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autodiff gaussian width parameter #4782

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autodiff gaussian width parameter #4782

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0d13a9e
autodiff gaussian width parameter
gf712 Oct 23, 2019
e7f2e62
include only the necessary header
gf712 Oct 23, 2019
0b0de2e
moved var instantiation outside the loop
gf712 Oct 24, 2019
e9bced7
autodiff gaussian width parameter
gf712 Oct 23, 2019
5815a3d
include only the necessary header
gf712 Oct 23, 2019
a35cf20
use eigen instead of stanmath
gf712 Nov 5, 2019
bdcebbf
generic kernel function for AD and kernel computation
gf712 Nov 6, 2019
bb85e1b
make expression template depend on class member
gf712 Nov 6, 2019
f94af02
fix race condition
gf712 Nov 6, 2019
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37 changes: 31 additions & 6 deletions src/shogun/kernel/GaussianKernel.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -12,6 +12,7 @@
#include <shogun/distance/EuclideanDistance.h>
#include <shogun/mathematics/Math.h>


using namespace shogun;

CGaussianKernel::CGaussianKernel() : CShiftInvariantKernel()
Expand Down Expand Up @@ -86,23 +87,42 @@ void CGaussianKernel::set_width(float64_t w)
{
require(w>0, "width ({}) must be positive",w);
m_log_width = std::log(w / 2.0) / 2.0;
m_eigen_log_width.value() = m_log_width;
}

auto CGaussianKernel::kernel_function(int32_t idx_a, int32_t idx_b)
{
// this could be written as Eigen::Matrix<float64_t, n_differentiable_params, 1>;
m_eigen_log_width.value() = m_log_width;

// this could be written as
// eigen_log_width.derivatives() = EigenScalar::Unit(n_differentiable_params, i);
// where i is the idx of the adjoint
m_eigen_log_width.derivatives() = Eigen::VectorXd::Unit(1,0);
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This is the derivative of the log width wrt the log width itself?

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this the derivative of the kernel function wrt to the log with, df/dw. It gives the same result as the manual derivative that was in the loop before in get_parameter_gradient

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Then kernel function should be equal to the log width (for the derivative to be one), no?

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what do you mean? The derivative is set to one, so that when you apply the chain rule, you get it wrt to this parameter, i.e. you initialise the dependent variable. Like shown here https://eigen.tuxfamily.org/bz_attachmentbase/attachment.cgi?id=395. The same happens in stan gradient function: https://github.com/stan-dev/math/blob/b42294a57318a27d2b6723b96a0b620485ba83e0/stan/math/rev/core/grad.hpp#L39


auto el = CShiftInvariantKernel::distance(idx_a, idx_b);
return exp(-el / (exp(m_eigen_log_width * 2.0) * 2.0));
}

SGMatrix<float64_t> CGaussianKernel::get_parameter_gradient(const TParameter* param, index_t index)
{
using std::exp;

require(lhs, "Left hand side features must be set!");
require(rhs, "Rightt hand side features must be set!");
require(rhs, "Right hand side features must be set!");

if (!strcmp(param->m_name, "log_width"))
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so I guess a next step could be to start thinking about getting rid of this explicit code, and rather automatically offer this derivative through registering something in the ctors ....

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I think for that we should maybe have a base class for classes that have parameters that we can take the derivative wrt. This class registers the gradient parameters in some vector and then we can get the index from there.
Basically when we do watch_param(...) this would add the variable in such a vector if it has the flag GRADIENT

{
SGMatrix<float64_t> derivative=SGMatrix<float64_t>(num_lhs, num_rhs);

for (int k=0; k<num_rhs; k++)
{
#pragma omp parallel for
// #pragma omp parallel for
for (int j=0; j<num_lhs; j++)
{
float64_t element=distance(j, k);
derivative(j, k) = std::exp(-element) * element * 2.0;
auto kernel = kernel_function(j, k);
// 0 is the index of the width parameter
derivative(j, k) = kernel.derivatives()(0);
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this seems pretty automatable to me (at least say for scalar valued kernels with scalar parameters)

}
}
return derivative;
Expand All @@ -116,9 +136,14 @@ SGMatrix<float64_t> CGaussianKernel::get_parameter_gradient(const TParameter* pa

float64_t CGaussianKernel::compute(int32_t idx_a, int32_t idx_b)
{
float64_t result=distance(idx_a, idx_b);
return std::exp(-result);
float64_t result;
#pragma omp critical
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@karlnapf the issue now is that this is not thread safe anymore

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because i assign the value of m_eigen_log_width in kernel_function. Basically would have to do the assignment outside the function, but if a user does ->put("log_width", ..) there is no way of tracking this.. hence the gradient dependent parameters would have to be added to the parameter framework somehow. Or AutoDiffScalar would have a reference instead of a value..

{
auto kernel = kernel_function(idx_a, idx_b);
result = kernel.value();
}
return result;
}

void CGaussianKernel::load_serializable_post() noexcept(false)
{
Expand Down
12 changes: 12 additions & 0 deletions src/shogun/kernel/GaussianKernel.h
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Original file line number Diff line number Diff line change
Expand Up @@ -11,6 +11,8 @@

#include <shogun/lib/config.h>
#include <shogun/kernel/ShiftInvariantKernel.h>
#include <shogun/mathematics/eigen3.h>
#include <unsupported/Eigen/AutoDiff>

namespace shogun
{
Expand Down Expand Up @@ -123,6 +125,15 @@ class CGaussianKernel: public CShiftInvariantKernel
return std::exp(m_log_width * 2.0) * 2.0;
}

#ifndef SWIG
/**
* Returns a lazily evaluated Eigen expression template
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If it is already evaluated, then it won't be lazily evaluated (at least not from the point of view of deferring evaluation after this method has been executed).

What about without the lazily evaluated part, or refactoring to "to be lazily evaluated" if you really want to keep that part.

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yes, good point, i'll change that

* that tracks the gradient of differentiable hyperparameters
*
* @return expression template of kernel function
*/
auto kernel_function(int32_t idx_a, int32_t idx_b);
#endif
/** return derivative with respect to specified parameter
*
* @param param the parameter
Expand Down Expand Up @@ -174,6 +185,7 @@ class CGaussianKernel: public CShiftInvariantKernel
protected:
/** width */
float64_t m_log_width;
Eigen::AutoDiffScalar<Eigen::VectorXd> m_eigen_log_width;
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this idea is actually not too bad: just make the parameters one can diff wrt class members. They just wrap the other member if I understand correctly? These two getting out of sync is he problem you mean with the user putting a parameter? Callback stuff might help? Should be possible to automate something for that or?

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@karlnapf karlnapf Nov 7, 2019 •
edited

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a more consequent version of this would be to make all model parameters live in eigen, and all the "model" function simply returning composed versions of those... but i guess that goes too far ;)

};

}
Expand Down