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import torch
from torch import Tensor
import torch.distributions as dist
from utils import GetterReturnType
def get_simple_regression(device: torch.device) -> GetterReturnType:
N = 10
K = 10
loc_beta = 0.
scale_beta = 1.
beta_prior = dist.Normal(loc_beta, scale_beta)
X = torch.rand(N, K + 1, device=device)
Y = torch.rand(N, 1, device=device)
# X.shape: (N, K + 1), Y.shape: (N, 1), beta_value.shape: (K + 1, 1)
beta_value = beta_prior.sample((K + 1, 1))
beta_value.requires_grad_(True)
def forward(beta_value: Tensor) -> Tensor:
mu = X.mm(beta_value)
# We need to compute the first and second gradient of this score with respect
# to beta_value. We disable Bernoulli validation because Y is a relaxed value.
score = (dist.Bernoulli(logits=mu, validate_args=False).log_prob(Y).sum() +
beta_prior.log_prob(beta_value).sum())
return score
return forward, (beta_value.to(device),)
def get_robust_regression(device: torch.device) -> GetterReturnType:
N = 10
K = 10
# X.shape: (N, K + 1), Y.shape: (N, 1)
X = torch.rand(N, K + 1, device=device)
Y = torch.rand(N, 1, device=device)
# Predefined nu_alpha and nu_beta, nu_alpha.shape: (1, 1), nu_beta.shape: (1, 1)
nu_alpha = torch.rand(1, 1, device=device)
nu_beta = torch.rand(1, 1, device=device)
nu = dist.Gamma(nu_alpha, nu_beta)
# Predefined sigma_rate: sigma_rate.shape: (N, 1)
sigma_rate = torch.rand(N, 1, device=device)
sigma = dist.Exponential(sigma_rate)
# Predefined beta_mean and beta_sigma: beta_mean.shape: (K + 1, 1), beta_sigma.shape: (K + 1, 1)
beta_mean = torch.rand(K + 1, 1, device=device)
beta_sigma = torch.rand(K + 1, 1, device=device)
beta = dist.Normal(beta_mean, beta_sigma)
nu_value = nu.sample()
nu_value.requires_grad_(True)
sigma_value = sigma.sample()
sigma_unconstrained_value = sigma_value.log()
sigma_unconstrained_value.requires_grad_(True)
beta_value = beta.sample()
beta_value.requires_grad_(True)
def forward(nu_value: Tensor, sigma_unconstrained_value: Tensor, beta_value: Tensor) -> Tensor:
sigma_constrained_value = sigma_unconstrained_value.exp()
mu = X.mm(beta_value)
# For this model, we need to compute the following three scores:
# We need to compute the first and second gradient of this score with respect
# to nu_value.
nu_score = dist.StudentT(nu_value, mu, sigma_constrained_value).log_prob(Y).sum() \
+ nu.log_prob(nu_value)
# We need to compute the first and second gradient of this score with respect
# to sigma_unconstrained_value.
sigma_score = dist.StudentT(nu_value, mu, sigma_constrained_value).log_prob(Y).sum() \
+ sigma.log_prob(sigma_constrained_value) \
+ sigma_unconstrained_value
# We need to compute the first and second gradient of this score with respect
# to beta_value.
beta_score = dist.StudentT(nu_value, mu, sigma_constrained_value).log_prob(Y).sum() \
+ beta.log_prob(beta_value)
return nu_score.sum() + sigma_score.sum() + beta_score.sum()
return forward, (nu_value.to(device), sigma_unconstrained_value.to(device), beta_value.to(device))
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