Bag of Little Bootstraps
Our Approach: BLB
X1, . . . , Xn
.
.
.
.
.
.
X⇤(1)
1
, . . . , X⇤(1)
n
X⇤(2)
1
, . . . , X⇤(2)
n
ˆ
✓⇤(1)
n
ˆ
✓⇤(2)
n
.
.
.
.
.
.
X⇤(1)
1
, . . . , X⇤(1)
n
X⇤(2)
1
, . . . , X⇤(2)
n
ˆ
✓⇤(1)
n
ˆ
✓⇤(2)
n
.
.
.
ˇ
X(1)
1
, . . . , ˇ
X(1)
b(n)
avg(⇠⇤
1
, . . . , ⇠⇤
s
)
ˇ
X(s)
1
, . . . , ˇ
X(s)
b(n)
X⇤(r)
1
, . . . , X⇤(r)
n
X⇤(r)
1
, . . . , X⇤(r)
n
ˆ
✓⇤(r)
n
ˆ
✓⇤(r)
n
⇠(ˆ
✓⇤(1)
n
, . . . , ˆ
✓⇤(r)
n
) = ⇠⇤
1
⇠(ˆ
✓⇤(1)
n
, . . . , ˆ
✓⇤(r)
n
) = ⇠⇤
s
Divide into
random subsets
Resample* each subset
and compute estimate
Compute bootstrap
metric
Image from “Bootstrapping Big Data”, Ariel Kleiner, et. al.
* with n replicates