CS 2710 Foundations of AI Lecture 22. Machine learning. Machine Learning

Transcription

1 CS 7 Foudatos of AI Lecture Mache learg Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square Mache Learg The feld of mache learg studes the desg of computer programs (agets) capable of learg from past eperece or adaptg to chages the evromet The eed for buldg agets capable of learg s everywhere predctos medce, tet ad web page classfcato, speech recogto, mage/tet retreval, commercal software

2 Learg Learg process: Learer (a computer program) processes data D represetg past epereces ad tres to ether to develop a approprate respose to future data, or descrbe some meagful way the data see Eample: Learer sees a set of patet cases (patet records) wth correspodg dagoses. It ca ether try: to predct the presece of a dsease for future patets descrbe the depedeces betwee dseases, symptoms Types of learg Supervsed learg Learg mappg betwee puts ad desred outputs y Teacher gves me y s for the learg purposes Usupervsed learg Learg relatos betwee data compoets No specfc outputs gve by a teacher Reforcemet learg Learg mappg betwee puts ad desred outputs y Crtc does ot gve me y s but stead a sgal (reforcemet) of how good my aswer was Other types of learg: Cocept learg, actve learg, deep learg,

3 Data: D { d, d,.., d d, y Supervsed learg a set of eamples s put vector, ad y s desred output (gve by a teacher) Objectve: lear the mappg f : X Y s.t. y f ( ) for all,.., Two types of problems: Regresso: X dscrete or cotuous Y s cotuous Classfcato: X dscrete or cotuous Y s dscrete } Supervsed learg eamples Regresso: Y s cotuous Debt/equty Eargs Future product orders Stock prce Data: Debt/equty Eargs Future prod orders Stock prce

4 Supervsed learg eamples Classfcato: Y s dscrete Label 3 Hadwrtte dgt (array of,s) Data: mage dgt Usupervsed learg Data: D { d, d,.., d} d vector of values No target value (output) y Objectve: lear relatos betwee samples, compoets of samples Types of problems: Clusterg Group together smlar eamples, e.g. patet cases Desty estmato Model probablstcally the populato of samples

5 Usupervsed learg eample Clusterg. Group together smlar eamples d Usupervsed learg eample Clusterg. Group together smlar eamples d

6 Usupervsed learg eample Desty estmato. We wat to buld a probablty model P() of a populato from whch we drew eamples d Usupervsed learg. Desty estmato A probablty desty of a pot the two dmesoal space Model used here: Mture of Gaussas

7 Reforcemet learg We wat to lear: f : X Y We see eamples of puts but ot y We select y for observed from avalable choces We get a feedback (reforcemet) from a crtc about how good our choce of y was Iput Learer Output/acto y reforcemet Crtc The goal s to select outputs that lead to the best reforcemet Learg: frst look Assume we see eamples of pars (, y) D ad we wat to lear the mappg f : X Y to predct y for some future We get the data D - what should we do? y

8 Learg: frst look Problem: may possble fuctos f : X Y ests for represetg the mappg betwee ad y Whch oe to choose? May eamples stll usee! y Learg: frst look Soluto: make a assumpto about the model, say, f ( ) a b y

9 Learg: frst look Choosg a parametrc model or a set of models s ot eough Stll too may fuctos f ( ) a b Oe for every par of parameters a, b y Learg: frst look We wat the best set of model parameters reduce the msft betwee the model M ad observed data D Or, ( other words) epla the data the best How to measure the msft? y

10 Learg: frst look We wat the best set of model parameters reduce the msft betwee the model M ad observed data D Or, ( other words) epla the data the best How to measure the msft? y - The dfferece observed value of y ad model predcto Learg: frst look We wat the best set of model parameters reduce the msft betwee the model M ad observed data D Or, ( other words) epla the data the best How to measure the msft? y

11 Learg: frst look We wat the best set of model parameters reduce the msft betwee the model M ad observed data D Or, ( other words) epla the data the best How to measure the msft? Objectve fucto: Error fucto: Measures the msft betwee D ad M Eamples of error fuctos: Average Square Error Average Absolute Error ( y y f ( )) f ( ) Learg: frst look Lear regresso problem Mmzes the squared error fucto for the lear model ( y f ( )) y

12 Learg: frst look Applcato: A ew eample wth ukow value y s checked agast the model, ad y s calculated as y f ( ) a b yy y =? Supervsed learg: Classfcato Data D: pars (, y) where y s a class label: y eamples: patet wll be readmtted or o, has dsease (case) or o (cotrol) case cotrol

13 Supervsed learg: Classfcato Fd a model f: X R, say f ( ) a b c that defes a decso boudary f () = that separates well the two classes Note that some eamples are ot correctly classfed case f () = cotrol Supervsed learg: Classfcato A ew eample wth ukow class label s checked agast the model, the class label s assged case cotrol? 3

14 Learg: frst look. Data: D { d, d,.., d}. Model selecto: Select a model or a set of models (wth parameters) E.g. y a b 3. Choose the objectve fucto Squared error ( y f ( )). Learg: Fd the set of parameters optmzg the error fucto The model ad parameters wth the smallest error 5. Applcato Apply the leared model to ew data E.g. predct ys for ew puts usg leared f () CS 75 Mache Learg Learg: frst look. Data: D { d, d,.., d}. Model selecto: Select a model or a set of models (wth parameters) E.g. y a y b 3. Choose the objectve fucto Squared error ( y f ( )) -. Learg: Fd the set of parameters optmzg the error fucto - The model ad parameters wth the smallest error 5. Applcato: Apply the leared model to ew data E.g. predct ys for ew puts usg leared f () CS 75 Mache Learg

15 A learg system: basc cycle. Data: D { d, d,.., d}. Model selecto: Select a model or a set of models (wth parameters) E.g. y a b 3. Choose the objectve fucto Squared error y ( y f ( )). Learg: Fd the set of parameters optmzg the error fucto The model ad parameters wth the smallest error - 5. Applcato Apply the leared model to ew data - E.g. predct ys for ew puts usg leared f () CS 75 Mache Learg Learg: frst look. Data: D { d, d,.., d}. Model selecto: Select a model or a set of models (wth parameters) E.g. y a b 3. Choose the objectve fucto Squared error ( y f ( )). Learg: Fd the set of parameters optmzg the error fucto The model ad parameters wth the smallest error 5. Applcato Apply the leared - model to ew data E.g. predct ys for - ew puts usg leared f () CS 75 Mache Learg 5

16 Learg: frst look. Data: D { d, d,.., d}. Model selecto: Select a modelor a set of models (wth parameters) - E.g. y a b - 3. Choose the objectve fucto Squared error ( y f ( )). Learg: Fd the set of parameters optmzg the error fucto The model ad parameters wth the smallest error 5. Applcato: Apply the leared model to ew data E.g. predct ys for ew puts usg leared f () Learg: frst look. Data: D { d, d,.., d}. Model selecto: Select a model or a set of models (wth parameters) E.g. y a b 3. Choose the objectve fucto Squared error ( y f ( )). Learg: - Fd the set of parameters - optmzg the error fucto The model ad - parameters wth the smallest error Applcato: Apply the leared model to ew data E.g. predct ys for ew puts usg leared f ()

17 Learg: frst look. Data: D { d, d,.., d}. Model selecto: Select a model or a set of models (wth parameters) E.g. y a b 3. Choose the objectve fucto Squared error ( y f ( )). Learg: Fd the set of parameters optmzg the error fucto The model ad parameters wth the smallest error 5. Applcato Apply the leared model to ew data Looks straghtforward, but there are problems. Learg Problem We ft the model based o past eperece (past eamples see) But ultmately we are terested learg the mappg that performs well o the whole populato of eamples Trag data: Data used to ft the parameters of the model Trag error: ( y f ( )) True (geeralzato) error (over the whole ukow populato): E(, y )( y f ( )) Epected squared error Trag error tres to appromate the true error!!!! Does a good trag error mply a good geeralzato error? 7

18 Overfttg Assume we have a set of pots ad we cosder polyomal fuctos as our possble models Overfttg Fttg a lear fucto wth the square error Error s ozero

19 Overfttg Fttg a lear fucto wth mea-squares error Error s ozero Overfttg Lear vs. cubc polyomal Hgher order polyomal leads to a better ft, smaller error

20 Overfttg Is t always good to mmze the error of the observed data? Overfttg For data pots, degree 9 polyomal gves a perfect ft (Lagrage terpolato). Error s zero. Is t always good to mmze the trag error?

21 Overfttg For data pots, degree 9 polyomal gves a perfect ft (Lagrage terpolato). Error s zero. Is t always good to mmze the trag error? NO!! More mportat: How do we perform o the usee data? Overfttg Stuato whe the trag error s low ad the geeralzato error s hgh. Causes of the pheomeo: Model wth more degrees of freedom (more parameters) Small data sze (as compared to the complety of model)

22 How to evaluate the learer s performace? Geeralzato error s the true error for the populato of eamples we would lke to optmze E (, y )( y f ( )) But t caot be computed eactly Optmzg (mea) trag error ca lead to overft,.e. trag error may ot reflect properly the geeralzato error ( y f ( )),.. So how to test the geeralzato error? How to assess the learer s performace? Geeralzato error s the true error for the populato of eamples we would lke to optmze E [( y f ( )) ] (, y ) Sample mea oly appromates t How to measure the geeralzato error? Two ways: Theoretcal: Law of Large umbers statstcal bouds o the dfferece betwee the true ad sample mea errors Practcal: Use a separate data set wth m data samples to test (Mea) test error ( y j f ( j )) m j,.. m

23 Testg of learg models Smple holdout method Dvde the data to the trag ad test data Dataset Trag set Testg set Evaluate Lear (ft) Predctve model Typcally /3 trag ad /3 testg Testg of models Data set Trag set Test set case cotrol case cotrol Lear o the trag set The model Evaluate o the test set 3

24 Data: Desty estmato D { D, D,.., D} D a vector of attrbute values Objectve: estmate the model of the uderlyg probablty dstrbuto over varables X, p(x), usg eamples D true dstrbuto samples p (X) D D, D,.., D } { estmate pˆ ( X) Desty estmato true dstrbuto samples p (X) D D, D,.., D } { estmate pˆ ( X) Stadard (d) assumptos: Samples are depedet of each other come from the same (detcal) dstrbuto (fed p(x) ) Idepedetly draw staces from the same fed dstrbuto

25 Learg va parameter estmato I ths lecture we cosder parametrc desty estmato Basc settgs: A set of radom varables X { X, X,, Xd} A model of the dstrbuto over varables X wth parameters Data D D, D,.., D } { Objectve: fd parameters ˆ that ft the data the best What s the best set of parameters? There are varous crtera oe ca apply here. Parameter estmato. Basc crtera. Mamum lkelhood (ML) mamze p( D, ) - represets pror (backgroud) kowledge Mamum a posteror probablty (MAP) mamze p( D, ) Selects the mode of the posteror p( D, ) p( D, ) p( ) p( D ) 5