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exp_1_convergence_fig3.py
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exp_1_convergence_fig3.py
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# -*- coding: utf-8 -*-
#
# Copyright (c) 2023 Pablo Moreno-Munoz
# CogSys Section --- (pabmo@dtu.dk)
# Technical University of Denmark (DTU)
# Running command: ~ python exp_1_convergence_fig2.py -d 50 -p 200
import time
from tqdm import tqdm
from tqdm import trange
from torch.autograd import Variable
from datetime import datetime
import sys
import argparse
from math import nan, isnan
from scipy.special import binom
import statistics
import numpy as np
import random
import torch
from torch.distributions import MultivariateNormal as Normal
import argparse
import matplotlib.pyplot as plt
font = {'family' : 'serif',
'size' : 20}
plt.rc('text', usetex=True)
plt.rc('font', **font)
plt.rc('text.latex', preamble=r'\usepackage{bm}')
color_palette_1 = ['#335c67','#fff3b0','#e09f3e','#9e2a2b','#540b0e']
color_palette_2 = ['#177e89','#084c61','#db3a34','#ef8354','#323031']
color_palette_3 = ['#bce784','#5dd39e','#348aa7','#525274','#513b56']
color_palette_4 = ['#002642','#840032','#e59500','#e5dada','#02040e']
color_palette_5 = ['#202c39','#283845','#b8b08d','#f2d449','#f29559']
palette_red = ["#03071e","#370617","#6a040f","#9d0208","#d00000","#dc2f02","#e85d04","#f48c06","#faa307","#ffba08"]
palette_blue = ["#012a4a","#013a63","#01497c","#014f86","#2a6f97","#2c7da0","#468faf","#61a5c2","#89c2d9","#a9d6e5"]
palette_green = ['#99e2b4','#88d4ab','#78c6a3','#67b99a','#56ab91','#469d89','#358f80','#248277','#14746f','#036666']
palette_pink = ["#ea698b","#d55d92","#c05299","#ac46a1","#973aa8","#822faf","#6d23b6","#6411ad","#571089","#47126b"]
palette_super_red = ["#641220","#6e1423","#85182a","#a11d33","#a71e34","#b21e35","#bd1f36","#c71f37","#da1e37","#e01e37"]
palette = color_palette_1
parser = argparse.ArgumentParser()
parser.add_argument('--n', '-n', type=int, default=100)
parser.add_argument('--dim', '-d', type=int, default=3)
parser.add_argument('--precision', '-b', type=float, default=5)
parser.add_argument('--max_perm', '-p', type=int, default=1)
parser.add_argument('--latent_dim', '-k', type=int, default=2)
parser.add_argument('--fix_mask', '-fm', type=bool, default=False)
parser.add_argument('--plot', '-plot', type=bool, default=True)
args = parser.parse_args()
print(binom(512,76))
# Dimensions
N = args.n
D = args.dim
K = args.latent_dim
beta = args.precision
max_permutations = args.max_perm
range_max_perm = [*range(max_permutations)]
[x+1 for x in range_max_perm]
torch.manual_seed(111)
np.random.seed(111)
############################################
# PPCA: GENERATIVE PROCESS
###########################################
# true weights
W = torch.randn(D,K)
Z = torch.randn(N,K)
epsilon = (1/beta) * torch.randn(N,1)
# how data is generated
x = Z @ W.T + epsilon
############################################
# EXACT LOG-MARGINAL LIKELIHOOD
############################################
S_lml = W @ W.T + (1/beta)*torch.eye(D)
lml_dist = Normal(torch.zeros(D), S_lml)
lml = lml_dist.log_prob(x).sum()
print('Mean Log-marginal Likelihood (MLML) =', lml.item()/N)
list_of_seeds = [4,44,444,4444,44444]
list_of_diffs = []
list_of_mean = []
list_of_std = []
for seed in list_of_seeds:
torch.manual_seed(seed)
np.random.seed(seed)
############################################
# MASKED PRE-TRAINING LOSS
############################################
def active_set_permutation(x, W):
""" Description: Does a random permutation of data and selects a subset
Input: Data observations X (NxD)
Return: Active Set X_A and X_rest / X_A U X_rest = X
"""
permutation = torch.randperm(x.size()[1])
W_perm = W[permutation]
x_perm = x[:, permutation]
return x_perm, W_perm
diff = []
for max_permutations in range_max_perm:
# sum over sizes of masked tokens --
masked_loss = 0.0
if args.fix_mask:
############################################
# 1) FIXED MASK RATIO
############################################
m = 76
loss_pred = torch.zeros_like(x[:,0])
for p in range(max_permutations):
x_p, W_p = active_set_permutation(x, W)
S_p = W_p @ W_p.T + (1/beta)*torch.eye(D)
# Computation // forgetting other extra elements
x_r = x_p[:,m:]
iS_rr = torch.inverse(S_p[m:,m:])
m_pred = S_p[:m,m:] @ iS_rr @ x_r.T
v_pred = torch.diagonal(S_p[:m,:m] - S_p[:m,m:] @ iS_rr @ S_p[:m,m:].T)
m_pred = m_pred.T
v_pred = torch.tile(v_pred.unsqueeze(1),(1,N)).T
log_p_masked = -0.5*torch.log(v_pred) - 0.5*np.log(2*np.pi) - (0.5*(x_p[:,:m] - m_pred)**2 / v_pred)
loss_pred += log_p_masked.sum(1)
loss_pred = loss_pred/(max_permutations * m)
masked_loss += loss_pred.sum()
else:
############################################
# 2) UNFIXED MASK RATIO
############################################
for a in range(D):
# m = a+1
m = 76
# average over permutations --
loss_pred = torch.zeros_like(x[:,0])
for p in range(max_permutations):
x_p, W_p = active_set_permutation(x, W)
S_p = W_p @ W_p.T + (1/beta)*torch.eye(D)
# Computation // forgetting other extra elements
x_r = x_p[:,m:]
iS_rr = torch.inverse(S_p[m:,m:])
m_pred = S_p[:m,m:] @ iS_rr @ x_r.T
v_pred = torch.diagonal(S_p[:m,:m] - S_p[:m,m:] @ iS_rr @ S_p[:m,m:].T)
m_pred = m_pred.T
v_pred = torch.tile(v_pred.unsqueeze(1),(1,N)).T
log_p_masked = -0.5*torch.log(v_pred) - 0.5*np.log(2*np.pi) - (0.5*(x_p[:,:m] - m_pred)**2 / v_pred)
loss_pred += log_p_masked.sum(1)
loss_pred = loss_pred/(max_permutations * m)
masked_loss += loss_pred.sum()
print(max_permutations, ' -- Masked pre-training loss (MPTL) =', masked_loss.item()/N)
loss_diff = lml.item()/N - masked_loss.item()/N
diff.append(loss_diff)
list_of_diffs.append(diff)
############################################
# PLOTTING
############################################
if args.plot:
fig, ax = plt.subplots(figsize=(8, 6))
for i, diff in enumerate(list_of_diffs):
ax.plot(range_max_perm, diff, lw=4.5, alpha=0.4, color=palette_blue[3+i])
ax.set_xlim(1.0,range_max_perm[-1])
ax.legend([r'\textsc{mpt} loss'])
plt.title(r'Convergence of \textsc{mpt} vs. \textsc{lml}')
plt.ylabel('Difference')
plt.xlabel('Num. of permutations')
plt.show()