dr sanchez - slides - 2

7/24/2019 Dr Sanchez - Slides - 2

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University of Maryland1Center for Advanced Life Cycle Engineering

NTRODUCT ON TO

MACH NE LEARN NG

[email protected]

Dr. Gusta! "#nchez


Reca$$

%as&c c!nce'ts( L&near A$ge%ra)

Unc!nstra&ned O't&m&zat&!n and

*r!%a%&$&t&es

Understand

%as&c c!nce'ts a%!ut regress&!n

Ana$+se the 'r!'ert&es !, the Least "-uaresMeth!d

G!a$ ,!r t!da+


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Least "-uares Meth!d

The Least "-uares Meth!d L"M/ &s 0&de$+used t! determ&ne m!de$s su&ta%$e t! ,&t

e1'er&menta$ data.

It 0as &nented %+ 2.33333 33333



In4567

) Legendre

'u%$&shed th&s

%!!8

He&ntr!duced

and

named

theL"M


3/40


In4569

) Gauss

'u%$&shed th&s

%!!8

He stated thathe

had used

the

meth!d s&nce

4:97




;e$&ee &t !r n!t


4/40


Reca$$

Three &m'!rtant resu$ts(

L&near E-uat&!ns

Unc!nstra&ned O't&m&zat&!n

*r!%a%&$&t&es


L&near "+stems


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L&near "+stems

I, M &sn!n

s&ngu$ar) th&s

e-uat&!n has !n$+

!ne s!$ut&!n




6/40


Grad&ent


The!rem


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Grad&ent

he gradient points in the direction of the greatest

rate of increase!


A %!!8 &ntended,!r 'e!'$e

&nterested &n

s!$&ng

!'t&m&zat&!n

'r!%$ems


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*r!%a%&$&t+ The!r+

Let , , , %e a set !, &nde'endentrand!m ar&a%$es) 0&th gauss&an

d&str&%ut&!n

1

2

,


"tandard N!rma$ D&str&%ut&!n


9/40


The>!&nt 'r!%a%&$&t+

can %e c!m'uted as(

, , , ,

?!&nt *r!%a%&$&t+


"t!'=

N! m!re) ,!r n!0(

L&near E-uat&!ns


*r!%a%&$&t&es


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*r!%$em !rmu$at&!n

e need a m!de$ that+&e$ds a Bg!!d

est&mat&!n !, the des&red

res'!nse( !ut'ut /0hen g&en an attr&%ute

ar&a%$e as&n'ut

/

Target unct&!n

Attr&%ute ar&a%$e

Res'!nse ar&a%$e


Learn&ng *r!cess

De,&ne the Learn&ng *r!%$em C!$$ect Data *re*r!cess "e$ect m!de$) tra&n&ng a$g!r&thm) etc.Tra&n&nga$&date


11/40


Data

( O$+m'&cs 466m 0&nn&ng t&me

R!gers and G&r!$an&


12/40


L&near M!de$s

The s&m'$est m!de$ 0e can

assume &s the$&near(

&nn&ng t&me

!ut'ut/

O$+m'&cs

num%er

&n'ut/

Un8n!0n

*arameters


hat &s a g!!d m!de$3

?ust &n er+ s&m'$e cases a $&near m!de$0&$$ +&e$d !ut'uts that

match

e1act$+ the

des&red !ut'uts.

&rst ans0er

( a g!!d m!de$ +&e$ds

!ut'uts as near as '!ss&%$e t! des&reda$ues g&en &n'ut a$ues


13/40


L!ss unct&!n

@!r an+ data 'a&r , de,&ne a L!ssunct&!n(

,! " #, #

$! " #, #


Aerage L!ss unct&!n

1% & ,! " #, #

Aerage $!ss acr!ssthe 0h!$e data set


14/40


&rst *r!%$em !rmu$at&!n

@&nd&ng a g!!d m!de$ &s e-u&a$ent t! s!$e(

'()#, #

#, #%+ Legendre

0here &s c!nt&nu!s$+ d&,,erent&a%$e &n


H!0 t! ,&nd a s!$ut&!n3

"u''!se 0e 8n!0 the s!$ut&!n+) then %+the The!rem 0e 8n!0 that(

# +

-

# +

-


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A g!!d cand&date

#+. $1% . .

. $1% .

#+

1

% & $

#+

% &


Data



16/40


## /0 1

! " #, # /0

ect!r !rmu$at&!n


ect!r !rmu$at&!n

1% & $ /0

/3

/45/6

75


17/40


8 + =87"u''!se 0e 8n!0 the s!$ut&!n+) then %+the The!rem 0e 8n!0 that(

"+stem !,

L&near E-uat&!ns

ect!r !rmu$at&!n



18/40



19/40


E1am'$e( ne0 data



20/40


=FG -@2A2


:; -@-H

CD=>FG -@-2

Data



21/40


hat &s a g!!d m!de$3

A Bg!!d m!de$ must a$s! %e a%$e t!generate the m!st

accurate 'red&ct&!ns

e sa+ that &t mustgenera$&se

%e+!nd

the data 0e hae used ,!r tra&n&ng


Oer,&tt&ng

The th !rder m!de$ ,&ts the tra&n&ngdata accurate$+) %ut &ts 'red&ct&!ns ,!r

ne1t O$+m'&cs are '!!r=

Th&s &s 8n!0n as!er,&tt&ng


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One 0a+ t! detect

!er,&tt&ng &s t! use

aa$&dat&!n data set

n!t used ,!r

tra&n&ng/ t! test the

'red&ct&e

'er,!rmance

!, the

m!de$

a$&dat&!n Data


Cr!ss a$&dat&!n

Aa&$a%$e

Data

4"et 4

"et ect&e,!rmu$at&!n/


C!mments

Th&s 'resentat&!n) c!de and dataMat$a%/ 0&$$ %e aa&$a%$e !n Canas

dr sanchez - slides - 2

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