[PPT] - Lea rning F rom Data Y aser S. Abu-Mostafa Califo PowerPoint Presentation

SLIDE 1 Outline

f

the Course 1. The Lea rning Problem (Ap ril 3 ) 2. Is Lea rning F easible? (Ap ril 5 ) 3. The Linea r Mo del I (Ap ril 10 ) 4. Erro r and Noise (Ap ril 12 ) 5. T raining versus T esting (Ap ril 17 ) 6. Theo ry

f

Generalization (Ap ril 19 ) 7. The V C Dimension (Ap ril 24 ) 8. Bias-V a rian e T radeo (Ap ril 26 ) 9. The Linea r Mo del I I (Ma y 1 ) 10. Neural Net w

rks

(Ma y 3 ) 11. Overtting (Ma y 8 ) 12. Regula rization (Ma y 10 ) 13. V alidation (Ma y 15 ) 14. Supp

rt

V e to r Ma hines (Ma y 17 ) 15. Kernel Metho ds (Ma y 22 ) 16. Radial Basis F un tions (Ma y 24 ) 17. Three Lea rning Prin iples (Ma y 29 ) 18. Epilogue (Ma y 31 )

theo

ry; mathemati al

te hnique;

p ra ti al

analysis;
n eptual

SLIDE 2 Lea rning F rom Data Y aser S. Abu-Mostafa Califo rnia Institute

f

T e hnology Le ture 1: The Lea rning Problem Sp

nso

red b y Calte h's Provost O e, E&AS Division, and IST

T

uesda y , Ap ril 3, 2012

SLIDE 3 The lea rning p roblem

Outline
Example
f

ma hine lea rning

Comp
nents
f

Lea rning

A

simple mo del

T

yp es

f

lea rning

Puzzle

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 2/19

SLIDE 4 Example: Predi ting ho w a view er will rate a movie 10% imp rovement = 1 million dolla r p rize The essen e

f

ma hine lea rning:

A

pattern exists.

W

e annot pin it do wn mathemati ally .

W

e have data

n

it.

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 3/19

SLIDE 5 Movie rating

a

solution Mat h movie and view er fa to rs p redi ted rating

medy
ntent

a tion

ntent

blo kbuster? T

m

Cruise in it? lik es T

m

Cruise? p refers blo kbusters? lik es a tion? lik es

medy?

movie view er add

ntributions

from ea h fa to r

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 4/19

SLIDE 6 The lea rning app roa h

v i e w e r m o v i e

top bottom

rating

LEARNING

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 5/19

SLIDE 7 Comp

nents
f

lea rning Metapho r: Credit app roval Appli ant info rmation: age 23 y ea rs gender male annual sala ry $30,000 y ea rs in residen e 1 y ea r y ea rs in job 1 y ea r urrent debt $15,000

· · · · · ·

App rove redit?

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 6/19

SLIDE 8 Comp

nents
f

lea rning F

rmalization:
Input: x

( ustomer appli ation )

Output: y

(go

d/bad

ustomer? )

T

a rget fun tion: f : X → Y (ideal redit app roval fo rmula)

Data: (x1, y1), (x2, y2), · · · , (xN, yN)

(histo ri al re o rds )

↓ ↓ ↓

Hyp
thesis: g : X → Y

(fo rmula to b e used )

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 7/19

SLIDE 9

f:

(ideal credit approval function) (historical records of credit customers) HYPOTHESIS SET (set of candidate formulas) ALGORITHM LEARNING FINAL HYPOTHESIS UNKNOWN TARGET FUNCTION (final credit approval formula) TRAINING EXAMPLES X Y

x y x y

N N 1 1

( , ), ... , ( , ) H A

g ~ f ~

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 8/19

SLIDE 10 Solution

mp
nents

f:

(ideal credit approval function) (historical records of credit customers) HYPOTHESIS SET (set of candidate formulas) ALGORITHM LEARNING FINAL HYPOTHESIS UNKNOWN TARGET FUNCTION (final credit approval formula) TRAINING EXAMPLES X Y

x y x y

N N 1 1

( , ), ... , ( , ) H A

g ~ f ~

The 2 solution

mp
nents
f

the lea rning p roblem:

The

Hyp

thesis

Set

H = {h} g ∈ H

The

Lea rning Algo rithm T

gether,

they a re referred to as the lea rning mo del .

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 9/19

SLIDE 11 A simple hyp

thesis

set

the

`p er eptron' F

r

input x = (x1, · · · , xd) `attributes

f

a ustomer' App rove redit if

d

i=1

wixi >

threshold, Deny redit if

d

i=1

wixi <

threshold. This linea r fo rmula h ∈ H an b e written as

h(x) =

sign

d

i=1

wixi

−

threshold

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 10/19

SLIDE 12

+ + + + _ _ _ _ + + + + + _ _ _ _ +

`linea rly sepa rable' data

h(x) =

sign

d

i=1

wi xi

+

w0

Intro

du e an a rti ial

rdinate x0 = 1:

h(x) =

sign

d

i=0

wi xi

In

ve to r fo rm, the p er eptron implements

h(x) =

sign(w Tx)

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 11/19

SLIDE 13 A simple lea rning algo rithm

PLA

The p er eptron implements

h(x) =

sign(w Tx) Given the training set:

(x1, y1), (x2, y2), · · · , (xN, yN)

pi k a mis lassied p

int:

sign(w Txn) = yn and up date the w eight ve to r:

w ← w + ynxn

w+ x y y w+ x y= +1 x w x w −1 y=

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 12/19

SLIDE 14 Iterations

f

PLA

+ + + + + _ _ _ _

One

iteration

f

the PLA:

w ← w + yx

where (x, y) is a mis lassied training p

int.
A

t iteration t = 1, 2, 3, · · · , pi k a mis lassied p

int

from

(x1, y1), (x2, y2), · · · , (xN, yN)

and run a PLA iteration

n

it.

That's

it!

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 13/19

SLIDE 15 The lea rning p roblem

Outline
Example
f

ma hine lea rning

Comp
nents
f

lea rning

A

simple mo del

T

yp es

f

lea rning

Puzzle

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 14/19

SLIDE 16 Basi p remise

f

lea rning using a set

f
bservations

to un over an underlying p ro ess b road p remise =

⇒

many va riations

Sup

ervised Lea rning

Unsup

ervised Lea rning

Reinfo

r ement Lea rning

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 15/19

SLIDE 17 Sup ervised lea rning Example from vending ma hines

in

re ognition

25 5 1

Mass Size

10 25 5 1

Mass Size

10

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 16/19

SLIDE 18 Unsup ervised lea rning Instead

f

(input, o rre t

utput),

w e get (input, ? )

Mass Size

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 17/19

SLIDE 19 Reinfo r ement lea rning Instead

f

(input, o rre t

utput),

w e get (input,some

utput,grade

fo r this

utput)

The w

rld

hampion w as a neural net w

rk!

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 18/19

SLIDE 20 A Lea rning puzzle

f = −1 f = +1 f = ?

A

M L

Creato r: Y aser Abu-Mostafa

LFD

Le ture 1 19/19