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蔚落 2022-01-29 13:59 222阅读 0赞

# 1 [FM模型][FM] #

y ^ ( x ) : = w 0 + ∑ i = 1 n w i x i + ∑ i = 1 n ∑ j = i + 1 n ⟨ v i , v j ⟩ x i x j \\hat\{y\}(\\mathbf\{x\}) :=w\_\{0\}+\\sum\_\{i=1\}^\{n\} w\_\{i\} x\_\{i\}+\\sum\_\{i=1\}^\{n\} \\sum\_\{j=i+1\}^\{n\}\\left\\langle\\mathbf\{v\}\_\{i\}, \\mathbf\{v\}\_\{j\}\\right\\rangle x\_\{i\} x\_\{j\} y^(x):=w0\+i=1∑nwixi\+i=1∑nj=i\+1∑n⟨vi,vj⟩xixj

# 2 [FFM模型][FFM] #

y ( x ) = w 0 + ∑ i = 1 n w i x i + ∑ i = 1 n ∑ j = i + 1 n ⟨ v i , f j , v j , f i ⟩ x i x j y(\\mathbf\{x\})=w\_\{0\}+\\sum\_\{i=1\}^\{n\} w\_\{i\} x\_\{i\}+\\sum\_\{i=1\}^\{n\} \\sum\_\{j=i+1\}^\{n\}\\left\\langle\\mathbf\{v\}\_\{i, f\_\{j\}\}, \\mathbf\{v\}\_\{j, f\_\{i\}\}\\right\\rangle x\_\{i\} x\_\{j\} y(x)=w0\+i=1∑nwixi\+i=1∑nj=i\+1∑n⟨vi,fj,vj,fi⟩xixj

# 3 [DeepFM模型][DeepFM] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70]  
 y ^ = sigmoid ⁡ ( y F M + y D N N ) \\hat\{y\}=\\operatorname\{sigmoid\}\\left(y\_\{F M\}+y\_\{D N N\}\\right) y^=sigmoid(yFM\+yDNN)  
 y F M = ⟨ w , x ⟩ + ∑ i = 1 d ∑ j = i + 1 d ⟨ V i , V j ⟩ x i ⋅ x j y\_\{F M\}=\\langle w, x\\rangle+\\sum\_\{i=1\}^\{d\} \\sum\_\{j=i+1\}^\{d\}\\left\\langle V\_\{i\}, V\_\{j\}\\right\\rangle x\_\{i\} \\cdot x\_\{j\} yFM=⟨w,x⟩\+i=1∑dj=i\+1∑d⟨Vi,Vj⟩xi⋅xj  
 y D N N = W ∣ H ∣ + 1 ⋅ a ∣ H ∣ + b ∣ H ∣ + 1 y\_\{D N N\}=W^\{|H|+1\} \\cdot a^\{|H|\}+b^\{|H|+1\} yDNN=W∣H∣\+1⋅a∣H∣\+b∣H∣\+1

# 4 [XDeepFM模型][XDeepFM] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 1]  
 y ∧ = σ ( w linear T a + w dnn T x dnn k + w c i n T p + + b ) y^\{\\wedge\}=\\sigma\\left(w\_\{\\text \{linear\}\}^\{T\} a+w\_\{\\text \{ dnn \}\}^\{T\} x\_\{\\text \{dnn\}\}^\{k\}+w\_\{c i n\}^\{T\} p^\{+\}+b\\right) y∧=σ(wlinearTa\+w dnn Txdnnk\+wcinTp\+\+b)

# 5 [GBDT+LR模型][GBDT_LR] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 2]

# 6 Deep&Wide模型 #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 3]  
 P ( Y = 1 ∣ x ) = σ ( w w i d e T \[ x , ϕ ( x ) \] + w d e e p T a ( l f ) + b ) P(Y=1 | \\mathbf\{x\})=\\sigma\\left(\\mathbf\{w\}\_\{w i d e\}^\{T\}\[\\mathbf\{x\}, \\phi(\\mathbf\{x\})\]+\\mathbf\{w\}\_\{d e e p\}^\{T\} a^\{\\left(l\_\{f\}\\right)\}+b\\right) P(Y=1∣x)=σ(wwideT\[x,ϕ(x)\]\+wdeepTa(lf)\+b)

# 7 [NCF模型][NCF] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 4]  
 ϕ G M F = p u G ⊙ q i G \\phi^\{G M F\}=\\mathbf\{p\}\_\{u\}^\{G\} \\odot \\mathbf\{q\}\_\{i\}^\{G\} ϕGMF=puG⊙qiG  
 ϕ M L P = a L ( W L T ( a L − 1 ( … a 2 ( W 2 T \[ p u M q i M \] + b 2 ) … ) ) + b L ) \\phi^\{M L P\}=a\_\{L\}\\left(\\mathbf\{W\}\_\{L\}^\{T\}\\left(a\_\{L-1\}\\left(\\ldots 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) \\ldots\\right)\\right)+\\mathbf\{b\}\_\{L\}\\right) ϕMLP=aL(WLT(aL−1(…a2(W2T\[puMqiM\]\+b2)…))\+bL)  
 y ^ u i = σ ( h T \[ ϕ G M F ϕ M L P \] ) \\hat\{y\}\_\{u i\}=\\sigma\\left(\\mathbf\{h\}^\{T\} \\left\[ \\begin\{array\}\{c\}\{\\phi^\{G M F\}\} \\\\ \{\\phi^\{M L P\}\}\\end\{array\}\\right\]\\right) y^ui=σ(hT\[ϕGMFϕMLP\])

# 8 [AFM模型][AFM] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 5]  
 y ^ A F M ( x ) = w 0 + ∑ i = 1 n w i x i + p T ∑ i = 1 n ∑ j = i + 1 n a i j ( v i ⊙ v j ) x i x j a i j ′ = h T Re ⁡ L U ( W ( v i ⊙ v j ) x i x j + b ) a i j = exp ⁡ ( a i j ′ ) ∑ ( i , j ) ∈ R x exp ⁡ ( a i j ′ ) \\begin\{aligned\} \\hat\{y\}\_\{A F M\}(\\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\_\{i j\}\\left(\\mathbf\{v\}\_\{i\} \\odot \\mathbf\{v\}\_\{j\}\\right) x\_\{i\} x\_\{j\} \\\\ a\_\{i j\}^\{\\prime\} &=\\mathbf\{h\}^\{T\} \\operatorname\{Re\} L U\\left(\\mathbf\{W\}\\left(\\mathbf\{v\}\_\{i\} \\odot \\mathbf\{v\}\_\{j\}\\right) x\_\{i\} x\_\{j\}+\\mathbf\{b\}\\right) \\\\ a\_\{i j\} &=\\frac\{\\exp \\left(a\_\{i j\}^\{\\prime\}\\right)\}\{\\sum\_\{(i, j) \\in \\mathcal\{R\}\_\{x\}\} \\exp \\left(a\_\{i j\}^\{\\prime\}\\right)\} \\end\{aligned\} y^AFM(x)aij′aij=w0\+i=1∑nwixi\+pTi=1∑nj=i\+1∑naij(vi⊙vj)xixj=hTReLU(W(vi⊙vj)xixj\+b)=∑(i,j)∈Rxexp(aij′)exp(aij′)

# 9 [PNN模型][PNN] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 6]  
 y ^ = σ ( W 3 l 2 + b 3 ) \\hat\{y\}=\\sigma\\left(\\boldsymbol\{W\}\_\{3\} l\_\{2\}+b\_\{3\}\\right) y^=σ(W3l2\+b3)  
 l 2 = relu ⁡ ( W 2 l 1 + b 2 ) l 1 = relu ⁡ ( l z + l p + b 1 ) \\begin\{array\}\{c\}\{l\_\{2\}=\\operatorname\{relu\}\\left(\\boldsymbol\{W\}\_\{2\} \\boldsymbol\{l\}\_\{1\}+\\boldsymbol\{b\}\_\{2\}\\right)\} \\\\ \{l\_\{1\}=\\operatorname\{relu\}\\left(\\boldsymbol\{l\}\_\{z\}+\\boldsymbol\{l\}\_\{p\}+\\boldsymbol\{b\}\_\{1\}\\right)\}\\end\{array\} l2=relu(W2l1\+b2)l1=relu(lz\+lp\+b1)  
 l z = ( l z 1 , l z 2 , … , l z n , … , l z D 1 ) , l z n = W z n ⊙ z l p = ( l p 1 , l p 2 , … , l p n , … , l p D 1 ) , l p n = W p n ⊙ p \\begin\{aligned\} l\_\{z\}=\\left(l\_\{z\}^\{1\}, l\_\{z\}^\{2\}, \\ldots, l\_\{z\}^\{n\}, \\ldots, l\_\{z\}^\{D\_\{1\}\}\\right), & l\_\{z\}^\{n\}=\\boldsymbol\{W\}\_\{z\}^\{n\} \\odot \\boldsymbol\{z\} \\\\ l\_\{p\}=\\left(l\_\{p\}^\{1\}, l\_\{p\}^\{2\}, \\ldots, l\_\{p\}^\{n\}, \\ldots, l\_\{p\}^\{D\_\{1\}\}\\right), & l\_\{p\}^\{n\}=\\boldsymbol\{W\}\_\{p\}^\{n\} \\odot \\boldsymbol\{p\} \\end\{aligned\} lz=(lz1,lz2,…,lzn,…,lzD1),lp=(lp1,lp2,…,lpn,…,lpD1),lzn=Wzn⊙zlpn=Wpn⊙p

# 10 [NFM模型][NFM] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 7]  
 y ^ N F M ( x ) = w 0 + ∑ i = 1 n w i x i + h T σ L ( W L ( … σ 1 ( W 1 f B I ( V x ) + b 1 ) … ) + b L ) \\begin\{aligned\} \\hat\{y\}\_\{N F M\}(\\mathbf\{x\}) &=w\_\{0\}+\\sum\_\{i=1\}^\{n\} w\_\{i\} x\_\{i\} +\\mathbf\{h\}^\{T\} \\sigma\_\{L\}\\left(\\mathbf\{W\}\_\{L\}\\left(\\ldots \\sigma\_\{1\}\\left(\\mathbf\{W\}\_\{1\} f\_\{B I\}\\left(\\mathcal\{V\}\_\{x\}\\right)+\\mathbf\{b\}\_\{1\}\\right) \\ldots\\right)+\\mathbf\{b\}\_\{L\}\\right) \\end\{aligned\} y^NFM(x)=w0\+i=1∑nwixi\+hTσL(WL(…σ1(W1fBI(Vx)\+b1)…)\+bL)  
 f B I ( V x ) = 1 2 \[ ( ∑ i = 1 n x i v i ) 2 − ∑ i = 1 n ( x i v i ) 2 \] f\_\{B I\}\\left(\\mathcal\{V\}\_\{x\}\\right)=\\frac\{1\}\{2\}\\left\[\\left(\\sum\_\{i=1\}^\{n\} x\_\{i\} \\mathbf\{v\}\_\{i\}\\right)^\{2\}-\\sum\_\{i=1\}^\{n\}\\left(x\_\{i\} \\mathbf\{v\}\_\{i\}\\right)^\{2\}\\right\] fBI(Vx)=21⎣⎡(i=1∑nxivi)2−i=1∑n(xivi)2⎦⎤

# 11 MLR模型 #

p ( y = 1 ∣ x ) = ∑ i = 1 m exp ⁡ ( u i T x ) ∑ j = 1 m exp ⁡ ( u j T x ) ⋅ 1 1 + exp ⁡ ( − w i T x ) 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)\} p(y=1∣x)=i=1∑m∑j=1mexp(ujTx)exp(uiTx)⋅1\+exp(−wiTx)1

# 12 [DIN模型][DIN]![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 8] #

# 13 [DCN模型][DCN] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 9]  
 p = σ ( \[ x L 1 T , h L 2 T \] w logits ) p=\\sigma\\left(\\left\[\\mathbf\{x\}\_\{L\_\{1\}\}^\{T\}, \\mathbf\{h\}\_\{L\_\{2\}\}^\{T\}\\right\] \\mathbf\{w\}\_\{\\text \{ logits \}\}\\right) p=σ(\[xL1T,hL2T\]w logits )  
 h l + 1 = f ( W l h l + b l ) \\mathbf\{h\}\_\{l+1\}=f\\left(W\_\{l\} \\mathbf\{h\}\_\{l\}+\\mathbf\{b\}\_\{l\}\\right) hl\+1=f(Wlhl\+bl)  
 x l + 1 = x 0 x l T w l + b l + x l = f ( x l , w l , b l ) + x l \\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\} xl\+1=x0xlTwl\+bl\+xl=f(xl,wl,bl)\+xl  
 x 0 = \[ x embed, 1 T , … , x embed , k T , x dense T \] \\mathbf\{x\}\_\{0\}=\\left\[\\mathbf\{x\}\_\{\\text \{ embed, \} 1\}^\{T\}, \\ldots, \\mathbf\{x\}\_\{\\text \{ embed \}, k\}^\{T\}, \\mathbf\{x\}\_\{\\text \{ dense \}\}^\{T\}\\right\] x0=\[x embed, 1T,…,x embed ,kT,x dense T\]

# 14 [DKN模型][DKN] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 10]

# 15 [RippleNet][] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 11]

# 16 [MKR模型][MKR] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 12]

# 17 [CMN模型][CMN] #

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 13]

[FM]: https://blog.csdn.net/qq_40006058/article/details/88532970
[FFM]: https://blog.csdn.net/qq_40006058/article/details/88656959
[DeepFM]: https://blog.csdn.net/qq_40006058/article/details/88723614
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70]: /images/20220129/b2133bc5fcda4c828c0a2bb39ff9d63b.png
[XDeepFM]: https://blog.csdn.net/qq_40006058/article/details/88870482
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 1]: /images/20220129/f3867b707e304f8eb2363298b032bfff.png
[GBDT_LR]: https://blog.csdn.net/qq_40006058/article/details/88978380
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 2]: /images/20220129/ac40d8590ae946d5912c86e99c6eba9b.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 3]: /images/20220129/a2d36be3d3584ddb972618ad60398784.png
[NCF]: https://blog.csdn.net/qq_40006058/article/details/89074172
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 4]: /images/20220129/9f5b1b81e36b42d9ba4a72966e1e1033.png
[AFM]: https://blog.csdn.net/qq_40006058/article/details/89172784
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 5]: /images/20220129/afa00ccfba504988bc70fa4d253c5511.png
[PNN]: https://blog.csdn.net/qq_40006058/article/details/89176343
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 6]: /images/20220129/6994e0e6636b454b889fc95401ecf3bc.png
[NFM]: https://blog.csdn.net/qq_40006058/article/details/89182442
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 7]: /images/20220129/018153d4a80a430892b052787ff32957.png
[DIN]: https://blog.csdn.net/qq_40006058/article/details/89305162
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 8]: /images/20220129/73c2d229fe1540ff82742da269848f60.png
[DCN]: https://blog.csdn.net/qq_40006058/article/details/89332465
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 9]: /images/20220129/966eefb4e8a745819a0f068b2c6f8eb3.png
[DKN]: https://blog.csdn.net/qq_40006058/article/details/89678866
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 10]: /images/20220129/8835275aa8414f0e8454d5e136e8e574.png
[RippleNet]: https://blog.csdn.net/qq_40006058/article/details/89742816
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 11]: /images/20220129/5fda3a9c90d44f56ad7269f2ddeb34a8.png
[MKR]: https://blog.csdn.net/qq_40006058/article/details/89977929
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 12]: /images/20220129/e313c5293d474b1bbdd64b48ee50307e.png
[CMN]: https://blog.csdn.net/qq_40006058/article/details/90018931
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQwMDA2MDU4_size_16_color_FFFFFF_t_70 13]: /images/20220129/1604b6d16f7b4959b2488b520611917a.png