Oshita Noriaki
November 03, 2018
3.8k

# 情報幾何の応用と最近の機械学習の動向

## Oshita Noriaki

November 03, 2018

## Transcript

1. ৘ใزԿͷԠ༻ͱ
࠷ۙͷػցֶशͷಈ޲
େԼൣߊ

2. ൃදͷ֓ཁ
ɾػցֶशʹ࢖ΘΕΔ͜ͱͷ͋Δ਺ֶ
ɾ৘ใزԿͱͦͷԠ༻ࣄྫͷઆ໌
ɾΧʔωϧ๏ͱͦͷԠ༻ࣄྫͷઆ໌
ɾΨ΢εաఔͷجૅͱͦͷԠ༻ࣄྫͷઆ໌
˞ࢲ͸਺ֶͷॳ৺ऀͳҝɼؒҧ͍΍ࢦఠ಺༰͕͋Ε
͹ɼൃද్தͰ΋͝ࢦఠ͍ͩ͘͞ɽ

3. ʢ࢖ΘΕΔ͜ͱ͕͋Δ͔ʣ
શ෦ཧղ͢Δඞཁ͸ͳ͍ɽ

4. ʢ࢖ΘΕΔ͜ͱ͕͋Δ͔ʣ

5. ৘ใزԿͱ͸
w ৘ใزԿͷ૑ઃऀ
w ࠎ૊Έ͸म࢜ͱത࢜Ͱߟ
͑ͨͦ͏Ͱ͢ɽ
؁རढ़Ұઌੜ

6. ৘ใزԿͱ͸
w ૒ରΞϑΝΠϯ઀ଓͷඍ෼زԿ
w ύϥϝʔλۭؒͷزԿֶʢ㱠σʔλۭؒͷزԿֶʣ

7. ඍ෼زԿͱ͸
w ͻͱ͜ͱͰݴ͑͹ඍ෼Λ༻͍ͨزԿɽ

8. ۂ཰ɾᎇ཰ʢΕ͍Γͭʣ
w ۂ཰
ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹΛ࣍ݩϢʔΫϦουۭؒ
தͷۂઢͱ͢Δɽʢ·ͨۂઢ1 T
ʹΑͬͯද͞ΕΔӡಈͷ଎
͞͸ҰఆͰʹͳΔΑ͏ʹύϥϝʔλΛͱͬͯ͋Δɽʣ
͢ͳΘͪ଎౓ϕΫτϧ
͕௕͞Ͱ͋Δͱ͢Δɽ۩ମతʹ͸
ͱͳ͍ͬͯΔͱ͢Δɽ
p(s) = (x(s), y(s), z(s))(a ≤ s ≤ b)
e1
(s) = p′(s) = (x′(s), y′(s), z′(s))
e1
(s) ⋅ e1
(s) = x′(s)2 + y′(s)2 + z′(s)2 = 1

9. ۂ཰ɾᎇ཰ʢΕ͍Γͭʣ
ͦͷͱ͖Ճ଎౓ϕΫτϧΛߟ͑ͯΈΔͱ
Ͱ͋Δ͔Βɼɹɹ͕ɹɹɹʹ௚ަ͍ͯ͠Δɽɹɹͷ௕͞Λ
ͱॻ͖ɼۂઢ1 T
ͷۂ཰ͱݺͿɽ͢ͳΘͪ
ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɾ
e′
1
(s)
0 =
d (e1
(s) ⋅ e1
(s))
ds
= 2e′
i
(s) ⋅ e1
(s)
e′
1
(s) e1
(s) e′
1
(s) k(s)
κ(s) = e′
1
(s) ⋅ e′
1
(s)
= x′′(s)2 + y′′(s)2 + z′′(s)2

10. ۂ཰ɾᎇ཰ʢΕ͍Γͭʣ
w ᎇ཰
e′
1
e′
2
e′
3
=
0 k 0
−κ 0 τ
0 −τ 0
e1
e2
e3
ಋग़͸লུ͠·͢ɽ

11. ૒ରΞϑΝΠϯ઀ଓ
ΞϑΝΠϯ઀ଓ∇Λ࣋ͭ3JFNBOOଟ༷ମ(M, g)ʹ͓͍ͯ
Xg
(Y, Z) = g(∇X
Y, Z) + g(Y, ∇*
X
Z) (X, Y, Z) ∈ (M)
Ͱఆٛ͞ΕΔΞϑΝΠϯ઀ଓ∇*Λܭྔgʹؔ͢Δ∇ͷ૒ରΞϑΝΠϯ઀ଓͱ͍͏ɽ

12. ৘ใزԿͷԠ༻
w ࣗવޯ഑๏
w αϙʔτϕΫτϧϚγϯ
w #PPTUJOH
w ओ੒෼෼ੳ
w ͳͲɼ͋Γͱ͋ΒΏΔ΋ͷʹԠ༻͞Ε͍ͯΔ
w ৄ͘͠͸৘ใزԿֶͷ৽ల։

13. ৘ใزԿͷԠ༻
w #BZFTJBOTISJOLBHFQSFEJDUJPOGPSUIFSFHSFTTJPO
QSPCMFNʢਖ਼ن෼෍ͷϕΠζ༧ଌʹ͓͚Δࣄલ෼෍ͷߏ
੒ʣ
IUUQTXXXTDJFODFEJSFDUDPNTDJFODFBSUJDMFQJJ
49
w 4UBUJTUJDBM*OGFSFODFXJUI6OOPSNBMJ[FE%JTDSFUF
.PEFMTBOE-PDBMJ[FE)PNPHFOFPVT%JWFSHFODFT ඇ
ਖ਼نԽϞσϧͷਪఆཧ࿦

IUUQKNMSPSHQBQFSTWIUN

14. ਖ਼ن෼෍ͷϕΠζ༧ଌʹ
͓͚Δࣄલ෼෍ͷߏ੒
w͜ͷ࿦จͷجૅ
ࠓҎԼͷଟมྔਖ਼ن෼෍͕؍ଌ͞ΕΔͱ͢Δɽ
y ∼ Nd
(y; μ, Σ)
Nd ͸ฏۉЖɼڞ෼ࢄЄ͔ΒͳΔɼ
̳࣍ݩͷଟมྔਖ਼ن෼෍ͷີ౓ؔ਺Ͱ͋Δɽ

15. Χʔωϧ๏ͷ؆୯ͳઆ໌

16. Χʔωϧ๏ͷॏཁͳఆཧ
L Y Z
ू߹Њ্ͷਖ਼ఆ஋Χʔωϧ
Њ্ͷؔ਺͔ΒͳΔώϧϕϧτۭؒͰ࣍ͷࡾͭΛຬͨ͢
΋ͷ͕Ұҙʹଘࡏ͢Δɻ

͸೚ҙʹݻఆ

༗ݶ࿨ͷܗͷݩ͸ͷதͰ᜚ີ

࠶ੜੑ ⟨f, k( ⋅ , x)⟩ℋ
= f(x) (∀x ∈ , ∀f ∈ ℋ)
ʢ.PPSF"SPOT[KOͷఆཧʣ
Hk
k(·
,x) ∈ Hk x ∈ Ω
f =
n

i=1
ci
k(·
,xi
)
Hk

17. ਖ਼ఆ஋Χʔωϧ
ɽɽɹਖ਼ఆ஋Χʔωϧͷఆٛͱجຊతੑ࣭
·ͣɼ࣮਺஋ͷਖ਼ఆ஋Χʔωϧ͔Βఆٛ͢Δɽ
Λू߹ͱ͢Δͱ͖ɼ࣍ͷ৚݅Λຬͨ͢Χʔωϧ
ɹɹɹɹɹɹɹɹΛਖ਼ఆ஋Χʔωϧ QPTJUJWF
EFpOFLFSOFM
ͱ͍͏ɽ
w ରশੑɿ೚ҙͷɹɹɹɹɹɹʹର͠ɹɹ
w ਖ਼஋ੑɿ೚ҙͷ
ʹର͠ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ
ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɽ

k : × → ℝ (্ͷ)
x, y ∈ k(x, y) = k(y, x)
n ∈ ℕ, x1
, …, xn
∈ , c1
, …, cn
∈ ℝ
n

i,j=1
ci
cj
k (xi
, xj) ≥ 0

18. άϥϜߦྻ
ରশੑͷ΋ͱɼਖ਼஋ੑͷ৚݅͸ରশߦྻ
͕൒ਖ਼ఆ஋Ͱ͋Δ͜ͱΛҙຯ͢Δɽ
͜ͷରশߦྻΛάϥϜߦྻͱ͍͏ɽ

19. ਖ਼ఆ஋ɾ൒ਖ਼ఆ஋
zTMz > 0
zTMz ≥ 0
͕ඞͣͳΓͨͭͱ͖ਖ਼ఆ஋ͱ͍͏ɽ
͕੒Γཱͭͱ͖൒ਖ਼ఆ஋ͱ͍͏ɽ
z ≡ ඇθϩྻϕΫτϧ
M ≡ OºOͷ࣮਺ରশߦྻ
.͕ਖ਼ఆ஋ͱ͸
.͕ਖ਼ఆ஋ͱ͸
zTMz = [z1
, z2
, ⋯, zn]
m11
m12
⋯ m1n
⋮ ⋱
mn1
m21
⋯ mnn
z1
z2

zn

20. "-JOFBS5JNF,FSOFM(PPEOFTTPG'JU5FTU
w/*14ͷϕετϖʔύʔʂʂ
w ෼෍ͷ෼͔Βͳ͍ͱ͜ΖΛਪఆ͢Δɽ
w ྫ͑͹͜Ε͸ඪ४ਖ਼ن෼෍ͱ͍ͬͯྑ͍ͷ͔Ͳ͏͔Λ൑
ఆ͢Δ
w ",FSOFMJ[FE4UFJO%JTDSFQBODZGPS(PPEOFTTPGpU
5FTUTʢ2JBOH-JV +BTPO%-FF .JDIBFM*+PSEBOʣ
ͱ͍͏ख๏Λ༻͍ͯʢޙ೔2JJUBʹ֓ཁΛॻ͘༧ఆ
ͭͷ
֬཰෼෍͕ࣅ͍ͯΔ͔Λઢܗ࣌ؒͰଌఆ͢Δɽ
IUUQTBSYJWPSHBCT

21. A Linear-Time Kernel Goodness-of-Fit Test
Wittawat Jitkrittum1 Wenkai Xu1 Zolt´
an Szab´
o2 Kenji Fukumizu3 Arthur Gretton1
1Gatsby Unit, University College London 2CMAP, ´
Ecole Polytechnique 3The Institute of Statistical Mathematics
A Linear-Time Kernel Goodness-of-Fit Test
Wittawat Jitkrittum1 Wenkai Xu1 Zolt´
an Szab´
o2 Kenji Fukumizu3 Arthur Gretton1
1Gatsby Unit, University College London 2CMAP, ´
Ecole Polytechnique 3The Institute of Statistical Mathematics
Summary
•Given: {x
i}n
i=1 ⇠ q (unknown), and a density p.
•Goal: Test H0 : p = q vs H1 : p 6= q quickly.
•New multivariate goodness-of-ﬁt test (FSSD):
1.Nonparametric: arbitrary, unnormalized p. x 2 Rd.
2.Linear-time: O(n) runtime complexity. Fast.
3.Interpretable: tell where p does not ﬁt the data.
Previous: Kernel Stein Discrepancy (KSD)
•Let x(x, v) := 1
p(x)rx[k(x, v)p(x)] 2 Rd.
Stein witness function: g(v) = E
x⇠q
[x(x, v)] where
g = (g1
, . . . , gd
) and each gi 2 F, an RKHS associated
with kernel k.
- 4 - 2 2 4
- 0.2
0.2
0.4
p(x)
q(x)
g(x)
Known: Under some conditions, kgkFd
= 0 () p = q.
[Chwialkowski et al., 2016, Liu et al., 2016]
Statistic: KSD2 = kgk2
Fd
=
double sums
z }| {
E
x⇠q
E
y⇠q hp
(x, y) ⇡
2
n(n 1)
P
ihp
(x
i
, x
j
). where
hp
(x, y) := [rx log p(x)] k(x, y) [ry log p(y)] + rxryk(x, y)
+ [ry log p(y)] rxk(x, y) + [rx log p(x)] ryk(x, y).
Characteristics of KSD:
3 Nonparametric. Applicable to a wide range of p.
3 Do not need the normalizer of p.
7 Runtime: O(n
2). Computationally expensive.
Linear-Time KSD (LKS) Test: [Liu et al., 2016]
kgk2
Fd

2
n
P
n/2
i=1 hp
(x2i 1
, x2i
).
3 Runtime: O(n). 7 High variance. Low test power.
The Finite Set Stein Discrepancy (FSSD)
Idea: Evaluate witness g at J locations {v1
, . . . , v
J}. Fast.
FSSD2 =
1
dJ
J
X
j=1
kg(v
j
)k
2
2
.
Proposition (FSSD is a discrepancy measure).
Main conditions:
1.(Nice kernel) Kernel k is C0
-universal, and real analytic
(Taylor series at any point converges) e.g., Gaussian kernel.
2.(Vanishing boundary) lim
kxk!1 p(x)g(x) = 0.
3.(Avoid “blind spots”
) Locations {v1
, . . . , v
J} are drawn
from a distribution h which has a density.
Then, for any J 1, h-a.s. FSSD2 = 0 () p = q.
Characteristics of FSSD:
3 Nonparametric. 3 Do not need the normalizer of p.
3 Runtime: O(n). 3 Higher test power than LKS.
Model Criticism with FSSD
Proposal: Optimize locations {v1
, . . . , v
J} and kernel
bandwidth by arg max score = FSSD2/s
H1
(runtime: O(n)).
Proposition: This procedure maximizes the true positive
rate = P(detect di↵erence | p 6= q).
score: 0.034 score: 0.44
Interpretable Features for Model Criticism
12K robbery
events in Chicago
in 2016
Model p =
10-component
Gaussian mixture
F = v⇤ = where model
does not ﬁt well.
Maximization objective
FSSD2/s
H1
.
Optimized v⇤
is highly
interpretable.
•Bahadur slope u rate of p-value ! 0 of statistic Tn
under H1
. High = good.
•Bahadur e ciency = ratio slope(1)
slope(2)
of slopes of two tests. > 1 means test(1) better.
•Results: Slopes of FSSD and LKS tests when p = N(0, 1) and q = N(µ
q
, 1).
0 50 100
n
0.0
0.5
1.0
p-value
T(1)
n
T(2)
n
Proposition. Let s2
k
, k2 be kernel bandwidths of
FSSD and LKS. Fix s2
k
= 1. Then, 8
µ
q 6= 0,
9v 2 R, 8
k2 > 0, the Bahadur e ciency
slope(FSSD)(µ
q
, v, s2
k
)
slope(LKS)(µ
q
, k2)
> 2. FSSD is statistically
more e cient than LKS.
Experiment: Restricted Boltzmann Machine
•40 binary hidden units. d = 50 visible units. Signiﬁcance level a = 0.05.
· · ·
· · ·
Model p
Perturb one
weight to get q.
2000 4000
Sample size n
0.00
0.25
0.50
0.75
Rejection rate
1000 2000 3000 4000
Sample size n
0
100
200
300
Time (s)
2000 4000
Sample size n
0.0
0.5
1.0
Rejection rate
FSSD-opt
FSSD-rand
KSD
LKS
MMD-opt
ME-opt
Better
•FSSD-opt, (FSSD-rand) = Proposed tests. J = 5 optimized, (random) locations.
•MMD-opt [Gretton et al., 2012] = State-of-the-art two-sample test (quadratic-time).
•ME-opt [Jitkrittum et al., 2016] = Linear-time two-sample test with optimized locations.
•Key: FSSD (O(n)), KSD (O(n
2)) have comparable power. FSSD is much faster.
WJ, WX, and AG thank the Gatsby Charitable Foundation
for the ﬁnancial support. ZSz was ﬁnancially supported
by the Data Science Initiative. KF has been supported by
KAKENHI Innovative Areas 25120012.
Contact: [email protected]
Code: github.com/wittawatj/kernel-gof

22. Ψ΢εաఔͷجૅ
w ·ͣɼΨ΢εաఔͰ͸ͳ͍ྫͰߟ͑ͯΈ·͠ΐ͏ɽ
ͨͱ͑͹ɼ࣍ݩͷೖྗʹ͍ͭͯɹɹɹɹɹɹɹɹͱ͍͏ಛ
௃ϕΫτϧΛߟ͑Ε͹ɼͷ࣍ؔ਺

͸ɼରԠ͢ΔॏΈΛ࢖ͬͨઢܗճؼϞσϧ
Λ
ͱද͢͜ͱ͕ग़དྷΔɽ
ͱఆٛ͢Δɽ
y = WTϕ(x)
y = w0
+ w1
x + w2
x2 + w3
x3
ϕ(x) = (1,x, x2, x3)T
x
x
w = (w0
, w1
, w2
, w3
)T

23. Ψ΢εաఔͷجૅ
ઌ΄Ͳͷճؼؔ਺Λ
ͱͭͷجఈؔ਺Ͱද͍ͯ͠ΔͱΈΔ͜ͱ͕Ͱ͖Δɽ
·ͨɼجఈؔ਺Λ࣍ͷΑ͏ʹఆٛ͠ɼ೚ҙͷؔ਺Λද͢͜ͱ
Λߟ͑Δɽ
ϕ(x) = exp(−
x − μ
σ2
)
ϕ(x) ϕ0
(x) = 1,ϕ1
(x) = x, ϕ2
(x) = x2, ϕ3
(x) = x3

24. Ψ΢εաఔͷجૅ

25. Ψ΢εաఔͷجૅ

26. Ψ΢εաఔͷجૅ
͔͠͠ɼ͜ͷํ๏Ͱ͸͇ͷ࣍ݩ͕খ͍͞ͱ͖͔͠ར༻Ͱ͖ͳ
͍ɽ͇ͷ࣍ݩ͕ͷ৔߹ɼ͔Β·ͰɼִؒɽͰج
ఈؔ਺ͷத৺ͳΒ΂ͨͱ͠·͠ΐ͏ɽ
͜ΕʹରԠ͢ΔϕΫτϧ͸ʹͳΓ·͢ɽ
͢ͳΘͪ

μm
y = WTϕ(x)
w

27. Ψ΢εաఔͷجૅ
Ͱ͸͇͕࣍ݩͷ৔߹͸Ͳ͏ͳΔͰ͠ΐ͏
౴͑͸
EJN

EJN

EJN

y = WTϕ(x1
, x2
)
212 = 441
213 = 9261

2110 = 16,679,880,978,201

28. Ψ΢εաఔͷجૅ
͇͕ߴ࣍ݩͷ৔߹Ͱ΋͖͞΄ͲͷਤͷΑ͏ʹॊೈͳճؼϞσ
ϧΛ࣮ݱ͢Δʹ͸Ͳ͏͢Ε͹͍͍Ͱ͠ΐ͏ɽ
ղܾ๏͸ઢܗճؼϞσϧͷύϥϝʔλʹ͍ͭͯظ଴஋Λ
ͱͬͯɼϞσϧ͔Βੵ෼ফڈͯ͠͠·͏͜ͱͰ͢ɽ
ઢܗճؼϞσϧ͸࣍ͷΑ͏ʹॻ͘͜ͱ΋ग़དྷ·͢ɽ
w
̂
y1
̂
y2

̂
yN
=
ϕ0
(x1
) ϕ1
(x1
) ⋯ ϕM
(x1
)
⋮ ⋱
ϕ0
(xN
) ϕ0
(xN
) ⋯ ϕM
(xN
)
w0
w1

wM

29. Ψ΢εաఔͷجૅ
ɹ
্ͷΑ͏ʹஔ͖׵͑Δͱͱදͤ·͢ɽ
࣍ʹࠓճ͸؆୯ͳͨΊʹZ͕Y͔Βਖ਼֬ʹޡࠩͳ͘ճؼ͞ΕΔͱ͢Δͱ
͕੒ΓཱͭͱԾఆ͠·͢ɽ
̂
y1
̂
y2

̂
yN
=
ϕ0
(x1
) ϕ1
(x1
) ⋯ ϕM
(x1
)
⋮ ⋱
ϕ0
(xN
) ϕ0
(xN
) ⋯ ϕM
(xN
)
w0
w1

wM
̂
y ϕ w
̂
y = ϕw
y = ϕw

30. Ψ΢εաఔͷجૅ
͜͜ͰॏΈ͕
Ͱੜ੒͞ΕΔͱ͠·͢ɽ୯Ґߦྻ
͜ͷͱ͖ɼڞ෼ࢄߦྻ͸࣍ͷΑ͏ʹͳΓ·͢ɽ
݁Ռͱͯ͠Zͷ෼෍͸࣍ͷଟมྔΨ΢ε෼෍ʹ͕͍ͨ͠·͢ɽ
ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ

w
w ∼ N(0,λ2I)
I
[yyT] − [y][y]T = [(Φw)(Φw)T] = Φ [wwT] ΦT
= λ2ΦΦT
y ∼ (0, λ2ΦΦT)
8͕ফ͑·ͨ͠ʂʂ
ظ଴஋ΛऔΔ͜ͱ͸ੵ෼͢Δ͜ͱͱΠίʔϧ

31. Ψ΢εաఔ
w ఆٛ
ͲΜͳ/ݸͷೖྗͷू߹ʹ͍ͭͯ΋ɼରԠ͢
Δग़ྗͷಉ࣌෼෍͕ଟมྔΨ΢ε෼෍ʹ
ै͏ͱ͖ɼ͸Ψ΢εաఔ (BVTTJBOQSPDFTT
ʹै͏ͱ
͍͍·͢ɽ
(x1
, x2
, ⋯, xN
)
y = (y1
, y2
, ⋯, yN
)
p(y)

32. Ψ΢εաఔͷ·ͱΊ
w ֬཰աఔͱ͸΋ͱ΋ͱ͸࣌ܥྻʹର͢Δཧ࿦ͱͯ͠ੜ·Ε
·͕ͨ͠ɼඞͣ͠΋࣌ܥྻͰ͋Δ͜ͱΛཁ੥͍ͯ͠ΔΘ͚
Ͱ͸͋Γ·ͤΜɽ
w ࣌ܥྻͰ͸ͳͯ͘΋ཧ࿦͸ಉ༷ʹ੒Γཱͭɽ
w ೖྗͷݸ਺/ ͢ͳΘͪग़ྗͷ࣍ݩ/͸͍͘Βେ͖ͯ͘΋੒
Γཱͪ·͢ɽ
w Ψ΢εաఔͱ͸࣮͸ແݶ࣍ݩͷΨ΢ε෼෍ͷ͜ͱͰ͢ɽ

33. Ψ΢εաఔͷ
ͳʹ͕͏Ε͍͠ͷ͔
ࣜͷڞ෼ࢄߦྻΛ
ͱ͓͘ͱɼ O N
ཁૉ͸ɼਤͷΑ͏ʹ
͇ͷಛ௃ϕΫτϧΛͱͯ͠ɼ
Ͱද͞Ε·͢ɽ
K = λ2ΦΦT
ϕ(x) = (ϕ0
, ⋯, ϕM
(x))T
Knm
= λ2ϕ (xn)
T
ϕ (xm)

34. Ψ΢εաఔͷ
ͳʹ͕͏Ε͍͠ͷ͔
ڞ෼ࢄߦྻɹɹɹɹɹɹɹ͕ޓ͍ʹࣅ͍ͯΕ͹
ಛ௃ϕΫτϧɹɹɹɹɹɹɹͷ಺ੵͷఆ਺ഒ͕ɼڞ෼ࢄߦྻ
,ͷ O N
ཁૉʹͳ͍ͬͯ·͢ɽ
͢ͳΘͪಛ௃ϕΫτϧۭؒʹ͓͍͕ͯࣅ͍ͯΔͳΒ
ରԠ͢Δɹ΋ࣅͨ஋Λ࣋ͭ͜ͱʹͳΓ·͢ɽ
K = λ2ΦΦT
ϕ(xn
)ͱϕ(xm
)
Knm
xn
ͱxm
yn
ͱym
େ͖͍ͳΒ͹
yn
ͱym
΋ࣅͨ஋ʹͳΔɽ
ೖྗY͕ࣅ͍ͯΔͳΒ͹͈΋ࣅͨ஋ʹͳΔ

35. Ψ΢εաఔͷԠ༻
7BSJBUJPOBM-FBSOJOHPO"HHSFHBUF0VUQVUTXJUI
(BVTTJBO1SPDFTTFT
IUUQTBSYJWPSHBCT
ɾڭࢣ͋Γֶश͸ೖྗͱग़ྗ͕ಉ༷ͷਫ਼౓Ͱ؍ଌ͞ΕΔ͜ͱ
Λ૝ఆ͍ͯ͠Δ͕ɼҰൠతͳڭࢣ͋ΓֶशͰ͸ೖྗΑΓ΋ग़
ྗͷํ͕ૈ͘؍ଌ͞ΕΔɽ͜ͷ໰୊ʹର͢ΔɼΞϓϩʔνΛ
Ψ΢εաఔΛ༻͍ͨม෼ֶशΛఏҊ͍ͯ͠Δɽ

36. ࢀߟจݙ
w ৘ใزԿֶͷ৽ల։ɿ؁རढ़Ұ
w ৘ใزԿֶͷجૅɿ౻ݪজ෉
w ۂઢͱۂ໘ͷඍ෼زԿɿখྛতࣣ
w Χʔωϧ๏ೖ໳ɿ෱ਫ݈࣍
w (BVTTJBO1SPDFTTGPS.BDIJOF-FBSOJOH
ʢIUUQXXXHBVTTJBOQSPDFTTPSHHQNMʣɹ

w Ψ΢εաఔͷجૅͱڭࢣͳֶ͠श
IUUQXXXJTNBDKQdEBJDIJMFDUVSFT)(BVTTJBO1SPDFTTHQMFDUVSFEBJDIJQEG

w ʰΨ΢εաఔͱػցֶशʱαϙʔτϖʔδ
IUUQDIBTFOPSHdEBJUJNHQCPPL