// Copyright (C) 2011 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#undef DLIB_STRUCTURAL_SVM_PRObLEM_ABSTRACT_Hh_
#ifdef DLIB_STRUCTURAL_SVM_PRObLEM_ABSTRACT_Hh_
#include "../optimization/optimization_oca_abstract.h"
#include "sparse_vector_abstract.h"
#include "../matrix.h"
namespace dlib
{
// ----------------------------------------------------------------------------------------
template <
typename matrix_type_,
typename feature_vector_type_ = matrix_type_
>
class structural_svm_problem : public oca_problem<matrix_type_>
{
public:
/*!
REQUIREMENTS ON matrix_type_
- matrix_type_ == a dlib::matrix capable of storing column vectors
REQUIREMENTS ON feature_vector_type_
- feature_vector_type_ == a dlib::matrix capable of storing column vectors
or an unsorted sparse vector type as defined in dlib/svm/sparse_vector_abstract.h.
INITIAL VALUE
- get_epsilon() == 0.001
- get_max_iterations() == 10000
- get_max_cache_size() == 5
- get_c() == 1
- get_cache_based_epsilon() == std::numeric_limits<scalar_type>::infinity()
(I.e. the cache based epsilon feature is disabled)
- num_nuclear_norm_regularizers() == 0
- This object will not be verbose
WHAT THIS OBJECT REPRESENTS
This object is a tool for solving the optimization problem associated with
a structural support vector machine. A structural SVM is a supervised
machine learning method for learning to predict complex outputs. This is
contrasted with a binary classifier which makes only simple yes/no
predictions. A structural SVM, on the other hand, can learn to predict
complex outputs such as entire parse trees or DNA sequence alignments. To
do this, it learns a function F(x,y) which measures how well a particular
data sample x matches a label y. When used for prediction, the best label
for a new x is given by the y which maximizes F(x,y).
To use this object you inherit from it, provide implementations of its four
pure virtual functions, and then pass your object to the oca optimizer.
Also, you should only pass an instance of this object to the oca optimizer
once. That is, the act of using a structural_svm_problem instance with the
oca solver "uses" the structural_svm_problem instance. If you want to
solve the same problem multiple times then you must use a fresh instance of
your structural_svm_problem.
To define the optimization problem precisely, we first introduce some notation:
- let PSI(x,y) == the joint feature vector for input x and a label y.
- let F(x,y|w) == dot(w,PSI(x,y)).
- let LOSS(idx,y) == the loss incurred for predicting that the idx-th training
sample has a label of y. Note that LOSS() should always be >= 0 and should
become exactly 0 when y is the correct label for the idx-th sample.
- let x_i == the i-th training sample.
- let y_i == the correct label for the i-th training sample.
- The number of data samples is N.
Then the optimization problem solved using this object is the following:
Minimize: h(w) == 0.5*dot(w,w) + C*R(w)
Where R(w) == sum from i=1 to N: 1/N * sample_risk(i,w)
and sample_risk(i,w) == max over all Y: LOSS(i,Y) + F(x_i,Y|w) - F(x_i,y_i|w)
and C > 0
For an introduction to structured support vector machines you should consult
the following paper:
Predicting Structured Objects with Support Vector Machines by
Thorsten Joachims, Thomas Hofmann, Yisong Yue, and Chun-nam Yu
For a more detailed discussion of the particular algorithm implemented by this
object see the following paper:
T. Joachims, T. Finley, Chun-Nam Yu, Cutting-Plane Training of Structural SVMs,
Machine Learning, 77(1):27-59, 2009.
Note that this object is essentially a tool for solving the 1-Slack structural
SVM with margin-rescaling. Specifically, see Algorithm 3 in the above referenced
paper.
!*/
typedef matrix_type_ matrix_type;
typedef typename matrix_type::type scalar_type;
typedef feature_vector_type_ feature_vector_type;
structural_svm_problem (
);
/*!
ensures
- this object is properly initialized
!*/
void set_epsilon (
scalar_type eps
);
/*!
requires
- eps > 0
ensures
- #get_epsilon() == eps
!*/
const scalar_type get_epsilon (
) const;
/*!
ensures
- returns the error epsilon that determines when training should stop.
Smaller values may result in a more accurate solution but take longer
to execute. Specifically, the algorithm stops when the average sample
risk (i.e. R(w) as defined above) is within epsilon of its optimal value.
Also note that sample risk is an upper bound on a sample's loss. So
you can think of this epsilon value as saying "solve the optimization
problem until the average loss per sample is within epsilon of it's
optimal value".
!*/
scalar_type get_cache_based_epsilon (
) const;
/*!
ensures
- if (get_max_cache_size() != 0) then
- The solver will not stop when the average sample risk is within
get_epsilon() of its optimal value. Instead, it will keep running
but will run the optimizer completely on the cache until the average
sample risk is within #get_cache_based_epsilon() of its optimal
value. This means that it will perform this additional refinement in
the solution accuracy without making any additional calls to the
separation_oracle(). This is useful when using a nuclear norm
regularization term because it allows you to quickly solve the
optimization problem to a high precision, which in the case of a
nuclear norm regularized problem means that many of the learned
matrices will be low rank or very close to low rank due to the
nuclear norm regularizer. This may not happen without solving the
problem to a high accuracy or their ranks may be difficult to
determine, so the extra accuracy given by the cache based refinement
is very useful. Finally, note that we include the nuclear norm term
as part of the "risk" for the purposes of determining when to stop.
- else
- The value of #get_cache_based_epsilon() has no effect.
!*/
void set_cache_based_epsilon (
scalar_type eps
);
/*!
requires
- eps > 0
ensures
- #get_cache_based_epsilon() == eps
!*/
void set_max_iterations (
unsigned long max_iter
);
/*!
ensures
- #get_max_iterations() == max_iter
!*/
unsigned long get_max_iterations (
);
/*!
ensures
- returns the maximum number of iterations the SVM optimizer is allowed to
run before it is required to stop and return a result.
!*/
void set_max_cache_size (
unsigned long max_size
);
/*!
ensures
- #get_max_cache_size() == max_size
!*/
unsigned long get_max_cache_size (
) const;
/*!
ensures
- Returns the number of joint feature vectors per training sample kept in
the separation oracle cache. This cache is used to avoid unnecessary
calls to the user supplied separation_oracle() function. Note that a
value of 0 means that caching is not used at all. This is appropriate
if the separation oracle is cheap to evaluate.
!*/
void add_nuclear_norm_regularizer (
long first_dimension,
long rows,
long cols,
double regularization_strength
);
/*!
requires
- 0 <= first_dimension < get_num_dimensions()
- 0 <= rows
- 0 <= cols
- first_dimension+rows*cols <= get_num_dimensions()
- 0 < regularization_strength
ensures
- Adds a nuclear norm regularization term to the optimization problem
solved by this object. That is, instead of solving:
Minimize: h(w) == 0.5*dot(w,w) + C*R(w)
this object will solve:
Minimize: h(w) == 0.5*dot(w,w) + C*R(w) + regularization_strength*nuclear_norm_of(part of w)
where "part of w" is the part of w indicated by the arguments to this
function. In particular, the part of w included in the nuclear norm is
exactly the matrix reshape(rowm(w, range(first_dimension, first_dimension+rows*cols-1)), rows, cols).
Therefore, if you think of the w vector as being the concatenation of a
bunch of matrices then you can use multiple calls to add_nuclear_norm_regularizer()
to add nuclear norm regularization terms to any of the matrices packed into w.
- #num_nuclear_norm_regularizers() == num_nuclear_norm_regularizers() + 1
!*/
unsigned long num_nuclear_norm_regularizers (
) const;
/*!
ensures
- returns the number of nuclear norm regularizers that are currently a part
of this optimization problem. That is, returns the number of times
add_nuclear_norm_regularizer() has been called since the last call to
clear_nuclear_norm_regularizers() or object construction, whichever is
most recent.
!*/
void clear_nuclear_norm_regularizers (
);
/*!
ensures
- #num_nuclear_norm_regularizers() == 0
!*/
void be_verbose (
);
/*!
ensures
- This object will print status messages to standard out so that a
user can observe the progress of the algorithm.
!*/
void be_quiet(
);
/*!
ensures
- this object will not print anything to standard out
!*/
scalar_type get_c (
) const;
/*!
ensures
- returns the SVM regularization parameter. It is the parameter that
determines the trade off between trying to fit the training data
exactly or allowing more errors but hopefully improving the
generalization of the resulting classifier. Larger values encourage
exact fitting while smaller values of C may encourage better
generalization.
!*/
void set_c (
scalar_type C
);
/*!
requires
- C > 0
ensures
- #get_c() == C
!*/
// --------------------------------
// User supplied routines
// --------------------------------
virtual long get_num_dimensions (
) const = 0;
/*!
ensures
- returns the dimensionality of a joint feature vector
!*/
virtual long get_num_samples (
) const = 0;
/*!
ensures
- returns the number of training samples in this problem.
!*/
virtual void get_truth_joint_feature_vector (
long idx,
feature_vector_type& psi
) const = 0;
/*!
requires
- 0 <= idx < get_num_samples()
ensures
- #psi == PSI(x_idx, y_idx)
(i.e. the joint feature vector for the idx-th training sample its true label.)
!*/
virtual void separation_oracle (
const long idx,
const matrix_type& current_solution,
scalar_type& loss,
feature_vector_type& psi
) const = 0;
/*!
requires
- 0 <= idx < get_num_samples()
- current_solution.size() == get_num_dimensions()
ensures
- runs the separation oracle on the idx-th sample. We define this as follows:
- let X == the idx-th training sample.
- let PSI(X,y) == the joint feature vector for input X and an arbitrary label y.
- let F(X,y) == dot(current_solution,PSI(X,y)).
- let LOSS(idx,y) == the loss incurred for predicting that the idx-th sample
has a label of y. Note that LOSS() should always be >= 0 and should
become exactly 0 when y is the correct label for the idx-th sample.
Then the separation oracle finds a Y such that:
Y = argmax over all y: LOSS(idx,y) + F(X,y)
(i.e. It finds the label which maximizes the above expression.)
Finally, we can define the outputs of this function as:
- #loss == LOSS(idx,Y)
- #psi == PSI(X,Y)
!*/
};
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_STRUCTURAL_SVM_PRObLEM_ABSTRACT_Hh_