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\NQ nPMPb[PQ^TV\NQ^F

">Q^[PQ MPbFrQ

~

w, b

^izhvS

nPX j ELnPn

δ

Z)E.hTVZ)EW izhvAV

pF j Q n s|TVWV_

y ₁ 1

|| w ~ || [ w ~ · x ~ ₁ + b] ≥ δ, . . . , y _` 1

|| w ~ || [ w ~ · x ~ _` + b] ≥ δ

^izhvAW

- - 9

J\\TVWj pFszhvzhv'EyQ^TVFTVsRQ j Q^[ Z…ILs|WVTYMcbrQ^F [PQ^FFrQ^\NQ^FrQ^F t'\yXLK_]TVZ)EWYQ<DOZ8KNQ^[PQ^\Q^FrQ|t Q^TVFsRQ ‡

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KXL[]_ (Q M^_PXL[Pn 5sRQ^FGEFFd_xvefb[ l\rn]_cEF j TYnP_ sRQ^FGEp

δ

^{t j vb v j TYQ!w} psRQ^brIL[]TVsRQykJFs|WYQ^TYMcbdpFs TYn]_ KNQ^[

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giELMcbrQ^[PQ?`GXL[]Z sRQ^\[cELMcbd_xv SUTYQ T oFsRQ j Q n E+Q TYMcbd_Pn]mRQ^O8_PXL[Pn

|| w ~ ||

^\Q Q^TVFrprncn]_ j TYQ T EsRQ j Q^[

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δ = _{|| w||} ¹ _~

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δ

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~

w, b

^izhv3u

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~

w · w ~

ZBTVFTVZ)EW izhvl

pF j Q n s|TVWV_

y ₁ [ w ~ · x ~ ₁ + b] ≥ 1, . . . , y ` [ w ~ · x ~ ` + b] ≥ 1

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j

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j

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gXL[]Zy_xv

_rF j Q

α ₁ , . . . , α _`

^{izhvD {}

nPX j ELnPn

−

`

X

i=1

α _i + 1 2

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j=1

y _i y _j α _i α _j ( x ~ _i · x ~ _j )

ZBTVFTVZ)EW izhv D D

pF j Q n s|TVWV_

`

X

i=1

y _i α _i = 0

^{pF j}

∀ i : 0 ≤ α _i

^{izhvD z}

ns|TVWV_…Q^TVFrQ ">Q^WYQ^s|pFsg%[ j TYQ (%E[]TE\WYQ^F

α ₁ , . . . , α `

w p _rF j Q^F tnPX j ELnPn j Q^[ lprn j []prMPO TVF

zhv

D D

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α _i

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D

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α ^∗ ₁ , . . . , α ^∗ _`

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j

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h(x) = sign b +

`

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i=0

α ^∗ _i y _i x ~ _i · ~ x

!

izhvD }

S+Q^[pE+Q TYMcbd_Pn]mRQ^O8_PXL[

~

w

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~ w =

`

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α ^∗ _i y _i x ~ _i

^{izhvD S}

5XL\Q^T-Fdp[ j TYQ ˆ_%_]w mRQ^O8_PXL[PQ^F ZBTV_

α ^∗ _i > 0

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b = y _i − w ~ · x ~ _i

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j

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j

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ξ _i

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">Q^[PQ McbFrQ

~

w, b

^{izhvD V}

ncX j ELnPn

w ∗ w + C

l

X

i=1

ξ _i

ZBTVFTVZ)EW izhv

D

W

pF j Q n s|TVWV_

y ₁ [ w ~ ∗ x ~ ₁ + b] ≥ 1 − ξ ₁ , . . . , y _l [ w ~ ∗ x ~ _l + b] ≥ 1 − ξ _l

^{izhvD u}

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ξ _i

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j

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∀ : 0 ≤ α _i

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Q^[PnPQ^_]w _xv

&(')('*&('-0; 2 <2

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k

^{H+WELncnPQ^F}

C ₁ , C ₂ , . . . , C _k

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m

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x ₁ , x ₂ , . . . , x _m ,

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X

^w prncEZBZ…Q^FsRQ g†ELnPn]_-Q^[

j

Q^F v

Pr(C i | X)

^s|TV\_

j TYQEb[PnPMcbrQ^TVFWVTYMPbORQ^TV_BEF t j ELncn j ELn ol\ Q^O8_!ZBTV_ j Q^Z sRQ^sRQ^\Q^FrQ^F„?Q^[]OZ)EWYnPmRQ^O_PXL[

X

^{w p[}

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C _i

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C _i

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- - 9

-Q^FF Q^[BQ^TVFFol\]Q^O_ZBTV_

j

Q^Z „/Q^[]O8Z)EWYn]mRQ^O8_PXL[

X

^{j Q^[BH+WELnPnPQw p 5Q^TYn]_xt g&%[ j TYQ}

Pr(C i | X )

Z)E.8TVZ)EW TYnP_xv

H BAY ES (X ) = argmax

C i ∈C

Pr(C i | X )

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Pr(C _i | X)

TVF<w -Q^T Q^TVWYQyEphgw prn]KGEWV_PQ^F v

Pr(C i | X) = Pr(X | C _i ) ∗ Pr(C i ) P

C i ∈C Pr(X | C i ) ∗ Pr(C i )

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Pr(C i )

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C _i

^TYn]_xv

Pr(X | C _i )

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C _i

^{j ELn ol\} Q^O8_…ZBTV_ j Q^Z „?Q^[]O8Z)EWYn]mRQ^O_PXL[

X

\Q XL\GELMcbd_PQ^_ TV[ j v

Pr(C ˆ i )

^{t j} Q^[5ˆ8MPbGo_]w 5Q^[]_%g&%[

Pr(C i )

tROLEFF…mRXLF

j

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Pr(C ˆ i ) = | C i | P

C ⁰ ∈C | C ⁰ |

izhvz|{

S+E\NQ^T TYn]_

| C _i |

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C _i

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Pr(X | C _i )

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j

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Pr(X | C _i )

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X

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x _j

^{\NQ^[PQ MPbFrQ^_ -Q^[ j Q^F}

Pr(X | C _i ) =

|C i |

Y

j=1

Pr(x j | C _i )

^{izhvz D}

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e S!} &%M !<-M

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'Fd_PnPMcbrQ^T

j

pFsRn]\GopZ…Q^F v''TVF 'Fd_PnPMcbrQ^T

j

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pF j ‡fDUQ^[][PnPMPbrQ‡ ˆ_][cE_PQ^s|TYQ|v ˆ8Q^TYQ^F

C = { C ₁ , C ₂ , . . . }

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T

^{Q^TVFrQ}

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T _i

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j

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j

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Pr(m)

^{E\bGoFs|_ pF j TVF} "-TV_PnJsRQ^Z…Q nPnPQ^F 5Q^[ j Q^FCO|EFF

− log ₂ Pr(m)

^{\TV_Pn izhvz|z}

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X

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n

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T

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T ₁ , T ₂ , . . . , T _n

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f req(C _j , T )

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T

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C _j

sRQ^brIL[PQ^F<pF

j

nPQ^T

| T |

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C j

sRQ^brIL[]_ \Q^_][cos|_(

f req(C j , T )

| T |

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− log ₂ f req(C _j , T )

| T |

\TV_Pn izhvz;S

- - 9

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Inf o(T ) = − X

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f req(C j , T )

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