Can someone help me derive this equation?

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I have read this paper Translation-based Recommendations and I have some question about the derivation. I'm not familiar with the derivative of vector.



I want to derive $$fracpartial (hatp_u,_i,_j - hatp_u,_i,_jprime)partial Theta$$
for all of the model parameters $$Theta = beta_i , vecgamma_i,vect_u, vect $$



where $$hatp_u,_i,_j$$ is a shorthand of
$$Prob(j | u,i) propto beta_j - d(vecgamma_i+vect_u + vect,vecgamma_j)$$



Can anyone help me to derive this? Thank you very much.




derivatives partial-derivative machine-learning gradient-descent




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  • It's better to write the math in the question directly using MathJax rather than linking to images.
    – littleO
    Jul 24 at 6:13










  • @littleO thank you. I have already edited it.
    – Plafishy Phannakan
    Jul 24 at 6:44














up vote
0
down vote

favorite












I have read this paper Translation-based Recommendations and I have some question about the derivation. I'm not familiar with the derivative of vector.



I want to derive $$fracpartial (hatp_u,_i,_j - hatp_u,_i,_jprime)partial Theta$$
for all of the model parameters $$Theta = beta_i , vecgamma_i,vect_u, vect $$



where $$hatp_u,_i,_j$$ is a shorthand of
$$Prob(j | u,i) propto beta_j - d(vecgamma_i+vect_u + vect,vecgamma_j)$$



Can anyone help me to derive this? Thank you very much.




derivatives partial-derivative machine-learning gradient-descent




share|cite|improve this question





















  • It's better to write the math in the question directly using MathJax rather than linking to images.
    – littleO
    Jul 24 at 6:13










  • @littleO thank you. I have already edited it.
    – Plafishy Phannakan
    Jul 24 at 6:44












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have read this paper Translation-based Recommendations and I have some question about the derivation. I'm not familiar with the derivative of vector.



I want to derive $$fracpartial (hatp_u,_i,_j - hatp_u,_i,_jprime)partial Theta$$
for all of the model parameters $$Theta = beta_i , vecgamma_i,vect_u, vect $$



where $$hatp_u,_i,_j$$ is a shorthand of
$$Prob(j | u,i) propto beta_j - d(vecgamma_i+vect_u + vect,vecgamma_j)$$



Can anyone help me to derive this? Thank you very much.




derivatives partial-derivative machine-learning gradient-descent




share|cite|improve this question













I have read this paper Translation-based Recommendations and I have some question about the derivation. I'm not familiar with the derivative of vector.



I want to derive $$fracpartial (hatp_u,_i,_j - hatp_u,_i,_jprime)partial Theta$$
for all of the model parameters $$Theta = beta_i , vecgamma_i,vect_u, vect $$



where $$hatp_u,_i,_j$$ is a shorthand of
$$Prob(j | u,i) propto beta_j - d(vecgamma_i+vect_u + vect,vecgamma_j)$$



Can anyone help me to derive this? Thank you very much.





derivatives partial-derivative machine-learning gradient-descent





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 24 at 6:44
























asked Jul 24 at 6:10









Plafishy Phannakan

61




61











  • It's better to write the math in the question directly using MathJax rather than linking to images.
    – littleO
    Jul 24 at 6:13










  • @littleO thank you. I have already edited it.
    – Plafishy Phannakan
    Jul 24 at 6:44
















  • It's better to write the math in the question directly using MathJax rather than linking to images.
    – littleO
    Jul 24 at 6:13










  • @littleO thank you. I have already edited it.
    – Plafishy Phannakan
    Jul 24 at 6:44















It's better to write the math in the question directly using MathJax rather than linking to images.
– littleO
Jul 24 at 6:13




It's better to write the math in the question directly using MathJax rather than linking to images.
– littleO
Jul 24 at 6:13












@littleO thank you. I have already edited it.
– Plafishy Phannakan
Jul 24 at 6:44




@littleO thank you. I have already edited it.
– Plafishy Phannakan
Jul 24 at 6:44















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