Why does the video say the earlier example 'cheated' by sampling directly from $g^*$?

Conditions

• The context is comparing the improved cross-entropy method to the original cross-entropy method.
• The rare event in the earlier example had a relatively high probability.

Reasoning, step by step

1. Recall the earlier example where direct rejection sampling was used.
2. Note that the rare event was not very rare in that specific case.
3. Understand that for genuinely rare events, direct sampling is too slow.
4. Conclude that the cross-entropy method is needed to adaptively find a good proposal.

Example

The speaker says that in the earlier example they kind of cheated because the rare event was not very rare, so they could sample from g star directly using rejection sampling, but in general this would take too long.

Common misconceptions

• Thinking that direct rejection sampling is always the preferred method.
• Assuming the cross-entropy method is used because it is mathematically simpler than direct sampling.

Watch the explanation

Explore next

• What is the purpose of the original cross-entropy method?
• How is the iteration threshold $\gamma_i$ defined and when does the cross-entropy loop stop?