Added Adjusted R2

HISTORY.md

@@ -1,5 +1,7 @@
 ### mlpack ?.?.?
 ###### ????-??-??
+  * Add Adjusted R squared functionality to R2Score::Evaluate (#2624).
+
   * Added an implementation to Stratify Data (#2671).
 
   * Add `BUILD_DOCS` CMake option to control whether Doxygen documentation is

src/mlpack/core/cv/metrics/r2_score.hpp

@@ -42,12 +42,17 @@ namespace cv {
  * where @f$ \bar{y} = frac{1}{y}\sum_{i=1}^{n} y_i @f$.
  * For example, a model having R2Score = 0.85, explains 85 \% variability of
  * the response data around its mean.
+ * 
+ * @tparam AdjustedR2 If true, then the Adjusted R2 score will be used.
+ * 	Otherwise, the regular R2 score is used.
  */
+
+template<bool AdjustedR2>
 class R2Score
 {
  public:
   /**
-   * Run prediction and calculate the R squared error.
+   * Run prediction and calculate the R squared or Adjusted R squared error.
    *
    * @param model A regression model.
    * @param data Column-major data containing test items.

src/mlpack/core/cv/metrics/r2_score_impl.hpp

@@ -15,10 +15,11 @@
 namespace mlpack {
 namespace cv {
 
+template<bool AdjustedR2>
 template<typename MLAlgorithm, typename DataType, typename ResponsesType>
-double R2Score::Evaluate(MLAlgorithm& model,
-                         const DataType& data,
-                         const ResponsesType& responses)
+double R2Score<AdjustedR2>::Evaluate(MLAlgorithm& model,
+                                     const DataType& data,
+                                     const ResponsesType& responses)
 {
   if (data.n_cols != responses.n_cols)
   {
@@ -46,7 +47,18 @@ double R2Score::Evaluate(MLAlgorithm& model,
   if (residualSumSquared == 0.0)
     return totalSumSquared ? 1.0 : DBL_MIN;
 
-  return 1 - residualSumSquared / totalSumSquared;
+  if (AdjustedR2)
+  {
+    // Returning adjusted R-squared.
+    double rsq = 1 - (residualSumSquared / totalSumSquared);
+    return (1 - ((1 - rsq) * ((data.n_cols - 1) /
+        (data.n_cols - data.n_rows - 1))));
+  }
+  else
+  {
+    // Returning R-squared
+    return 1 - residualSumSquared / totalSumSquared;
+  }
 }
 
 } // namespace cv

src/mlpack/tests/cv_test.cpp

@@ -187,10 +187,31 @@ TEST_CASE("R2ScoreTest", "[CVTest]")
 
   double expectedR2 = 0.99999779;
 
-  REQUIRE(R2Score::Evaluate(lr, data, responses)
+  REQUIRE(R2Score<false>::Evaluate(lr, data, responses)
           == Approx(expectedR2).epsilon(1e-7));
 }
 
+/**
+ * Test the Adjusted R squared metric.
+ */
+TEST_CASE("AdjR2ScoreTest", "[CVTest]")
+{
+  // Making two variables that define the linear function is
+  // f(x1, x2) = x1 + x2.
+  arma::mat X;
+  X << 1 << 2 << 3 << 4 << 5 << 6 << arma::endr
+    << 2 << 3 << 4 << 5 << 6 << 7 << arma::endr;
+  arma::rowvec Y;
+  Y << 3 << 5 << 7 << 9 << 11 << 13;
+
+  LinearRegression lr(X, Y);
+
+  // Theoretically Adjusted R squared should be equal 1
+  double expAdjR2 = 1;
+  REQUIRE(std::abs(R2Score<true>::Evaluate(lr, X, Y) - expAdjR2)
+          <= 1e-7);
+}
+
 /**
  * Test the mean squared error with matrix responses.
  */