ISYE 7406 QUIZ #4 DATA MINING&STAT LEARN
- ISYE-7406-OAN QUESTIONS AND ANSWERS
LATEST 2025-2026 UPDATE
What is the form of B-spline basis Bi=1,d=1 of order d = 1? - Answer-
x*I(0 <= x < 1) + (2 - x)*I(1 <= x < 2)
Assume that we observe four data points of (Yi, Xi) as (1, 0), (2, 1), (1,
2), and (3, 3).
Consider the B-spline basis of order d. There are n = 4 points, and the
four xi values are called knots. Thus, there are 4 B-spline basis of order
d = 0,
Bi,0(x) = I(xi <= x < xi+1), i.e., (= 1 if inside this interval and = 0 if
outside this interval), and x1=0, x2=1, x3=2, x4=3.
Now, using the formula that:
Bi,d(x) = ((x-xi)/(xi+d - xi))Bi,d-1(x) + ((xi+d+1 - x)/(xi+d+1 -
xi+1))Bi+1,d-1(x)
we can compute the 3 B-spline basis of order d = 1, and 2 B-spline basis
of order d = 2, etc.
What is the form of B-spline basis Bi=2,d=1 of order d = 1? - Answer-(x
- 1)*I(1 <= x < 2) + (3 - x)*I(2 <= x < 3)
Assume that we observe four data points of (Yi, Xi) as (1, 0), (2, 1), (1,
2), and (3, 3).
, Consider the B-spline basis of order d. There are n = 4 points, and the
four xi values are called knots. Thus, there are 4 B-spline basis of order
d = 0,
Bi,0(x) = I(xi <= x < xi+1), i.e., (= 1 if inside this interval and = 0 if
outside this interval), and x1=0, x2=1, x3=2, x4=3.
Now, using the formula that:
Bi,d(x) = ((x-xi)/(xi+d - xi))Bi,d-1(x) + ((xi+d+1 - x)/(xi+d+1 -
xi+1))Bi+1,d-1(x)
we can compute the 3 B-spline basis of order d = 1, and 2 B-spline basis
of order d = 2, etc.
What is the form of B-spline basis Bi=1,d=2 of order d = 2 in the
interval [1, 2)? - Answer-0.5*(-3 + 6*(x - 2)*x^2)
In the example of solving the equation system:
2x1 + x2 = 1 and x1 + 2x2 = 2
we can also write:
x2 = 1 - 2x1 and x1 = 2 - 2x2
Based on these relationships, is it a backfitting algorithm if we
recursively update (x1, x2) by:
x1_new ← 2 - 2x2 and x2_new ← 1 - 2x1
with initialization x1 = x2 = 0? - Answer-Yes, it is still a backfitting
algorithm, but it no longer converges to a meaningful solution.
T/F: The tree-based model can be thought of as a special case of the
additive model? - Answer-True
- ISYE-7406-OAN QUESTIONS AND ANSWERS
LATEST 2025-2026 UPDATE
What is the form of B-spline basis Bi=1,d=1 of order d = 1? - Answer-
x*I(0 <= x < 1) + (2 - x)*I(1 <= x < 2)
Assume that we observe four data points of (Yi, Xi) as (1, 0), (2, 1), (1,
2), and (3, 3).
Consider the B-spline basis of order d. There are n = 4 points, and the
four xi values are called knots. Thus, there are 4 B-spline basis of order
d = 0,
Bi,0(x) = I(xi <= x < xi+1), i.e., (= 1 if inside this interval and = 0 if
outside this interval), and x1=0, x2=1, x3=2, x4=3.
Now, using the formula that:
Bi,d(x) = ((x-xi)/(xi+d - xi))Bi,d-1(x) + ((xi+d+1 - x)/(xi+d+1 -
xi+1))Bi+1,d-1(x)
we can compute the 3 B-spline basis of order d = 1, and 2 B-spline basis
of order d = 2, etc.
What is the form of B-spline basis Bi=2,d=1 of order d = 1? - Answer-(x
- 1)*I(1 <= x < 2) + (3 - x)*I(2 <= x < 3)
Assume that we observe four data points of (Yi, Xi) as (1, 0), (2, 1), (1,
2), and (3, 3).
, Consider the B-spline basis of order d. There are n = 4 points, and the
four xi values are called knots. Thus, there are 4 B-spline basis of order
d = 0,
Bi,0(x) = I(xi <= x < xi+1), i.e., (= 1 if inside this interval and = 0 if
outside this interval), and x1=0, x2=1, x3=2, x4=3.
Now, using the formula that:
Bi,d(x) = ((x-xi)/(xi+d - xi))Bi,d-1(x) + ((xi+d+1 - x)/(xi+d+1 -
xi+1))Bi+1,d-1(x)
we can compute the 3 B-spline basis of order d = 1, and 2 B-spline basis
of order d = 2, etc.
What is the form of B-spline basis Bi=1,d=2 of order d = 2 in the
interval [1, 2)? - Answer-0.5*(-3 + 6*(x - 2)*x^2)
In the example of solving the equation system:
2x1 + x2 = 1 and x1 + 2x2 = 2
we can also write:
x2 = 1 - 2x1 and x1 = 2 - 2x2
Based on these relationships, is it a backfitting algorithm if we
recursively update (x1, x2) by:
x1_new ← 2 - 2x2 and x2_new ← 1 - 2x1
with initialization x1 = x2 = 0? - Answer-Yes, it is still a backfitting
algorithm, but it no longer converges to a meaningful solution.
T/F: The tree-based model can be thought of as a special case of the
additive model? - Answer-True
