LATeX 插入脚注：
使用 footnote{...注释内容} 命令：
To maximize the lower-bound in $Equ.3$ we employ conjugate gradient method. We first fix all latent vectors for the item $footnote{We use the supscript $t$ for parameters in the $t^{th}$ round}$, and apply $ log sum_k u_k i_k geq frac{sum_k i_k log u_k}{sum_k i_k} + log sum_k i_k,forall i_k geq 0.$ Let's compute $c^t(d,i,j)=sum_k u_k^ti_k^t + sum_k u_k^tj_k^t$,$c_k^t(d,i,j)=frac{i_k^t + j_k^t}{c^t(d,i,j)}$, and $ f_k^t(d,i)=frac{i_k^t}{sum_k i_k^t} $ for all pairwise ranking observations in $d$ using the $t$-th round parameters, we have
效果如下：
