) =2Y T(Yab)50/E V a(1)a(k + 1) = a(k)kY T(Yab)4k =1k T1 i b12 T MY(=)5s Bhl9 i% V| E “ a(1)a(k + 1) = a(k)k(a(k)Tyk bk)ykk “k9F7vhl E l bB4k = 1kyk - 5f “EB“ K ps “b 4.13 1 T(A + xxT)1 = A1 A1xxTA11 + xTA1x 2 kT T 4-98b 1(A + xxT)(A1 A1xxT
14、A11 + xTA1x)= (A + xxT)(I A1xxT1 + xTA1x)A1=(A + xxT xxT1 + xTA1x xxTA1xxT1 + xTA1x)A1= AA1= I(A + xxT)1 = A1 A1xxTA11 + xTA1x 2R(k + 1)1 = R(k)1 + ykyTk T VR(k + 1) = R(k) R(k)ykyTk R(k)1 + yTk R(k)yk 4.14 I n5f J(a) =yY (a)(aTy b)2Y (a) PaTy b“b !y1 Y (a)B“5J(a)0J(a) =2(aTk y1 b)y1= D = 2y1yT1b N
15、K4k =|J(a)|2JT(a)DJ(a) H0/E Tak+1 = ak + baTk y1|y1|2 y1 y1 Y (a)B“55f J(a) =yY (a)(aTy b)2 = (aTy1 b)2J(a) = 2(aTy1 b)y1= D = 2y1yT1b0/ Tak+1 = akkJ(ak)k = 4(aTk y1 b)2|y1|28(aTk y1 b)2yT1 y1yT1 y1 =12|y1|2|k 0/ Tak+1 = ak + baTk y1|y1|2 y113 T MY(=)5s 4.15 |b =NN1,.,NN1| z N1, NN2,., NN2| z N2MSEN
16、Fisherb Y =yT1yT2.yTN= 11 X11 2 X2a = w0,wT5Y TYa = Y Tb1 T1 1 T2XT1 XT2 11 X11 2 X2w0w=1 T1 1 T2XT1 XT2NN11 1NN11 2!m1 = 1N1iC1xi,m2 = 1N2iC2xi T V N (N1m1 + N2m2)T(N1m1 + N2m2) Sw + N1m1mT1 + N2m2mT2w0w= 0N(m1 m2)TSw =2i=1jCi(xj mi)(xj mi)T O(N1m1 + N2m2)T = NmTm =Ni=1xi T Vs TBw0 = mTw|w0 = T V 1
17、N (N1m1 + N2m2)(N1m1 + N2m2)T + Sw + N1m1mT1 + N2m2mT2w = N(m1 m2) 1NSw +N1N2N2 (m1 m2)(m1 m2)Tw = m1 m2iyN1N2N (m1 m2)(m1 m2)Twm1 m2Z_ T VSww = (m1 m2)FisherMb 4.16 (1) T(4-113)V U_ y aTy|w|20wV UyX bW gb (2)gX bW b 15 _ X bW y (y aTy|w|20w)_ X bW E_ bX bW Zg(x) = wTx +14 T MY(=)5sx0 = 1,wTx0x= aTy
18、 = 0|_ g(x)aTy aTy|w|2aT0w= aTy aTy|w|2|w|2 = 0yy (y aTy|w|20w)= aTy|w|20w 4.17 5 TBF“ V$BL s 5F“ LVsb iwi T ?B wi “ “s 7 598L Vsb 98L VsAL VsQ ba cbabccbam3:98L VsAL Vsm4:L VsA98L Vs 4.18 !BF“b ic(c 1)/2 Hij PHij wi “ wj“s 75F“ L Vsb L Vs“BL Vsbm5:L VsBL Vs15 T MY(=)5s5dL Yf 5.1 s Ls V/= Yf w bs Lf
19、 B + ydLf % F V/ w b 5.2X 5 m6 U V Uw1 “ V Uw2 “b (1)s“P (2)s“M “ “H (3)L ! “ Ms “H 3z(x)b1050105m6:B 5s: 1US V U“w1“(4,6)w2“(5,5) (3,4)(3,2) (2,5)(1,3)9 b m7 U 2 m8 U6 #E 6.1 K # % s Lbs Lf % Fb F yNB 6.2 T(614) (618)b :ci=1P2(wi|x) = P2(wm|x) +i=mP2(wi|x)16 T MY(=)5s1050105m7: 6.3 I f /K # (Pr 6.5
20、7=_ x1 = (1,0)T,x2 = (0,1)T,x3 = (0,1)T,x4 = (0,0)T,x5 =(0,2)T,x6 = (0,2)T,x7 = (2,0)TL - w1 w2 b (1)K #E % (2) p“ (m1,m2 “ ( vls k % bB n51 I oK #Ep$ L= Bs L Yf b= “ ( s n5 p “ (s % “( D(x,Mp) D(x,xi) D(x,Mp)D(xi,Mp) T - # x BD(x,xi) D(x,Mp)D(xi,Mp) BB + D(xi,Mp) c, PJeKls b0“b L !iB b0“Xk,1 6 k 6 c PJeKl Vs 0“ bs PJelb22
