# $F \in \mathbb{R}^{M \times N}$ is a Gaussian random matrix.
# You can build the perceptron directly, or use the `glm_generative` model builder.
teacher = glm_generative(N=1000,
alpha=1.7,
ensemble_type="gaussian",
prior_type="binary",
output_type="sgn")
scenario = BayesOptimalScenario(teacher, x_ids=["x"])
scenario.setup(seed=42)
scenario.student.plot()
# %%
# EP dynamics
ep_evo = scenario.ep_convergence(metrics=["mse"],
max_iter=30,
callback=EarlyStoppingEP())
qplot(ep_evo, x="iter", y=["mse", "v"], y_markers=[".", "-"], y_legend=True)
# %%
# Recovered signal
plot_compare(scenario.x_true["x"], scenario.x_pred["x"])
# %%
# Compare EP vs SE
# ----------------
# See `data/perceptron_ep_vs_se.py` for the corresponding script.
rename = {
"alpha": r"$\alpha$",
"n_iter": "iterations",
"p_pos": r"$p_+$",
"source=": ""
)
axes[2].set_title(r'$z = \textrm{DFT}(x)$')
axes[2].set_xlim(0, 25)
for axe in axes:
axe.legend(fancybox=True, shadow=False, loc="lower center", fontsize=20)
fig.tight_layout()
# %%
# Parameters
N, rho, noise_var, seed = 100, 0.02, 0.1, 1
prior_var, fft_var = 1, 18.75
# %%
# We create the teacher student scenario
teacher = SparseFFT_Teacher(N, noise_var)
teacher.info()
student = build_sparse_fft_student(N, prior_var, rho, fft_var, noise_var)
scenario = TeacherStudentScenario(teacher, student, x_ids=["x", "z"])
scenario.setup(seed=seed)
# %%
# Run EP
_ = scenario.run_ep(
max_iter=1000, damping=0.1, callback=EarlyStoppingEP(tol=1e-2)
)
# %%
# Plot
plot_sparse_fft(scenario)
teacher = SparseGradTeacher(size=N, grad_rho=rho, noise_var=1e-2)
# Build the student
student = build_sparse_grad_student(size=N, grad_rho=rho, noise_var=1e-2)
# Create a Teacher Student Scenario
# Variables to track #
x_ids = ["x", "x'"]
scenario = TeacherStudentScenario(teacher, student, x_ids=x_ids)
scenario.setup(seed=seed)
# %%
# Run EP
# Max number of EP iterations #
max_iter = 1000
# Damping value #
damping = 0.1
scenario.run_ep(max_iter=max_iter,
damping=damping,
callback=EarlyStoppingEP(tol=1e-2)
)
dic = {'model': 'sparse_gradient', 'N': N, 'rho': rho, 'seed': seed,
'y': scenario.observations["y"], 'x': scenario.x_true, 'x_pred': scenario.x_pred}
# %%
# Plot
plot_sparse_gradient(dic, save_fig=False)