CS计算机代考程序代写 algorithm Circle your tutorial section: • TCTOlOl Thu 1-3

Circle your tutorial section: • TCTOlOl Thu 1-3
• TFT0102 Thu -1-6
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ECE 4::!1F –
Introdudiou lo 1\lachinc Lcarniug i\lidTcrm F”\.amination
Wed Oct llith , 20lfl 4: 10-6:00 p.lll.
Iu~trudor At-hit-h h.hbli
Instructions
• Please read the folio”° ing m:.-truclions carefully.
• You have I hour fift) minute:; ll:50) to complete the exnm.
• Plea…«e make sure that rnu haw a complete exmn booklet.
• Plea…«e .’.\lli-,n,r all qut:5tions. Read each question carefully.
• The value of each QUlSt.ion is indicated. Allocate your time wisely1
• ~o additional pages will be collected beyond this answer book. You may use the reverse side of each page if needed to show additional work.
• This examination is closed-book; One 8.5 ‘< 11 aid-sheet is permitted. A non-programmable calculator is also allowed. • Good lucid PAGE l OF 1,1 10 marks 1 (40 MARKS) C'on idc-r n multi cl ll11r:1t dn ific ton prob! m h r th ,j t po n onnl 1 .x (r1 :r2) IR2 11d th" I hcl ll c {I 2,3} Throughout th1 rrob m ,nth f lk1w1n fiv polnls· whJ('thei11putdntnVC'Cto1 on'gi,,nb) X1 { 1,0)7', X2 (1,0)1, X1 {l.l)T, Xt ( ) lf X (0 3)1 nnd llu ussocL,1 Nl lnht,Js an given by Y1=I. Y2=2. y3=2, y4=l, yr,=3 Om aim is to find a linear clas.sification rule: u•o + w1x1 + w2x2 with weight vector w = ( ) that classifies this dataset. (a) Suppose we implement the perceptron learning algorithm for binary classification that finl\ted as a mi:;..c)n..,.,ifil’d point nnd th<' nlgorithm visits the points in tlw follov.ing order: ' ,. --- .1 -f" ' \ •' ' \ '\ '\ ~' \. -:: -= - l ll ... \ ''\ ' e<,nt'mt p!U't h) ht l't' '\ ' - \ \ ") .\\ '- \ \\\\\ "' \ '<. -\\ ~ ,, C ~ '"'\ "I ~t\ l 'I l>
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‘< ~,(Jc.') f ") , $ fu._(,t) X• t1 \ '5 P.\GE 6 CW l l Ill rnorkJ Cd) S11p11u,c v:c \vi Ii lo unplonr111 a multi-cla."3 logistic regression model for clossif);ng !ht' tlltining 11> l.,ct H {w(I).w(2).w(3)} dl•11olc tIll’ mo:j
Please note that C, is a diagonal matrix where the j-th diagonal entry is A· G ~ fl
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2. (30 MARKS) Co11Hidcr o. li1wflr rc•grcsHiou model whPrc the trnining set, is specified by
with x, E R_il 1 1 and Iii E JR. We usHume Llrnt, each rlnt,,t vector iH in t.h<' augrnent0rl dimension i.e.. x, (.r,,o - l,;i:,,1, ....r,,,,). We aim to fi11d a weight vector w E JRtl+J t.lw.L aims to minimized n wcight.cd i-.quttr<'d error losH function A1~T2 E111(w)= NL.,>..,•(w x,-Yi),
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where A = (>..1, … , AN )7′ is a prc-spocifiecl vccLor of non-negative constunts t.hat. determine t.lw importance of each Hampl0.
Suppose that. w• mi11imi7,es Lho weighted squared error loss i.e., w•=arg min E~(w).
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