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full_repr.py
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"""
This code implements the (stochastic) GenSparseUOT algorithm with full
representations ie. gamma is of size m x n.
"""
import torch
import numpy as np
from torch import sqrt
from torch.linalg import norm
tol = 1e-6
eps = 1e-9
def seed_everything(seed=0):
import random
random.seed(seed)
np.random.seed(seed)
torch.manual_seed(seed)
torch.cuda.manual_seed(seed)
torch.backends.cudnn.deterministic = True
torch.backends.cudnn.benchmark = False
def get_marginals(gamma):
gamma1 = torch.sum(gamma, 1)
gammaT1 = torch.sum(gamma, 0)
return gamma1, gammaT1
def get_obj(C, G1, G2, v1, v2, gamma, lda, vparts=None):
def get_mmdsq_reg(gamma1, gammaT1, v1, v2, vparts, G1, G2):
reg_1 = torch.mv(G1, gamma1-2*v1).dot(gamma1) + vparts[1]
reg_2 = torch.mv(G2, gammaT1-2*v2).dot(gammaT1) + vparts[2]
return reg_1, reg_2
if vparts is None:
g1 = torch.mv(G1, v1)
g2 = torch.mv(G2, v2)
vparts = {1: g1.dot(v1), 2: g2.dot(v2)}
gamma1, gammaT1 = get_marginals(gamma)
reg_1, reg_2 = get_mmdsq_reg(gamma1, gammaT1, v1, v2, vparts, G1, G2)
obj = torch.tensordot(gamma, C) + lda*(reg_1+reg_2)
return obj
def get_gamma(C, G1, G2, v1, v2, max_itr, lda, K, s=0, seed=0, ws=0,
all_gamma=0):
"""Computes sparse gamma using K-sparse-OT-dash algorithm.
Args:
C (_array_like_): cost matrix between source and target.
G1 (_array_like_): Gram matrix with samples from source.
G2 (_array_like_): Gram matrix with samples from target.
v1 (_vector_): source distribution over samples.
v2 (_vector_): target distribution over samples.
max_itr (_int_): for APGD.
lda (_float_): lambda regularization hyperparameter.
K (_int_): Cardinality of the support set.
s (None or _int_): None if non-stochastic else
cardinality of set R in the sparseotdash. Defaults to None.
seed (int, optional): To seed for reproducibility. Defaults to 0.
ws (int): Warm start or not. Defaults to 0.
all_gamma (int): To return gamma of all iterations or not.
Defaults to 0.
Returns:
if all_gamma, returns list of K sparse OT plans of
else returns the final.
"""
if K is not None:
assert K <= C.shape[0]*C.shape[1], "K should be less than m*n"
vparts = None # {1: torch.dot(torch.mv(G1, v1), v1), 2: torch.dot(torch.mv(G2, v2), v2)}
if not s:
if ws:
return get_gamma_dash_ws(C, G1, G2, v1, v2, max_itr, lda,
seed, all_gamma, K, vparts)
else:
return get_gamma_dash(C, G1, G2, v1, v2, max_itr, lda,
seed, all_gamma, K, vparts)
else:
if ws:
return get_gamma_sdash_ws(C, G1, G2, v1, v2, max_itr, lda,
s, seed, all_gamma, K, vparts)
else:
return get_gamma_sdash(C, G1, G2, v1, v2, max_itr, lda,
s, seed, all_gamma, K, vparts)
def get_gamma_dash(C, G1, G2, v1, v2, max_itr, lda, seed, allg,
K, vparts):
"""Implements Sparse-OT-Dash algorithm.
Returns:
all_gamma: list of K sparse OT plans corresponding to cardinalities
1 to K.
"""
seed_everything(seed)
m, n = C.shape
device = C.device
g1 = torch.mv(G1, v1)
g2 = torch.mv(G2, v2)
fixed_grd = C-2*lda*(g1[:, None] + g2)
V_minus_L = torch.arange(m*n, device=device)
S_i = torch.zeros(K, dtype=torch.long, device=device) # to avoid memory leak
S_j = torch.zeros(K, dtype=torch.long, device=device) # to avoid memory leak
gamma0 = torch.zeros((m, n), dtype=fixed_grd.dtype,
device=fixed_grd.device)
g1_0 = gamma0[:, 0].clone()
g2_0 = gamma0[0, :].clone()
all_gamma = []
gamma = None
u_0 = torch.argmin(fixed_grd)
for k in range(K):
if k:
S_i_R = torch.div(V_minus_L, n, rounding_mode='floor')
S_j_R = V_minus_L % n
gamma1, gammaT1 = get_marginals(gamma)
unq_i_R = torch.unique(S_i_R)
unq_j_R = torch.unique(S_j_R)
g1 = torch.mv(G1[unq_i_R], gamma1)
g2 = torch.mv(G2[unq_j_R], gammaT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i_R, g1)
g2_new = g2_new.index_copy(0, unq_j_R, g2)
u_0 = torch.argmin((fixed_grd+2*lda*(g1_new[:, None] + g2_new)
).take(V_minus_L))
chosen = V_minus_L[u_0]
S_i[k] = torch.div(chosen, n, rounding_mode='floor')
S_j[k] = chosen % n
S_i_S = S_i[:k+1]
S_j_S = S_j[:k+1]
V_minus_L = torch.cat([V_minus_L[:u_0], V_minus_L[u_0+1:]])
# upd unique, upd ss
unq_i = torch.unique(S_i_S)
unq_j = torch.unique(S_j_S)
G1_ss = G1[unq_i, :][:, unq_i]
G2_ss = G2[unq_j, :][:, unq_j]
ss = 1/(2*lda*(sqrt(len(unq_j)**2*norm(G1_ss)**2 +
len(unq_i)**2*norm(G2_ss)**2 +
2*(torch.sum(G1_ss)*torch.sum(G2_ss)))))
# solve for gamma using apgd
G1_u = G1[unq_i]
G2_u = G2[unq_j]
y = gamma0.clone()
gamma = gamma0.clone()
x_old = y.clone()
t = 1
grd_S = fixed_grd[S_i_S, S_j_S].clone()
for _ in range(max_itr):
gamma[S_i_S, S_j_S] = torch.clamp(y[S_i_S, S_j_S]-ss*grd_S, min=0)
t_new = (1+np.sqrt(1+4*t**2))/2
t_dash = (t-1)/t_new
y[S_i_S, S_j_S] = (t_dash+1)*gamma[S_i_S, S_j_S] - \
t_dash*x_old[S_i_S, S_j_S]
x_old = gamma.clone()
t = t_new
y1, yT1 = get_marginals(y)
g1 = torch.mv(G1_u, y1)
g2 = torch.mv(G2_u, yT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i, g1)
g2_new = g2_new.index_copy(0, unq_j, g2)
grd_S = (fixed_grd+2*lda*(g1_new[:, None] + g2_new)
)[S_i_S, S_j_S]
if allg:
all_gamma.append(gamma)
return all_gamma if allg else gamma
def get_gamma_sdash(C, G1, G2, v1, v2, max_itr, lda, s, seed,
allg, K, vparts):
"""Implements Stochastic Sparse-OT-Dash algorithm
Returns:
all_gamma: list of K sparse OT plans corresponding to cardinalities
1 to K.
"""
seed_everything(seed)
m, n = C.shape
device = C.device
g1 = torch.mv(G1, v1)
g2 = torch.mv(G2, v2)
fixed_grd = C-2*lda*(g1[:, None] + g2)
V_minus_L = torch.arange(m*n, device=device)
S_i = torch.zeros(K, dtype=torch.long, device=device) # to avoid memory leak
S_j = torch.zeros(K, dtype=torch.long, device=device) # to avoid memory leak
gamma0 = torch.zeros((m, n), dtype=fixed_grd.dtype,
device=fixed_grd.device)
g1_0 = gamma0[:, 0].clone()
g2_0 = gamma0[0, :].clone()
all_gamma = []
gamma = None
for k in range(K):
R = V_minus_L[torch.randint(m*n-k, (s,))]
if k:
S_i_R = torch.div(R, n, rounding_mode='floor')
S_j_R = R % n
gamma1, gammaT1 = get_marginals(gamma)
unq_i_R = torch.unique(S_i_R)
unq_j_R = torch.unique(S_j_R)
g1 = torch.mv(G1[unq_i_R], gamma1)
g2 = torch.mv(G2[unq_j_R], gammaT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i_R, g1)
g2_new = g2_new.index_copy(0, unq_j_R, g2)
u_0 = torch.argmin((fixed_grd+2*lda*(g1_new[:, None] + g2_new)
).take(R))
else:
u_0 = torch.argmin(fixed_grd.take(R))
chosen = R[u_0]
S_i[k] = torch.div(chosen, n, rounding_mode='floor')
S_j[k] = chosen % n
S_i_S = S_i[:k+1]
S_j_S = S_j[:k+1]
index = torch.where(V_minus_L != chosen)[0]
V_minus_L = V_minus_L[index]
unq_i = torch.unique(S_i_S)
unq_j = torch.unique(S_j_S)
G1_ss = G1[unq_i, :][:, unq_i]
G2_ss = G2[unq_j, :][:, unq_j]
ss = 1/(2*lda*(sqrt(len(unq_j)**2*norm(G1_ss)**2 +
len(unq_i)**2*norm(G2_ss)**2 +
2*(torch.sum(G1_ss)*torch.sum(G2_ss)))))
# solve for gamma using apgd
G1_u = G1[unq_i]
G2_u = G2[unq_j]
y = gamma0.clone()
gamma = gamma0.clone()
x_old = y.clone()
t = 1
grd_S = fixed_grd[S_i_S, S_j_S].clone()
for _ in range(max_itr):
gamma[S_i_S, S_j_S] = torch.clamp(y[S_i_S, S_j_S]-ss*grd_S, min=0)
t_new = (1+np.sqrt(1+4*t**2))/2
t_dash = (t-1)/t_new
y[S_i_S, S_j_S] = (t_dash+1)*gamma[S_i_S, S_j_S] - \
t_dash*x_old[S_i_S, S_j_S]
x_old = gamma.clone()
t = t_new
y1, yT1 = get_marginals(y)
g1 = torch.mv(G1_u, y1)
g2 = torch.mv(G2_u, yT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i, g1)
g2_new = g2_new.index_copy(0, unq_j, g2)
grd_S = (fixed_grd+2*lda*(g1_new[:, None] + g2_new)
)[S_i_S, S_j_S]
if allg:
all_gamma.append(gamma)
return all_gamma if allg else gamma
def get_gamma_dash_ws(C, G1, G2, v1, v2, max_itr, lda, seed, allg,
K, vparts):
"""Implements Sparse-OT-Dash algorithm with warm start.
Returns:
all_gamma: list of K sparse OT plans corresponding to cardinalities
1 to K.
"""
seed_everything(seed)
m, n = C.shape
device = C.device
g1 = torch.mv(G1, v1)
g2 = torch.mv(G2, v2)
fixed_grd = C-2*lda*(g1[:, None] + g2)
V_minus_L = torch.arange(m*n, device=device)
S_i = torch.zeros(K, dtype=torch.long, device=device) # to avoid memory leak
S_j = torch.zeros(K, dtype=torch.long, device=device) # to avoid memory leak
gamma = torch.zeros((m, n), dtype=fixed_grd.dtype,
device=fixed_grd.device)
g1_0 = gamma[:, 0].clone()
g2_0 = gamma[0, :].clone()
all_gamma = []
u_0 = torch.argmin(fixed_grd)
for k in range(K):
if k:
# R: V_minus_L
S_i_R = torch.div(V_minus_L, n, rounding_mode='floor')
S_j_R = V_minus_L % n
gamma1, gammaT1 = get_marginals(gamma)
unq_i_R = torch.unique(S_i_R)
unq_j_R = torch.unique(S_j_R)
g1 = torch.mv(G1[unq_i_R], gamma1)
g2 = torch.mv(G2[unq_j_R], gammaT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i_R, g1)
g2_new = g2_new.index_copy(0, unq_j_R, g2)
u_0 = torch.argmin((fixed_grd+2*lda*(g1_new[:, None] + g2_new)
).take(V_minus_L))
chosen = V_minus_L[u_0]
S_i[k] = torch.div(chosen, n, rounding_mode='floor')
S_j[k] = chosen % n
S_i_S = S_i[:k+1]
S_j_S = S_j[:k+1]
V_minus_L = torch.cat([V_minus_L[:u_0], V_minus_L[u_0+1:]])
# upd unique, upd ss
unq_i = torch.unique(S_i_S)
unq_j = torch.unique(S_j_S)
G1_ss = G1[unq_i, :][:, unq_i]
G2_ss = G2[unq_j, :][:, unq_j]
ss = 1/(2*lda*(sqrt(len(unq_j)**2*norm(G1_ss)**2 +
len(unq_i)**2*norm(G2_ss)**2 +
2*(torch.sum(G1_ss)*torch.sum(G2_ss)))))
# solve for gamma using apgd
G1_u = G1[unq_i]
G2_u = G2[unq_j]
y = gamma.clone()
x_old = y.clone()
t = 1
if k:
y1, yT1 = get_marginals(y)
g1 = torch.mv(G1_u, y1)
g2 = torch.mv(G2_u, yT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i, g1)
g2_new = g2_new.index_copy(0, unq_j, g2)
grd_S = (fixed_grd+2*lda*(g1_new[:, None] + g2_new)
)[S_i_S, S_j_S]
else:
grd_S = fixed_grd[S_i_S, S_j_S].clone()
for _ in range(max_itr):
gamma[S_i_S, S_j_S] = torch.clamp(y[S_i_S, S_j_S]-ss*grd_S, min=0)
t_new = (1+np.sqrt(1+4*t**2))/2
t_dash = (t-1)/t_new
y[S_i_S, S_j_S] = (t_dash+1)*gamma[S_i_S, S_j_S] - \
t_dash*x_old[S_i_S, S_j_S]
x_old = gamma.clone()
t = t_new
y1, yT1 = get_marginals(y)
g1 = torch.mv(G1_u, y1)
g2 = torch.mv(G2_u, yT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i, g1)
g2_new = g2_new.index_copy(0, unq_j, g2)
grd_S = (fixed_grd+2*lda*(g1_new[:, None] + g2_new)
)[S_i_S, S_j_S]
if allg:
all_gamma.append(gamma)
return all_gamma if allg else gamma
def get_gamma_sdash_ws(C, G1, G2, v1, v2, max_itr, lda, s, seed,
allg, K, vparts):
"""Implements Stochastic Sparse-OT-Dash algorithm with warm start.
Returns:
all_gamma: list of K sparse OT plans corresponding to cardinalities
1 to K.
"""
seed_everything(seed)
m, n = C.shape
device = C.device
g1 = torch.mv(G1, v1)
g2 = torch.mv(G2, v2)
fixed_grd = C-2*lda*(g1[:, None] + g2)
V_minus_L = torch.arange(m*n, device=device)
S_i = torch.zeros(K, dtype=torch.long, device=device) # to avoid memory leak
S_j = torch.zeros(K, dtype=torch.long, device=device) # to avoid memory leak
gamma = torch.zeros((m, n), dtype=fixed_grd.dtype,
device=fixed_grd.device)
g1_0 = gamma[:, 0].clone()
g2_0 = gamma[0, :].clone()
all_gamma = []
for k in range(K):
R = V_minus_L[torch.randint(m*n-k, (s,))]
if k:
S_i_R = torch.div(R, n, rounding_mode='floor')
S_j_R = R % n
gamma1, gammaT1 = get_marginals(gamma)
unq_i_R = torch.unique(S_i_R)
unq_j_R = torch.unique(S_j_R)
g1 = torch.mv(G1[unq_i_R], gamma1)
g2 = torch.mv(G2[unq_j_R], gammaT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i_R, g1)
g2_new = g2_new.index_copy(0, unq_j_R, g2)
u_0 = torch.argmin((fixed_grd+2*lda*(g1_new[:, None] + g2_new)
).take(R))
else:
u_0 = torch.argmin(fixed_grd.take(R))
chosen = R[u_0]
S_i[k] = torch.div(chosen, n, rounding_mode='floor')
S_j[k] = chosen % n
S_i_S = S_i[:k+1]
S_j_S = S_j[:k+1]
index = torch.where(V_minus_L != chosen)[0]
V_minus_L = V_minus_L[index]
unq_i = torch.unique(S_i_S)
unq_j = torch.unique(S_j_S)
G1_ss = G1[unq_i, :][:, unq_i]
G2_ss = G2[unq_j, :][:, unq_j]
ss = 1/(2*lda*(sqrt(len(unq_j)**2*norm(G1_ss)**2 +
len(unq_i)**2*norm(G2_ss)**2 +
2*(torch.sum(G1_ss)*torch.sum(G2_ss)))))
# solve for gamma using apgd
G1_u = G1[unq_i]
G2_u = G2[unq_j]
y = gamma.clone()
x_old = y.clone()
t = 1
if k:
y1, yT1 = get_marginals(y)
g1 = torch.mv(G1_u, y1)
g2 = torch.mv(G2_u, yT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i, g1)
g2_new = g2_new.index_copy(0, unq_j, g2)
grd_S = (fixed_grd+2*lda*(g1_new[:, None] + g2_new)
)[S_i_S, S_j_S]
else:
grd_S = fixed_grd[S_i_S, S_j_S].clone()
for _ in range(max_itr):
gamma[S_i_S, S_j_S] = torch.clamp(y[S_i_S, S_j_S]-ss*grd_S, min=0)
t_new = (1+np.sqrt(1+4*t**2))/2
t_dash = (t-1)/t_new
y[S_i_S, S_j_S] = (t_dash+1)*gamma[S_i_S, S_j_S] - \
t_dash*x_old[S_i_S, S_j_S]
x_old = gamma.clone()
t = t_new
y1, yT1 = get_marginals(y)
g1 = torch.mv(G1_u, y1)
g2 = torch.mv(G2_u, yT1)
g1_new = g1_0.clone()
g2_new = g2_0.clone()
g1_new = g1_new.index_copy(0, unq_i, g1)
g2_new = g2_new.index_copy(0, unq_j, g2)
grd_S = (fixed_grd+2*lda*(g1_new[:, None] + g2_new)
)[S_i_S, S_j_S]
if allg:
all_gamma.append(gamma)
return all_gamma if allg else gamma