text: /*
   * 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
   * https://github.com/emtiyaz/VariationalApproxExample
   * and the reference paper is
   * Marlin, Benjamin M., Mohammad Emtiyaz Khan, and Kevin P. Murphy.
   * "Piecewise Bounds for Estimating Bernoulli-Logistic Latent Gaussian Models." ICML. 2011.
   */
  
  #ifndef _LOGITVGPIECEWISEBOUNDLIKELIHOOD_H_
  #define _LOGITVGPIECEWISEBOUNDLIKELIHOOD_H_
  
  #include <shogun/lib/config.h>
  
  
  #include <shogun/machine/gp/LogitLikelihood.h>
  #include <shogun/machine/gp/VariationalGaussianLikelihood.h>
  
  namespace shogun
  {
  /** @brief Class that models Logit likelihood and
   * uses variational piecewise bound to approximate
   * the following variational expection of log likelihood
   * \f[
   * \sum_{{i=1}^n}{E_{q(f_i|{\mu}_i,{\sigma}^2_i)}[logP(y_i|f_i)]}
   * \f] where
   * \f[
   * p(y_i|f_i) = \frac{exp(y_i*f_i)}{1+exp(f_i)}, y_i \in \{0,1\}
   * \f]
   *
   * The memory requirement for this class is O(n*m), where
   * n is the size of sample, which is the size of mu or sigma2 passed in set_distribution
   * m is the size of the pre-defined bound, which is the num_rows of bound passed in set_bound
   * (In the reference Matlab code, m is 20)
   */
  class CLogitVGPiecewiseBoundLikelihood : public CVariationalGaussianLikelihood
  {
  public:
  	CLogitVGPiecewiseBoundLikelihood();
  
  	virtual ~CLogitVGPiecewiseBoundLikelihood();
  
  	/** returns the name of the likelihood model
  	 *
  	 * @return name LogitVGPiecewiseBoundLikelihood
  	 */
  	virtual const char* get_name() const { return "LogitVGPiecewiseBoundLikelihood"; }
  
  	/** set the variational piecewise bound for logit likelihood
  	 *
  	 *  @param bound variational piecewise bound
  	 */
  	virtual void set_variational_bound(SGMatrix<float64_t> bound);
  
  	/** set the variational normal distribution given data and parameters
  	 *
  	 * @param mu mean of the variational normal distribution
  	 * @param s2 variance of the variational normal distribution
  	 * @param lab labels/data used
  	 * @return true if variational parameters are valid
  	 *
  	 */
  	virtual bool set_variational_distribution(SGVector<float64_t> mu, SGVector<float64_t> s2, const CLabels* lab);
  
  	/** returns the expection of the logarithm of a logit distribution
  	 * wrt the variational distribution using piecewise bound
  	 *
  	 * For each sample i, using the piecewise bound to
  	 * approximate \f[
  	 * E_{q(f_i|{\mu}_i,{\sigma}^2_i)}[logP(y_i|f_i)]
  	 * \f] given mu_i and sigma2_i
  	 *
  	 * @return expection
  	 */
  	virtual SGVector<float64_t> get_variational_expection();
  
  	/** get derivative of the variational expection of log LogitLikelihood
  	 * using the piecewise bound with respect to given parameter
  	 *
  	 * compute the derivative of \f[
  	 * E_{q(f_i|{\mu}_i,{\sigma}^2_i)}[logP(y_i|f_i)]
  	 * \f] given mu_i and sigma2_i with repect to param using the piecewise bound
  	 *
  	 * @param param parameter(mu or sigma2)
  	 *
  	 * @return derivative
  	 */
  	virtual SGVector<float64_t> get_variational_first_derivative(const TParameter* param) const;
  
  	/** return whether likelihood function supports
  	 * computing the derivative wrt hyperparameter
  	 * Note that variational parameters are NOT considered as hyperparameters
  	 *
  	 * @return boolean
  	 */
  	virtual bool supports_derivative_wrt_hyperparameter() const { return false; }
  
  
  	/** get derivative of log likelihood \f$log(p(y|f))\f$ with respect to given
  	 * hyperparameter
  	 * Note that variational parameters are NOT considered as hyperparameters
  	 *
  	 * @param param parameter
  	 *
  	 * @return derivative
  	 */
  	virtual SGVector<float64_t> get_first_derivative_wrt_hyperparameter(const TParameter* param) const;
  
  	/** initialize the default bound for this class */
  	void set_default_variational_bound();
  
  protected:
  
  	/** The function used to initialize m_likelihood*/
  	virtual void init_likelihood();
  
  private:
  	/** initialize private data members for this class */
  	void init();
  
  	/** compute common variables later used in get_variational_expection
  	 * and get_variational_first_derivative.
  	 * Note that this method will automatically be called when set_variational_distribution is called
  	 */
  	void precompute();
  
  	/** Variational piecewise bound for logit likelihood */
  	SGMatrix<float64_t> m_bound;
  
  	/** The pdf given the lower range and parameters(mu and variance) */
  	SGMatrix<float64_t> m_pl;
  
  	/** The pdf given the higher range and parameters(mu and variance) */
  	SGMatrix<float64_t> m_ph;
  
  	/** The CDF difference between the lower and higher range given the parameters(mu and variance) */
  	SGMatrix<float64_t> m_cdf_diff;
  
  	/** The result of l^2 + sigma^2 */
  	SGMatrix<float64_t> m_l2_plus_s2;
  
  	/** The result of h^2 + sigma^2 */
  	SGMatrix<float64_t> m_h2_plus_s2;
  
  	/** The result of l*pdf(l_norm)-h*pdf(h_norm) */
  	SGMatrix<float64_t> m_weighted_pdf_diff;
  };
  }
  #endif /* _LOGITVGPIECEWISEBOUNDLIKELIHOOD_H_ */
  