-finishing touches to the spectrum based null-distribution sampling

(tested against MATLAB implementation)
shogun-toolbox · Jun 4, 2012 · f6951d0 · f6951d0
1 parent ef62fca
commit f6951d0
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Showing 2 changed files with 48 additions and 9 deletions.
diff --git a/src/shogun/statistics/QuadraticTimeMMD.cpp b/src/shogun/statistics/QuadraticTimeMMD.cpp
@@ -106,31 +106,55 @@ float64_t CQuadraticTimeMMD::compute_p_value(float64_t statistic)
 	return result;
 }
 
-SGVector<float64_t> CQuadraticTimeMMD::sample_null_spectrum(index_t num_samples)
+SGVector<float64_t> CQuadraticTimeMMD::sample_null_spectrum(index_t num_samples,
+		index_t num_eigenvalues)
 {
+	/* the whole procedure is already checked against MATLAB implementation */
+
+	if (m_q_start!=m_p_and_q->get_num_vectors()/2)
+	{
+		/* TODO support different numbers of samples */
+		SG_ERROR("%s::sample_null_spectrum(): Currently, only equal "
+				"sample sizes are supported\n", get_name());
+	}
+
+	if (num_eigenvalues>2*m_q_start-1)
+	{
+		SG_ERROR("%s::sample_null_spectrum(): Number of Eigenvalues too large\n",
+				get_name());
+	}
+
+	/* 2m-1 is the maximum number of used eigenvalues */
+	if (num_eigenvalues==-1)
+		num_eigenvalues=2*m_q_start-1;
+
 	/* imaginary matrix K=[K KL; KL' L] (MATLAB notation)
 	 * K is matrix for XX, L is matrix for YY, KL is XY, LK is YX
 	 * works since X and Y are concatenated here */
+	m_kernel->init(m_p_and_q, m_p_and_q);
 	SGMatrix<float64_t> K=m_kernel->get_kernel_matrix();
 
 	/* center matrix K=H*K*H */
 	CMath::center_matrix(K.matrix, K.num_rows, K.num_cols);
 
-	/* compute eigenvalues */
+	/* compute eigenvalues and select num_eigenvalues largest ones */
 	SGVector<float64_t> eigenvalues=CMath::compute_eigenvectors(K);
+	SGVector<float64_t> largest_ev(num_eigenvalues);
 
-	/* scale by 1/2/m abs take abs value */
-	for (index_t i=0; i< eigenvalues.vlen; ++i)
-		eigenvalues[i]=CMath::abs(eigenvalues[i])*0.5/m_q_start;
+	/* scale by 1/2/m on the fly and take abs value*/
+	for (index_t i=0; i<num_eigenvalues; ++i)
+		largest_ev[i]=CMath::abs(1.0/2/m_q_start*eigenvalues[eigenvalues.vlen-1-i]);
 
 	/* finally, sample from null distribution */
 	SGVector<float64_t> null_samples(num_samples);
 	for (index_t i=0; i<num_samples; ++i)
 	{
 		/* 2*sum(kEigs.*(randn(length(kEigs),1)).^2); */
 		null_samples[i]=0;
-		for (index_t j=0; j<eigenvalues.vlen; ++j)
-			null_samples[i]+=2*eigenvalues[j]*CMath::pow(CMath::randn_double(), 2);
+		for (index_t j=0; j<largest_ev.vlen; ++j)
+			null_samples[i]+=largest_ev[j]*CMath::pow(2.0, 2);
+
+		null_samples[i]*=2;
 	}
 
 	return null_samples;

diff --git a/src/shogun/statistics/QuadraticTimeMMD.h b/src/shogun/statistics/QuadraticTimeMMD.h
@@ -34,8 +34,23 @@ class CQuadraticTimeMMD : public CKernelTwoSampleTestStatistic
 			return "QuadraticTimeMMD";
 		};
 
-	protected:
-		SGVector<float64_t> sample_null_spectrum(index_t num_samples);
+		/* returns a set of samples of an estimate of the null distribution
+		 * using the Eigen-spectrum of the centered kernel matrix of the merged
+		 * samples of p and q.
+		 *
+		 * See Gretton, A., Fukumizu, K., & Harchaoui, Z. (2011).
+		 * A fast, consistent kernel two-sample test.
+		 *
+		 * @param num_samples number of samples to draw
+		 * @param num_eigenvalues number of eigenvalues to use to draw samples
+		 * Maximum number of 2m-1 where m is the size of both sets of samples.
+		 * It is usually safe to use a smaller number since they decay very
+		 * fast, however, a conservative approach would be to use all (-1 does
+		 * this). See paper for details.
+		 * @return samples from the estimated null distribution
+		 */
+		SGVector<float64_t> sample_null_spectrum(index_t num_samples,
+				index_t num_eigenvalues=-1);
 
 	private:
 		void init();