def sample(
self,
tensors,
n_samples=1,
library_size=1,
) -> np.ndarray:
r"""
Generate observation samples from the posterior predictive distribution.
The posterior predictive distribution is written as :math:`p(\hat{x} \mid x)`.
Parameters
----------
tensors
Tensors dict
n_samples
Number of required samples for each cell
library_size
Library size to scale scamples to
Returns
-------
x_new : :py:class:`torch.Tensor`
tensor with shape (n_cells, n_genes, n_samples)
"""
inference_kwargs = dict(n_samples=n_samples)
inference_outputs, generative_outputs, = self.forward(
tensors,
inference_kwargs=inference_kwargs,
compute_loss=False,
)
px_r = generative_outputs["px_r"]
px_rate = generative_outputs["px_rate"]
px_dropout = generative_outputs["px_dropout"]
if self.gene_likelihood == "poisson":
l_train = px_rate
l_train = torch.clamp(l_train, max=1e8)
dist = torch.distributions.Poisson(
l_train) # Shape : (n_samples, n_cells_batch, n_genes)
elif self.gene_likelihood == "nb":
dist = NegativeBinomial(mu=px_rate, theta=px_r)
elif self.gene_likelihood == "zinb":
dist = ZeroInflatedNegativeBinomial(mu=px_rate,
theta=px_r,
zi_logits=px_dropout)
else:
raise ValueError(
"{} reconstruction error not handled right now".format(
self.module.gene_likelihood))
if n_samples > 1:
exprs = dist.sample().permute(
[1, 2, 0]) # Shape : (n_cells_batch, n_genes, n_samples)
else:
exprs = dist.sample()
return exprs.cpu()
def loss(
self,
tensors,
inference_outputs,
generative_outputs,
kl_weight: float = 1.0,
):
x = tensors[REGISTRY_KEYS.X_KEY]
y = tensors[REGISTRY_KEYS.LABELS_KEY]
qz_m = inference_outputs["qz_m"]
qz_v = inference_outputs["qz_v"]
px_rate = generative_outputs["px_rate"]
px_r = generative_outputs["px_r"]
mean = torch.zeros_like(qz_m)
scale = torch.ones_like(qz_v)
kl_divergence_z = kl(Normal(qz_m, torch.sqrt(qz_v)),
Normal(mean, scale)).sum(dim=1)
reconst_loss = -NegativeBinomial(px_rate,
logits=px_r).log_prob(x).sum(-1)
scaling_factor = self.ct_weight[y.long()[:, 0]]
loss = torch.mean(scaling_factor *
(reconst_loss + kl_weight * kl_divergence_z))
return LossRecorder(loss, reconst_loss, kl_divergence_z,
torch.tensor(0.0))
def get_reconstruction_loss(
self,
x: torch.Tensor,
px_rate: torch.Tensor,
px_r: torch.Tensor,
px_dropout: torch.Tensor,
bernoulli_params: torch.Tensor,
eps_log: float = 1e-8,
**kwargs,
) -> torch.Tensor:
# LLs for NB and ZINB
ll_zinb = torch.log(1.0 - bernoulli_params +
eps_log) + ZeroInflatedNegativeBinomial(
mu=px_rate, theta=px_r,
zi_logits=px_dropout).log_prob(x)
ll_nb = torch.log(bernoulli_params + eps_log) + NegativeBinomial(
mu=px_rate, theta=px_r).log_prob(x)
# Reconstruction loss using a logsumexp-type computation
ll_max = torch.max(ll_zinb, ll_nb)
ll_tot = ll_max + torch.log(
torch.exp(ll_nb - ll_max) + torch.exp(ll_zinb - ll_max))
reconst_loss = -ll_tot.sum(dim=-1)
return reconst_loss
def loss(
self,
tensors,
inference_outputs,
generative_outputs,
kl_weight: float = 1.0,
n_obs: int = 1.0,
):
x = tensors[REGISTRY_KEYS.X_KEY]
px_rate = generative_outputs["px_rate"]
px_o = generative_outputs["px_o"]
gamma = generative_outputs["gamma"]
reconst_loss = -NegativeBinomial(px_rate,
logits=px_o).log_prob(x).sum(-1)
# eta prior likelihood
mean = torch.zeros_like(self.eta)
scale = torch.ones_like(self.eta)
glo_neg_log_likelihood_prior = -Normal(mean, scale).log_prob(
self.eta).sum()
glo_neg_log_likelihood_prior += torch.var(self.beta)
# gamma prior likelihood
if self.mean_vprior is None:
# isotropic normal prior
mean = torch.zeros_like(gamma)
scale = torch.ones_like(gamma)
neg_log_likelihood_prior = (
-Normal(mean, scale).log_prob(gamma).sum(2).sum(1))
else:
# vampprior
# gamma is of shape n_latent, n_labels, minibatch_size
gamma = gamma.unsqueeze(1) # minibatch_size, 1, n_labels, n_latent
mean_vprior = torch.transpose(self.mean_vprior, 0, 1).unsqueeze(
0) # 1, p, n_labels, n_latent
var_vprior = torch.transpose(self.var_vprior, 0, 1).unsqueeze(
0) # 1, p, n_labels, n_latent
pre_lse = (Normal(mean_vprior,
torch.sqrt(var_vprior)).log_prob(gamma).sum(-1)
) # minibatch, p, n_labels
log_likelihood_prior = torch.logsumexp(pre_lse, 1) - np.log(
self.p) # minibatch, n_labels
neg_log_likelihood_prior = -log_likelihood_prior.sum(
1) # minibatch
# mean_vprior is of shape n_labels, p, n_latent
loss = (
n_obs *
torch.mean(reconst_loss + kl_weight * neg_log_likelihood_prior) +
glo_neg_log_likelihood_prior)
return LossRecorder(loss, reconst_loss, neg_log_likelihood_prior,
glo_neg_log_likelihood_prior)
def get_reconstruction_loss_expression(self, x, px_rate, px_r, px_dropout):
rl = 0.0
if self.gene_likelihood == "zinb":
rl = (-ZeroInflatedNegativeBinomial(
mu=px_rate, theta=px_r,
zi_logits=px_dropout).log_prob(x).sum(dim=-1))
elif self.gene_likelihood == "nb":
rl = -NegativeBinomial(mu=px_rate,
theta=px_r).log_prob(x).sum(dim=-1)
elif self.gene_likelihood == "poisson":
rl = -Poisson(px_rate).log_prob(x).sum(dim=-1)
return rl
def get_reconstruction_loss(self, x, px_rate, px_r,
px_dropout) -> torch.Tensor:
if self.gene_likelihood == "zinb":
reconst_loss = (-ZeroInflatedNegativeBinomial(
mu=px_rate, theta=px_r,
zi_logits=px_dropout).log_prob(x).sum(dim=-1))
elif self.gene_likelihood == "nb":
reconst_loss = (-NegativeBinomial(
mu=px_rate, theta=px_r).log_prob(x).sum(dim=-1))
elif self.gene_likelihood == "poisson":
reconst_loss = -Poisson(px_rate).log_prob(x).sum(dim=-1)
return reconst_loss
def sample(
self,
tensors,
n_samples=1,
) -> np.ndarray:
r"""
Generate observation samples from the posterior predictive distribution.
The posterior predictive distribution is written as :math:`p(\hat{x} \mid x)`.
Parameters
----------
tensors
Tensors dict
n_samples
Number of required samples for each cell
Returns
-------
x_new : :py:class:`torch.Tensor`
tensor with shape (n_cells, n_genes, n_samples)
"""
inference_kwargs = dict(n_samples=n_samples)
generative_outputs = self.forward(
tensors,
inference_kwargs=inference_kwargs,
compute_loss=False,
)[1]
px_r = generative_outputs["px_r"]
px_rate = generative_outputs["px_rate"]
dist = NegativeBinomial(px_rate, logits=px_r)
if n_samples > 1:
exprs = dist.sample().permute(
[1, 2, 0]) # Shape : (n_cells_batch, n_genes, n_samples)
else:
exprs = dist.sample()
return exprs.cpu()
def sample(self, tensors, n_samples=1):
inference_kwargs = dict(n_samples=n_samples)
with torch.no_grad():
inference_outputs, generative_outputs, = self.forward(
tensors,
inference_kwargs=inference_kwargs,
compute_loss=False,
)
px_ = generative_outputs["px_"]
py_ = generative_outputs["py_"]
rna_dist = NegativeBinomial(mu=px_["rate"], theta=px_["r"])
protein_dist = NegativeBinomialMixture(
mu1=py_["rate_back"],
mu2=py_["rate_fore"],
theta1=py_["r"],
mixture_logits=py_["mixing"],
)
rna_sample = rna_dist.sample().cpu()
protein_sample = protein_dist.sample().cpu()
return rna_sample, protein_sample
def get_reconstruction_loss(
self,
x: torch.Tensor,
y: torch.Tensor,
px_dict: Dict[str, torch.Tensor],
py_dict: Dict[str, torch.Tensor],
pro_batch_mask_minibatch: Optional[torch.Tensor] = None,
) -> Tuple[torch.Tensor, torch.Tensor]:
"""Compute reconstruction loss."""
px_ = px_dict
py_ = py_dict
# Reconstruction Loss
if self.gene_likelihood == "zinb":
reconst_loss_gene = (
-ZeroInflatedNegativeBinomial(
mu=px_["rate"], theta=px_["r"], zi_logits=px_["dropout"]
)
.log_prob(x)
.sum(dim=-1)
)
else:
reconst_loss_gene = (
-NegativeBinomial(mu=px_["rate"], theta=px_["r"])
.log_prob(x)
.sum(dim=-1)
)
py_conditional = NegativeBinomialMixture(
mu1=py_["rate_back"],
mu2=py_["rate_fore"],
theta1=py_["r"],
mixture_logits=py_["mixing"],
)
reconst_loss_protein_full = -py_conditional.log_prob(y)
if pro_batch_mask_minibatch is not None:
temp_pro_loss_full = torch.zeros_like(reconst_loss_protein_full)
temp_pro_loss_full.masked_scatter_(
pro_batch_mask_minibatch.bool(), reconst_loss_protein_full
)
reconst_loss_protein = temp_pro_loss_full.sum(dim=-1)
else:
reconst_loss_protein = reconst_loss_protein_full.sum(dim=-1)
return reconst_loss_gene, reconst_loss_protein
def reconstruction_loss(
self,
x: torch.Tensor,
px_rate: torch.Tensor,
px_r: torch.Tensor,
px_dropout: torch.Tensor,
mode: int,
) -> torch.Tensor:
reconstruction_loss = None
if self.gene_likelihoods[mode] == "zinb":
reconstruction_loss = (-ZeroInflatedNegativeBinomial(
mu=px_rate, theta=px_r,
zi_logits=px_dropout).log_prob(x).sum(dim=-1))
elif self.gene_likelihoods[mode] == "nb":
reconstruction_loss = (-NegativeBinomial(
mu=px_rate, theta=px_r).log_prob(x).sum(dim=-1))
elif self.gene_likelihoods[mode] == "poisson":
reconstruction_loss = -Poisson(px_rate).log_prob(x).sum(dim=1)
return reconstruction_loss
def test_zinb_distribution():
theta = 100.0 + torch.rand(size=(2, ))
mu = 15.0 * torch.ones_like(theta)
pi = torch.randn_like(theta)
x = torch.randint_like(mu, high=20)
log_p_ref = log_zinb_positive(x, mu, theta, pi)
dist = ZeroInflatedNegativeBinomial(mu=mu, theta=theta, zi_logits=pi)
log_p_zinb = dist.log_prob(x)
assert (log_p_ref - log_p_zinb).abs().max().item() <= 1e-8
torch.manual_seed(0)
s1 = dist.sample((100, ))
assert s1.shape == (100, 2)
s2 = dist.sample(sample_shape=(4, 3))
assert s2.shape == (4, 3, 2)
log_p_ref = log_nb_positive(x, mu, theta)
dist = NegativeBinomial(mu=mu, theta=theta)
log_p_nb = dist.log_prob(x)
assert (log_p_ref - log_p_nb).abs().max().item() <= 1e-8
s1 = dist.sample((1000, ))
assert s1.shape == (1000, 2)
assert (s1.mean(0) - mu).abs().mean() <= 1e0
assert (s1.std(0) - (mu + mu * mu / theta)**0.5).abs().mean() <= 1e0
size = (50, 3)
theta = 100.0 + torch.rand(size=size)
mu = 15.0 * torch.ones_like(theta)
pi = torch.randn_like(theta)
x = torch.randint_like(mu, high=20)
dist1 = ZeroInflatedNegativeBinomial(mu=mu,
theta=theta,
zi_logits=pi,
validate_args=True)
dist2 = NegativeBinomial(mu=mu, theta=theta, validate_args=True)
assert dist1.log_prob(x).shape == size
assert dist2.log_prob(x).shape == size
with pytest.raises(ValueError):
ZeroInflatedNegativeBinomial(mu=-mu,
theta=theta,
zi_logits=pi,
validate_args=True)
with pytest.warns(UserWarning):
dist1.log_prob(-x) # ensures neg values raise warning
with pytest.warns(UserWarning):
dist2.log_prob(0.5 * x) # ensures float values raise warning
def generative(self, x, size_factor, design_matrix=None):
# x has shape (n, g)
delta = torch.exp(self.delta_log) # (g, c)
theta_log = F.log_softmax(self.theta_logit, dim=-1) # (c)
# compute mean of NegBin - shape (n_cells, n_genes, n_labels)
n_cells = size_factor.shape[0]
base_mean = torch.log(size_factor) # (n, 1)
base_mean = base_mean.unsqueeze(-1).expand(n_cells, self.n_genes,
self.n_labels) # (n, g, c)
# compute beta (covariate coefficent)
# design_matrix has shape (n,p)
if design_matrix is not None:
covariates = torch.einsum("np,gp->gn", design_matrix,
self.beta) # (g, n)
covariates = torch.transpose(covariates, 0,
1).unsqueeze(-1) # (n, g, 1)
covariates = covariates.expand(n_cells, self.n_genes,
self.n_labels)
base_mean = base_mean + covariates
# base gene expression
b_g_0 = self.b_g_0.unsqueeze(-1).expand(n_cells, self.n_genes,
self.n_labels)
delta_rho = delta * self.rho
delta_rho = delta_rho.expand(n_cells, self.n_genes,
self.n_labels) # (n, g, c)
log_mu_ngc = base_mean + delta_rho + b_g_0
mu_ngc = torch.exp(log_mu_ngc) # (n, g, c)
# compute phi of NegBin - shape (n_cells, n_genes, n_labels)
a = torch.exp(self.log_a) # (B)
a = a.expand(n_cells, self.n_genes, self.n_labels, B)
b_init = 2 * ((self.basis_means[1] - self.basis_means[0])**2)
b = torch.exp(torch.ones(B, device=x.device) *
(-torch.log(b_init))) # (B)
b = b.expand(n_cells, self.n_genes, self.n_labels, B)
mu_ngcb = mu_ngc.unsqueeze(-1).expand(n_cells, self.n_genes,
self.n_labels, B) # (n, g, c, B)
basis_means = self.basis_means.expand(n_cells, self.n_genes,
self.n_labels, B) # (n, g, c, B)
phi = ( # (n, g, c)
torch.sum(a * torch.exp(-b * torch.square(mu_ngcb - basis_means)),
3) + LOWER_BOUND)
# compute gamma
nb_pdf = NegativeBinomial(mu=mu_ngc, theta=phi)
x_ = x.unsqueeze(-1).expand(n_cells, self.n_genes, self.n_labels)
x_log_prob_raw = nb_pdf.log_prob(x_) # (n, g, c)
theta_log = theta_log.expand(n_cells, self.n_labels)
p_x_c = torch.sum(x_log_prob_raw, 1) + theta_log # (n, c)
normalizer_over_c = torch.logsumexp(p_x_c, 1)
normalizer_over_c = normalizer_over_c.unsqueeze(-1).expand(
n_cells, self.n_labels)
gamma = torch.exp(p_x_c - normalizer_over_c) # (n, c)
return dict(
mu=mu_ngc,
phi=phi,
gamma=gamma,
p_x_c=p_x_c,
s=size_factor,
)