1. Greedy Importance Sampling
Dale Shuurmans

2. Generalized importance sampling
We are interested in computing expectation
Draw independent points from a simpler “proposal” distribution
Weight these points by to obtain a “fair” representation of

3. Block Importance Sampling
Importance sampling is effective when Q approximates P over most of the domain.
It fails when Q misses high probability regions of P and systematically yields samples with small weights.
To overcome this problem it is critical to obtain data points from importance regions of P.
Explicitly searching for significant regions in the target distribution P.
Sampling blocks of points instead of just individual points.
Let B be a partition of X into finite blocks B where

4. “Block” importance sampling
Draw independently from
For , recover block
Create a large sample out of the blocks
Weight each by
For a random variable , estimate by
For discrete spaces

5. “Sliding window” importance sampling
allow countably infinite blocks that each have a discrete total order
unbiased estimator

6. “Sliding window” importance sampling
Draw independently from
For , recover block and let
Get ‘s successors by climbing up
m-1 steps from
Get predecessors by climbing down
Weight
Create final sample from successor points
For a random variable , estimate

7. Greedy importance sampling : 1-dimensional case
Draw independently from
For , let
compute successors by taking
m-1 size steps in the direction of increase
compute predecessors by taking
m-1 size steps in the direction of decrease.
If an improper ascent or descent occurs, truncate paths
Weight
Create final sample from successor points
For a random variable , estimate

8. Greedy importance sampling
optimal proposal distribution for importance sampling
which minimize variance
follow direction of increasing ,taking fixed size steps
nontrivial issue : maintain disjoint search paths
At a collision, the largest ascent point must be allocated to a single path.

9. Experimental Result Direct Greed Imprtn Metropolis
mean
bias
stdev