![Page 1: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/1.jpg)
MachineLearning
DecisionTrees:Representation
1SomeslidesfromTomMitchell,DanRothandothers
![Page 2: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/2.jpg)
Keyissuesinmachinelearning
• ModelingHowtoformulateyourproblemasamachinelearningproblem?Howtorepresentdata?Whichalgorithmstouse?Whatlearningprotocols?
• RepresentationGoodhypothesisspacesandgoodfeatures
• Algorithms– Whatisagoodlearningalgorithm?– Whatissuccess?– Generalizationvs overfitting– Thecomputationalquestion:Howlongwilllearningtake?
2
![Page 3: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/3.jpg)
Comingup…(therestofthesemester)
Differenthypothesisspacesandlearningalgorithms– DecisiontreesandtheID3algorithm– Linearclassifiers
• Perceptron• SVM• Logisticregression
– Combiningmultipleclassifiers• Boosting,bagging
– Non-linearclassifiers– Nearestneighbors
3
![Page 4: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/4.jpg)
Comingup…(therestofthesemester)
Differenthypothesisspacesandlearningalgorithms– DecisiontreesandtheID3algorithm– Linearclassifiers
• Perceptron• SVM• Logisticregression
– Combiningmultipleclassifiers• Boosting,bagging
– Non-linearclassifiers– Nearestneighbors
4
Importantissuestoconsider
1. Whatdothesehypothesesrepresent?
2. Implicitassumptionsandtradeoffs
3. Generalization?
4. Howdowelearn?
![Page 5: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/5.jpg)
Thislecture:LearningDecisionTrees
1. Representation:Whataredecisiontrees?
2. Algorithm:Learningdecisiontrees– TheID3algorithm:Agreedyheuristic
3. Someextensions
5
![Page 6: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/6.jpg)
Thislecture:LearningDecisionTrees
1. Representation:Whataredecisiontrees?
2. Algorithm:Learningdecisiontrees– TheID3algorithm:Agreedyheuristic
3. Someextensions
6
![Page 7: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/7.jpg)
Representingdata
Datacanberepresentedasabigtable,withcolumnsdenotingdifferentattributes
Name Label
ClaireCardie -PeterBartlett +EricBaum +Haym Hirsh -LesliePackKaelbling +Yoav Freund -
7
![Page 8: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/8.jpg)
Representingdata
Datacanberepresentedasabigtable,withcolumnsdenotingdifferentattributes
Name Namehaspunctuation?
Secondcharacteroffirstname
Lengthoffirst
name>5?
Samefirstletterintwonames?
Label
ClaireCardie No l Yes Yes -PeterBartlett No e No No +EricBaum No r No No +Haym Hirsh No a No Yes -LesliePackKaelbling
No e Yes No +
Yoav Freund No o No No -8
![Page 9: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/9.jpg)
Name Namehaspunctuation?
Secondcharacteroffirstname
Lengthoffirst
name>5?
Samefirstletterintwonames?
Label
ClaireCardie No l Yes Yes -PeterBartlett No e No No +EricBaum No r No No +Haym Hirsh No a No Yes -LesliePackKaelbling
No e Yes No +
Yoav Freund No o No No -
Representingdata
Datacanberepresentedasabigtable,withcolumnsdenotingdifferentattributes
Withthesefourattributes,howmanyuniquerowsarepossible?2· 26· 26· 2=2704
Ifthereare100attributes,allbinary,howmanyuniquerowsarepossible?2100
9
![Page 10: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/10.jpg)
Name Namehaspunctuation?
Secondcharacteroffirstname
Lengthoffirst
name>5?
Samefirstletterintwonames?
Label
ClaireCardie No l Yes Yes -PeterBartlett No e No No +EricBaum No r No No +Haym Hirsh No a No Yes -LesliePackKaelbling
No e Yes No +
Yoav Freund No o No No -
Representingdata
Datacanberepresentedasabigtable,withcolumnsdenotingdifferentattributes
Withthesefourattributes,howmanyuniquerowsarepossible?2×26×2×2 = 208
Ifthereare100attributes,allbinary,howmanyuniquerowsarepossible?2100
10
![Page 11: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/11.jpg)
Name Namehaspunctuation?
Secondcharacteroffirstname
Lengthoffirst
name>5?
Samefirstletterintwonames?
Label
ClaireCardie No l Yes Yes -PeterBartlett No e No No +EricBaum No r No No +Haym Hirsh No a No Yes -LesliePackKaelbling
No e Yes No +
Yoav Freund No o No No -
Representingdata
Datacanberepresentedasabigtable,withcolumnsdenotingdifferentattributes
Withthesefourattributes,howmanyuniquerowsarepossible?2×26×2×2 = 208
Ifthereare100attributes,allbinary,howmanyuniquerowsarepossible?2100
11
![Page 12: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/12.jpg)
Name Namehaspunctuation?
Secondcharacteroffirstname
Lengthoffirst
name>5?
Samefirstletterintwonames?
Label
ClaireCardie No l Yes Yes -PeterBartlett No e No No +EricBaum No r No No +Haym Hirsh No a No Yes -LesliePackKaelbling
No e Yes No +
Yoav Freund No o No No -
Representingdata
Datacanberepresentedasabigtable,withcolumnsdenotingdifferentattributes
Withthesefourattributes,howmanyuniquerowsarepossible?2×26×2×2 = 208
Ifthereare100attributes,allbinary,howmanyuniquerowsarepossible?(100times)2×2×2×⋯×2 = 2)**
12
![Page 13: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/13.jpg)
Name Namehaspunctuation?
Secondcharacteroffirstname
Lengthoffirst
name>5?
Samefirstletterintwonames?
Label
ClaireCardie No l Yes Yes -PeterBartlett No e No No +EricBaum No r No No +Haym Hirsh No a No Yes -LesliePackKaelbling
No e Yes No +
Yoav Freund No o No No -
Representingdata
Datacanberepresentedasabigtable,withcolumnsdenotingdifferentattributes
Withthesefourattributes,howmanyuniquerowsarepossible?2×26×2×2 = 208
Ifthereare100attributes,allbinary,howmanyuniquerowsarepossible?(100times)2×2×2×⋯×2 = 2)**
13
Ifwewantedtostoreallpossiblerows,thisnumberistoolarge.
Weneedtofigureouthowtorepresentdatainabetter,moreefficientway
![Page 14: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/14.jpg)
Whataredecisiontrees?
Ahierarchicaldatastructurethatrepresentsdatausingadivide-and-conquerstrategy
Canbeusedashypothesisclassfornon-parametricclassificationorregression
Generalidea:Givenacollectionofexamples,learnadecisiontreethatrepresentsit
14
![Page 15: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/15.jpg)
Whataredecisiontrees?
• Decisiontreesareafamilyofclassifiersforinstancesthatarerepresentedbycollectionsofattributes(i.e.features)
• Nodes aretestsforfeaturevalues
• Thereisonebranch foreveryvaluethatthefeaturecantake
• Leaves ofthetreespecifytheclasslabels
15
![Page 16: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/16.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
Label=ALabel=C Label=B
16
![Page 17: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/17.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
17
Beforebuildingadecisiontree:
Whatisthelabelforaredtriangle?Andwhy?
Label=ALabel=C Label=B
![Page 18: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/18.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?
18
Label=ALabel=C Label=B
![Page 19: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/19.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?Color,Shape
19
Label=ALabel=C Label=B
![Page 20: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/20.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?Color,Shape Color?
20
Label=ALabel=C Label=B
![Page 21: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/21.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?Color,Shape Color?
Blue Red Green
21
Label=ALabel=C Label=B
![Page 22: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/22.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?Color,Shape Color?
Blue Red Green
B
22
Label=ALabel=C Label=B
![Page 23: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/23.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?Color,Shape Color?
Blue Red Green
B
squaretriangle circle
CAB
Shape?
23
Label=ALabel=C Label=B
![Page 24: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/24.jpg)
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?Color,Shape Color?
Shape?circlesquare
AB
Blue Red Green
B
squaretriangle circle
CAB
Shape?
24
Label=ALabel=C Label=B
![Page 25: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/25.jpg)
Label=ALabel=C Label=B
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?Color,Shape Color?
Shape?circlesquare
AB
Blue Red Green
squaretriangle circle
CAB
Shape?
1. Howdowelearn adecisiontree?Comingupsoon…
2. Howtouseadecisiontreeforprediction?• Whatisthelabelforared triangle?
• Justfollowapathfromtheroottoaleaf
• Whataboutagreentriangle?
25
B
![Page 26: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/26.jpg)
Label=ALabel=C Label=B
Let’sbuildadecisiontreeforclassifyingshapes
Whataresomeattributesoftheexamples?Color,Shape Color?
Shape?circlesquare
AB
Blue Red Green
squaretriangle circle
CAB
Shape?
1. Howdowelearn adecisiontree?Comingupsoon…
2. Howtouseadecisiontreeforprediction?• Whatisthelabelforared triangle?
• Justfollowapathfromtheroottoaleaf
• Whataboutagreen triangle?
26
B
![Page 27: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/27.jpg)
ExpressivityofDecisiontrees
WhatBooleanfunctionscandecisiontreesrepresent?– AnyBooleanfunction
(Color=blue ANDShape=triangle) Label=B)AND(Color=blue ANDShape=square) Label=A) AND(Color=blueANDShape=circle) Label=C)AND….
Everypathfromthetreetoarootisarule
Thefulltreeisequivalenttotheconjunctionofalltherules
AnyBooleanfunctioncanberepresentedasadecisiontree.
27
![Page 28: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/28.jpg)
ExpressivityofDecisiontrees
WhatBooleanfunctionscandecisiontreesrepresent?– AnyBooleanfunction
(Color=blue ANDShape=triangle) Label=B)AND(Color=blue ANDShape=square) Label=A) AND(Color=blueANDShape=circle) Label=C)AND….
AnyBooleanfunctioncanberepresentedasadecisiontree.
28
Everypathfromthetreetoarootisarule
Thefulltreeisequivalenttotheconjunctionofalltherules
![Page 29: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/29.jpg)
ExpressivityofDecisiontrees
WhatBooleanfunctionscandecisiontreesrepresent?– AnyBooleanfunction
(Color=blue ANDShape=triangle) Label=B)AND(Color=blue ANDShape=square) Label=A) AND(Color=blueANDShape=circle) Label=C)AND….
AnyBooleanfunctioncanberepresentedasadecisiontree.
29
Everypathfromthetreetoarootisarule
Thefulltreeisequivalenttotheconjunctionofalltherules
![Page 30: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/30.jpg)
DecisionTrees
• Outputsarediscretecategories
• Butrealvaluedoutputsarealsopossible(regressiontrees)
• Wellstudiedmethodsforhandlingnoisydata(noiseinthelabelorinthefeatures)andforhandlingmissingattributes– Pruningtreeshelpswithnoise– Moreonthislater…
30
![Page 31: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/31.jpg)
Numericattributesanddecisionboundaries
• Wehaveseeninstancesrepresentedasattribute-valuepairs(color=blue,secondletter=e,etc.)– Valueshavebeencategorical
• Howdowedealwithnumericfeaturevalues?(eg length=?)– Discretizethemorusethresholdsonthenumericvalues– Thisexampledividesthefeaturespaceintoaxisparallelrectangles
31
![Page 32: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/32.jpg)
Numericattributesanddecisionboundaries
• Wehaveseeninstancesrepresentedasattribute-valuepairs(color=blue,secondletter=e,etc.)– Valueshavebeencategorical
• Howdowedealwithnumericfeaturevalues?(eg length=?)– Discretizethemorusethresholdsonthenumericvalues– Thisexampledividesthefeaturespaceintoaxisparallelrectangles
32
![Page 33: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/33.jpg)
Numericattributesanddecisionboundaries
• Wehaveseeninstancesrepresentedasattribute-valuepairs(color=blue,secondletter=e,etc.)– Valueshavebeencategorical
• Howdowedealwithnumericfeaturevalues?(eg length=?)– Discretizethemorusethresholdsonthenumericvalues– Thisexampledividesthefeaturespaceintoaxisparallelrectangles
13X
7
5
Y
- +
+ +
+ +
-
-
+
33
![Page 34: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/34.jpg)
Numericattributesanddecisionboundaries
• Wehaveseeninstancesrepresentedasattribute-valuepairs(color=blue,secondletter=e,etc.)– Valueshavebeencategorical
• Howdowedealwithnumericfeaturevalues?(eg length=?)– Discretizethemorusethresholdsonthenumericvalues– Thisexampledividesthefeaturespaceintoaxisparallelrectangles
13X
7
5
Y
- +
+ +
+ +
-
-
+
34
X<3
Y<5
no yes
Y>7yesno
X<1
no yes
- + +
+ -yesno
![Page 35: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/35.jpg)
Numericattributesanddecisionboundaries
• Wehaveseeninstancesrepresentedasattribute-valuepairs(color=blue,secondletter=e,etc.)– Valueshavebeencategorical
• Howdowedealwithnumericfeaturevalues?(eg length=?)– Discretizethemorusethresholdsonthenumericvalues– Thisexampledividesthefeaturespaceintoaxisparallelrectangles
13X
7
5
Y
- +
+ +
+ +
-
-
+Decisionboundariescanbenon-linear
35
X<3
Y<5
no yes
Y>7yesno
X<1
no yes
- + +
+ -yesno
![Page 36: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/36.jpg)
Summary:Decisiontrees
• DecisiontreescanrepresentanyBooleanfunction• Awaytorepresentlotofdata• Anaturalrepresentation(think20questions)• Predicting withadecisiontreeiseasy
• Clearly,givenadataset,therearemanydecisiontreesthatcanrepresentit.[Exercise:Why?]
• Learningagoodrepresentationfromdataisthenextquestion
36
![Page 37: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/37.jpg)
Summary:Decisiontrees
• DecisiontreescanrepresentanyBooleanfunction• Awaytorepresentlotofdata• Anaturalrepresentation(think20questions)• Predicting withadecisiontreeiseasy
• Clearly,givenadataset,therearemanydecisiontreesthatcanrepresentit.[Exercise:Why?]
• Learningagoodrepresentationfromdataisthenextquestion
37
![Page 38: Decision Trees: Representation - svivek · Let’s build a decision tree for classifying shapes What are some attributes of the examples? Color, Shape Color? Shape? square circle](https://reader034.vdocument.in/reader034/viewer/2022050205/5f5860fa1af89f4c3b659663/html5/thumbnails/38.jpg)
Exercises
1. WritedownthedecisiontreefortheshapesdataiftherootnodewasShape insteadofColor.
2. Willthetwotreesmakethesamepredictionsforunseenshapes/colorcombinations?
3. ShowthatmultiplestructurallydifferentdecisiontreescanrepresentthesameBooleanfunctionoftwoormorevariables.
38
Label=ALabel=C Label=B
(thinkaboutwhatitmeansfortwotreestobestructurallydifferent)