If we knew the distribution function of Y, let's call it F, we would simply determine ξ i from equation 1, where P i =Σp k , k ≤ i : and we would know that in each partition p i the name perplexity is between ξ i-1 and ξ i, with ξ 0 = 0.
we do not know F. Fortunately, we can estimate ξ i .