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Numerical Stability and Conditioning
Numerical Stability and Conditioning
4 questions
Difficulty 3-3
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Foundation
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compute
To add probabilities computed in log-space, you need the log-sum-exp trick:
lo
g
(
p
+
q
)
=
?
given
lo
g
p
and
lo
g
q
. What is the identity?
Hide and think first
A.
lo
g
(
p
+
q
)
=
lo
g
p
⋅
lo
g
q
, following the distributive property of logarithms
B.
lo
g
(
p
+
q
)
=
m
+
lo
g
(
e
l
o
g
p
−
m
+
e
l
o
g
q
−
m
)
where
m
=
max
(
lo
g
p
,
lo
g
q
)
C.
lo
g
(
p
+
q
)
=
lo
g
p
+
lo
g
q
, since logs of a sum equal the sum of logs
D.
lo
g
(
p
+
q
)
=
max
(
lo
g
p
,
lo
g
q
)
, since the dominant term determines the result
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