def test_result_does_not_depend_on_position_in_feature_dimension(self):
norms1 = self.variance.transform(X=self.x)
variance2 = OnlineVariance(self.n_features, rate=self.rate)
norms2 = variance2.transform(X=np.fliplr(self.x))
np.testing.assert_allclose(norms1, np.fliplr(norms2))
def setUp(self):
self.n_features = 3
self.rate = 0.02
self.variance = OnlineVariance(self.n_features, rate=self.rate)
self.rng = np.random.default_rng(33)
self.n_samples = 500
self.x = self.rng.normal(size=(self.n_samples, self.n_features))
def test_result_in_one_seq_independent_of_other_seqs(self):
X1 = self.x
norms1 = self.variance.transform(X=X1)
X2 = np.copy(self.x)
X2[:, 1] = self.x[:, 2]
variance2 = OnlineVariance(self.n_features, rate=self.rate)
norms2 = variance2.transform(X=X2)
np.testing.assert_allclose(norms1[:, 0], norms2[:, 0])
def setUp(self):
self.n_features = 4
self.order = 4
self.rate = 0.01
self.variance = OnlineVariance(self.n_features, rate=self.rate)
self.rng = np.random.default_rng(33)
self.n_samples = 500
self.x = self.rng.normal(size=(self.n_samples, self.n_features))
self.norms = self.variance.transform(X=self.x)
def test_repeated_transform_same_as_single_transform_on_combined_input(self):
norms = self.variance.transform(X=self.x)
n1 = self.n_samples // 2
x1 = self.x[:n1]
x2 = self.x[n1:]
variance_alt = OnlineVariance(self.n_features, rate=self.rate)
norms1 = variance_alt.transform(X=x1)
norms2 = variance_alt.transform(X=x2)
norms_exp = np.row_stack((norms1, norms2))
np.testing.assert_allclose(norms, norms_exp)
def __init__(
self,
weights: Optional[Sequence] = None,
n_models: Optional[int] = None,
n_features: Optional[int] = None,
rng: Union[int, np.random.Generator] = 0,
variance_kws: Optional[dict] = None,
):
""" Initialize the variance-based regressor.
This chains together a `PredictionError` instance with an `OnlineVariance`.
Parameters
----------
weights
Regression coefficients for each model, shape `(n_models, n_features)`. If
this is provided, `n_models` and `n_features` need not be provided. If
`weights` is not provided, it will be initialized randomly, using a standard
normal distribution. See `rng`.
n_models
Number of models. If `weights` is provided, `n_models` need not be. However,
if both are provided, then `n_models` should be equal to the number of rows
in `weights`.
n_features
Number of predictor variables (features). If `weights` is provided,
`n_features` need not be. However, if both are provided, then `n_features`
should be equal to the number of columns in `weights`.
rng
Random number generator or seed to use for generating initial weight
values. If seed, a random number generator is created using
`np.random.default_rng`. If not provided, a seed of 0 is used. The random
number generator is not used at all if `weights` is provided.
variance_kws
Additional keywords to pass to `OnlineVariance`. By default `negative` is set
to true.
"""
if weights is None:
if not hasattr(rng, "normal"):
rng = np.random.default_rng(rng)
weights = rng.normal(size=(n_models, n_features))
else:
if n_models is not None and n_models != np.shape(weights)[0]:
raise ValueError("n_models does not match shape(weights)[0]")
if n_features is not None and n_features != np.shape(weights)[1]:
raise ValueError("n_features does not match shape(weights)[1]")
self.n_models = len(weights)
self.prediction_error = PredictionError(weights)
if variance_kws is None:
variance_kws = {}
variance_kws.setdefault("negative", True)
self.variance_norm = OnlineVariance(self.n_models, **variance_kws)
super().__init__(["prediction_error", "variance_norm"])
class TestOnlineVarianceNegative(unittest.TestCase):
def setUp(self):
self.n_features = 4
self.order = 4
self.rate = 0.01
self.variance = OnlineVariance(self.n_features, rate=self.rate)
self.rng = np.random.default_rng(33)
self.n_samples = 500
self.x = self.rng.normal(size=(self.n_samples, self.n_features))
self.norms = self.variance.transform(X=self.x)
def test_negative_returned_when_asked_for(self):
variance_neg = OnlineVariance(self.n_features, rate=self.rate, negative=True)
norms_neg = variance_neg.transform(X=self.x)
np.testing.assert_allclose(norms_neg, -self.norms)
def setUp(self):
self.n_features = 3
self.rate = 0.02
self.variance = OnlineVariance(self.n_features, rate=self.rate)
class TestOnlineVarianceTransform(unittest.TestCase):
def setUp(self):
self.n_features = 3
self.rate = 0.02
self.variance = OnlineVariance(self.n_features, rate=self.rate)
self.rng = np.random.default_rng(33)
self.n_samples = 500
self.x = self.rng.normal(size=(self.n_samples, self.n_features))
def test_all_outputs_are_non_negative(self):
norms = self.variance.transform(X=self.x)
self.assertGreaterEqual(np.min(norms), 0)
def test_result_does_not_depend_on_position_in_feature_dimension(self):
norms1 = self.variance.transform(X=self.x)
variance2 = OnlineVariance(self.n_features, rate=self.rate)
norms2 = variance2.transform(X=np.fliplr(self.x))
np.testing.assert_allclose(norms1, np.fliplr(norms2))
def test_result_in_one_seq_independent_of_other_seqs(self):
X1 = self.x
norms1 = self.variance.transform(X=X1)
X2 = np.copy(self.x)
X2[:, 1] = self.x[:, 2]
variance2 = OnlineVariance(self.n_features, rate=self.rate)
norms2 = variance2.transform(X=X2)
np.testing.assert_allclose(norms1[:, 0], norms2[:, 0])
def test_initial_estimate_is_zero(self):
norms = self.variance.transform(X=self.x)
np.testing.assert_allclose(norms[0], self.rate * self.x[0] ** 2)
def test_one_step_update_end(self):
norms = self.variance.transform(X=self.x)
diffs = np.diff(norms, axis=0)
expected_last_diff = self.rate * (self.x[-1] ** 2 - norms[-2])
np.testing.assert_allclose(diffs[-1], expected_last_diff)
def test_shape_of_output_correct(self):
norms = self.variance.transform(X=self.x)
self.assertEqual(norms.shape, self.x.shape)
def test_repeated_transform_same_as_single_transform_on_combined_input(self):
norms = self.variance.transform(X=self.x)
n1 = self.n_samples // 2
x1 = self.x[:n1]
x2 = self.x[n1:]
variance_alt = OnlineVariance(self.n_features, rate=self.rate)
norms1 = variance_alt.transform(X=x1)
norms2 = variance_alt.transform(X=x2)
norms_exp = np.row_stack((norms1, norms2))
np.testing.assert_allclose(norms, norms_exp)
def test_output_is_set_properly(self):
norms = self.variance.transform(X=self.x)
np.testing.assert_allclose(self.variance.output_, norms[-1])
def test_monitor_output(self):
monitor = AttributeMonitor(["output_"])
norms = self.variance.transform(X=self.x, monitor=monitor)
np.testing.assert_allclose(monitor.history_.output_, norms)
def test_negative_returned_when_asked_for(self):
variance_neg = OnlineVariance(self.n_features, rate=self.rate, negative=True)
norms_neg = variance_neg.transform(X=self.x)
np.testing.assert_allclose(norms_neg, -self.norms)