def evaluate(method: storch.method.Method, model: DiscreteVAE, data, optimizer):
# Compute expected gradient
optimizer.zero_grad()
z = generative_story(storch.method.Expect("z"), model, data)
storch.backward()
expected_gradient = z.param_grads["probs"]
# Collect gradient samples
gradients = []
for i in range(100):
optimizer.zero_grad()
z = generative_story(method, model, data)
elbo = storch.backward()
gradients.append(z.param_grads["probs"])
gradients = storch.gather_samples(gradients, "gradients")
mean_gradient = storch.reduce_plates(gradients, "gradients")
bias_gradient = (
storch.reduce_plates((mean_gradient - expected_gradient) ** 2)
).sum()
print(
"Training ELBO "
+ str(elbo.item())
+ " Gradient variance "
+ str(storch.variance(gradients, "gradients")._tensor.item())
+ " Gradient bias "
+ str(bias_gradient._tensor.item())
)
def experiment(method):
optim.zero_grad()
b = Bernoulli(logits=eta.repeat(3))
x = method(b)
cost = torch.sum((x - p)**2, -1)
storch.add_cost(cost, "cost")
storch.backward()
return eta.grad.clone()
def experiment(method):
for i in range(2000):
optim.zero_grad()
b = Bernoulli(logits=eta)
x = method(b)
cost = torch.sum((x - p)**2, -1)
storch.add_cost(cost, "cost")
storch.backward()
optim.step()
if i % 100 == 0:
print(eta)
def estimate_variance(method):
gradient_samples = []
for i in range(1000):
f, c = compute_f(method)
storch.add_cost(f, "f")
storch.backward()
gradient_samples.append(c.grad)
gradients = storch.gather_samples(gradient_samples, "gradients")
# print(gradients)
print("variance", storch.variance(gradients, "gradients"))
print("mean", storch.reduce_plates(gradients, "gradients"))
print("st dev", torch.sqrt(storch.variance(gradients, "gradients")))
print(type(gradients))
print(gradients.shape)
print(gradients.plates)
def train(method: storch.method.Method, train_loader):
model = DiscreteVAE()
optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)
for epoch in range(5):
print("Epoch:" + str(epoch + 1))
for i, (data, _) in enumerate(train_loader):
# if i % 300 == 0:
# evaluate(method, model, data, optimizer)
optimizer.zero_grad()
generative_story(method, model, data)
elbo = storch.backward()
optimizer.step()
if i % 300 == 0:
print("Training ELBO " + str(elbo.item()))
import storch
import torch
from torch.distributions import Bernoulli
from storch.method import GumbelSoftmax
torch.manual_seed(0)
p = torch.tensor(0.5, requires_grad=True)
for i in range(10000):
sample = GumbelSoftmax(f"sample_{i}")(Bernoulli(p))
storch.add_cost(sample, f"cost_{i}")
storch.backward()
print("Finished")
score_method = storch.method.ScoreFunction("white_noise_1", n_samples=2)
infer_method = storch.method.Infer("white_noise_2", Normal)
def loss(v):
return torch.nn.MSELoss(reduction="none")(v, theta).mean(dim=-1)
mu = lax_method(Normal(mu_prior, 1))
k = expect(
Categorical(probs=torch.tensor([[0.1, 0.3, 0.6], [0.1, 0.8, 0.1]],
requires_grad=True)), )
agg_v = 0.0
s1 = 1.0
for i in range(2):
k1, k2 = 0, 0
if i == 1:
k1 = k[:, 0]
k2 = k[:, 1]
s1 = score_method(Normal(mu + k1, 1))
aaa = -mu + s1 * k2
s2 = infer_method(Normal(-mu + s1 * k2, 1))
# plus = lambda a, b: a + b
# plus = storch.deterministic(plus)
agg_v = agg_v + s1 + s2 * mu
print(isinstance(agg_v, Iterable))
storch.add_cost(loss(agg_v), "loss")
storch.backward(debug=False, print_costs=True)
import storch
import torch
from torch.distributions import Bernoulli, OneHotCategorical
expect = storch.method.Expect("x")
probs = torch.tensor([0.95, 0.01, 0.01, 0.01, 0.01, 0.01], requires_grad=True)
indices = torch.tensor([1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
b = OneHotCategorical(probs=probs)
z = expect.sample(b)
c = (2.4 * z * indices).sum(-1)
storch.add_cost(c, "no_baseline_cost")
storch.backward()
expect_grad = z.grad["probs"].clone()
def eval(grads):
print("----------------------------------")
grad_samples = storch.gather_samples(grads, "variance")
mean = storch.reduce_plates(grad_samples, plates=["variance"])
print("mean grad", mean)
print("expected grad", expect_grad)
print("specific_diffs", (mean - expect_grad)**2)
mse = storch.reduce_plates((grad_samples - expect_grad)**2).sum()
print("MSE", mse)
bias = (storch.reduce_plates((mean - expect_grad)**2)).sum()
print("bias", bias)
return bias
d = a + b
# Sample e from a normal distribution using reparameterization
normal_distribution = Normal(b + c, 1)
e = method(normal_distribution)
f = d * e * e
return f, c
# e*e follows a noncentral chi-squared distribution https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
# exp_f = d * (1 + mu * mu)
repar = Reparameterization("e", n_samples=1)
f, c = compute_f(repar)
storch.add_cost(f, "f")
print(storch.backward())
print("first derivative estimate", c.grad)
f, c = compute_f(repar)
storch.add_cost(f, "f")
print(storch.backward())
print("second derivative estimate", c.grad)
def estimate_variance(method):
gradient_samples = []
for i in range(1000):
f, c = compute_f(method)
storch.add_cost(f, "f")
def train(epoch, model, train_loader, device, optimizer, args, writer):
model.train()
train_loss = 0
for batch_idx, (data, _) in enumerate(train_loader):
data = data.to(device)
optimizer.zero_grad()
storch.reset()
# Denote the minibatch dimension as being independent
data = storch.denote_independent(data.view(-1, 784), 0, "data")
recon_batch, KLD, z = model(data)
storch.add_cost(loss_function(recon_batch, data), "reconstruction")
cost = backward()
train_loss += cost.item()
optimizer.step()
cond_log = batch_idx % args.log_interval == 0
if cond_log:
step = 100.0 * batch_idx / len(train_loader)
global_step = 100 * (epoch - 1) + step
# Variance of expect method is 0 by definition.
variances = {}
if args.method != "expect" and args.variance_samples > 1:
_consider_param = "probs"
if args.latents < 3:
old_method = model.sampling_method
model.sampling_method = Expect("z")
optimizer.zero_grad()
recon_batch, _, z = model(data)
storch.add_cost(loss_function(recon_batch, data),
"reconstruction")
backward()
expect_grad = storch.reduce_plates(
z.grad[_consider_param]).detach_tensor()
optimizer.zero_grad()
model.sampling_method = old_method
grads = {n: [] for n in z.grad}
for i in range(args.variance_samples):
optimizer.zero_grad()
recon_batch, _, z = model(data)
storch.add_cost(loss_function(recon_batch, data),
"reconstruction")
backward()
for param_name, grad in z.grad.items():
# Make sure to reduce the data dimension and detach, for memory reasons.
grads[param_name].append(
storch.reduce_plates(grad).detach_tensor())
variances = {}
for param_name, gradz in grads.items():
# Create a new independent dimension for the different gradient samples
grad_samples = storch.gather_samples(gradz, "variance")
# Compute the variance over this independent dimension
variances[param_name] = storch.variance(
grad_samples, "variance")._tensor
if param_name == _consider_param and args.latents < 3:
mean = storch.reduce_plates(grad_samples, "variance")
mse = storch.reduce_plates(
(grad_samples - expect_grad)**2).sum()
bias = (storch.reduce_plates(
(mean - expect_grad)**2)).sum()
print("mse", mse._tensor.item())
# Should approach 0 when increasing variance_samples for unbiased estimators.
print("bias", bias._tensor.item())
writer.add_scalar("train/probs_bias", bias._tensor,
global_step)
writer.add_scalar("train/probs_mse", mse._tensor,
global_step)
print(
"Train Epoch: {} [{}/{} ({:.0f}%)]\tCost: {:.6f}\t Logits var {}"
.format(
epoch,
batch_idx * len(data),
len(train_loader.dataset),
step,
cost.item(),
variances,
))
writer.add_scalar("train/ELBO", cost, global_step)
for param_name, var in variances.items():
writer.add_scalar("train/variance/" + param_name, var,
global_step)
avg_train_loss = train_loss / (batch_idx + 1)
print("====> Epoch: {} Average loss: {:.4f}".format(epoch, avg_train_loss))
return avg_train_loss
