Small fix on S4 macro not called

This commit is contained in:
Aaron Huber 2020-12-20 16:00:50 -05:00
parent 35d894243f
commit 6f3fb7798e

View file

@ -412,7 +412,7 @@ It turns out that for proof of~\Cref{lem:sample}, we need to argue that when $\e
%Algorithm ~\ref{alg:sample} takes $\etree$ as input, samples an arbitrary $(\monom, \coef)$ from $\expandtree{\etree}$ with probabilities $\stree_\lchild.\wght$ and $\stree_\rchild.\wght$ for each subtree $\stree$ with $\stree.\type = +$, outputting the tuple $(\monom, \sign(\coef))$. While one cannot compute $\expandtree{\etree}$ in time better than $O(N^k)$, the algorithm, similar to \textsc{OnePass}, uses a technique on $\etree$ which produces a sample from $\expandtree{\etree}$ without ever materializing $\expandtree{\etree}$.
A naive (slow) implementation of \sampmon\ would first compute $E(T)$ and then sample from it.
A naive (slow) implementation of \sampmon\ would first compute $\expandtree{\etree}$ and then sample from it.
% However, this would be too time consuming.
%
Instead, \Cref{alg:sample} selects a monomial from $\expandtree{\etree}$ by top-down traversal.