def test_2sls(self):
n = 50000
e = np.random.uniform(low=-0.5, high=0.5, size=(n, 1))
z = np.random.uniform(size=(n, 1))
x = np.random.uniform(size=(n, 1)) + e
p = x + z * e + np.random.uniform(size=(n, 1))
y = p * x + e
losses = []
marg_effs = []
z_fresh = np.random.uniform(size=(n, 1))
e_fresh = np.random.uniform(low=-0.5, high=0.5, size=(n, 1))
x_fresh = np.random.uniform(size=(n, 1)) + e_fresh
p_fresh = x_fresh + z_fresh * e_fresh + np.random.uniform(size=(n, 1))
for (dt, dx, dz) in [(0, 0, 0), (1, 1, 1), (5, 5, 5), (10, 10, 10),
(3, 3, 10), (10, 10, 3)]:
np2sls = NonparametricTwoStageLeastSquares(
HermiteFeatures(dt), HermiteFeatures(dx), HermiteFeatures(dz),
HermiteFeatures(dt, shift=1))
np2sls.fit(y, p, x, z)
effect = np2sls.effect(x_fresh, np.zeros(shape(p_fresh)), p_fresh)
losses.append(np.mean(np.square(p_fresh * x_fresh - effect)))
marg_effs.append(
np2sls.marginal_effect(np.array([[0.3], [0.5], [0.7]]),
np.array([[0.4], [0.6], [0.2]])))
print("losses: {}".format(losses))
print("marg_effs: {}".format(marg_effs))
def test_hermite_results(self):
inputs = np.random.normal(size=(5, 1))
hf = HermiteFeatures(3).fit_transform(inputs)
# first polynomials are 1, x, x*x-1, x*x*x-3*x
ones = np.ones(shape(inputs))
polys = np.hstack([ones, inputs, inputs * inputs - ones, inputs * inputs * inputs - 3 * inputs])
assert(np.allclose(hf, polys * np.exp(-inputs * inputs / 2)))
for j in [True, False]:
hf = HermiteFeatures(1, shift=1, joint=j).fit_transform(inputs)
# first derivatives are -x, -x^2+1 (since there's just one column, joint-ness doesn't matter)
polys = np.hstack([-inputs, -inputs * inputs + ones])
assert(np.allclose(hf, reshape(polys * np.exp(-inputs * inputs / 2), (5, 1, 2))))
def test_hermite_shape(self):
for d, s in [(3, 0), (4, 2)]:
for j in [True, False]:
for n, x in [(5, 1), (7, 3)]:
last_dim = (d + 1)**x if j else (d + 1) * x
correct_shape = (n,) + (x,) * s + (last_dim,)
output_shape = shape(HermiteFeatures(d, s, j).fit_transform(np.zeros((n, x))))
assert output_shape == correct_shape
def test_2sls(self):
n = 50000
d_w = 2
d_z = 1
d_x = 1
d_t = 1
d_y = 1
e = np.random.uniform(low=-0.5, high=0.5, size=(n, d_x))
z = np.random.uniform(size=(n, 1))
w = np.random.uniform(size=(n, d_w))
a = np.random.normal(size=(d_w, d_t))
b = np.random.normal(size=(d_w, d_y))
x = np.random.uniform(size=(n, d_x)) + e
p = x + z * e + w @ a + np.random.uniform(size=(n, d_t))
y = p * x + e + w @ b
losses = []
marg_effs = []
z_fresh = np.random.uniform(size=(n, d_z))
e_fresh = np.random.uniform(low=-0.5, high=0.5, size=(n, d_x))
x_fresh = np.random.uniform(size=(n, d_x)) + e_fresh
w_fresh = np.random.uniform(size=(n, d_w))
p_fresh = x_fresh + z_fresh * e_fresh + np.random.uniform(size=(n, d_t))
for (dt, dx, dz) in [(0, 0, 0), (1, 1, 1), (5, 5, 5), (10, 10, 10), (3, 3, 10), (10, 10, 3)]:
np2sls = NonparametricTwoStageLeastSquares(t_featurizer=HermiteFeatures(dt),
x_featurizer=HermiteFeatures(dx),
z_featurizer=HermiteFeatures(dz),
dt_featurizer=HermiteFeatures(dt, shift=1))
np2sls.fit(y, p, X=x, W=w, Z=z)
effect = np2sls.effect(x_fresh, np.zeros(shape(p_fresh)), p_fresh)
losses.append(np.mean(np.square(p_fresh * x_fresh - effect)))
marg_effs.append(np2sls.marginal_effect(np.array([[0.3], [0.5], [0.7]]), np.array([[0.4], [0.6], [0.2]])))
print("losses: {}".format(losses))
print("marg_effs: {}".format(marg_effs))
def err(k, j):
hf = HermiteFeatures(k, joint=j)
m = LinearRegression()
m.fit(hf.fit_transform(x[:n // 2, :]), y[:n // 2])
return ((y[n // 2:] -
m.predict(hf.fit_transform(x[n // 2:, :])))**2).mean()
