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About the ot_loss why optimizing the dual term's derivate instead of the OT distance ? #29

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Lynyanyu opened this issue May 4, 2022 · 1 comment
Open

About the ot_loss why optimizing the dual term's derivate instead of the OT distance ? #29

Lynyanyu opened this issue May 4, 2022 · 1 comment

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@Lynyanyu
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Lynyanyu commented May 4, 2022 •
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Why setting the optimal target equals the dual term "<β*, z^>"s derivate times the prediction instead of the original OT distance? It makes sense to optimize the entire OT loss term "W(z, z^)" or its dual term "<β*, z^>" to force dot regression more sparse and accurate, but why the derivate? Is it mentioned in the paper or supplements?
@Lynyanyu Lynyanyu changed the title About the ot_loss why did you use the prediction's derivative times itself instead of the OT distance ? About the ot_loss why did you use the prediction's derivate times itself instead of the OT distance ? May 4, 2022
@Lynyanyu Lynyanyu changed the title About the ot_loss why did you use the prediction's derivate times itself instead of the OT distance ? About the ot_loss why optimizing the dual term's derivate instead of the OT distance ? May 4, 2022
@henvh
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henvh commented Jan 24, 2024

I actually had the same question. And why is the distance matrix for the ot computation defined like that?

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@Lynyanyu @henvh