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实数集合： $\mathbb{R}$

$$\underset{p_i,q_j}{\underbrace{argmin}}\sum _{i,j}(m_{ij}-\mu -b_i-b_j-q_j^T{p}_i–q_j^T|N(i){|}^{-1/2}\sum _{s\in N(i)}{y}_s{)}^2+\lambda (||p_i|{|}_2^2+||q_j|{|}_2^2+||b_i|{|}_2^2+||b_j|{|}_2^2+\sum _{s\in N(i)}||y_s|{|}_2^2)$$

$$Bilinear(x,y)=x\odot W\times y+b$$

$$\begin{array}{rl}P(z|G,S)\log P(G|S)& =\log \int P(G|z,S)P(z|S)dz\\ & =\log \int P(G|z,S)P(z|S)\frac{q(z)}{q(z)}dz\\ & =\log {\mathbb{E}}_{z\sim q(z)}\left[\frac{P(G|z,S)P(z|S)}{q(z)}\right]\\ & \ge {\mathbb{E}}_{z\sim q(z)}\left[\log \frac{P(G|z,S)P(z|S)}{q(z)}\right]\\ & ={\mathbb{E}}_{z\sim q(z)}\left[\log P(G|z,S)\right]+{\mathbb{E}}_{z\sim q(z)}\left[\log \frac{P(z|S)}{q(z)}\right]\\ & ={\mathbb{E}}_{z\sim q(z)}\left[\log P(G|z,S)\right]-\mathrm{K}\mathrm{L}\left[q(z)||P(z|S)\right]\end{array}$$

$$\begin{array}{rl}\log P(G|S)& \ge {\mathbb{E}}_{z\sim q(z)}\left[\log P(G|z,S)\right]-\mathrm{K}\mathrm{L}\left[q(z)||P(z|S)\right]\end{array}$$

$$\begin{array}{r}{\mathbb{E}}_{z\sim q(z)}\left[\log P(G|z,S)\right]={\mathbb{E}}_{ϵ\sim N(0,1)}\left[\log P(G|\mu +ϵ\sigma ,S)\right]\end{array}$$

$$\frac{\partial J}{\partial \mathbf{\theta }}=-\frac{1}{m}\sum _{i=1}^m\frac{\partial J_i}{\partial \mathbf{\theta }}=\frac{1}{m}\sum _{i=1}^m(h^{(i)}-y^{(i)}){\mathbf{x}}^{(i)}\text{\hspace{1em}(11)}$$

$$\frac{log(P(A))\times le{n}^{0.6}+log(P(B))}{(len+1{)}^{0.6}}$$