推荐系统 | 已看论文阶段性整理

1 FM模型

$$\hat{y}(\mathbf{x}):=w_0+\sum _{i=1}^n{w}_i{x}_i+\sum _{i=1}^n\sum _{j=i+1}^n⟨{\mathbf{v}}_i,{\mathbf{v}}_j⟩x_i{x}_j$$

2 FFM模型

$$y(\mathbf{x})=w_0+\sum _{i=1}^n{w}_i{x}_i+\sum _{i=1}^n\sum _{j=i+1}^n⟨{\mathbf{v}}_{i,f_j},{\mathbf{v}}_{j,f_i}⟩x_i{x}_j$$

3 DeepFM模型

$$\hat{y}=\mathrm{sigmoid}\left(y_{FM}+y_{DNN}\right)$$
$$y_{FM}=⟨w,x⟩+\sum _{i=1}^d\sum _{j=i+1}^d⟨V_i,V_j⟩x_i\cdot x_j$$
$$y_{DNN}=W^{|H|+1}\cdot a^{|H|}+b^{|H|+1}$$

4 XDeepFM模型

$$y^{\wedge }=\sigma \left(w_{\text{linear}}^{T}a+w_{\text{ dnn }}^T{x}_{\text{dnn}}^k+w_{cin}^T{p}^{+}+b\right)$$

5 GBDT+LR模型

6 Deep&Wide模型

$$P(Y=1|\mathbf{x})=\sigma \left({\mathbf{w}}_{wide}^T[\mathbf{x},\varphi (\mathbf{x})]+{\mathbf{w}}_{deep}^T{a}^{\left(l_f\right)}+b\right)$$

7 NCF模型

$${\varphi }^{GMF}={\mathbf{p}}_u^G\odot {\mathbf{q}}_i^G$$
$${\varphi }^{MLP}=a_L\left({\mathbf{W}}_L^T\left(a_{L-1}\left(\dots a_2\left({\mathbf{W}}_2^T\left[\begin{array}{c}{\mathbf{p}}_u^M\\ {\mathbf{q}}_i^M\end{array}\right]+{\mathbf{b}}_2\right)\dots \right)\right)+{\mathbf{b}}_L\right)$$
$${\hat{y}}_{ui}=\sigma \left({\mathbf{h}}^T\left[\begin{array}{c}{\varphi }^{GMF}\\ {\varphi }^{MLP}\end{array}\right]\right)$$

8 AFM模型

$$\begin{array}{rl}{\hat{y}}_{AFM}(\mathbf{x})& =w_0+\sum _{i=1}^n{w}_i{x}_i+{\mathbf{p}}^T\sum _{i=1}^n\sum _{j=i+1}^n{a}_{ij}\left({\mathbf{v}}_i\odot {\mathbf{v}}_j\right)x_i{x}_j\\ a_{ij}^{\prime }& ={\mathbf{h}}^T\mathrm{Re}LU\left(\mathbf{W}\left({\mathbf{v}}_i\odot {\mathbf{v}}_j\right)x_i{x}_j+\mathbf{b}\right)\\ a_{ij}& =\frac{\exp \left(a_{ij}^{\prime }\right)}{{\sum }_{(i,j)\in {\mathcal{R}}_x}\exp \left(a_{ij}^{\prime }\right)}\end{array}$$

9 PNN模型

$$\hat{y}=\sigma \left({\mathbf{W}}_3{l}_2+b_3\right)$$
$$\begin{array}{c}{l}_2=\mathrm{relu}\left({\mathbf{W}}_2{\mathbf{l}}_1+{\mathbf{b}}_2\right)\\ l_1=\mathrm{relu}\left({\mathbf{l}}_z+{\mathbf{l}}_p+{\mathbf{b}}_1\right)\end{array}$$
$$\begin{array}{rl}{l}_z=\left(l_z^1,l_z^2,\dots ,l_z^n,\dots ,l_z^{D_1}\right),& l_z^n={\mathbf{W}}_z^n\odot \mathbf{z}\\ l_p=\left(l_p^1,l_p^2,\dots ,l_p^n,\dots ,l_p^{D_1}\right),& l_p^n={\mathbf{W}}_p^n\odot \mathbf{p}\end{array}$$

10 NFM模型

$$\begin{array}{rl}{\hat{y}}_{NFM}(\mathbf{x})& =w_0+\sum _{i=1}^n{w}_i{x}_i+{\mathbf{h}}^T{\sigma }_L\left({\mathbf{W}}_L\left(\dots {\sigma }_1\left({\mathbf{W}}_1{f}_{BI}\left({\mathcal{V}}_x\right)+{\mathbf{b}}_1\right)\dots \right)+{\mathbf{b}}_L\right)\end{array}$$
$$f_{BI}\left({\mathcal{V}}_x\right)=\frac{1}{2}\left[{\left(\sum _{i=1}^n{x}_i{\mathbf{v}}_i\right)}^2-\sum _{i=1}^n{\left(x_i{\mathbf{v}}_i\right)}^2\right]$$

11 MLR模型

$$p(y=1|x)=\sum _{i=1}^m\frac{\exp \left(u_i^{T}x\right)}{{\sum }_{j=1}^m\exp \left(u_j^{T}x\right)}\cdot \frac{1}{1+\exp \left(-w_i^{T}x\right)}$$

12 DIN模型

13 DCN模型

$$p=\sigma \left(\left[{\mathbf{x}}_{L_1}^T,{\mathbf{h}}_{L_2}^T\right]{\mathbf{w}}_{\text{ logits }}\right)$$
$${\mathbf{h}}_{l+1}=f\left(W_l{\mathbf{h}}_l+{\mathbf{b}}_l\right)$$
$${\mathbf{x}}_{l+1}={\mathbf{x}}_0{\mathbf{x}}_l^T{\mathbf{w}}_l+{\mathbf{b}}_l+{\mathbf{x}}_l=f\left({\mathbf{x}}_l,{\mathbf{w}}_l,{\mathbf{b}}_l\right)+{\mathbf{x}}_l$$
$${\mathbf{x}}_0=\left[{\mathbf{x}}_{\text{ embed, }1}^T,\dots ,{\mathbf{x}}_{\text{ embed },k}^T,{\mathbf{x}}_{\text{ dense }}^T\right]$$

14 DKN模型

15 RippleNet

16 MKR模型

17 CMN模型