def run_interpolation_with_various_betas(points,
kernel=RBF(10, (1e-2, 1e2)) * C(1)):
"""
Runs Interpolation with number of picked points(beta) from 1 to all points-1 picked and using uniform distribution in
the picking in 1 Dimesnsion
"""
rmse_data = []
for i in range(
1, len(points)
): # runs through all number of picked points starting at 1 and ending with all points picked-1
sum_rmse = 0
for j in range(
0, 3
): # runs every interpolation with a certain beta 5 times and averages the results
picked_points = pick_uniform_random_points(points, i)
interpolated_points = interpolate_unknown_points(
picked_points, points, kernel)
sum_rmse = sum_rmse + root_mean_square_error(interpolated_points)
rmse_data.append(sum_rmse / 5)
plot_numbers(rmse_data, range(1, len(points)))
return rmse_data
def run_experiment_with_various_length_scales_log(bottom_bound, top_bound,
side_length, mean, std,
pick_number, number_of_maps):
"""
Experiment to see rmse of cheating and not cheating regreassion on varous length scales (traverses by powers of 10) in 2D. Uses uniform point selection and RBF kernel
:param bottom_bound: bottom bound of length scale
:param top_bound: top bound of length scale not inclusive
:param side_length: number of points on one side of the square of points
:param mean: Mean pollution value to be set
:param std: Standard Deviation
:param pick_number: the Beta (the number of points to select to be measured)
:param number_of_maps: Number of trials for each length scale
:return:
"""
not_cheating_data = []
cheating_data = []
length_scale = bottom_bound
length_scale_list = []
while length_scale <= top_bound: # runs through each length scale
points = create_points_with_spatially_correlated_pollution_2d(
side_length, mean, std, length_scale,
number_of_maps) # Creates all points
picked_points = pick_uniform_random_points_on_map_of_maps(
points, pick_number, 0, std) # Picks points to be measured
interpolated_points = interpolate_unknown_points_of_a_map_of_maps_of_points(
picked_points,
points,
# Interpolates using noncheating method
RBF(np.random.randint(1e-05, 100 + 1)),
fixed=False)
not_cheating_data.append(
average_rmse_of_maps(interpolated_points)
) # adds average rms of all the trials for the noncheating method
interpolated_points = interpolate_unknown_points_of_a_map_of_maps_of_points(
picked_points,
points,
# Interpolates using cheating method
RBF(length_scale, ),
fixed=True)
cheating_data.append(
average_rmse_of_maps(interpolated_points)
) # adds average rmse of all the trials for the cheating method
length_scale_list.append(length_scale)
length_scale = length_scale * 10
plot_numbers(
length_scale_list,
not_cheating_data,
length_scale_list,
cheating_data,
# Plots the data Red is not cheating, Green Cheating
"Length Scale",
"RMSE",
x_log_scale=True)
def run_interpolations_with_random_betas_1d():
"""
Runs Interpolation with random picking of the value of Beta
"""
rmse_values = []
picked_points_values = []
number_of_times = 100 # this will be the number of points displayed on the graph
random = np.random.default_rng()
for i in range(0, number_of_times):
test_points = create_points_with_random_pollution_1d(100, 100, 10)
test_picked_points = pick_uniform_random_points(
test_points,
random.integers(1, 100)) # picks a random number of known points
test_interpolated_points = interpolate_unknown_points(
test_picked_points, test_points)
test_rmse = root_mean_square_error(test_interpolated_points)
rmse_values.append(test_rmse)
picked_points_values.append(len(test_picked_points))
plot_numbers(rmse_values, picked_points_values)