def build_model(self):
self.prior = GaussBernouilliPrior(size=(self.N, ), rho=self.rho)
ensemble = GaussianEnsemble(self.M, self.N)
self.A = ensemble.generate()
model = self.prior @ V(id="x") @ LinearChannel(W=self.A) @ V(
id='z') @ GaussianChannel(var=self.Delta) @ O(id="y")
model = model.to_model()
return model
def build_sparse_fft_student(size, prior_var, fft_rho, fft_var, noise_var):
x_shape = (size, )
fft_shape = (2, ) + x_shape
student = (GaussianPrior(size=size, var=prior_var) @ SIMOVariable(
id="x", n_next=2) @ (GaussianChannel(var=noise_var) @ O("y") +
(DFTChannel(real=True) + GaussBernouilliPrior(
size=fft_shape, var=fft_var, rho=fft_rho))
@ MILeafVariable(id="z", n_prev=2))).to_model()
return student
def build_sparse_grad_student(N, rho, noise_var):
x_shape = (N, )
z_shape = (1, N)
student = (GaussianPrior(size=x_shape) @ SIMOVariable(id="x", n_next=2) @ (
GaussianChannel(var=noise_var) @ O("y") +
(GradientChannel(shape=x_shape) + GaussBernoulliPrior(
size=z_shape, rho=rho)) @ MILeafVariable(id="z", n_prev=2))
).to_model()
return student
def run_benchmark(alpha, algo, seed):
# create scenario
N, rho, noise_var = 1000, 0.05, 1e-2
M = int(alpha * N)
A = GaussianEnsemble(M=M, N=N).generate()
t0 = time()
model = (GaussBernoulliPrior(size=N, rho=rho) @ V("x") @ LinearChannel(A)
@ V("z") @ GaussianChannel(var=noise_var) @ O("y")).to_model()
t1 = time()
record = {"svd_time": t1 - t0} # svd precomputation time
scenario = BayesOptimalScenario(model, x_ids=["x"])
scenario.setup(seed)
y = scenario.observations["y"]
# run algo
t0 = time()
if algo == "SE":
x_data = scenario.run_se(max_iter=1000, damping=0.1)
record["mse"] = x_data["x"]["v"]
record["n_iter"] = x_data["n_iter"]
if algo == "EP":
x_data = scenario.run_ep(max_iter=1000, damping=0.1)
x_pred = x_data["x"]["r"]
record["n_iter"] = x_data["n_iter"]
if algo == "LassoCV":
lasso = LassoCV(cv=5)
lasso.fit(A, y)
x_pred = lasso.coef_
record["param_scikit"] = lasso.alpha_
record["n_iter"] = lasso.n_iter_
if algo == "Lasso":
optim = pd.read_csv("optimal_param_lasso.csv")
param_scaled = np.interp(alpha, optim["alpha"], optim["param_scaled"])
param_scikit = noise_var * param_scaled / (M * rho)
lasso = Lasso(alpha=param_scikit)
lasso.fit(A, y)
x_pred = lasso.coef_
record["param_scikit"] = param_scikit
record["n_iter"] = lasso.n_iter_
if algo == "pymc3":
with pm.Model():
ber = pm.Bernoulli("ber", p=rho, shape=N)
nor = pm.Normal("nor", mu=0, sd=1, shape=N)
x = pm.Deterministic("x", ber * nor)
likelihood = pm.Normal("y",
mu=pm.math.dot(A, x),
sigma=np.sqrt(noise_var),
observed=y)
trace = pm.sample(draws=1000, chains=1, return_inferencedata=False)
x_pred = trace.get_values('x').mean(axis=0)
t1 = time()
record["time"] = t1 - t0
if algo != "SE":
record["mse"] = mean_squared_error(x_pred, scenario.x_true["x"])
return record
def sample_from_prior(self, prior_x):
if self.plot_prior_sample:
model = prior_x @ O(id="y")
model = model.to_model_dag()
prior_sample = model.to_model()
fig, axs = plt.subplots(4, 4, figsize=(4, 4))
for ax in axs.ravel():
sample = prior_sample.sample()['y']
ax.set_axis_off()
ax.imshow(sample.reshape(28, 28), cmap="gray")
plt.show()
def mse_lasso(alpha, param_scaled, seed):
# create scenario
N, rho, noise_var = 1000, 0.05, 1e-2
M = int(alpha * N)
A = GaussianEnsemble(M=M, N=N).generate()
model = (GaussBernoulliPrior(size=N, rho=rho) @ V("x") @ LinearChannel(A)
@ V("z") @ GaussianChannel(var=noise_var) @ O("y")).to_model()
scenario = BayesOptimalScenario(model, x_ids=["x"])
scenario.setup(seed)
y = scenario.observations["y"]
# run lasso
param_scikit = noise_var * param_scaled / (M * rho)
lasso = Lasso(alpha=param_scikit)
lasso.fit(A, y)
x_pred = lasso.coef_
mse = mean_squared_error(x_pred, scenario.x_true["x"])
return mse
def sample_from_prior(self, prior_x):
""" sample from prior """
model = prior_x @ O(id="y")
model = model.to_model()
prior_sample = model.to_model()
fig, axs = plt.subplots(4, 4, figsize=(4, 4))
for ax in axs.ravel():
sample = prior_sample.sample()['y']
ax.set_axis_off()
ax.imshow(sample.reshape(28, 28), cmap="gray")
dir_fig = 'Figures/'
os.makedirs(dir_fig) if not os.path.exists(dir_fig) else 0
file_name = f"/{dir_fig}Prior_{self.prior_params['name']}_{self.prior_params['type']}_{self.prior_params['id']}.pdf"
plt.savefig(file_name, format='pdf', dpi=1000,
bbox_inches="tight", pad_inches=0.1)
plt.show(block=True)
input("...")
plt.close()
def conv_sensing(measurement_ratios,
filter_size,
solver="AMP",
sparse_in_dct=False,
width=50,
depth=20,
delta=1e-2,
sparsity=0.5,
n_rep=10):
N = width * depth
signal = GaussBernouilliPrior(size=(N, ), rho=sparsity)
def sample_trnsf():
if (sparse_in_dct):
D = scipy.linalg.block_diag(
*[dctmtx(width).T for _ in range(depth)])
else:
D = np.eye(N)
return D
recovery_per_alpha = []
for alpha in measurement_ratios:
recoveries = []
for rep in range(n_rep):
out_channels = int(np.rint(alpha * depth))
ensemble = ChannelConvEnsemble(width=width,
in_channels=depth,
out_channels=out_channels,
k=filter_size)
A = ensemble.generate()
C = sample_trnsf()
teacher = conv_model(
A, C, signal) @ GaussianChannel(var=delta) @ O(id="y")
teacher = teacher.to_model()
sample = teacher.sample()
if (solver == "AMP"):
max_iter = 20
damping = 0.1
student = conv_model(A, C, signal) @ GaussianLikelihood(
y=sample['y'], var=delta)
student = student.to_model_dag()
student = student.to_model()
ep = ExpectationPropagation(student)
ep.iterate(max_iter=max_iter,
damping=damping,
callback=EarlyStopping(tol=1e-8))
data_ep = ep.get_variables_data((['x']))
mse = np.mean((data_ep['x']['r'] - sample['x'])**2)
recoveries.append(mse)
elif (solver == "CVX"):
reg_param = 0.001
x = cp.Variable(shape=(N, ), name="x")
lmbda = cp.Parameter(nonneg=True)
objective = cp.norm2(A @ C @ x -
sample['y'])**2 + lmbda * cp.norm1(x)
problem = cp.Problem(cp.Minimize(objective))
lmbda.value = reg_param
problem.solve(abstol=1e-6)
mse = np.mean((x.value - sample['x'])**2)
recoveries.append(mse)
else:
raise ValueError("Solver must be 'AMP' or 'CVX'")
recovery_per_alpha.append(recoveries)
return recovery_per_alpha
def recovery(measurement_ratios,
filter_size,
solver="AMP",
prior="conv",
sparse_in_dct=False,
N=1000,
delta=1e-2,
sparsity=0.5,
n_rep=10):
signal = GaussBernouilliPrior(size=(N, ), rho=sparsity)
prior_conv_ens = ConvEnsemble(N, filter_size)
def sample_trnsf():
if (sparse_in_dct):
D = dctmtx(N).T
else:
D = np.eye(N)
if (prior == "conv"):
C = prior_conv_ens.generate()
elif (prior == "sparse"):
C = np.eye(N)
else:
raise ValueError("Prior must be 'conv' or 'sparse'")
return D @ C
recovery_per_alpha = []
for alpha in measurement_ratios:
recoveries = []
for rep in range(n_rep):
M = int(alpha * N)
ensemble = GaussianEnsemble(M, N)
A = ensemble.generate()
C = sample_trnsf()
teacher = conv_model(
A, C, signal) @ GaussianChannel(var=delta) @ O(id="y")
teacher = teacher.to_model()
sample = teacher.sample()
if (solver == "AMP"):
max_iter = 20
damping = 0.1
student = conv_model(A, C, signal) @ GaussianLikelihood(
y=sample['y'], var=delta)
student = student.to_model_dag()
student = student.to_model()
ep = ExpectationPropagation(student)
ep.iterate(max_iter=max_iter,
damping=damping,
callback=EarlyStopping(tol=1e-8))
data_ep = ep.get_variables_data((['x']))
mse = np.mean((data_ep['x']['r'] - sample['x'])**2)
recoveries.append(mse)
elif (solver == "CVX"):
reg_param = 0.001
x = cp.Variable(shape=(N, ), name="x")
lmbda = cp.Parameter(nonneg=True)
objective = cp.norm2(A @ C @ x -
sample['y'])**2 + lmbda * cp.norm1(x)
problem = cp.Problem(cp.Minimize(objective))
lmbda.value = reg_param
problem.solve(abstol=1e-6)
mse = np.mean((x.value - sample['x'])**2)
recoveries.append(mse)
else:
raise ValueError("Solver must be 'AMP' or 'CVX'")
recovery_per_alpha.append(recoveries)
return recovery_per_alpha
self.size = x.shape
def math(self):
return "coon"
def sample(self):
return self.x
coon = CoonPrior()
x_shape = coon.size
noise = GaussianChannel(var=0.5)
grad_shape = (2,) + x_shape
teacher = (
coon @ SIMOVariable("x", n_next=2) @ (
GradientChannel(x_shape) @ O("x'") +
noise @ O("y")
)
).to_model()
# teacher.plot()
sample = teacher.sample()
plot_histograms(sample)
plot_data(sample, sample["y"])
# %%
# Sparse gradient denoising
# sparse grad denoiser
grad_shape = (2,) + x_shape
def __init__(self):
x = face(gray=True).astype(np.float32)
x = (x - x.mean()) / x.std()
self.x = x
self.size = x.shape
def sample(self):
return self.x
prior = RaccoonPrior()
x_shape = prior.size
noise = GaussianChannel(var=0.5)
grad_shape = (2, ) + x_shape
teacher = (prior @ SIMOVariable("x", n_next=2)
@ (GradientChannel(x_shape) @ O("x'") + noise @ O("y"))).to_model()
sample = teacher.sample()
plot_histograms(sample)
plot_data(sample, sample["y"])
# %%
# Sparse gradient denoising
grad_shape = (2, ) + x_shape
sparse_grad = (GaussianPrior(size=x_shape) @ SIMOVariable(id="x", n_next=2)
@ (noise @ O("y") +
(GradientChannel(shape=x_shape) +
GaussBernoulliPrior(size=grad_shape, var=0.7, rho=0.9))
@ MILeafVariable(id="x'", n_prev=2))).to_model()
scenario = TeacherStudentScenario(teacher, sparse_grad, x_ids=["x", "x'"])
scenario.setup(seed=1)
scenario.student.plot()
