Usage of the SimulationWrapper class

We illustrate how the SimmulationWrapper class can be used to simplify the process of creating a Montecarlo simmulation for analying the performance of the Landweber method.

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import EarlyStopping as es
import pandas as pd

np.random.seed(42)
sns.set_theme()

Gererate synthetic data using the SimulationData class. Other options besides diagonal_data include ‘gravity’, ‘heat’, ‘deriv2’, ‘phillips’

design_smooth, response_noiseless_smooth, true_signal_smooth = es.SimulationData.diagonal_data(
    sample_size=1000, type="smooth"
)

Setup and verify the Simulation paramters for the Simulation

parameters_smooth = es.SimulationParameters(
    design=design_smooth,
    true_signal=true_signal_smooth,
    true_noise_level=0.01,
    monte_carlo_runs=3,
    cores=3,
)

UserWarning: PARAMETER WARNING: The design matrix is sparse. Escaping from __validate().

Create a SimulationWrapper object based on the SimulationParameters and run the simulation based on the desired estimation method. The data_set_name parameter is optional and is used to save the results of the simulation. Since the parameter is not specified, the results will not be saved and are simply returned as a pd.DataFrame.

simulation_smooth = es.SimulationWrapper(**parameters_smooth.__dict__)
simmulation_results = simulation_smooth.run_simulation_landweber(max_iteration=1000)

pd.set_option("display.max_rows", None, "display.max_columns", None)  # Display all rows and columns of the DataFrame
print(simmulation_results)

Running Monte-Carlo simulation for Landweber.
   strong_empirical_risk_es  weak_empirical_risk_es  weak_relative_efficiency  \
0                 19.952893                0.087339                  0.742983
1                 23.146479                0.107895                  0.737363
2                 21.187514                0.097031                  0.759895

   strong_relative_efficiency  \
0                    0.898375
1                    0.890932
2                    0.889724

                                        strong_bias2  \
0  [9182.427732573386, 4665.676312893388, 3697.39...
1  [9182.427732573386, 4665.676312893388, 3697.39...
2  [9182.427732573386, 4665.676312893388, 3697.39...

                                     strong_variance  \
0  [0.0, 0.0007485470860550343, 0.002456820157913...
1  [0.0, 0.0007485470860550343, 0.002456820157913...
2  [0.0, 0.0007485470860550343, 0.002456820157913...

                                         strong_risk  \
0  [9182.427732573386, 4665.677061440474, 3697.40...
1  [9182.427732573386, 4665.677061440474, 3697.40...
2  [9182.427732573386, 4665.677061440474, 3697.40...

                                          weak_bias2  \
0  [3716.6807943847025, 557.7151148768934, 316.87...
1  [3716.6807943847025, 557.7151148768934, 316.87...
2  [3716.6807943847025, 557.7151148768934, 316.87...

                                       weak_variance  \
0  [0.0, 0.00016439345666815605, 0.00028498358854...
1  [0.0, 0.00016439345666815605, 0.00028498358854...
2  [0.0, 0.00016439345666815605, 0.00028498358854...

                                           weak_risk  \
0  [3716.6807943847025, 557.71527927035, 316.8717...
1  [3716.6807943847025, 557.71527927035, 316.8717...
2  [3716.6807943847025, 557.71527927035, 316.8717...

                                           residuals  discrepancy_stop  \
0  [3718.3327812372677, 558.0901478259906, 317.01...               273
1  [3715.9371777596866, 557.306219720411, 316.583...               270
2  [3716.7133946758336, 557.4296163744252, 316.75...               269

   balanced_oracle_weak  balanced_oracle_strong
0                   325                     312
1                   325                     312
2                   325                     312