Add comment regarding stochastic trace estimation tests

test/test_stochastic_log_det_estimation.py

@@ -25,13 +25,16 @@ def log_det_jac_f(self, inputs):
 
 @pytest.mark.parametrize('n_hutchinson_samples', [*list(range(25, 40))])
 @pytest.mark.parametrize('n_iterations', [4, 10, 25, 100])
-def test_hutchinson(n_iterations, n_hutchinson_samples):
+def test_hutchinson_power_series(n_iterations, n_hutchinson_samples):
     # This test checks for validity of the hutchinson power series trace estimator.
     # The estimator computes log|det(Jac_f)| where f(x) = x + g(x) and x is Lipschitz continuous with Lip(g) < 1.
     # In this example: a Lipschitz continuous function with constant < 1 is g(x) = 1/2 * x; Lip(g) = 1/2.
 
     # The reference jacobian of f is I * 1.5, because d/dx f(x) = d/dx x + g(x) = d/dx x + 1/2 * x = 1 + 1/2 = 1.5
 
+    # TODO: use the analytical variance of the Monte Carlo Hutchinson trace estimator to compute the variance of the
+    #  Hutchinson power series estimator. Then make sure that the power series error is below 4 * variance.
+
     n_data = 1
     n_dim = 1
 
@@ -56,7 +59,7 @@ def test_hutchinson(n_iterations, n_hutchinson_samples):
 
 
 @pytest.mark.parametrize('p', [0.01, 0.1, 0.5, 0.9, 0.99])
-def test_roulette(p):
+def test_roulette_power_series(p):
     # an example of a Lipschitz continuous function with constant < 1: g(x) = 1/2 * x
 
     n_data = 100