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