Update objective computation: multiply quadratic biases with (1-alpha)

dwave/plugins/sklearn/transformers.py

@@ -198,22 +198,18 @@ def correlation_cqm(
                 dtype=np.result_type(X, y),
                 mode="w+",
                 shape=(X_copy.shape[1], X_copy.shape[1]),
-                )
-
+                )            
             # main calculation. It modifies X_copy in-place
             corrcoef(X_copy, out=correlations, rowvar=False, copy=False)
-
             # we don't care about the direction of correlation in terms of
             # the penalty/quality
             np.absolute(correlations, out=correlations)
-
+            # multiplying all but last columns and rows with (1 - alpha)
+            np.multiply(correlations[:-1, :-1], (1 - alpha), out=correlations[:-1, :-1])
             # our objective
-            # we multiply by 2 because the matrix is symmetric
-            np.fill_diagonal(correlations, correlations[:, -1] * (-2 * alpha * num_features))
-
-            # Note: the full symmetric matrix (with both upper- and lower-diagonal
-            # entries for each correlation coefficient) is retained for consistency with
-            # the original formulation from Milne et al.
+            # we multiply by num_features to have consistent performance 
+            # with the increase of the number of features
+            np.fill_diagonal(correlations, correlations[:, -1] * (- alpha * num_features))
             it = np.nditer(correlations[:-1, :-1], flags=['multi_index'], op_flags=[['readonly']])
             cqm.set_objective((*it.multi_index, x) for x in it if x)
 

releasenotes/notes/algorithm-update-d73cd4f7c854a8b3.yaml

@@ -0,0 +1,3 @@
+---
+fixes:
+  - Multiply off-diagonal terms of the correlation matrix with 1-alpha.

tests/test_transformer.py

@@ -126,6 +126,10 @@ def test_alpha_0(self):
         cqm = SelectFromQuadraticModel.correlation_cqm(self.X, self.y, num_features=3, alpha=0)
         self.assertTrue(not any(cqm.objective.linear.values()))
 
+    def test_alpha_1_no_quadratic(self):
+        cqm = SelectFromQuadraticModel.correlation_cqm(self.X, self.y, num_features=3, alpha=1)
+        self.assertTrue(not any(cqm.objective.quadratic.values()))
+
     def test_alpha_1(self):
         rng = np.random.default_rng(42)