. . : =L distance functions Possible Euclidean . - PDF document

Midterm the Since Topics ÷ based Instance and classification ] learning NN . regression Kernel . mgohssien ... ] ' , margin than Peru " learning , . .←dy←u,¢ online approaches trick kernel kernel based ^ , SVM . K means . - ] unsupervised Learning PCA . GMM e for GMM EM . optimal Classifier structural models Bayes . ] Bayes Naive ' ' Nets Bayes . learning Deny . ÷ N nearest neighbors Predict of K . using avg . . a a € • . . : =L distance functions Possible Euclidean . Manhattan - other .

tradeoff K ? function of Bids 1 Variance as discontinuities Note has : KNN regression . ke-ssiacldsfhdt.tn ' ' nearest H ' ' neighbors s . function Given Kernel kx , xq ) i&Vkt ( ×i yc . , I = , i#xx ' dsl bandwidth Kernel d : b. variance exyf.lt#lh) ( ) kernel K : Gaussian ' ' = i. xq , Boxcar kernel others ,

Payton boundary dnjonghisien ;±meqsg" and Leg Training : wcd =c t : At each ' 't xD F+=s:gn( . a y^+ If =Y+ nothing Do Else wltl ' ) wct ' ← + Y+X+ function less Perception : ntzo if ycx 0 wI={ . Cx YG.nl }+ L [ , ⇒ ycw.xle.tn . w ) LC x. go.lt#ycw.x based a ' stance from boundary

nt § , ,L(w , xi ) : Todd C # Minimize njn = year - . + - yx D= %LCx , |¥w4w,xl=d ← ohfinud ) nlcx a- Batch : hinge min 't "l 't it ,t{ - ' , .l±c]%.xi{ Illydwct w 7 .x P=tnasq)forh loss :#

Kernel yeruytran ÷ ¢C×| not linearly : compute a sez xtq ) daily .xl } ' # ' xl wct sign ( w . 'gn[;{m+y , ⇒ G. aegis i. ( 's x . . ; ← DG ) with Replace x ) ) As × ) ( wl !gmxi Cdcxiodcxlltofgajlikcxi dcx ii. sign , , → No computing ¢ This . ' ' trick is the ' kernel ' ' MCH 't Instead of track of just remember keeping n . , Kennel functions Many . . .

-1 = w.xi.no Svm : =/ Vie - If f. \ § | t \ - Max - margin wxetwail ± Ethan . objective ! SVM \ llwlljh s .t . min . n Wa , ) ( N I yi w xi + we . ... , , not : Data linearly separable - yi(w nd 0 if c I x , + < { . violation = well at yilwxi I - + .w . Trade off violation ' llwll margin us . . + C§| ( l Hwllah ) data ( xitnd dsiectia when ← Min - n yi . + ' nearly not 1. 4 w we . , te ( loss regularized similar hinge minimitns SVM ) perception slicks details do trick for SGD Kennel can ' see , , .

1£ Means - - K j=iiiti=j Xi Had C { llyj : minimize - distortion " " kink look for plat ' K Choosing . , t.t.pt# uu ) select data basis Cu D K < Given . a , ... , , , , X÷ Xc xi I " that best ' the ' projection of lower gives 'm - of Projection is zi . ~ assume ( ( K ] ) }=x 4 data till } zi[ with zii ' .u z , ; ; ... , , , arr centered maan - =y§ Reconstruct from ]u zil x ; xnc z as ; . ; , , " that best projection ! the ' ' minimizes one Itai E. in . .

best that result nesters The the : Big u give use ... , , K eigenvectors , reconstruction of the are ← flex . .xiT eigenvalwes with areyngartionoel the largest The egenralms . data onto each the of the to projected variance ui , . 's Gin Generative ' process . catch Ke Sampler class - ^ a Ek ,\ data ~N( sample X yk . , . , , : Likelihood S ;) , top Gilt , ,§ Pcxiiol = ; , multimodal lets angneseet complex why GMM : you , distributions . Et Motivation old unwed ' GMM has ° xe zi . , , } ;k= O={ it parameters 9 µ ; ; ; , , , want talk best at to 0 learn zi guess . ,

a good Intuition Alternate blw updating : O using at and at updating Z our 7 guess guess , current O our using . " ' of had ' make Instead making assignments ti , ' ' " salt assignments rij . details far slides See more component onto mixture of collapse A Pathologies EM an : paint single a cluster lelustyry 2 ← *a Waives Features Y X tyut class a- . , i ] I Y ] 1 [ C ' assumption Fi X ' Naive Bayes X , ; . , , the distribution factories Thus !PtM×[d}lA according to . PlX[d]ly\ YI ) MY PCX xD = ... , , , , . . # predict To ) : I = PG y argqax

MLE counts ' just for Nain Bayes . . g) ' ] count 2×5 ; } xc y ]=x[ = |y=§= PCXC ;] , ; T.tw unrealistic often but well practice performs NB in is . , Bayesiannetwerks CDAG ) alienated distribution Represent joint graph acyclic as Random variables Vertices ! Conditional dependencies Edges : lgarenfs ) variable variable PC ! each One for CPT 1>431 PCA @ @ 1×1 ~@p( \~d PCxliTPCXilpamntsCXil@PCctt.B it ) , DKPCAIPCBI I Put , B. c. ) 131 PCDK ) Pktt Dlc ,

HHerg@ @ variable Assume each is binary ) . d sin@ needed specify # parameters to yourself ) joint check : the io Headd %@ without # yaaamet gneyh .rs knowing 25 structure ' 1=31 - . . Marker Assumption : Local independent given parents X - descendants of is man Headache Flu 1 Nose Sinus Allergy 1 , , independent : , allergy Flu Explaining marginally away are . about why\ dependent cthink b. Homer they came gyms . , ,