diff --git a/bayesnet/ensembles/BoostA2DE.cc b/bayesnet/ensembles/BoostA2DE.cc
index 209173b..4738358 100644
--- a/bayesnet/ensembles/BoostA2DE.cc
+++ b/bayesnet/ensembles/BoostA2DE.cc
@@ -155,7 +155,7 @@ namespace bayesnet {
             }
         }
         if (pairSelection.size() > 0) {
-            notes.push_back("Used pairs not used in train: " + std::to_string(pairSelection.size()));
+            notes.push_back("Pairs not used in train: " + std::to_string(pairSelection.size()));
             status = WARNING;
         }
         notes.push_back("Number of models: " + std::to_string(n_models));
diff --git a/bayesnet/utils/BayesMetrics.cc b/bayesnet/utils/BayesMetrics.cc
index 85645c7..b4b12cc 100644
--- a/bayesnet/utils/BayesMetrics.cc
+++ b/bayesnet/utils/BayesMetrics.cc
@@ -198,24 +198,20 @@ namespace bayesnet {
         }
         return entropyValue;
     }
-    // H(Y|X,C) = sum_{x in X, c in C} p(x,c) H(Y|X=x,C=c)
+    // H(X|Y,C) = sum_{y in Y, c in C} p(x,c) H(X|Y=y,C=c)
     double Metrics::conditionalEntropy(const torch::Tensor& firstFeature, const torch::Tensor& secondFeature, const torch::Tensor& labels, const torch::Tensor& weights)
     {
         // Ensure the tensors are of the same length
         assert(firstFeature.size(0) == secondFeature.size(0) && firstFeature.size(0) == labels.size(0) && firstFeature.size(0) == weights.size(0));
-
         // Convert tensors to vectors for easier processing
         auto firstFeatureData = firstFeature.accessor<int, 1>();
         auto secondFeatureData = secondFeature.accessor<int, 1>();
         auto labelsData = labels.accessor<int, 1>();
         auto weightsData = weights.accessor<double, 1>();
-
         int numSamples = firstFeature.size(0);
-
         // Maps for joint and marginal probabilities
         std::map<std::tuple<int, int, int>, double> jointCount;
         std::map<std::tuple<int, int>, double> marginalCount;
-
         // Compute joint and marginal counts
         for (int i = 0; i < numSamples; ++i) {
             auto keyJoint = std::make_tuple(firstFeatureData[i], labelsData[i], secondFeatureData[i]);
@@ -224,34 +220,29 @@ namespace bayesnet {
             jointCount[keyJoint] += weightsData[i];
             marginalCount[keyMarginal] += weightsData[i];
         }
-
         // Total weight sum
         double totalWeight = torch::sum(weights).item<double>();
         if (totalWeight == 0)
             return 0;
-
         // Compute the conditional entropy
         double conditionalEntropy = 0.0;
-
         for (const auto& [keyJoint, jointFreq] : jointCount) {
             auto [x, c, y] = keyJoint;
             auto keyMarginal = std::make_tuple(x, c);
-
             //double p_xc = marginalCount[keyMarginal] / totalWeight;
             double p_y_given_xc = jointFreq / marginalCount[keyMarginal];
-
             if (p_y_given_xc > 0) {
                 conditionalEntropy -= (jointFreq / totalWeight) * std::log(p_y_given_xc);
             }
         }
         return conditionalEntropy;
     }
-    // I(X;Y) = H(Y) - H(Y|X)
+    // I(X;Y) = H(Y) - H(Y|X) ; I(X;Y) >= 0
     double Metrics::mutualInformation(const torch::Tensor& firstFeature, const torch::Tensor& secondFeature, const torch::Tensor& weights)
     {
-        return entropy(firstFeature, weights) - conditionalEntropy(firstFeature, secondFeature, weights);
+        return std::max(entropy(firstFeature, weights) - conditionalEntropy(firstFeature, secondFeature, weights), 0.0);
     }
-    // I(X;Y|C) = H(Y|C) - H(Y|X,C)
+    // I(X;Y|C) = H(X|C) - H(X|Y,C) >= 0
     double Metrics::conditionalMutualInformation(const torch::Tensor& firstFeature, const torch::Tensor& secondFeature, const torch::Tensor& labels, const torch::Tensor& weights)
     {
         return std::max(conditionalEntropy(firstFeature, labels, weights) - conditionalEntropy(firstFeature, secondFeature, labels, weights), 0.0);
diff --git a/tests/TestBayesMetrics.cc b/tests/TestBayesMetrics.cc
index 755a4a0..f2eeebf 100644
--- a/tests/TestBayesMetrics.cc
+++ b/tests/TestBayesMetrics.cc
@@ -11,7 +11,6 @@
 #include "TestUtils.h"
 #include "Timer.h"
 
-
 TEST_CASE("Metrics Test", "[Metrics]")
 {
     std::string file_name = GENERATE("glass", "iris", "ecoli", "diabetes");
@@ -28,8 +27,8 @@ TEST_CASE("Metrics Test", "[Metrics]")
         {"diabetes", 0.0345470614}
     };
     map<pair<std::string, int>, std::vector<pair<int, int>>> resultsMST = {
-        { {"glass", 0}, { {0, 6}, {0, 5}, {0, 3}, {5, 1}, {5, 8}, {5, 4}, {6, 2}, {6, 7} } },
-        { {"glass", 1}, { {1, 5}, {5, 0}, {5, 8}, {5, 4}, {0, 6}, {0, 3}, {6, 2}, {6, 7} } },
+        { {"glass", 0}, { {0, 6}, {0, 5}, {0, 3}, {3, 4}, {5, 1}, {5, 8}, {6, 2}, {6, 7} } },
+        { {"glass", 1}, { {1, 5}, {5, 0}, {5, 8}, {0, 6}, {0, 3}, {3, 4}, {6, 2}, {6, 7} } },
         { {"iris", 0}, { {0, 1}, {0, 2}, {1, 3} } },
         { {"iris", 1}, { {1, 0}, {1, 3}, {0, 2} } },
         { {"ecoli", 0}, { {0, 1}, {0, 2}, {1, 5}, {1, 3}, {5, 6}, {5, 4} } },
diff --git a/tests/TestBoostA2DE.cc b/tests/TestBoostA2DE.cc
index b0f6b4a..b841bc3 100644
--- a/tests/TestBoostA2DE.cc
+++ b/tests/TestBoostA2DE.cc
@@ -22,7 +22,7 @@ TEST_CASE("Build basic model", "[BoostA2DE]")
     REQUIRE(clf.getNumberOfEdges() == 684);
     REQUIRE(clf.getNotes().size() == 3);
     REQUIRE(clf.getNotes()[0] == "Convergence threshold reached & 15 models eliminated");
-    REQUIRE(clf.getNotes()[1] == "Used pairs not used in train: 20");
+    REQUIRE(clf.getNotes()[1] == "Pairs not used in train: 20");
     REQUIRE(clf.getNotes()[2] == "Number of models: 38");
     auto score = clf.score(raw.Xv, raw.yv);
     REQUIRE(score == Catch::Approx(0.919271).epsilon(raw.epsilon));