# $y = \mathrm{sgn}(Fx) \in \pm^M$, where
# $F \in \mathbb{R}^{M \times N}$ 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"$p_+$",
prior_type="gauss_bernouilli",
output_type="modulus",
prior_mean=0.01,
prior_rho=0.5)
scenario = BayesOptimalScenario(model, x_ids=["x"])
scenario.setup()
scenario.student.plot()
for factor in scenario.student.factors:
print(factor.id, factor)
# %%
# EP dyanmics
# Damping is needed
# really bad without damping
ep_evo = scenario.ep_convergence(metrics=["mse", "phase_mse"], max_iter=20)
qplot(ep_evo,
x="iter",
y=["phase_mse", "v"],
y_markers=["x", "-"],
y_legend=True)
ep_evo = scenario.ep_convergence(metrics=["mse", "phase_mse"],
max_iter=70,
damping=0.3)
qplot(ep_evo,
x="iter",
y=["mse", "phase_mse", "v"],
y_markers=[".", "x", "-"],
y_legend=True)
plot_compare_complex(scenario.x_true["x"], scenario.x_pred["x"])
prior_type="binary",
output_type="door",
output_width=1.,
prior_p_pos=0.51)
for factor in teacher.factors:
print(factor)
scenario = BayesOptimalScenario(teacher, x_ids=["x", "z"])
scenario.setup(seed=42)
scenario.student.plot()
# %%
# EP dyanmics
ep_evo = scenario.ep_convergence(metrics=["mse", "sign_mse"],
damping=0.1,
max_iter=40)
qplot(ep_evo,
x="iter",
y=["mse", "sign_mse", "v"],
y_markers=["x", ".", "-"],
column="id",
y_legend=True)
plot_compare(scenario.x_true["x"], scenario.x_pred["x"])
# %%
# MSE curve
# See data/door_mse_curves.py for the code
rename = {
"alpha": r"$\alpha$",
"output_width": "K",
alpha = 2.
N = 1000
teacher = glm_generative(
N=N, alpha=alpha, ensemble_type="gaussian", prior_type="gauss_bernoulli",
output_type="relu", prior_rho=0.5
)
for factor in teacher.factors:
print(factor)
scenario = BayesOptimalScenario(teacher, x_ids=["x", "z"])
scenario.setup(seed=42)
scenario.student.plot()
# %%
# EP dyanmics
ep_evo = scenario.ep_convergence(metrics=["mse"], max_iter=10)
qplot(
ep_evo, x="iter", y=["mse", "v"],
y_markers=[".", "-"], column="id", y_legend=True
)
plot_compare(scenario.x_true["x"], scenario.x_pred["x"])
# %%
# MSE curve
# See data/relu_mse_curves.py for the code
rename = {
"alpha": r"$\alpha$", "v": "MSE", "n_iter": "iter", "a0": r"$a_0$",
"prior_rho": r"$\rho$", "x_id=": "", "n_iter": "iterations"
}
mse_curves = pd.read_csv("data/relu_mse_curves.csv")