def linear_model_ground_truth(model,
design,
observation_labels,
target_labels,
eig=True):
if isinstance(target_labels, str):
target_labels = [target_labels]
w_sd = torch.cat(list(model.w_sds.values()), dim=-1)
prior_cov = torch.diag(w_sd**2)
design_shape = design.shape
posterior_covs = [
analytic_posterior_cov(prior_cov, x, model.obs_sd)
for x in torch.unbind(
design.reshape(-1, design_shape[-2], design_shape[-1]))
]
target_indices = get_indices(target_labels, tensors=model.w_sds)
target_posterior_covs = [
S[target_indices, :][:, target_indices] for S in posterior_covs
]
output = torch.tensor([
0.5 * torch.logdet(2 * math.pi * math.e * C)
for C in target_posterior_covs
])
if eig:
prior_entropy = mean_field_entropy(model, [design],
whitelist=target_labels)
output = prior_entropy - output
return output.reshape(design.shape[:-2])
def true_ape(ns):
"""Analytic APE"""
true_ape = []
prior_cov = torch.diag(prior_sds**2)
designs = [group_assignment_matrix(torch.tensor([n1, N-n1])) for n1 in ns]
for i in range(len(ns)):
x = designs[i]
posterior_cov = analytic_posterior_cov(prior_cov, x, torch.tensor(1.))
true_ape.append(0.5*torch.logdet(2*np.pi*np.e*posterior_cov))
return torch.tensor(true_ape)