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：

LATeX 插入脚注_LaTeX