Outline of the Course 11. Over�tting ( Ma y 8 ) 12. Regula rization ( Ma y 10 ) 1. The Lea rning Problem ( Ap ril 3 ) 13. V alidation ( Ma y 15 ) 2. Is Lea rning F easible? ( Ap ril 5 ) 14. Supp o rt V e to r Ma hines ( Ma y 17 ) 3. The Linea r Mo del I ( Ap ril 10 ) 15. Kernel Metho ds ( Ma y 22 ) 4. Erro r and Noise ( Ap ril 12 ) 16. Radial Basis F un tions ( Ma y 24 ) 5. T raining versus T esting ( Ap ril 17 ) 17. Three Lea rning Prin iples ( Ma y 29 ) 6. Theo ry of Generalization ( Ap ril 19 ) 18. Epilogue ( Ma y 31 ) 7. The V C Dimension ( Ap ril 24 ) theo ry; mathemati al 8. Bias-V a rian e T radeo� ( Ap ril 26 ) te hnique; p ra ti al 9. The Linea r Mo del I I ( Ma y 1 ) analysis; on eptual 10. Neural Net w o rks ( Ma y 3 ) • • •
Lea rning F rom Data Y aser S. Abu-Mostafa Califo rnia Institute of T e hnology Le ture 1 : The Lea rning Problem Sp onso red b y Calte h's Provost O� e, E&AS Division, and IST T uesda y , Ap ril 3, 2012 •
The lea rning p roblem - Outline Example of ma hine lea rning Comp onents of Lea rning • A simple mo del • T yp es of lea rning • Puzzle • • Creato r: Y aser Abu-Mostafa - LFD Le ture 1 2/19 M � A L
Example: Predi ting ho w a view er will rate a movie 10% imp rovement = 1 million dolla r p rize The essen e of ma hine lea rning: A pattern exists. W e annot pin it do wn mathemati ally . • W e have data on it. • Creato r: Y aser Abu-Mostafa - LFD Le ture 1 3/19 • M � A L
Movie rating - a solution kbusters? Cruise? omedy? a tion? om blo T refers es es es lik lik lik p view er add ontributions p redi ted Mat h movie and from ea h fa to r rating view er fa to rs movie T omedy a tion blo om kbuster? Cruise ontent ontent in it? Creato r: Y aser Abu-Mostafa - LFD Le ture 1 4/19 M � A L
The lea rning app roa h top v i e w e r m o v i e LEARNING rating Creato r: Y aser Abu-Mostafa - LFD Le ture 1 5/19 bottom M � A L
Comp onents of 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? · · · · · · Creato r: Y aser Abu-Mostafa - LFD Le ture 1 6/19 M � A L
Comp onents of lea rning F o rmalization: Input: x ( ustomer appli ation ) Output: y ( go o d/bad ustomer? ) • T a rget fun tion: f : X → Y ( ideal redit app roval fo rmula ) • Data: ( x 1 , y 1 ) , ( x 2 , y 2 ) , · · · , ( x N , y N ) ( histo ri al re o rds ) • • Hyp othesis: g : X → Y ( fo rmula to b e used ) ↓ ↓ ↓ Creato r: Y aser Abu-Mostafa - LFD Le ture 1 7/19 • M � A L
UNKNOWN TARGET FUNCTION f: X Y (ideal credit approval function) TRAINING EXAMPLES x y x y ( , ), ... , ( , ) N N 1 1 (historical records of credit customers) FINAL LEARNING HYPOTHESIS ALGORITHM g ~ f ~ A (final credit approval formula) HYPOTHESIS SET Creato r: Y aser Abu-Mostafa - LFD Le ture 1 8/19 H (set of candidate formulas) M � A L
Solution omp onents The 2 solution omp onents of the lea rning p roblem: UNKNOWN TARGET FUNCTION f: The Hyp othesis Set X Y (ideal credit approval function) TRAINING EXAMPLES x y x y ( , ), ... , ( , ) • N N 1 1 The Lea rning Algo rithm (historical records of credit customers) H = { h } g ∈ H FINAL LEARNING HYPOTHESIS ALGORITHM g ~ f ~ T ogether, they a re referred to as the lea rning A • (final credit approval formula) mo del . HYPOTHESIS SET H (set of candidate formulas) Creato r: Y aser Abu-Mostafa - LFD Le ture 1 9/19 M � A L
A simple hyp othesis set - the `p er eptron' F o r input x = ( x 1 , · · · , x d ) `attributes of a ustomer' App rove redit if threshold , d Deny redit if threshold . � w i x i > i =1 d This linea r fo rmula h ∈ H an b e written as � w i x i < i =1 sign threshold �� d � � � h ( x ) = − w i x i Creato r: Y aser Abu-Mostafa - LFD Le ture 1 10/19 i =1 M � A L
sign �� d � � � h ( x ) = + w i x i w 0 Intro du e an a rti� ial o o rdinate x 0 = 1 : i =1 _ _ sign + + _ _ + + � d + + � + _ + `linea rly sepa rable' data _ � h ( x ) = w i x i In ve to r fo rm, the p er eptron implements + + _ _ i =0 T x ) sign ( w Creato r: Y aser Abu-Mostafa - LFD Le ture 1 11/19 h ( x ) = M � A L
A simple lea rning algo rithm - PLA The p er eptron implements T x ) sign ( w Given the training set: y= +1 w+ x y h ( x ) = x w pi k a mis lassi�ed p oint: ( x 1 , y 1 ) , ( x 2 , y 2 ) , · · · , ( x N , y N ) T x n ) � = y n sign ( w and up date the w eight ve to r: y= w −1 x w+ x y Creato r: Y aser Abu-Mostafa - LFD Le ture 1 12/19 w ← w + y n x n M � A L
Iterations of PLA One iteration of the PLA: where ( x , y ) is a mis lassi�ed training p oint. • w ← w + y x _ A t iteration t = 1 , 2 , 3 , · · · , pi k a mis lassi�ed p oint from + _ + + and • run a PLA iteration on it. _ + ( x 1 , y 1 ) , ( x 2 , y 2 ) , · · · , ( x N , y N ) + That's it! _ Creato r: Y aser Abu-Mostafa - LFD Le ture 1 13/19 • M � A L
The lea rning p roblem - Outline Example of ma hine lea rning Comp onents of lea rning • A simple mo del • T yp es of lea rning • Puzzle • • Creato r: Y aser Abu-Mostafa - LFD Le ture 1 14/19 M � A L
Basi p remise of lea rning �using a set of observations 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 • Creato r: Y aser Abu-Mostafa - LFD Le ture 1 15/19 • M � A L
Sup ervised lea rning Example from vending ma hines � oin re ognition 25 25 Mass Mass 5 5 1 1 10 10 Creato r: Y aser Abu-Mostafa - LFD Le ture 1 16/19 Size Size M � A L
Unsup ervised lea rning Instead of (input, o rre t output) , w e get (input, ? ) Mass Creato r: Y aser Abu-Mostafa - LFD Le ture 1 17/19 Size M � A L
Reinfo r ement lea rning Instead of (input, o rre t output) , w e get (input, some output,grade fo r this output) The w o rld hampion w as a neural net w o rk! Creato r: Y aser Abu-Mostafa - LFD Le ture 1 18/19 M � A L
A Lea rning puzzle f = − 1 f = +1 Creato r: Y aser Abu-Mostafa - LFD Le ture 1 19/19 f = ? M � A L
Recommend
More recommend
