def basis_plot(formula: gammy.formulae.Formula,
grid_limits,
input_maps,
gridsize=20):
"""Plot all basis functions
"""
# Figure definition
N = len(formula)
fig = plt.figure(figsize=(8, max(4 * N // 2, 8)))
gs = fig.add_gridspec(N, 1)
# Data and predictions
grid = (pipe(grid_limits,
utils.listmap(lambda x: np.linspace(x[0], x[1], gridsize)),
lambda x: np.array(x).T))
# Plot stuff
for i, (basis, input_map) in enumerate(zip(formula.terms, input_maps)):
ax = fig.add_subplot(gs[i])
x = input_map(grid)
for f in basis:
ax.plot(x, f(grid))
return fig
def predict_variance_marginal(self, input_data, i):
# Not refactored with predict_marginals for perf reasons
X = self.formula.build_Xi(input_data, i=i)
F = bp.nodes.SumMultiply("i,i", self.theta_marginal(i), X)
mu = np.dot(X, self.mean_theta[i])
sigma = pipe(F, utils.solve_covariance, np.diag)
return (mu, sigma)
def predict_variance_marginals(self, input_data):
Xs = self.formula.build_Xs(input_data)
Fs = [
bp.nodes.SumMultiply("i,i", theta, X)
for X, theta in zip(Xs, self.theta_marginals)
]
mus = [np.dot(X, c) for X, c in zip(Xs, self.mean_theta)]
sigmas = [pipe(F, utils.solve_covariance, np.diag) for F in Fs]
return list(zip(mus, sigmas))
def predict_variance(self, input_data) -> tuple:
"""Predict observations with variance
Returns
-------
(μ, σ) : tuple([np.array, np.array])
``μ`` is mean of posterior predictive distribution
``σ`` is variances of posterior predictive + noise
"""
X = self.formula.build_X(input_data)
F = bp.nodes.SumMultiply("i,i", self.theta, X)
return (F.get_moments()[0],
pipe(F, utils.solve_covariance, np.diag) + self.inv_mean_tau)
def gaussian1d_density_plot(model, grid_limits=[0.5, 1.5]):
"""Plot 1-D density for each parameter
Parameters
----------
grid_limits : list
Grid of `tau` has endpoints `[grid_limits[0] * mu, grid_limits[1] * mu]`
where `mu` is the expectation of `tau`.
"""
N = len(model)
fig = plt.figure(figsize=(8, max(4 * N // 2, 8)))
gs = fig.add_gridspec(N + 1, 1)
# Plot inverse gamma
ax = fig.add_subplot(gs[0])
(b, a) = (-model.tau.phi[0], model.tau.phi[1])
mu = a / b
grid = np.arange(0.5 * mu, 1.5 * mu, mu / 300)
ax.plot(grid, model.tau.pdf(grid))
ax.set_title(r"$\tau$ = noise inverse variance")
ax.grid(True)
# Plot marginal thetas
for i, theta in enumerate(model.theta_marginals):
ax = fig.add_subplot(gs[i + 1])
mus = theta.get_moments()[0]
mus = np.array([mus]) if mus.shape == () else mus
cov = utils.solve_covariance(theta)
stds = pipe(
np.array([cov]) if cov.shape == () else np.diag(cov), np.sqrt)
left = (mus - 4 * stds).min()
right = (mus + 4 * stds).max()
grid = np.arange(left, right, (right - left) / 300)
for (mu, std) in zip(mus, stds):
node = bp.nodes.GaussianARD(mu, 1 / std**2)
ax.plot(grid, node.pdf(grid))
ax.set_title(r"$\theta_{0}$".format(i))
ax.grid(True)
fig.tight_layout()
return fig
def predict_variance_theta(self, input_data):
"""Predict observations with variance from model parameters
Returns
-------
(μ, σ) : tuple([np.array, np.array])
``μ`` is mean of posterior predictive distribution
``σ`` is variances of posterior predictive
"""
X = self.formula.build_X(input_data)
F = bp.nodes.SumMultiply("i,i", self.theta, X)
# Ensuring correct moments
#
# F = F._ensure_moments(
# F, bp.inference.vmp.nodes.gaussian.GaussianMoments, ndim=0
# )
#
# NOTE: See also bp.plot.plot_gaussian how std can be calculated
return (F.get_moments()[0], pipe(F, utils.solve_covariance, np.diag))
def gaussian1d_density_plot(model: gammy.bayespy.GAM):
"""Plot 1-D density for each parameter
"""
N = len(model.formula)
N_rows = 2 + (N + 1) // 2
fig = plt.figure(figsize=(8, 2 * N_rows))
gs = fig.add_gridspec(N + 1, 1)
# Plot inverse gamma
ax = fig.add_subplot(gs[0])
(b, a) = (-model.tau.phi[0], model.tau.phi[1])
mu = a / b
grid = np.arange(0.5 * mu, 1.5 * mu, mu / 300)
ax.plot(grid, model.tau.pdf(grid))
ax.set_title(r"$\tau$ = noise inverse variance")
ax.grid(True)
# Plot marginal thetas
for i, theta in enumerate(model.theta_marginals):
ax = fig.add_subplot(gs[i + 1])
mus = theta.get_moments()[0]
mus = np.array([mus]) if mus.shape == () else mus
cov = utils.solve_covariance(theta.get_moments())
stds = pipe(
np.array([cov]) if cov.shape == () else np.diag(cov), np.sqrt)
left = (mus - 4 * stds).min()
right = (mus + 4 * stds).max()
grid = np.arange(left, right, (right - left) / 300)
for (mu, std) in zip(mus, stds):
node = bp.nodes.GaussianARD(mu, 1 / std**2)
ax.plot(grid, node.pdf(grid))
ax.set_title(r"$\theta_{0}$".format(i))
ax.grid(True)
fig.tight_layout()
return fig
def validation_plot(model,
input_data,
y,
grid_limits,
input_maps,
index=None,
xlabels=None,
titles=None,
ylabel=None,
gridsize=20,
**kwargs):
"""Generic validation plot for a GAM
"""
# TODO: Support larger input dimensions
index = np.arange(len(input_data)) if index is None else index
# Figure definitions
N = len(model)
fig = plt.figure(figsize=(8, max(4 * N // 2, 8)))
gs = fig.add_gridspec(N // 2 + 3, 2)
xlabels = xlabels or [None] * len(model)
titles = titles or [None] * len(model)
# Data and predictions
grid = (pipe(grid_limits,
utils.listmap(lambda x: np.linspace(x[0], x[1], gridsize)),
lambda x: np.array(x).T) if len(input_data.shape) > 1 else
np.linspace(grid_limits[0], grid_limits[1], gridsize))
marginals = model.predict_variance_marginals(grid)
residuals = model.marginal_residuals(input_data, y)
# Time series plot
ax = fig.add_subplot(gs[0, :])
(mu, sigma_theta) = model.predict_variance_theta(input_data)
lower = mu - 2 * np.sqrt(sigma_theta + model.inv_mean_tau)
upper = mu + 2 * np.sqrt(sigma_theta + model.inv_mean_tau)
ax.plot(index, y, linewidth=0, marker="o", alpha=0.3)
ax.plot(index, mu, color="k")
ax.fill_between(index, lower, upper, color="k", alpha=0.3)
ax.grid(True)
# XY-plot
ax = fig.add_subplot(gs[1, :])
ax.plot(mu, y, alpha=0.3, marker="o", lw=0)
ax.plot([mu.min(), mu.max()], [mu.min(), mu.max()], c="k", label="x=y")
ax.legend(loc="best")
ax.grid(True)
ax.set_xlabel("Predictions")
ax.set_ylabel("Observations")
# Partial residual plots
for i, ((mu, sigma), res, input_map, xlabel, title) in enumerate(
zip(marginals, residuals, input_maps, xlabels, titles)):
x = input_map(grid)
if len(x.shape) == 1 or x.shape[1] == 1:
ax = fig.add_subplot(gs[2 + i // 2, i % 2])
(lower, upper) = (mu - 2 * np.sqrt(sigma), mu + 2 * np.sqrt(sigma))
ax.scatter(input_map(input_data), res, **kwargs)
ax.plot(x, mu, c='k', lw=2)
ax.fill_between(x, lower, upper, alpha=0.3, color="k")
ax.set_xlabel(xlabel)
elif x.shape[1] == 2:
ax = fig.add_subplot(gs[2 + i // 2, i % 2], projection="3d")
u, v = np.meshgrid(x[:, 0], x[:, 1])
w = np.hstack((u.reshape(-1, 1), v.reshape(-1, 1)))
# Override mu and sigma on purpose!
(mu, sigma) = model.predict_variance_marginal(w, i)
mu_mesh = mu.reshape(u.shape)
ax.plot_surface(u, v, mu_mesh)
else:
raise NotImplementedError("High-dimensional plots not supported.")
ax.set_title(title)
ax.grid(True)
fig.tight_layout()
return fig
def mean_theta(self):
return pipe(self.theta.get_moments()[0],
lambda x: utils.unflatten(x, self.formula.bases),
listmap(np.array))
[np.array([[1, 2], [4, 5]]), np.array([[9]])]),
(np.array([[1, 2], [3, 4]]),
[np.array([[np.nan, np.nan], [np.nan, np.inf]]),
np.array([])], [np.array([[1, 2], [3, 4]])])])
def test_extract_diag_blocks(x, y, expected):
assert all([
array_equal(*args)
for args in zip(expected, utils.extract_diag_blocks(x, y))
])
return
@pytest.mark.parametrize(
"mu,Sigma",
[(np.random.rand(23),
utils.pipe(np.random.randn(23, 23), lambda A: np.dot(A.T, A)))])
def test_solve_covariance(mu, Sigma):
node = bp.nodes.Gaussian(mu, np.linalg.inv(Sigma))
assert_almost_equal(utils.solve_covariance(node.get_moments()),
Sigma,
decimal=8)
return
@pytest.mark.parametrize("order,expected",
[(
1,
np.array([0, 1, 2, 3]),
), (2, np.array([-1, 0, 1, 2, 3, 4])),
(3, np.array([-2, -1, 0, 1, 2, 3, 4, 5]))])
def test_extend_spline_grid(order, expected):
