CTR Pre-estimate method: FM and FFM__ algorithm

Ctr Pre-estimate method: FFM

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CTR Pre-estimate method FFM 1FM 1 background 11 linear Model 122-item model 2 FM FM Fundamentals 22 data Analysis 23 parameter Count 24 compute time Complexity 25 gradient 26 Training time complexity 2FFM 1 background and Fundamentals 2 model and optimization problem 21 Model 22 Optimization Problem 23 Adaptive learning rate The final form of the FFM algorithm 3 complete algorithm flow 31 COMPUTE gradient 32 compute cumulative gradient squared and 33 update hidden variable 34 about initial parameter set 4 time complexity 41 computational time complexity 42 training time Complexity 5 calculation Speed optimization SSE3 parameterserver 6 model Optimization 61 feature encoding 621 consecutive item missing effect 63 sample normalization 64 feature normalization

Full code See: HTTPS://GITHUB.COM/LUJINHONG/FFM 1, FM 1.1 background 1.1.1 Linear model

Common linear models, such as linear regression and logistic regression, consider only the individual effects of each feature on the results, without regard to the effect of the combination of features on the results.

For a model with n-dimensional features, the linear regression is in the following form:
F (x) =ω0+ω1x1+ω2x2+...+ωnxn=ω0+∑i=1nωixi (1) \begin{aligned} f (x) &= \omega_0 + \omega_1x_1+\omega_2x_2+...+\omega _nx_n \ &=\omega_0+\sum_{i=1}^n{\omega_ix_i} \tag{1} \end{aligned}
Among them (ω0,ω1 ... ωn) (\omega_0,\omega_1...\omega_n) is a characteristic of model parameters, (X1,X2...XN) (x_1,x_2...x_n).
It can be seen from the (1) formula that the final calculation result of the model is the independent calculation result of each characteristic, and the relationship between the characteristics is not considered.

For example, our "USA" and "Thanksgiving", "China" and "Chinese New Year" such a combination of characteristics is very meaningful, in such a combination of characteristics, will show a greater willingness to buy some goods, and the individual consideration of the country and festivals are meaningless. 1.1.22-Item model

On the basis of the (1) formula, we consider the relationship between any 2 feature components and derive the following models:
F (x) =ω0+∑i=1nωixi+∑i=1n