def model_3D(data):
# Sampling mu and kappa
psi_1 = pyro.sample("psi_1", dist.VonMises(0, 0.1))
phi_2 = pyro.sample("phi_2", dist.VonMises(0, 0.1))
psi_2 = pyro.sample("psi_2", dist.VonMises(0, 0.1))
phi_3 = pyro.sample("phi_3", dist.VonMises(0, 0.1))
das = torch.tensor([[[0., psi_1, np.pi]],[[phi_2, psi_2, np.pi]],[[phi_3, 0., 0.]]])
coords_3d = pnerf(das)
_3a_x = coords_3d[2,:,0]
_4a_x = coords_3d[3,:,0]
_5a_x = coords_3d[4,:,0]
_6a_x = coords_3d[5,:,0]
_7a_x = coords_3d[6,:,0]
_8a_x = coords_3d[7,:,0]
_9a_x = coords_3d[8,:,0]
_3a_y = coords_3d[2,:,1]
_4a_y = coords_3d[3,:,1]
_5a_y = coords_3d[4,:,1]
_6a_y = coords_3d[5,:,1]
_7a_y = coords_3d[6,:,1]
_8a_y = coords_3d[7,:,1]
_9a_y = coords_3d[8,:,1]
_3a_z = coords_3d[2,:,2]
_4a_z = coords_3d[3,:,2]
_5a_z = coords_3d[4,:,2]
_6a_z = coords_3d[5,:,2]
_7a_z = coords_3d[6,:,2]
_8a_z = coords_3d[7,:,2]
_9a_z = coords_3d[8,:,2]
# Looping over the observed data in an independant manner
with pyro.plate('3D_coords'):
pyro.sample("obs_3D_3a_x", dist.Normal(_3a_x, 0.001), obs=data[2,:,0])
pyro.sample("obs_3D_4a_x", dist.Normal(_4a_x, 0.001), obs=data[3,:,0])
pyro.sample("obs_3D_5a_x", dist.Normal(_5a_x, 0.001), obs=data[4,:,0])
pyro.sample("obs_3D_6a_x", dist.Normal(_6a_x, 0.001), obs=data[5,:,0])
pyro.sample("obs_3D_7a_x", dist.Normal(_7a_x, 0.001), obs=data[6,:,0])
pyro.sample("obs_3D_8a_x", dist.Normal(_8a_x, 0.001), obs=data[7,:,0])
pyro.sample("obs_3D_9a_x", dist.Normal(_9a_x, 0.001), obs=data[8,:,0])
pyro.sample("obs_3D_3a_y", dist.Normal(_3a_y, 0.001), obs=data[2,:,1])
pyro.sample("obs_3D_4a_y", dist.Normal(_4a_y, 0.001), obs=data[3,:,1])
pyro.sample("obs_3D_5a_y", dist.Normal(_5a_y, 0.001), obs=data[4,:,1])
pyro.sample("obs_3D_6a_y", dist.Normal(_6a_y, 0.001), obs=data[5,:,1])
pyro.sample("obs_3D_7a_y", dist.Normal(_7a_y, 0.001), obs=data[6,:,1])
pyro.sample("obs_3D_8a_y", dist.Normal(_8a_y, 0.001), obs=data[7,:,1])
pyro.sample("obs_3D_9a_y", dist.Normal(_9a_y, 0.001), obs=data[8,:,1])
pyro.sample("obs_3D_3a_z", dist.Normal(_3a_z, 0.001), obs=data[2,:,2])
pyro.sample("obs_3D_4a_z", dist.Normal(_4a_z, 0.001), obs=data[3,:,2])
pyro.sample("obs_3D_5a_z", dist.Normal(_5a_z, 0.001), obs=data[4,:,2])
pyro.sample("obs_3D_6a_z", dist.Normal(_6a_z, 0.001), obs=data[5,:,2])
pyro.sample("obs_3D_7a_z", dist.Normal(_7a_z, 0.001), obs=data[6,:,2])
pyro.sample("obs_3D_8a_z", dist.Normal(_8a_z, 0.001), obs=data[7,:,2])
pyro.sample("obs_3D_9a_z", dist.Normal(_9a_z, 0.001), obs=data[8,:,2])
def guide_3D(data):
# Hyperparameters
mu_psi_1 = pyro.param('mu_psi_1', torch.tensor(0.))
kappa_psi_1 = pyro.param('kappa_psi_1', torch.tensor(0.01), constraint=constraints.positive)
mu_phi_2 = pyro.param('mu_phi_2', torch.tensor(0.))
kappa_phi_2 = pyro.param('kappa_phi_2', torch.tensor(0.01), constraint=constraints.positive)
mu_psi_2 = pyro.param('mu_psi_2', torch.tensor(0.))
kappa_psi_2 = pyro.param('kappa_psi_2', torch.tensor(0.01), constraint=constraints.positive)
mu_phi_3 = pyro.param('mu_phi_3', torch.tensor(0.))
kappa_phi_3 = pyro.param('kappa_phi_3', torch.tensor(0.01), constraint=constraints.positive)
# Sampling mu and kappa
psi_1 = pyro.sample("psi_1", dist.VonMises(mu_psi_1, 10 + kappa_psi_1))
phi_2 = pyro.sample("phi_2", dist.VonMises(mu_phi_2, 10 + kappa_phi_2))
psi_2 = pyro.sample("psi_2", dist.VonMises(mu_psi_2, 10 + kappa_psi_2))
phi_3 = pyro.sample("phi_3", dist.VonMises(mu_phi_3, 10 + kappa_phi_3))
def model(num_hidden=50):
zs = pyro.sample('zs', VSGP(OUKernel(drift, scale), inducing_set,
dist.MultivariateNormal, input_data=input_data))
decoder = torch.nn.GRU(30, num_hidden)
pyro.module('decoder', decoder)
mean_nn = torch.nn.Sequential(torch.nn.Linear(num_hidden, 1),
torch.nn.Sigmoid())
kappa_nn = torch.nn.Sequential(torch.nn.Linear(num_hidden, 1),
torch.nn.Softplus())
mean_nn2 = torch.nn.Sequential(torch.nn.Linear(num_hidden, 1),
torch.nn.Sigmoid())
kappa_nn2 = torch.nn.Sequential(torch.nn.Linear(num_hidden, 1),
torch.nn.Softplus())
pyro.module('param_nn', param_nn)
decoded = decoder(zs) # Should autoregress on zs
means1 = mean_nn(decoded)
kappas1 = kappa_nn(decoded)
means2 = mean_nn2(decoded)
kappas2 = kappa_nn2(decoded)
pyro.sample('phis', dist.VonMises(means1, kappas1), obs=observed_phis)
pyro.sample('psis', dist.VonMises(means2, kappas2), obs=observed_psis)
def model(self, x):
# register PyTorch module `decoder` with Pyro
pyro.module("decoder", self.decoder)
with pyro.plate("data", x.shape[0]):
# setup hyperparameters for prior p(z)
z_loc = x.new_zeros(torch.Size((x.shape[0], self.z_dim)))
z_scale = x.new_ones(torch.Size((x.shape[0], self.z_dim)))
# sample from prior (value will be sampled by guide when computing the ELBO)
z = pyro.sample("latent", dist.Normal(z_loc, z_scale).to_event(1))
# decode the latent code z
loc, k = self.decoder.forward(z)
# score against actual images
pyro.sample("obs", dist.VonMises(loc, k).to_event(1), obs=x)
def model_3DA(data):
# Sampling mu and kappa
mu_psi_1 = pyro.sample("mu_psi_1", dist.Uniform(-np.pi, np.pi))
inv_kappa_psi_1 = pyro.sample("inv_kappa_psi_1", dist.HalfNormal(1.))
kappa_psi_1 = 100 + 1/inv_kappa_psi_1
mu_phi_2 = pyro.sample("mu_phi_2", dist.Uniform(-np.pi, np.pi))
inv_kappa_phi_2 = pyro.sample("inv_kappa_phi_2", dist.HalfNormal(1.))
kappa_phi_2 = 100 + 1/inv_kappa_phi_2
mu_psi_2 = pyro.sample("mu_psi_2", dist.Uniform(-np.pi, np.pi))
inv_kappa_psi_2 = pyro.sample("inv_kappa_psi_2", dist.HalfNormal(1.))
kappa_psi_2 = 100 + 1/inv_kappa_psi_2
mu_phi_3 = pyro.sample("mu_phi_3", dist.Uniform(-np.pi, np.pi))
inv_kappa_phi_3 = pyro.sample("inv_kappa_phi_3", dist.HalfNormal(1.))
kappa_phi_3 = 100 + 1/inv_kappa_phi_3
# Looping over the observed data in an conditionally independant manner
with pyro.plate('dihedral_angles'):
pyro.sample("obs_psi_1", dist.VonMises(mu_psi_1, kappa_psi_1), obs=data[0,:,1])
pyro.sample("obs_phi_2", dist.VonMises(mu_phi_2, kappa_phi_2), obs=data[1,:,0])
pyro.sample("obs_psi_2", dist.VonMises(mu_psi_2, kappa_psi_2), obs=data[1,:,1])
pyro.sample("obs_phi_3", dist.VonMises(mu_phi_3, kappa_phi_3), obs=data[2,:,0])
def __init__(self, von_loc, von_conc, skewness):
base_dist = dist.VonMises(von_loc, von_conc).to_event(von_loc.ndim)
super().__init__(base_dist, skewness)
def random_pose_transform(transforms: transforms.TransformSequence,
device=torch.device("cpu")):
"""
Take a sequence of transformations and create a r.v corresponding to the co-ordinates of each.
Return the transformation corresponding to this that can be applied to an input image.
TODO: atm these classes have a cnn attached; this doesn't feel like a super clean abstraciton, but we'll see...
"""
params = []
for transform in transforms:
# sample the U and V corresponding to that transformation
sample_site_prefix = repr(type(transform)).split(".")[-1].strip("'>")
u_sample_name = sample_site_prefix + "_u"
v_sample_name = sample_site_prefix + "_v"
# todo: make this more sensible
ps = []
if transform.has_u:
if transform.periodic_u:
u = pyro.sample(
u_sample_name,
D.VonMises(
torch.tensor(0.0, device=device),
torch.tensor(1e-2, device=device),
),
)
else:
u = pyro.sample(
u_sample_name,
D.Normal(
torch.tensor(0.0, device=device),
torch.tensor(1.0, device=device),
),
)
ps.append(u)
if transform.has_v:
if transform.periodic_v:
v = pyro.sample(
v_sample_name,
D.VonMises(
torch.tensor(0.0, device=device),
torch.tensor(1e-2, device=device),
),
)
else:
v = pyro.sample(
v_sample_name,
D.Normal(
torch.tensor(0.0, device=device),
torch.tensor(1.0, device=device),
),
)
ps.append(v)
params.append(ps)
# we take the inverse transformation here because we want to use the order specified by
# the spatial transformer network, which uses the opposite convection to what make sense
# from a generative perspective
if len(params) > 0:
transform_grid = transforms.inverse_transform_from_params(params)
else:
# handle the edge case where we have an empty list of transformations.
transform_grid = ProjectiveGridTransform(torch.eye(3, device=device))
return transform_grid
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 model_generic(config):
"""Hierarchical mixed-effects hidden markov model"""
MISSING = config["MISSING"]
N_v = config["sizes"]["random"]
N_state = config["sizes"]["state"]
# initialize group-level random effect parameterss
if config["group"]["random"] == "discrete":
probs_e_g = pyro.param("probs_e_group",
lambda: torch.randn((N_v, )).abs(),
constraint=constraints.simplex)
theta_g = pyro.param("theta_group", lambda: torch.randn(
(N_v, N_state**2)))
elif config["group"]["random"] == "continuous":
loc_g = torch.zeros((N_state**2, ))
scale_g = torch.ones((N_state**2, ))
# initialize individual-level random effect parameters
N_c = config["sizes"]["group"]
if config["individual"]["random"] == "discrete":
probs_e_i = pyro.param("probs_e_individual",
lambda: torch.randn((
N_c,
N_v,
)).abs(),
constraint=constraints.simplex)
theta_i = pyro.param("theta_individual", lambda: torch.randn(
(N_c, N_v, N_state**2)))
elif config["individual"]["random"] == "continuous":
loc_i = torch.zeros((
N_c,
N_state**2,
))
scale_i = torch.ones((
N_c,
N_state**2,
))
# initialize likelihood parameters
# observation 1: step size (step ~ Gamma)
step_zi_param = pyro.param("step_zi_param", lambda: torch.ones(
(N_state, 2)))
step_concentration = pyro.param("step_param_concentration",
lambda: torch.randn((N_state, )).abs(),
constraint=constraints.positive)
step_rate = pyro.param("step_param_rate",
lambda: torch.randn((N_state, )).abs(),
constraint=constraints.positive)
# observation 2: step angle (angle ~ VonMises)
angle_concentration = pyro.param("angle_param_concentration",
lambda: torch.randn((N_state, )).abs(),
constraint=constraints.positive)
angle_loc = pyro.param("angle_param_loc", lambda: torch.randn(
(N_state, )).abs())
# observation 3: dive activity (omega ~ Beta)
omega_zi_param = pyro.param("omega_zi_param", lambda: torch.ones(
(N_state, 2)))
omega_concentration0 = pyro.param("omega_param_concentration0",
lambda: torch.randn((N_state, )).abs(),
constraint=constraints.positive)
omega_concentration1 = pyro.param("omega_param_concentration1",
lambda: torch.randn((N_state, )).abs(),
constraint=constraints.positive)
# initialize gamma to uniform
gamma = torch.zeros((N_state**2, ))
N_c = config["sizes"]["group"]
with pyro.plate("group", N_c, dim=-1):
# group-level random effects
if config["group"]["random"] == "discrete":
# group-level discrete effect
e_g = pyro.sample("e_g", dist.Categorical(probs_e_g))
eps_g = Vindex(theta_g)[..., e_g, :]
elif config["group"]["random"] == "continuous":
eps_g = pyro.sample(
"eps_g",
dist.Normal(loc_g, scale_g).to_event(1),
) # infer={"num_samples": 10})
else:
eps_g = 0.
# add group-level random effect to gamma
gamma = gamma + eps_g
N_s = config["sizes"]["individual"]
with pyro.plate(
"individual", N_s,
dim=-2), poutine.mask(mask=config["individual"]["mask"]):
# individual-level random effects
if config["individual"]["random"] == "discrete":
# individual-level discrete effect
e_i = pyro.sample("e_i", dist.Categorical(probs_e_i))
eps_i = Vindex(theta_i)[..., e_i, :]
# assert eps_i.shape[-3:] == (1, N_c, N_state ** 2) and eps_i.shape[0] == N_v
elif config["individual"]["random"] == "continuous":
eps_i = pyro.sample(
"eps_i",
dist.Normal(loc_i, scale_i).to_event(1),
) # infer={"num_samples": 10})
else:
eps_i = 0.
# add individual-level random effect to gamma
gamma = gamma + eps_i
y = torch.tensor(0).long()
N_t = config["sizes"]["timesteps"]
for t in pyro.markov(range(N_t)):
with poutine.mask(mask=config["timestep"]["mask"][..., t]):
gamma_t = gamma # per-timestep variable
# finally, reshape gamma as batch of transition matrices
gamma_t = gamma_t.reshape(
tuple(gamma_t.shape[:-1]) + (N_state, N_state))
# we've accounted for all effects, now actually compute gamma_y
gamma_y = Vindex(gamma_t)[..., y, :]
y = pyro.sample("y_{}".format(t),
dist.Categorical(logits=gamma_y))
# observation 1: step size
step_dist = dist.Gamma(
concentration=Vindex(step_concentration)[..., y],
rate=Vindex(step_rate)[..., y])
# zero-inflation with MaskedMixture
step_zi = Vindex(step_zi_param)[..., y, :]
step_zi_mask = pyro.sample(
"step_zi_{}".format(t),
dist.Categorical(logits=step_zi),
obs=(config["observations"]["step"][...,
t] == MISSING))
step_zi_zero_dist = dist.Delta(v=torch.tensor(MISSING))
step_zi_dist = dist.MaskedMixture(step_zi_mask, step_dist,
step_zi_zero_dist)
pyro.sample("step_{}".format(t),
step_zi_dist,
obs=config["observations"]["step"][..., t])
# observation 2: step angle
angle_dist = dist.VonMises(
concentration=Vindex(angle_concentration)[..., y],
loc=Vindex(angle_loc)[..., y])
pyro.sample("angle_{}".format(t),
angle_dist,
obs=config["observations"]["angle"][..., t])
# observation 3: dive activity
omega_dist = dist.Beta(
concentration0=Vindex(omega_concentration0)[..., y],
concentration1=Vindex(omega_concentration1)[..., y])
# zero-inflation with MaskedMixture
omega_zi = Vindex(omega_zi_param)[..., y, :]
omega_zi_mask = pyro.sample(
"omega_zi_{}".format(t),
dist.Categorical(logits=omega_zi),
obs=(config["observations"]["omega"][...,
t] == MISSING))
omega_zi_zero_dist = dist.Delta(v=torch.tensor(MISSING))
omega_zi_dist = dist.MaskedMixture(omega_zi_mask,
omega_dist,
omega_zi_zero_dist)
pyro.sample("omega_{}".format(t),
omega_zi_dist,
obs=config["observations"]["omega"][..., t])