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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 218
/
1
/
c
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2021
iii
Paper 218
1
c
2026-09-28
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The two
Lasso
problems are
min
β
∥
Y
−
x
β
∥
2
2
subject to
∣
β
∣
≤
t
(1)
and
min
β
1
,
β
2
∥
Y
−
x
(
β
1
+
β
2
)
∥
2
2
subject to
∣
β
1
∣
+
∣
β
2
∣
≤
t
.
(2)
If
β
solves the
first
problem, the complete solution
set
of the
second
is
{(
β
1
,
β
2
)
:
β
1
+
β
2
=
β
,
∣
β
1
∣
+
∣
β
2
∣
≤
t
}
.
(3)
Indeed, the feasible totals are exactly
[
−
t
,
t
]
, the same
as
in the
first
problem.
Ancestors
(11)
c
1
Paper 218
iii
2021
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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