/
evolve_oja_rule.py
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/
evolve_oja_rule.py
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import numpy as np
import matplotlib.pyplot as plt
import functools
import cgp
import pickle
import sympy
from evolution import *
from learning_rules import oja_rule
from functions import *
def f_target(x, w, y):
oja = y * (x - y * w)
return oja
if __name__ == "__main__":
seed = 10000
rng = np.random.RandomState(seed)
flag_save_figures = True
flag_save_data = True
# data parameters
n_datasets = 3
num_dimensions = 2
num_points = 5000
max_var_input = 1
# learning parameters
learning_rate = 0.005
# fitness parameters
fitness_mode = "variance"
alpha = num_dimensions * max_var_input # hyperparameter for weighting fitness function terms
population_params = {"n_parents": 10, "mutation_rate": 0.1, "seed": seed}
genome_params = {
"n_inputs": 3,
"n_outputs": 1,
"n_columns": 10,
"n_rows": 2,
"levels_back": 5,
"primitives": (cgp.Sub, cgp.Mul), # cgp.Add, cgp.Div
}
ea_params = {
"n_offsprings": 10,
"tournament_size": 2,
"n_processes": 2,
}
evolve_params = {
"max_generations": 10, # Todo: set to larger value
"min_fitness": 1000.0,
} #
# initialize datasets
datasets = []
pc0_per_dataset = []
pc0_empirical_per_dataset = []
initial_weights_per_dataset = []
for idx in range(n_datasets):
dataset, cov_mat = create_input_data(
num_points, num_dimensions, max_var_input, seed + idx
)
datasets.append(dataset)
initial_weights = initialize_weights(num_dimensions, rng)
initial_weights_per_dataset.append(initial_weights)
pc0 = calculate_eigenvector_for_largest_eigenvalue(cov_mat)
pc0_per_dataset.append(pc0)
pc0_empirical = compute_first_pc(dataset)
pc0_empirical_per_dataset.append(pc0_empirical)
[history, champion] = evolution(
datasets, pc0_per_dataset, initial_weights_per_dataset,
population_params, genome_params, ea_params, evolve_params,
learning_rate, alpha, fitness_mode)
rng.seed(seed)
champion_learning_rule = cgp.CartesianGraph(champion.genome).to_numpy()
champion_fitness, champion_weights_per_dataset = calculate_fitness(
champion_learning_rule,
datasets,
pc0_per_dataset,
initial_weights_per_dataset,
learning_rate, alpha, fitness_mode)
champion_sympy_expression = champion.to_sympy()
# evaluate hypothetical fitness of oja rule
rng.seed(seed)
oja_fitness, oja_weights_per_dataset = calculate_fitness(
oja_rule, datasets, pc0_per_dataset, initial_weights_per_dataset, learning_rate, alpha, fitness_mode)
# plot (works only for n_dimensions = 2 at the moment)
m = np.linspace(-1, 1, 1000)
champion_angle = np.zeros(n_datasets)
oja_angle = np.zeros(n_datasets)
for idx in range(n_datasets):
temp_champ_angle = compute_angle_weight_first_pc(
champion_weights_per_dataset[idx], pc0_per_dataset[idx], mode="degree"
)
champion_angle[idx] = calculate_smallest_angle(temp_champ_angle)
temp_oja_angle = compute_angle_weight_first_pc(
oja_weights_per_dataset[idx], pc0_per_dataset[idx], mode="degree"
)
oja_angle[idx] = calculate_smallest_angle(temp_oja_angle)
champion_as_line = np.zeros([num_dimensions, np.size(m)])
champion_as_line[0, :] = champion_weights_per_dataset[idx][0] * m
champion_as_line[1, :] = champion_weights_per_dataset[idx][1] * m
oja_as_line = np.zeros([num_dimensions, np.size(m)])
oja_as_line[0, :] = oja_weights_per_dataset[idx][0] * m
oja_as_line[1, :] = oja_weights_per_dataset[idx][1] * m
pc0_as_line = np.zeros([num_dimensions, np.size(m)])
pc0_as_line[0, :] = pc0_per_dataset[idx][0] * m
pc0_as_line[1, :] = pc0_per_dataset[idx][1] * m
# Todo: set learning rule as eg. plot title
fig, ax = plt.subplots()
plt.grid()
plt.plot(champion_as_line[0, :], champion_as_line[1, :])
plt.plot(oja_as_line[0, :], oja_as_line[1, :])
plt.plot(pc0_as_line[0, :], pc0_as_line[1, :])
plt.xlim(-3, 3)
plt.ylim(-3, 3)
plt.xlabel("w_0")
plt.ylabel("w_1")
plt.legend(
[
"champion angle:" + str(champion_angle[idx]),
"oja angle: " + str(oja_angle[idx]),
"true pc 1",
]
)
if flag_save_figures:
fig.savefig("figures/weight_vectors_seed" + str(seed+idx) + ".png")
if flag_save_data:
param_list = [ea_params, evolve_params, genome_params, population_params, seed, n_datasets, num_dimensions,
num_points, max_var_input, fitness_mode]
save_data = {'params': {
'ea_params': ea_params,
'evolve_params' : evolve_params,
'genome_params' : genome_params,
'population_params' : population_params,
'seed' : seed,
'n_datasets' : n_datasets,
'num_dimensions' : num_dimensions,
'num_points' : num_points,
'max_var_input' : max_var_input,
'fitness_mode' : fitness_mode,
},
'champion': champion,
'history': history,
'champion_sympy': champion_sympy_expression
}
# sympy expression purely for convenience
data_file = open('data/data_seed' + str(seed) + '.pickle', 'wb')
pickle.dump(save_data, data_file)