def quantile(self, level: Tensor) -> Tensor:
F = self.F
exp = F.exp(
self.mu
+ (self.sigma * F.sqrt(F.full(1, 2)) * erfinv(F, 2 * level - 1))
)
return exp / (1 + exp)
def test_erfinv() -> None:
try:
from scipy.special import erfinv as scipy_erfinv
except:
pytest.skip("scipy not installed skipping test for erf")
x = np.linspace(-1.0 + 1.0e-4, 1 - 1.0e-4, 11)
y_mxnet = util.erfinv(mx.nd, mx.nd.array(x)).asnumpy()
y_scipy = scipy_erfinv(x)
assert np.allclose(y_mxnet, y_scipy, rtol=1e-3)
def quantile(self, level: Tensor) -> Tensor:
F = self.F
# we consider level to be an independent axis and so expand it
# to shape (num_levels, 1, 1, ...)
for _ in range(self.all_dim):
level = level.expand_dims(axis=-1)
return F.broadcast_add(
self.mu,
F.broadcast_mul(self.sigma,
math.sqrt(2.0) * erfinv(F, 2.0 * level - 1.0)),
)
def test_erfinv() -> None:
try:
from scipy.special import erfinv as scipy_erfinv
except:
pytest.skip("scipy not installed skipping test for erf")
x = np.linspace(-1.0 + 1.0e-4, 1 - 1.0e-4, 11)
y_scipy = scipy_erfinv(x)
# Text np
y_np = erfinv(x)
assert np.allclose(y_np, y_scipy, rtol=1e-3)
def test_erfinv() -> None:
try:
from scipy.special import erfinv as scipy_erfinv
except:
pytest.skip("scipy not installed skipping test for erf")
x = np.linspace(-1.0 + 1.0e-4, 1 - 1.0e-4, 11)
y_scipy = scipy_erfinv(x)
# Test mx.nd
y_mxnet = util.erfinv(mx.nd, mx.nd.array(x)).asnumpy()
assert np.allclose(y_mxnet, y_scipy, rtol=1e-3)
# Test mx.sym
X = mx.symbol.Variable("x")
func = util.erfinv(mx.sym, X)
func_exec = func.bind(ctx=mx.cpu(), args={"x": mx.nd.array(x)})
func_exec.forward()
y_mxnet_sym = func_exec.outputs[0].asnumpy()
assert np.allclose(y_mxnet_sym, y_scipy, rtol=1e-3)
# Text np
y_np = util.erfinv(np, x)
assert np.allclose(y_np, y_scipy, rtol=1e-3)
def standard_gaussian_ppf(y: np.array) -> np.array:
y_clipped = np.clip(y, a_min=1.0e-6, a_max=1.0 - 1.0e-6)
return np.sqrt(2.0) * erfinv(2.0 * y_clipped - 1.0)
