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experiments.py
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experiments.py
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import sys
import matplotlib
import utils
from metrics import energy_dist
from utils import cached_function
#matplotlib.use('Agg')
matplotlib.use('pdf')
matplotlib.rcParams.update({
"pgf.texsystem": "pdflatex",
'font.family': 'serif',
'font.size': 10.95,
'text.usetex': True,
'pgf.rcfonts': False,
# 'legend.framealpha': 0.5,
'text.latex.preamble': r'\usepackage{times} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb}'
})
from algorithms import *
from pathlib import Path
import matplotlib.pyplot as plt
def plot_mc_logpartition(d: int, n_reps: int = 11):
colors = [u'#a06010', u'#d62728', u'#e377c2', u'#2ca02c', u'#ff7f0e', u'#9467bd', u'#17becf', u'#7f7f7f',
u'#bcbd22', u'#1f77b4', u'#44FF44', u'#000000']
# colors = [(0, 0, 0), (215, 0, 0), (140, 60, 255), (2, 136, 0), (0, 172, 199), (152, 255, 0), (255, 127, 209),
# (108, 0, 79), (255, 165, 48),
# (0,0,157), (134,112,104), (0,73,66), (79,42,0), (0,253,207), (188,183,255)]
# todo: put the legend to the right of the plot
# todo: use more distinct colors or less lines
plt.figure(figsize=(6, 4))
torch.manual_seed(0)
np.random.seed(0)
lip_consts = [4**k for k in range(12)]
ns = [2**k for k in range(20)]
# plot upper bounds first, such that they are in the background of the plot
for i, lip_const in enumerate(reversed(lip_consts)):
beta = lip_const / np.sqrt(d)
true_dist = LinearGibbsDistribution(params=torch.as_tensor([beta], dtype=torch.float32))
upper_bounds = []
for n in ns:
upper_bounds.append(mc_logpartition_upper_bound(n, d, lip_const, delta=0.5))
color = colors[i % len(colors)]
plt.loglog(ns, upper_bounds, linestyle='--', color=color)
for i, lip_const in enumerate(reversed(lip_consts)):
beta = lip_const / np.sqrt(d)
true_dist = LinearGibbsDistribution(params=torch.as_tensor([beta], dtype=torch.float32))
dist_str = f'linear_1d_{beta:g}'
# print(f'{lip_const=}')
mc_errors = []
upper_bounds = []
for n in ns:
apx_values = cached_function(f'{dist_str}_pc', 0,
lambda n, n_batch: MCLogPartition(
UniformCubeDistribution(d=d)).eval(true_dist, n_reps=n_batch, n=n).cpu(),
n=n, n_batch=n_reps)
ref_value = true_dist.log_partition()
errors = torch.abs(apx_values - ref_value)
mc_errors.append(torch.median(errors).item())
# upper_bounds.append(mc_logpartition_upper_bound(n, d, lip_const, delta=0.5))
color = colors[i % len(colors)]
plt.loglog(ns, mc_errors, linestyle='-', color=color, label=f'$|f|_1 = {lip_const}$')
# plt.loglog(ns, upper_bounds, linestyle='--', color=color)
plt.xlabel('$n$')
plt.ylabel(r'Median error $|L_f - \tilde L_f|$')
plt.legend(loc='upper left', bbox_to_anchor=(1.05, 1.0))
plt.tight_layout(pad=0.4)
plt.savefig(f'plots/mc_logpartition_{d}d_new.pdf')
plt.show()
plt.close()
def plot_logpartition_errors_ax(ax: plt.Axes, d: int = 3, beta: float = 5, n_batch: int = 1001, rerun: bool = False):
# d = 3
# true_dist = LinearGibbsDistribution(params=torch.as_tensor([20.0, 20.0, 20.0]))
# dist_str = f'linear_3d_20_20_20'
# plt.figure(figsize=(6, 4))
params = torch.as_tensor([beta] * d, dtype=torch.float64)
true_dist = LinearGibbsDistribution(params=params)
params_str = '_'.join([str(beta)] * d)
dist_str = f'linear_{d}d_{params_str}'
true_value = true_dist.log_partition()
n_per_dims = [1, 2, 3, 4, 6, 8, 10, 13, 16, 20, 26, 32]
n_arr = np.asarray([1, 2*n_per_dims[-1]**d])
factor = beta
ax.loglog(n_arr, factor * n_arr ** (-1 / 3), 'k--', label=r'$\beta n^{-1/3}$')
ax.loglog(n_arr, factor * n_arr ** (-1 / 2), '--', color='tab:orange', label=r'$\beta n^{-1/2}$')
ax.loglog(n_arr, factor * n_arr ** (-2 / 3), '--', color='tab:blue', label=r'$\beta n^{-2/3}$')
ax.loglog(n_arr, factor * n_arr ** (-5 / 6), '--', color='tab:green', label=r'$\beta n^{-5/6}$')
ns = []
errors = []
for n_per_dim in n_per_dims:
apx_value = cached_function(f'{dist_str}_pc', 0,
lambda n_per_dim: PiecewiseConstantGibbsDistribution(true_dist, n_per_dim).log_partition(),
rerun=rerun, n_per_dim=n_per_dim)
ns.append(n_per_dim**d)
errors.append(np.abs(apx_value - true_value))
ax.loglog(ns, errors, '.-', color='tab:blue', label='PC')
ns = []
errors = []
for n_per_dim in n_per_dims:
apx_value = cached_function(f'{dist_str}_mc', 0,
lambda n, n_batch: MCLogPartition(UniformCubeDistribution(d=d)).eval(
true_dist,
n_reps=n_batch,
n=n),
rerun=rerun, n=n_per_dim**d, n_batch=n_batch)
ns.append(n_per_dim ** d)
errors.append((apx_value - true_value).abs().median().item())
# print(errors)
ax.loglog(ns, errors, '.-', color='tab:orange', label='MC')
ns = []
errors = []
for n_per_dim in n_per_dims:
apx_value = cached_function(f'{dist_str}_pc_mc', 0,
lambda n_per_dim, n, n_batch: MCLogPartition(
PiecewiseConstantGibbsDistribution(true_dist, n_per_dim)).eval(true_dist,
n_reps=n_batch,
n=n),
rerun=rerun, n_per_dim=n_per_dim, n=n_per_dim**d, n_batch=n_batch)
ns.append(2 * n_per_dim ** d)
errors.append((apx_value - true_value).abs().median().item())
ax.loglog(ns, errors, '.-', color='tab:green', label='PC+MC')
def plot_logpartition_experiments(n_reps: int = 1001):
# fig = plt.figure(figsize=(6, 6))
# axs = fig.subplots(2, 2)
fig, axs = plt.subplots(2, 2, figsize=(6, 6))
plot_logpartition_errors_ax(ax=axs[0, 0], d=3, beta=10000, n_batch=n_reps)
plot_logpartition_errors_ax(ax=axs[0, 1], d=3, beta=40, n_batch=n_reps)
plot_logpartition_errors_ax(ax=axs[1, 0], d=3, beta=0.1, n_batch=n_reps)
for ax in [axs[0, 0], axs[0, 1], axs[1, 0]]:
ax.set_xlabel('Number of function evaluations $n$')
ax.set_ylabel(r'Median error $|L_f - \tilde L_f|$')
axs[0, 0].set_title(r'$\beta = 10^4$')
axs[0, 1].set_title(r'$\beta = 40$')
axs[1, 0].set_title(r'$\beta = 0.1$')
axs[-1, -1].axis('off')
fig.legend(*axs[0, 0].get_legend_handles_labels(), loc='center', bbox_to_anchor=(0.75, 0.3), ncol=1)
# plt.xlabel('Number of function evaluations $n$')
# plt.ylabel('Median log-partition estimation error')
plt.tight_layout(pad=0.4)
file_path = Path('plots') / 'logpartition_plot_large.pdf'
utils.ensureDir(file_path)
plt.savefig(file_path)
plt.show()
plt.close(fig)
def plot_sampling_errors_ax(ax: plt.Axes, beta: float, n_samples: int = 10000, d: int = 3, rerun: bool = False):
params = torch.as_tensor([beta] * d, dtype=torch.float64)
true_dist = LinearGibbsDistribution(params=params)
params_str = '_'.join([str(beta)] * d)
dist_str = f'linear_{d}d_{params_str}'
true_max = d * beta
slope_sum = true_max
# d = 4
# true_dist = LinearGibbsDistribution(params=torch.as_tensor([5.0, 5.0, 5.0, 5.0]))
# dist_str = f'linear_4d_5_5_5_5'
true_samples = cached_function(f'{dist_str}_true_samples', 1234,
lambda n_samples: true_dist.sample(n_samples).cpu(), rerun=rerun, n_samples=n_samples)
true_samples_ref = [cached_function(f'{dist_str}_true_samples', i,
lambda n_samples: true_dist.sample(n_samples).cpu(), rerun=rerun, n_samples=n_samples)
for i in range(3)]
# loss = geomloss.SamplesLoss(loss='sinkhorn', p=1, blur=1e-3, backend='multiscale')
# loss_name = 'error'
loss = lambda s1, s2: energy_dist(s1, s2, device=DefaultDevice.get())
loss_name = 'energy-dist'
# n_per_dims = [1, 2, 4, 8, 16]
n_per_dims = [1, 2, 3, 4, 6, 8, 10, 13, 16, 20, 26, 32]
n_arr = np.asarray([1, 2*n_per_dims[-1]**d])
colors = [u'#a06010', u'#d62728', u'#e377c2', u'#2ca02c', u'#ff7f0e', u'#9467bd', u'#17becf', u'#7f7f7f',
u'#bcbd22', u'#1f77b4', u'#44FF44', u'#000000']
ax.loglog(n_arr, n_arr ** (-1 / 3), '--', color='tab:green', label=r'$n^{-1/3}$')
ax.loglog(n_arr, n_arr ** (-1 / 2), '--', color='mediumpurple', label=r'$n^{-1/2}$')
ax.loglog(n_arr, n_arr ** (-2 / 3), '--', color='tab:pink', label=r'$n^{-2/3}$')
numerical_errors = [cached_function(f'{dist_str}_true_samples_{loss_name}', 0,
lambda idx, **kwargs: loss(true_samples, true_samples_ref[idx]).item(),
rerun=rerun, n_samples=n_samples, idx=i) for i in range(len(true_samples_ref))]
ax.loglog([1, 2*n_per_dims[-1]**d], [np.max(numerical_errors)] * 2, '--', color='#666666',
label='Numerical accuracy')
ns = []
errors = []
for n_per_dim in n_per_dims:
samples = cached_function(f'{dist_str}_pc_samples', 0,
lambda n_per_dim, n_samples: PiecewiseConstantGibbsDistribution(true_dist, n_per_dim).sample(n_samples).cpu(),
rerun=rerun, n_per_dim=n_per_dim, n_samples=n_samples)
error = cached_function(f'{dist_str}_pc_samples_{loss_name}', 0, lambda **kwargs: loss(true_samples, samples).item(),
rerun=rerun, n_per_dim=n_per_dim, n_samples=n_samples)
ns.append(n_per_dim**d)
errors.append(error)
ax.loglog(ns, errors, '.-', color='k', label='PC')
ns = []
errors = []
for n_per_dim in n_per_dims:
samples = cached_function(f'{dist_str}_mc_samples', 0,
lambda n, n_samples: MCSampler(UniformCubeDistribution(d=d)).sample(
true_dist,
n_samples=n_samples,
n=n).cpu(),
rerun=rerun, n=n_per_dim**d, n_samples=n_samples)
error = cached_function(f'{dist_str}_mc_samples_{loss_name}', 0, lambda **kwargs: loss(true_samples, samples).item(),
rerun=rerun, n=n_per_dim**d, n_samples=n_samples)
ns.append(n_per_dim ** d)
errors.append(error)
# print(errors)
ax.loglog(ns, errors, '.-', color='tab:blue', label='MC')
ns = []
errors = []
for n_per_dim in n_per_dims:
samples = cached_function(f'{dist_str}_rs_samples', 0,
lambda n, n_samples: RejectionSampler(UniformCubeDistribution(d=d).shift_by(true_max)).sample(
true_dist,
n_samples=n_samples,
n=n).cpu(),
rerun=rerun, n=n_per_dim ** d, n_samples=n_samples)
error = cached_function(f'{dist_str}_rs_samples_{loss_name}', 0, lambda **kwargs: loss(true_samples, samples).item(),
rerun=rerun, n=n_per_dim ** d, n_samples=n_samples)
ns.append(n_per_dim ** d)
errors.append(error)
# print(errors)
ax.loglog(ns, errors, '.-', color='tab:red', label='RS')
ns = []
errors = []
for n_per_dim in n_per_dims:
samples = cached_function(f'{dist_str}_pc_mc_samples', 0,
lambda n_per_dim, n, n_samples: MCSampler(
PiecewiseConstantGibbsDistribution(true_dist, n_per_dim)).sample(true_dist,
n_samples=n_samples,
n=n).cpu(),
rerun=rerun, n_per_dim=n_per_dim, n=n_per_dim**d, n_samples=n_samples)
ns.append(2 * n_per_dim ** d)
error = cached_function(f'{dist_str}_pc_mc_samples_{loss_name}', 0, lambda **kwargs: loss(true_samples, samples).item(),
rerun=rerun, n_per_dim=n_per_dim, n=n_per_dim**d, n_samples=n_samples)
errors.append(error)
ax.loglog(ns, errors, '.-', color='tab:cyan', label='PC+MC')
ns = []
errors = []
for n_per_dim in n_per_dims:
samples = cached_function(f'{dist_str}_pc_rs_samples', 0,
lambda n_per_dim, n, n_samples: RejectionSampler(
PiecewiseConstantGibbsDistribution(true_dist, n_per_dim).shift_by(slope_sum/(2*n_per_dim))).sample(true_dist,
n_samples=n_samples,
n=n).cpu(),
rerun=rerun, n_per_dim=n_per_dim, n=n_per_dim ** d, n_samples=n_samples)
ns.append(2 * n_per_dim ** d)
error = cached_function(f'{dist_str}_pc_rs_samples_{loss_name}', 0,
lambda **kwargs: loss(true_samples, samples).item(),
rerun=rerun, n_per_dim=n_per_dim, n=n_per_dim ** d, n_samples=n_samples)
errors.append(error)
ax.loglog(ns, errors, '.-', color='tab:orange', label='PC+RS')
def plot_sampling_errors(beta: float, n_samples: int = 10000, d: int = 3, rerun: bool = False):
fig, ax = plt.subplots(1, 1, figsize=(6, 4))
plot_sampling_errors_ax(ax, beta=beta, n_samples=n_samples, d=d, rerun=rerun)
plt.legend() # todo: better legend placement
ax.set_xlabel('$n$')
ax.set_ylabel('Empirical energy distance')
plt.tight_layout(pad=0.4)
params_str = '_'.join([f'{beta:g}'] * d)
dist_str = f'linear_{d}d_{params_str}'
plt.savefig(f'plots/sampling_plot_{dist_str}_energy-dist.pdf')
plt.show()
plt.close(fig)
if __name__ == '__main__':
if len(sys.argv) > 1:
device = sys.argv[1]
else:
device = 'cpu'
DefaultDevice.set(device)
plot_logpartition_experiments(n_reps=10001)
# plot_logpartition_errors(d=3, param=30)
# plot_logpartition_errors(d=3, param=20)
# plot_logpartition_errors(d=3, param=1)
# plot_logpartition_errors(d=3, param=0.1)
# plot_logpartition_errors(d=3, param=0.01)
# plot_logpartition_errors(d=3, param=5)
# plot_logpartition_errors(d=3, param=10000)
# plot_logpartition_errors(d=3, param=40)
# plot_mc_logpartition(d=1, n_reps=1001)
plot_mc_logpartition(d=1, n_reps=10001)
plot_sampling_errors(beta=15, n_samples=1000000)