def torus_dbn(phis=None,
psis=None,
lengths=None,
num_sequences=None,
num_states=55,
prior_conc=0.1,
prior_loc=0.0,
prior_length_shape=100.,
prior_length_rate=100.,
prior_kappa_min=10.,
prior_kappa_max=1000.):
# From https://pyro.ai/examples/hmm.html
with ignore_jit_warnings():
if lengths is not None:
assert num_sequences is None
num_sequences = int(lengths.shape[0])
else:
assert num_sequences is not None
transition_probs = pyro.sample(
'transition_probs',
dist.Dirichlet(
torch.ones(num_states, num_states, dtype=torch.float) *
num_states).to_event(1))
length_shape = pyro.sample('length_shape',
dist.HalfCauchy(prior_length_shape))
length_rate = pyro.sample('length_rate',
dist.HalfCauchy(prior_length_rate))
phi_locs = pyro.sample(
'phi_locs',
dist.VonMises(
torch.ones(num_states, dtype=torch.float) * prior_loc,
torch.ones(num_states, dtype=torch.float) *
prior_conc).to_event(1))
phi_kappas = pyro.sample(
'phi_kappas',
dist.Uniform(
torch.ones(num_states, dtype=torch.float) * prior_kappa_min,
torch.ones(num_states, dtype=torch.float) *
prior_kappa_max).to_event(1))
psi_locs = pyro.sample(
'psi_locs',
dist.VonMises(
torch.ones(num_states, dtype=torch.float) * prior_loc,
torch.ones(num_states, dtype=torch.float) *
prior_conc).to_event(1))
psi_kappas = pyro.sample(
'psi_kappas',
dist.Uniform(
torch.ones(num_states, dtype=torch.float) * prior_kappa_min,
torch.ones(num_states, dtype=torch.float) *
prior_kappa_max).to_event(1))
element_plate = pyro.plate('elements', 1, dim=-1)
with pyro.plate('sequences', num_sequences, dim=-2) as batch:
if lengths is not None:
lengths = lengths[batch]
obs_length = lengths.float().unsqueeze(-1)
else:
obs_length = None
state = 0
sam_lengths = pyro.sample('length',
dist.TransformedDistribution(
dist.GammaPoisson(
length_shape, length_rate),
AffineTransform(0., 1.)),
obs=obs_length)
if lengths is None:
lengths = sam_lengths.squeeze(-1).long()
for t in pyro.markov(range(lengths.max())):
with poutine.mask(mask=(t < lengths).unsqueeze(-1)):
state = pyro.sample(f'state_{t}',
dist.Categorical(transition_probs[state]),
infer={'enumerate': 'parallel'})
if phis is not None:
obs_phi = Vindex(phis)[batch, t].unsqueeze(-1)
else:
obs_phi = None
if psis is not None:
obs_psi = Vindex(psis)[batch, t].unsqueeze(-1)
else:
obs_psi = None
with element_plate:
pyro.sample(f'phi_{t}',
dist.VonMises(phi_locs[state],
phi_kappas[state]),
obs=obs_phi)
pyro.sample(f'psi_{t}',
dist.VonMises(psi_locs[state],
psi_kappas[state]),
obs=obs_psi)
def forward(self, x_data, idx, batch_index):
obs2sample = one_hot(batch_index, self.n_batch)
obs_plate = self.create_plates(x_data, idx, batch_index)
# =====================Cell abundances w_sf======================= #
# factorisation prior on w_sf models similarity in locations
# across cell types f and reflects the absolute scale of w_sf
with obs_plate:
n_s_cells_per_location = pyro.sample(
"n_s_cells_per_location",
dist.Gamma(
self.N_cells_per_location * self.N_cells_mean_var_ratio,
self.N_cells_mean_var_ratio,
),
)
y_s_groups_per_location = pyro.sample(
"y_s_groups_per_location",
dist.Gamma(self.Y_groups_per_location, self.ones),
)
# cell group loadings
shape = self.ones_1_n_groups * y_s_groups_per_location / self.n_groups_tensor
rate = self.ones_1_n_groups / (n_s_cells_per_location /
y_s_groups_per_location)
with obs_plate:
z_sr_groups_factors = pyro.sample(
"z_sr_groups_factors",
dist.Gamma(
shape,
rate), # .to_event(1)#.expand([self.n_groups]).to_event(1)
) # (n_obs, n_groups)
k_r_factors_per_groups = pyro.sample(
"k_r_factors_per_groups",
dist.Gamma(self.factors_per_groups,
self.ones).expand([self.n_groups, 1]).to_event(2),
) # (self.n_groups, 1)
c2f_shape = k_r_factors_per_groups / self.n_factors_tensor
x_fr_group2fact = pyro.sample(
"x_fr_group2fact",
dist.Gamma(c2f_shape, k_r_factors_per_groups).expand(
[self.n_groups, self.n_factors]).to_event(2),
) # (self.n_groups, self.n_factors)
with obs_plate:
w_sf_mu = z_sr_groups_factors @ x_fr_group2fact
w_sf = pyro.sample(
"w_sf",
dist.Gamma(
w_sf_mu * self.w_sf_mean_var_ratio_tensor,
self.w_sf_mean_var_ratio_tensor,
),
) # (self.n_obs, self.n_factors)
# =====================Location-specific detection efficiency ======================= #
# y_s with hierarchical mean prior
detection_mean_y_e = pyro.sample(
"detection_mean_y_e",
dist.Gamma(
self.ones * self.detection_mean_hyp_prior_alpha,
self.ones * self.detection_mean_hyp_prior_beta,
).expand([self.n_batch, 1]).to_event(2),
)
detection_hyp_prior_alpha = pyro.deterministic(
"detection_hyp_prior_alpha",
self.ones_n_batch_1 * self.detection_hyp_prior_alpha,
)
beta = (obs2sample @ detection_hyp_prior_alpha) / (
obs2sample @ detection_mean_y_e)
with obs_plate:
detection_y_s = pyro.sample(
"detection_y_s",
dist.Gamma(obs2sample @ detection_hyp_prior_alpha, beta),
) # (self.n_obs, 1)
# =====================Gene-specific additive component ======================= #
# per gene molecule contribution that cannot be explained by
# cell state signatures (e.g. background, free-floating RNA)
s_g_gene_add_alpha_hyp = pyro.sample(
"s_g_gene_add_alpha_hyp",
dist.Gamma(self.gene_add_alpha_hyp_prior_alpha,
self.gene_add_alpha_hyp_prior_beta),
)
s_g_gene_add_mean = pyro.sample(
"s_g_gene_add_mean",
dist.Gamma(
self.gene_add_mean_hyp_prior_alpha,
self.gene_add_mean_hyp_prior_beta,
).expand([self.n_batch, 1]).to_event(2),
) # (self.n_batch)
s_g_gene_add_alpha_e_inv = pyro.sample(
"s_g_gene_add_alpha_e_inv",
dist.Exponential(s_g_gene_add_alpha_hyp).expand([self.n_batch,
1]).to_event(2),
) # (self.n_batch)
s_g_gene_add_alpha_e = self.ones / s_g_gene_add_alpha_e_inv.pow(2)
s_g_gene_add = pyro.sample(
"s_g_gene_add",
dist.Gamma(s_g_gene_add_alpha_e, s_g_gene_add_alpha_e /
s_g_gene_add_mean).expand([self.n_batch,
self.n_vars]).to_event(2),
) # (self.n_batch, n_vars)
# =====================Gene-specific overdispersion ======================= #
alpha_g_phi_hyp = pyro.sample(
"alpha_g_phi_hyp",
dist.Gamma(self.alpha_g_phi_hyp_prior_alpha,
self.alpha_g_phi_hyp_prior_beta),
)
alpha_g_inverse = pyro.sample(
"alpha_g_inverse",
dist.Exponential(alpha_g_phi_hyp).expand(
[self.n_batch, self.n_vars]).to_event(2),
) # (self.n_batch, self.n_vars)
# =====================Expected expression ======================= #
# expected expression
mu = ((w_sf @ self.cell_state) +
(obs2sample @ s_g_gene_add)) * detection_y_s
alpha = obs2sample @ (self.ones / alpha_g_inverse.pow(2))
# convert mean and overdispersion to total count and logits
# total_count, logits = _convert_mean_disp_to_counts_logits(
# mu, alpha, eps=self.eps
# )
# =====================DATA likelihood ======================= #
# Likelihood (sampling distribution) of data_target & add overdispersion via NegativeBinomial
with obs_plate:
pyro.sample(
"data_target",
dist.GammaPoisson(concentration=alpha, rate=alpha / mu),
# dist.NegativeBinomial(total_count=total_count, logits=logits),
obs=x_data,
)
# =====================Compute mRNA count from each factor in locations ======================= #
with obs_plate:
mRNA = w_sf * (self.cell_state).sum(-1)
pyro.deterministic("u_sf_mRNA_factors", mRNA)
def forward(self, x_data, idx, batch_index, label_index,
extra_categoricals):
obs2sample = one_hot(batch_index, self.n_batch)
obs2label = one_hot(label_index, self.n_factors)
if self.n_extra_categoricals is not None:
obs2extra_categoricals = torch.cat(
[
one_hot(
extra_categoricals[:, i].view(
(extra_categoricals.shape[0], 1)),
n_cat,
) for i, n_cat in enumerate(self.n_extra_categoricals)
],
dim=1,
)
obs_plate = self.create_plates(x_data, idx, batch_index, label_index,
extra_categoricals)
# =====================Per-cluster average mRNA count ======================= #
# \mu_{f,g}
per_cluster_mu_fg = pyro.sample(
"per_cluster_mu_fg",
dist.Gamma(self.ones,
self.ones).expand([self.n_factors,
self.n_vars]).to_event(2),
)
# =====================Gene-specific multiplicative component ======================= #
# `y_{t, g}` per gene multiplicative effect that explains the difference
# in sensitivity between genes in each technology or covariate effect
if self.n_extra_categoricals is not None:
detection_tech_gene_tg = pyro.sample(
"detection_tech_gene_tg",
dist.Gamma(
self.ones * self.gene_tech_prior_alpha,
self.ones * self.gene_tech_prior_beta,
).expand([np.sum(self.n_extra_categoricals),
self.n_vars]).to_event(2),
)
# =====================Cell-specific detection efficiency ======================= #
# y_c with hierarchical mean prior
detection_mean_y_e = pyro.sample(
"detection_mean_y_e",
dist.Gamma(
self.ones * self.detection_mean_hyp_prior_alpha,
self.ones * self.detection_mean_hyp_prior_beta,
).expand([self.n_batch, 1]).to_event(2),
)
detection_y_c = obs2sample @ detection_mean_y_e # (self.n_obs, 1)
# =====================Gene-specific additive component ======================= #
# s_{e,g} accounting for background, free-floating RNA
s_g_gene_add_alpha_hyp = pyro.sample(
"s_g_gene_add_alpha_hyp",
dist.Gamma(self.ones * self.gene_add_alpha_hyp_prior_alpha,
self.ones * self.gene_add_alpha_hyp_prior_beta),
)
s_g_gene_add_mean = pyro.sample(
"s_g_gene_add_mean",
dist.Gamma(
self.gene_add_mean_hyp_prior_alpha,
self.gene_add_mean_hyp_prior_beta,
).expand([self.n_batch, 1]).to_event(2),
) # (self.n_batch)
s_g_gene_add_alpha_e_inv = pyro.sample(
"s_g_gene_add_alpha_e_inv",
dist.Exponential(s_g_gene_add_alpha_hyp).expand([self.n_batch,
1]).to_event(2),
) # (self.n_batch)
s_g_gene_add_alpha_e = self.ones / s_g_gene_add_alpha_e_inv.pow(2)
s_g_gene_add = pyro.sample(
"s_g_gene_add",
dist.Gamma(s_g_gene_add_alpha_e, s_g_gene_add_alpha_e /
s_g_gene_add_mean).expand([self.n_batch,
self.n_vars]).to_event(2),
) # (self.n_batch, n_vars)
# =====================Gene-specific overdispersion ======================= #
alpha_g_phi_hyp = pyro.sample(
"alpha_g_phi_hyp",
dist.Gamma(self.ones * self.alpha_g_phi_hyp_prior_alpha,
self.ones * self.alpha_g_phi_hyp_prior_beta),
)
alpha_g_inverse = pyro.sample(
"alpha_g_inverse",
dist.Exponential(alpha_g_phi_hyp).expand([1, self.n_vars
]).to_event(2),
) # (self.n_batch or 1, self.n_vars)
# =====================Expected expression ======================= #
# overdispersion
alpha = self.ones / alpha_g_inverse.pow(2)
# biological expression
mu = (
obs2label @ per_cluster_mu_fg +
obs2sample @ s_g_gene_add # contaminating RNA
) * detection_y_c # cell-specific normalisation
if self.n_extra_categoricals is not None:
# gene-specific normalisation for covatiates
mu = mu * (obs2extra_categoricals @ detection_tech_gene_tg)
# total_count, logits = _convert_mean_disp_to_counts_logits(
# mu, alpha, eps=self.eps
# )
# =====================DATA likelihood ======================= #
# Likelihood (sampling distribution) of data_target & add overdispersion via NegativeBinomial
with obs_plate:
pyro.sample(
"data_target",
dist.GammaPoisson(concentration=alpha, rate=alpha / mu),
# dist.NegativeBinomial(total_count=total_count, logits=logits),
obs=x_data,
)