LaplacianInferenceMethodWithLBFGS.h

/*
 * Copyright (c) The Shogun Machine Learning Toolbox
 * Written (w) 2014 Wu Lin
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright notice, this
 *    list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * The views and conclusions contained in the software and documentation are those
 * of the authors and should not be interpreted as representing official policies,
 * either expressed or implied, of the Shogun Development Team.
 *
 * Code adapted from Gaussian Process Machine Learning Toolbox
 * http://www.gaussianprocess.org/gpml/code/matlab/doc/
 */
#ifndef CLAPLACIANINFERENCEMETHODWITHLBFGS_H_
#define CLAPLACIANINFERENCEMETHODWITHLBFGS_H_

#include <shogun/lib/config.h>

#ifdef HAVE_EIGEN3

#include <shogun/machine/gp/LaplacianInferenceMethod.h>
#include <shogun/mathematics/eigen3.h>
#include <shogun/optimization/lbfgs/lbfgs.h>


namespace shogun
{

/** @brief The Laplace approximation inference method with LBFGS class.
 *
 * This inference method approximates the posterior likelihood function by using
 * Laplace's method. Here, we compute a Gaussian approximation to the posterior
 * via a Taylor expansion around the maximum of the posterior likelihood
 * function. We use the Limited-memory BFGS method to obtain the maximum of likelihood. 
 * Note that due to the Laplace approximation, the time complexity of the class still is O(n^3), 
 * where n is the number of training data points. 
 * However, in the optimization step we use L-BFGS method, which of the time complexity
 * is O(n*m) to replace the Newton method, which of the time complexity is O(n^3). 
 * Here L-BFGS only uses the last m (m<<n) function/gradient pairs to find the optimal pointer
 *
 * For more details, see Nocedal, Jorge, and Stephen J. Wright. 
 * "Numerical Optimization 2nd." (2006), Pages 177-180. 
 *
 * This specific implementation was based on the idea 
 * from Murphy, Kevin P. "Machine learning: a probabilistic perspective." (2012), Pages 251-252.
 */
class CLaplacianInferenceMethodWithLBFGS: public CLaplacianInferenceMethod
{
public:
	/* default constructor */
	CLaplacianInferenceMethodWithLBFGS();

	/* constructor
	 *
	 * @param kernel covariance function
	 * @param features features to use in inference
	 * @param mean mean function
	 * @param labels labels of the features
	 * @param model Likelihood model to use
	 */
	CLaplacianInferenceMethodWithLBFGS(CKernel* kernel,
			CFeatures* features,
			CMeanFunction* mean,
			CLabels* labels,
			CLikelihoodModel* model);

	virtual ~CLaplacianInferenceMethodWithLBFGS();

	/* returns the name of the inference method
	 *
	 * @return name LaplacianWithLBFGS
	 */
	virtual const char* get_name() const
	{return "LaplacianInferenceMethodWithLBFGS";}

	/* set L-BFGS parameters
	 * For details please see shogun/optimization/lbfgs/lbfgs.h
	 * @param m The number of corrections to approximate the inverse hessian matrix. 
	 * Default value is 100.
	 * @param max_linesearch The maximum number of trials to do line search for each L-BFGS update. 
	 * Default value is 1000.
	 * @param linesearch The line search algorithm. 
	 * Default value is using the Morethuente line search
	 * @param max_iterations The maximum number of iterations for L-BFGS update. 
	 * Default value is 1000.
	 * @param delta Delta for convergence test based on the change of function value.
	 * Default value is 0.  
	 * @param past Distance for delta-based convergence test.
	 * Default value is 0. 
	 * @param epsilon Epsilon for convergence test based on the change of gradient.
	 * Default value is 1e-5
	 * @param enable_newton_if_fail if LBFGS optimizer fails, should we use Newton method.
	 * Default value is true.  
	 * @param min_step The minimum step of the line search.
	 * The default value is 1e-20
	 * @param max_step The maximum step of the line search.
	 * The default value is 1e+20
	 * @param ftol A parameter used in Armijo condition.
	 * Default value is 1e-4
	 * @param wolfe A parameter used in curvature condition.
	 * Default value is 0.9
	 * @param gtol A parameter used in Morethuente linesearch to control the accuracy.
	 * Default value is 0.9
	 * @param xtol The machine precision for floating-point values.
	 * Default value is 1e-16.
	 * @param orthantwise_c Coeefficient for the L1 norm of variables.
	 * This parameter should be set to zero for standard minimization problems.
	 * Setting this parameter to a positive value activates 
	 * Orthant-Wise Limited-memory Quasi-Newton (OWL-QN) method. Default value is 0.
	 * @param orthantwise_start Start index for computing L1 norm of the variables.
	 * This parameter is valid only for OWL-QN method. Default value is 0.
	 * @param orthantwise_end End index for computing L1 norm of the variables.
	 * Default value is 1.
	 */
	virtual void set_lbfgs_parameters(int m = 100,
			int max_linesearch = 1000,
			int linesearch = LBFGS_LINESEARCH_DEFAULT,
			int max_iterations = 1000,
			float64_t delta = 0.0,
			int past = 0,
			float64_t epsilon = 1e-5,
			bool enable_newton_if_fail = true,
			float64_t min_step = 1e-20,
			float64_t max_step = 1e+20,
			float64_t ftol = 1e-4,
			float64_t wolfe = 0.9,
			float64_t gtol = 0.9,
			float64_t xtol = 1e-16,
			float64_t orthantwise_c = 0.0,
			int orthantwise_start = 0,
			int orthantwise_end = 1);


protected:
	/* update alpha using the LBFGS method*/
	virtual void update_alpha();

private:
	/* a parameter used to compute function value and gradient for LBFGS update*/
	SGVector<float64_t> * m_mean_f;

	/* should we enable the original Newton method
	 * if the L-BFGS method fails
	 * */
	bool m_enable_newton_if_fail;

	/* The number of corrections to approximate the inverse hessian matrix.*/
	int m_m;

	/* The maximum number of trials to do line search for each L-BFGS update.*/
	int m_max_linesearch;

	/* The line search algorithm.*/
	int m_linesearch;

	/* The maximum number of iterations for L-BFGS update.*/
	int m_max_iterations;

	/* Delta for convergence test based on the change of function value.*/
	float64_t m_delta;

	/* Distance for delta-based convergence test.*/
	int m_past;

	/* Epsilon for convergence test based on the change of gradient.*/
	float64_t m_epsilon;

	/* The minimum step of the line search.*/
	float64_t m_min_step;

	/* The maximum step of the line search.*/
	float64_t m_max_step;

	/* A parameter used in Armijo condition.*/
	float64_t m_ftol;

	/* A parameter used in curvature condition.*/
	float64_t m_wolfe;

	/* A parameter used in Morethuente linesearch to control the accuracy.*/
	float64_t m_gtol;

	/* The machine precision for floating-point values.*/
	float64_t m_xtol;

	/* Coeefficient for the L1 norm of variables.*/
	float64_t m_orthantwise_c;

	/* Start index for computing L1 norm of the variables.*/
	int m_orthantwise_start;

	/* End index for computing L1 norm of the variables.*/
	int m_orthantwise_end;

	void init();

	/* helper function is passed to the LBFGS API
	 * Note that this function should be static and
	 * private.
	 * */
	static float64_t evaluate(void *obj,
			const float64_t *alpha,
			float64_t *gradient,
			const int dim,
			const float64_t step);

	/* compute the gradient given the current alpha*/
	void get_gradient_wrt_alpha(Eigen::Map<Eigen::VectorXd>* alpha,
			Eigen::Map<Eigen::VectorXd>* gradient);

	/* compute the function value given the current alpha*/
	void get_psi_wrt_alpha(Eigen::Map<Eigen::VectorXd>* alpha,
			float64_t* psi);
};

} /* namespace shogun */
#endif /* HAVE_EIGEN3 */
#endif /* CLAPLACIANINFERENCEMETHODWITHLBFGS_H_ */