- #1
kiuhnm
- 66
- 1
Hi,
I need to minimize, with respect to [itex]\hat{y}(x)[/itex], the following function:
[tex]\tilde{J}_x = \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)^2] + \nu \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)tr(\nabla_x^2\hat{y}(x))] + \nu \mathbb{E}_{p(x,y)}[||\nabla_x\hat{y}(x)||^2],[/tex]
where [itex]x[/itex] is a vector and [itex]y[/itex] a scalar.
I found this in a book about Deep Learning (Machine Learning). I'm studying on my own and this math is a bit over my head. If you want more context, see pages 215-216 here: http://goodfeli.github.io/dlbook/contents/regularization.html
First of all, do I need to learn the Calculus of Variations to solve this?
The expression I wrote here is slightly different from the one on the book, because I think the authors forgot a "trace" (tr).
Thank you for your time.
I need to minimize, with respect to [itex]\hat{y}(x)[/itex], the following function:
[tex]\tilde{J}_x = \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)^2] + \nu \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)tr(\nabla_x^2\hat{y}(x))] + \nu \mathbb{E}_{p(x,y)}[||\nabla_x\hat{y}(x)||^2],[/tex]
where [itex]x[/itex] is a vector and [itex]y[/itex] a scalar.
I found this in a book about Deep Learning (Machine Learning). I'm studying on my own and this math is a bit over my head. If you want more context, see pages 215-216 here: http://goodfeli.github.io/dlbook/contents/regularization.html
First of all, do I need to learn the Calculus of Variations to solve this?
The expression I wrote here is slightly different from the one on the book, because I think the authors forgot a "trace" (tr).
Thank you for your time.
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