Re: Hinge Gradient

[Debasish Das]

Hi Weichen,

Traditionally svm are solved using quadratic programming solvers and most
likely that's why this idea is not so popular but since in mllib we are
using smooth methods to optimize linear svm, the idea of smoothing svm loss
become relevant.

The paper also mentions kernel svm using the same idea. In place of full
kernel, we can use random kitchen sink.

http://research.cs.wisc.edu/dmi/svm/ssvm/

I will go through Yuhao's work as well.

Thanks.
Deb


On Dec 16, 2017 6:35 PM, "Weichen Xu"  wrote:

Hi Deb,

Which library or paper do you find to use this loss function in SVM ?

But I prefer the implementation in LIBLINEAR which use coordinate descent
optimizer.

Thanks.

On Sun, Dec 17, 2017 at 6:52 AM, Yanbo Liang  wrote:

> Hello Deb,
>
> To optimize non-smooth function on LBFGS really should be considered
> carefully.
> Is there any literature that proves changing max to soft-max can behave
> well?
> I’m more than happy to see some benchmarks if you can have.
>
> + Yuhao, who did similar effort in this PR: https://github.com/apache/
> spark/pull/17862
>
> Regards
> Yanbo
>
> On Dec 13, 2017, at 12:20 AM, Debasish Das 
> wrote:
>
> Hi,
>
> I looked into the LinearSVC flow and found the gradient for hinge as
> follows:
>
> Our loss function with {0, 1} labels is max(0, 1 - (2y - 1) (f_w(x)))
> Therefore the gradient is -(2y - 1)*x
>
> max is a non-smooth function.
>
> Did we try using ReLu/Softmax function and use that to smooth the hinge
> loss ?
>
> Loss function will change to SoftMax(0, 1 - (2y-1) (f_w(x)))
>
> Since this function is smooth, gradient will be well defined and
> LBFGS/OWLQN should behave well.
>
> Please let me know if this has been tried already. If not I can run some
> benchmarks.
>
> We have soft-max in multinomial regression and can be reused for LinearSVC
> flow.
>
> Thanks.
> Deb
>
>
>

Re: Hinge Gradient

[Weichen Xu]

Hi Deb,

Which library or paper do you find to use this loss function in SVM ?

But I prefer the implementation in LIBLINEAR which use coordinate descent
optimizer.

Thanks.

On Sun, Dec 17, 2017 at 6:52 AM, Yanbo Liang  wrote:

> Hello Deb,
>
> To optimize non-smooth function on LBFGS really should be considered
> carefully.
> Is there any literature that proves changing max to soft-max can behave
> well?
> I’m more than happy to see some benchmarks if you can have.
>
> + Yuhao, who did similar effort in this PR: https://github.com/apache/
> spark/pull/17862
>
> Regards
> Yanbo
>
> On Dec 13, 2017, at 12:20 AM, Debasish Das 
> wrote:
>
> Hi,
>
> I looked into the LinearSVC flow and found the gradient for hinge as
> follows:
>
> Our loss function with {0, 1} labels is max(0, 1 - (2y - 1) (f_w(x)))
> Therefore the gradient is -(2y - 1)*x
>
> max is a non-smooth function.
>
> Did we try using ReLu/Softmax function and use that to smooth the hinge
> loss ?
>
> Loss function will change to SoftMax(0, 1 - (2y-1) (f_w(x)))
>
> Since this function is smooth, gradient will be well defined and
> LBFGS/OWLQN should behave well.
>
> Please let me know if this has been tried already. If not I can run some
> benchmarks.
>
> We have soft-max in multinomial regression and can be reused for LinearSVC
> flow.
>
> Thanks.
> Deb
>
>
>

Re: Hinge Gradient

[Yanbo Liang]

Hello Deb,

To optimize non-smooth function on LBFGS really should be considered carefully.
Is there any literature that proves changing max to soft-max can behave well?
I’m more than happy to see some benchmarks if you can have.

+ Yuhao, who did similar effort in this PR: 
https://github.com/apache/spark/pull/17862 


Regards
Yanbo   

> On Dec 13, 2017, at 12:20 AM, Debasish Das  wrote:
> 
> Hi,
> 
> I looked into the LinearSVC flow and found the gradient for hinge as follows:
> 
> Our loss function with {0, 1} labels is max(0, 1 - (2y - 1) (f_w(x)))
> Therefore the gradient is -(2y - 1)*x
> 
> max is a non-smooth function.
> 
> Did we try using ReLu/Softmax function and use that to smooth the hinge loss ?
> 
> Loss function will change to SoftMax(0, 1 - (2y-1) (f_w(x)))
> 
> Since this function is smooth, gradient will be well defined and LBFGS/OWLQN 
> should behave well. 
> 
> Please let me know if this has been tried already. If not I can run some 
> benchmarks.
> 
> We have soft-max in multinomial regression and can be reused for LinearSVC 
> flow.
> 
> Thanks.
> Deb