iii. "go.EE't) - - PowerPoint PPT Presentation

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iii. "go.EE't) - - PowerPoint PPT Presentation

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iii. "go.EE't)

slide-1
SLIDE 1
  • iii.

"go.EE't)

  • d = L

r a n k 2 ① sU{WT

DTD:wsutuewt

: we'wt

Problem s e t 3 Solutions Posted.

A i - - - A n

6 , . .- G ,

D

s ✓NUT:

VASVT

c i g

v s

Syd

D:uEwT

singular

v i e s

  • r D , squared

e i o o n i e s o f

①T D

slide-2
SLIDE 2
  • ⃗

:∥⃗ ∥

≤

⃗ ⃗ .

  • ←
slide-3
SLIDE 3

γ = σ−σ

σ

⃗ () =

  • /

γ

  • ∥⃗

() −⃗ ∥ ≤ . →

  • () · (/)

γ ·

  • =
  • · (/)

γ

  • .
  • F ,

E

ft's#It-D

  • Z
  • I

% )

  • numbero f n o n z e r o
slide-4
SLIDE 4

=

  • /

√γ

slide-5
SLIDE 5

=

  • /

√γ

  • σ σ ≥

⃗

() ∝ () ·⃗ () → (σ

) ·

  • X : coat
  • ✓Eat

✓

Tzco'

  • 6,2T

a > 6 ;

2 T

slide-6
SLIDE 6

=

  • /

√γ

  • σ σ ≥

⃗

() ∝ () ·⃗ () → (σ

) ·

⃗

() ∝ () ·⃗ () → (σ

) ·

  • =

3 (Xx) t

y (xx)t-tt 5(xix)"....

slide-7
SLIDE 7

=

  • /

√γ

  • σ σ ≥

⃗

() ∝ () ·⃗ () → (σ

) ·

⃗

() ∝ () ·⃗ () → (σ

) ·

  • 1

(6,2)ts(6iD

I
  • I"s[a,XT

xt<z(xtx)'t...at/x T x)tIz'"

I

×T×zMT(×Tx)xTxzkD-

slide-8
SLIDE 8
  • Gift

P t( 6

i t

i s .

slide-9
SLIDE 9
slide-10
SLIDE 10
slide-11
SLIDE 11
slide-12
SLIDE 12
  • ¥
slide-13
SLIDE 13
  • 1 1 ,

a s

pH=[o, oooo) pl":[00£'s}of

slide-14
SLIDE 14

⃗ () ∈ R ⃗ ()() = ( )

slide-15
SLIDE 15

⃗ () ∈ R ⃗ ()() = ( ) ⃗ () = [, , , . . . , ]

slide-16
SLIDE 16

⃗ () ∈ R ⃗ ()() = ( ) ⃗ () = [, , , . . . , ] ( ) =

  • ∈()

( ) ·

  • ()
  • it;io÷..
slide-17
SLIDE 17

⃗ () ∈ R ⃗ ()() = ( ) ⃗ () = [, , , . . . , ] ( ) =

  • ∈()

( ) ·

  • ()

= ⃗ ⃗ (−) ⃗ () =

  • () ∈ ()⃗

() = / ∈ ().

  • l
  • p"ki)-

I

⇒pot":co.ie#isooEi

  • q!÷÷÷÷÷§
slide-18
SLIDE 18

⃗ () ∈ R ⃗ ()() = ( ) ⃗ () = [, , , . . . , ] ( ) =

  • ∈()

( ) ·

  • ()

= ⃗ ⃗ (−) ⃗ () =

  • () ∈ ()⃗

() = / ∈ (). ⃗ −.

  • "" [÷⇒±⇒f(

"

' "''If

slide-19
SLIDE 19

⃗ () ∈ R ⃗ ()() = ( ) ⃗ () = [, , , . . . , ] ( ) =

  • ∈()

( ) ·

  • ()

= ⃗ ⃗ (−) ⃗ () =

  • () ∈ ()⃗

() = / ∈ (). ⃗ −. ⃗ () = −⃗ (−)

  • pco)

pits

= CAD")

+pm

slide-20
SLIDE 20

⃗ () ∈ R ⃗ ()() = ( ) ⃗ () = [, , , . . . , ] ( ) =

  • ∈()

( ) ·

  • ()

= ⃗ ⃗ (−) ⃗ () =

  • () ∈ ()⃗

() = / ∈ (). ⃗ −. ⃗ () = −⃗ (−) = −− . . . −

  • ⃗

()

  • [
.
slide-21
SLIDE 21

⃗ () = −− . . . −

  • ⃗

().

slide-22
SLIDE 22

⃗ () = −− . . . −

  • ⃗

(). −/⃗ () = (−/−/)(−/−/) . . . (−/−/)

  • (−/⃗

()).

  • Pi'
  • D-

'"pt: %A§AD¢AD"p°

slide-23
SLIDE 23

⃗ () = −− . . . −

  • ⃗

(). −/⃗ () = (−/−/)(−/−/) . . . (−/−/)

  • (−/⃗

()). −/⃗ () / −/⃗ ()

  • E
  • [

(Xt

x )

( E x ) . . .

Inditedadjacencymatrix

t

[Iij÷÷"It:i1

slide-24
SLIDE 24

⃗ () = −− . . . −

  • ⃗

(). −/⃗ () = (−/−/)(−/−/) . . . (−/−/)

  • (−/⃗

()). −/⃗ () / −/⃗ () −/−/ ⃗ () →

  • ¥ p l t )

p # t

  • →
slide-25
SLIDE 25

⃗ () = −− . . . −

  • ⃗

(). −/⃗ () = (−/−/)(−/−/) . . . (−/−/)

  • (−/⃗

()). −/⃗ () / −/⃗ () −/−/ ⃗ () → −/−/

  • 5

¥

slide-26
SLIDE 26
slide-27
SLIDE 27
slide-28
SLIDE 28
slide-29
SLIDE 29
  • [
slide-30
SLIDE 30
  • ⇐

flat,

slide-31
SLIDE 31

: R → R ⃗ θ⋆ (⃗ θ⋆) =

⃗ θ∈ (⃗

θ)

slide-32
SLIDE 32

: R → R ⃗ θ⋆ (⃗ θ⋆) =

⃗ θ∈ (⃗

θ) +

slide-33
SLIDE 33

: R → R ⃗ θ⋆ (⃗ θ⋆) =

⃗ θ∈ (⃗

θ) +

∥⃗

θ∥ ≤ ∥⃗ θ∥ ≤

⃗

θ ≤ ⃗

  • ⃗

θ⃗ θ ≥

⃗

⃗ θ =

= ⃗

θ() ≤

  • V, top singular

vector

  • f

×

f l u )

= vTXTX✓

s-t I N

11,51

slide-34
SLIDE 34
slide-35
SLIDE 35
slide-36
SLIDE 36
  • homeprice

=

g , A.

bathrooms

t

§#beds

slide-37
SLIDE 37
slide-38
SLIDE 38
slide-39
SLIDE 39

⃗

θ : R → R ⃗ θ(⃗

)

  • = ⟨⃗

θ,⃗ ⟩

  • s 04)

X( l ) t . . t@(d)

Nd)

slide-40
SLIDE 40

⃗

θ : R → R ⃗ θ(⃗

)

  • = ⟨⃗

θ,⃗ ⟩ = ⃗ θ() ·⃗ () + . . . + ⃗ θ() ·⃗ ()

slide-41
SLIDE 41

⃗

θ : R → R ⃗ θ(⃗

)

  • = ⟨⃗

θ,⃗ ⟩ = ⃗ θ() ·⃗ () + . . . + ⃗ θ() ·⃗ () ⃗ θ ∈ R

slide-42
SLIDE 42

⃗

θ : R → R ⃗ θ(⃗

)

  • = ⟨⃗

θ,⃗ ⟩ = ⃗ θ() ·⃗ () + . . . + ⃗ θ() ·⃗ () ⃗ θ ∈ R ⃗ , . . . ,⃗

  • ∈ R× , . . . , ∈ R ⃗

θ∗ (⃗ θ, ,⃗ ) =

  • =

ℓ(⃗

θ(⃗

), )

  • ℓ ⃗

θ(⃗

)

slide-43
SLIDE 43

⃗

θ : R → R ⃗ θ(⃗

)

  • = ⟨⃗

θ,⃗ ⟩ = ⃗ θ() ·⃗ () + . . . + ⃗ θ() ·⃗ () ⃗ θ ∈ R ⃗ , . . . ,⃗

  • ∈ R× , . . . , ∈ R ⃗

θ∗ (⃗ θ, ,⃗ ) =

  • =

ℓ(⃗

θ(⃗

), )

  • ℓ ⃗

θ(⃗

) ℓ(⃗

θ(⃗

), ) =

  • ⃗

θ(⃗

) − ∈ {−, } ℓ(⃗

θ(⃗

), ) =

  • + (−⃗

θ(⃗

))

  • .
  • I
slide-44
SLIDE 44

⃗

θ : R → R ⃗ θ(⃗

)

  • = ⟨⃗

θ,⃗ ⟩ = ⃗ θ() ·⃗ () + . . . + ⃗ θ() ·⃗ () ⃗ θ ∈ R ⃗ , . . . ,⃗

  • ∈ R× , . . . , ∈ R ⃗

θ∗ (⃗ θ, ,⃗ ) =

  • =

ℓ(⃗

θ(⃗

), ) + (⃗ θ) ℓ ⃗

θ(⃗

) ℓ(⃗

θ(⃗

), ) =

  • ⃗

θ(⃗

) − ∈ {−, } ℓ(⃗

θ(⃗

), ) =

  • + (−⃗

θ(⃗

))

slide-45
SLIDE 45

⃗

θ : R → R ⃗ θ(⃗

)

  • = ⟨⃗

θ,⃗ ⟩ = ⃗ θ() ·⃗ () + . . . + ⃗ θ() ·⃗ () ⃗ θ ∈ R ⃗ , . . . ,⃗

  • ∈ R× , . . . , ∈ R ⃗

θ∗ (⃗ θ, ,⃗ ) =

  • =

ℓ(⃗

θ(⃗

), ) + λ∥⃗ θ∥

  • ℓ ⃗

θ(⃗

) ℓ(⃗

θ(⃗

), ) =

  • ⃗

θ(⃗

) − ∈ {−, } ℓ(⃗

θ(⃗

), ) =

  • + (−⃗

θ(⃗

))

  • =
slide-46
SLIDE 46

⃗

θ : R → R ⃗ θ(⃗

)

  • = ⟨⃗

θ,⃗ ⟩ = ⃗ θ() ·⃗ () + . . . + ⃗ θ() ·⃗ () ⃗ θ ∈ R ⃗ , . . . ,⃗

  • ∈ R× , . . . , ∈ R ⃗

θ∗ ,(⃗ θ) = (⃗ θ, ,⃗ ) =

  • =

ℓ(⃗

θ(⃗

), ) + λ∥⃗ θ∥

  • ℓ ⃗

θ(⃗

) ℓ(⃗

θ(⃗

), ) =

  • ⃗

θ(⃗

) − ∈ {−, } ℓ(⃗

θ(⃗

), ) =

  • + (−⃗

θ(⃗

))

  • ninininiice

w e t

t o0

  • a
slide-47
SLIDE 47
slide-48
SLIDE 48

⃗

θ : R → R

  • ⃗

θ ∈ R(# )

  • ( x - ,
slide-49
SLIDE 49

⃗

θ : R → R ⃗ θ(⃗

) = ⟨⃗ , σ(σ(⃗ ))⟩ ⃗ θ ∈ R(# )

slide-50
SLIDE 50

⃗

θ : R → R ⃗ θ(⃗

) = ⟨⃗ , σ(σ(⃗ ))⟩ ⃗ θ ∈ R(# ) ⃗ , . . . ,⃗ , . . . , ∈ R ⃗ θ∗ ,⃗

(⃗

θ) =

  • =

ℓ(⃗

θ(⃗

), )

  • =
slide-51
SLIDE 51

,⃗

(⃗

θ) =

  • =

ℓ(⃗

θ(⃗

), ) , . . . ,

slide-52
SLIDE 52

,⃗

(⃗

θ) =

  • =

ℓ(⃗

θ(⃗

), ) , . . . ,

slide-53
SLIDE 53

,⃗

(⃗

θ) =

  • =

ℓ(⃗

θ(⃗

), ) , . . . ,

slide-54
SLIDE 54

,⃗

(⃗

θ) =

  • =

ℓ(⃗

θ(⃗

), ) , . . . ,

slide-55
SLIDE 55

,⃗

(⃗

θ) =

  • =

ℓ(⃗

θ(⃗

), ) , . . . , ,⃗

(⃗

θ)

slide-56
SLIDE 56

(⃗ θ) ⃗ θ ∥⃗ θ∥ < ,⃗

(⃗

θ) =

  • =

ℓ(⃗

θ(⃗

), )

  • →
slide-57
SLIDE 57

(⃗ θ) ⃗ θ ∥⃗ θ∥ < ,⃗

(⃗

θ) =

  • =

ℓ(⃗

θ(⃗

), )

  • K K T

"second o r , "

gradienetoodgesc ent

  • reentonsnetho

l i n k psyraming.

A D M M

  • bags

quadraticpogning.

A D A M ,Adaged (varierts m GD)

a c c r a t e d

G D .