What would you like to understand?

The iteration threshold $\gamma_i$ is defined as the empirical $(1-p)$-quantile of the current batch of samples drawn from the proposal distribution. The loop stops when this threshold $\gamma_i$ is greater than or equal to the target rare-event threshold $\gamma$.

Conditions: Samples are drawn from the current proposal distribution.; The elite fraction parameter $p$ is set to 0.05.; The target threshold is $\gamma=5$.

The iteration threshold $\gamma_i$ is defined as the empirical $(1-p)$-quantile of the current batch of samples drawn from the proposal distribution. The loop stops when this threshold $\gamma_i$ is greater than or equal to the target rare-event threshold $\gamma$.

Conditions: Samples are drawn from the current proposal distribution.; The elite fraction parameter $p$ is set to 0.05.; The target threshold is $\gamma=5$.

The video states that the earlier example 'cheated' because the rare event was not very rare, making direct rejection sampling from $g^*$ computationally feasible. In general, for truly rare events, direct rejection sampling would take too long, which motivates the use of the adaptive cross-entropy method.

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.

The video states that the earlier example 'cheated' because the rare event was not very rare, making direct rejection sampling from $g^*$ computationally feasible. In general, for truly rare events, direct rejection sampling would take too long, which motivates the use of the adaptive cross-entropy method.

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.