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7
Perceptron Convergence Proof 1 If dataset is separable there is a margin Margin yl best direction w't Kw w HI tyx 1w w glint x 215 w 1 8 3 Hw ll I Hw yall 11 112 4 1 Hw H't y4lxH't2y4w x Hut ll't I O

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Page 1: yl - cscheid.net

Perceptron Convergence Proof

1 If dataset is separable there is a margin

Margin ylbest direction w't

Kw w HI tyx1w w glint x

215 w 1 8

3 Hw llIHw yall 11 112 4 1Hw H't y4lxH't2y4w x

Hut ll't I O

Page 2: yl - cscheid.net

4 lui WHY KylHulk'll k k

HT 3 Hw ll I w w trial

fkill L

VT trial

78

K f ter B

Page 3: yl - cscheid.net

x zto w O O 2 b 2 a

µx six Y

t I l I I 4Xz X

I T l I O

I l I I O

i t I I 4

what a bat 3 dimensions D lwhat happens to the efficiency in votingtheperceptron updates

what abut K NNwhat about deep networks

Yao can solve the XOR problem

is 1 layers

Page 4: yl - cscheid.net

Averaged Perceptron

Assume bias term in xs

we want

c w dropping ItemWe have

cw c x Coke x4 EckCw v

wa

Page 5: yl - cscheid.net

K l

Z c w c Ix e ex

i i

i

c Krk

U dx t e x'e te x

2 Ic x c c XK

l

c r

k k

ow I xid I t e

2c XK

Ix t e ft c

i i i

Ex c ckx

Page 6: yl - cscheid.net

1,2 13,4 11

l 3 t 2.4 t 12

1.3 I 2 4 I I I

1.3 2.9 t 2.9.24 y l 2 7

I 3 1.9 I 3 2 4 t l 3 l

TF 2 wix 11 real L

LE xi wi 1112

f

Page 7: yl - cscheid.net

It

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ton