added kullback leibler for gaussian cases

2017-03-09 18:57:47 +01:00
parent 62087fe072
commit e48d3bafcd
9 changed files with 374 additions and 8 deletions
--- a/math/divergence/KullbackLeibler.h
+++ b/math/divergence/KullbackLeibler.h
@@ -0,0 +1,90 @@
+#ifndef KULLBACKLEIBLER_H
+#define KULLBACKLEIBLER_H
+
+#include "../distribution/Normal.h"
+#include "../distribution/NormalN.h"
+
+#include "../../Assertions.h"
+#include <string>
+
+namespace Divergence {
+
+    template <typename Scalar> class KullbackLeibler {
+
+        public:
+
+            /** Calculate the Kullback Leibler Distance for a univariate Gaussian distribution
+            *   Info: https://tgmstat.wordpress.com/2013/07/10/kullback-leibler-divergence/
+            */
+            static inline Scalar getUnivariateGauss(Distribution::Normal<Scalar> norm1, Distribution::Normal<Scalar> norm2){
+
+                auto sigma1Quad = norm1.getSigma() * norm1.getSigma();
+                auto sigma2Quad = norm2.getSigma() * norm2.getSigma();
+                auto mu12Quad = (norm1.getMu() - norm2.getMu()) * (norm1.getMu() - norm2.getMu());
+                auto log1 = std::log(norm1.getSigma());
+                auto log2 = std::log(norm2.getSigma());
+
+                // kl = log(sigma_2 / sigma_1) + ((sigma_1^2 + (mu_1 - mu_2)^2) / 2 * sigma_2^2) - 0.5
+                double klb = (log2 - log1) + ((sigma1Quad + mu12Quad)/(2.0 * sigma2Quad)) - 0.5;
+
+                //klb is always greater 0
+                if(klb < 0.0){
+                    Assert::doThrow("The Kullback Leibler Distance is < 0! Thats not possible");
+                }
+                return klb;
+            }
+
+            /** Calculate the Kullback Leibler Distance for a univariate Gaussian distribution symmetric*/
+            static inline Scalar getUnivariateGaussSymmetric(Distribution::Normal<Scalar> norm1, Distribution::Normal<Scalar> norm2){
+                return getUnivariateGauss(norm1, norm2) + getUnivariateGauss(norm2, norm1);
+            }
+
+            /** Calculate the Kullback Leibler Distance for a multivariate Gaussian distribution */
+            static inline Scalar getMultivariateGauss(Distribution::NormalDistributionN norm1, Distribution::NormalDistributionN norm2){
+
+                //both gaussian have the same dimension.
+                Assert::equal(norm1.getMu().rows(), norm2.getMu().rows(), "mean vectors do not have the same dimension");
+                Assert::equal(norm1.getSigma().rows(), norm2.getSigma().rows(), "cov matrices do not have the same dimension");
+                Assert::equal(norm1.getSigma().cols(), norm2.getSigma().cols(), "cov matrices do not have the same dimension");
+
+                //log
+                auto det1 = norm1.getSigma().determinant();
+                auto det2 = norm2.getSigma().determinant();
+                auto log1 = std::log(det1);
+                auto log2 = std::log(det2);
+
+                //trace
+                Eigen::MatrixXd toTrace(norm1.getSigma().rows(),norm1.getSigma().cols());
+                toTrace = norm2.getSigmaInv() * norm1.getSigma();
+                auto trace = toTrace.trace();
+
+                //transpose
+                Eigen::VectorXd toTranspose(norm1.getMu().rows());
+                toTranspose = norm2.getMu() - norm1.getMu();
+                auto transpose = toTranspose.transpose();
+
+                //rawdensity
+                auto rawDensity = transpose * norm2.getSigmaInv() * toTranspose;
+                auto dimension = norm1.getMu().rows();
+
+                //0.5 * ((log(det(cov_2)/det(cov_1)) + tr(cov_2^-1 cov_1) + (mu_2 - mu_1)^T * cov_2^-1 * (mu_2 - mu_1) - dimension)
+                double klb = 0.5 * ((log2 - log1) + trace + rawDensity - dimension);
+
+                //klb is always greater 0
+                if(klb < 0.0){
+                    Assert::doThrow("The Kullback Leibler Distance is < 0! Thats not possible");
+                }
+                return klb;
+            }
+
+             /** Calculate the Kullback Leibler Distance for a multivariate Gaussian distribution symmetric*/
+            static inline Scalar getMultivariateGaussSymmetric(Distribution::NormalDistributionN norm1, Distribution::NormalDistributionN norm2){
+                return getMultivariateGauss(norm1, norm2) + getMultivariateGauss(norm2, norm1);
+            }
+
+
+    };
+
+}
+
+#endif // KULLBACKLEIBLER_H