// 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_ > classstructural_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 !*/voidset_epsilon( scalar_type eps ); /*! requires - eps > 0 ensures - #get_epsilon() == eps !*/ const scalar_typeget_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 its optimal value". !*/ scalar_typeget_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. !*/voidset_cache_based_epsilon( scalar_type eps ); /*! requires - eps > 0 ensures - #get_cache_based_epsilon() == eps !*/voidset_max_iterations(unsignedlongmax_iter ); /*! ensures - #get_max_iterations() == max_iter !*/unsignedlongget_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. !*/voidset_max_cache_size(unsignedlongmax_size ); /*! ensures - #get_max_cache_size() == max_size !*/unsignedlongget_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. !*/voidadd_nuclear_norm_regularizer(longfirst_dimension,longrows,longcols,doubleregularization_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 !*/unsignedlongnum_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. !*/voidclear_nuclear_norm_regularizers( ); /*! ensures - #num_nuclear_norm_regularizers() == 0 !*/voidbe_verbose( ); /*! ensures - This object will print status messages to standard out so that a user can observe the progress of the algorithm. !*/voidbe_quiet( ); /*! ensures - this object will not print anything to standard out !*/ scalar_typeget_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. !*/voidset_c( scalar_type C ); /*! requires - C > 0 ensures - #get_c() == C !*/ // -------------------------------- // User supplied routines // -------------------------------- virtuallongget_num_dimensions( ) const = 0; /*! ensures - returns the dimensionality of a joint feature vector !*/ virtuallongget_num_samples( ) const = 0; /*! ensures - returns the number of training samples in this problem. !*/ virtualvoidget_truth_joint_feature_vector(longidx, 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.) !*/ virtualvoidseparation_oracle( constlongidx, 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_