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discreteRPM.py
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discreteRPM.py
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import torch
import numpy as np
class discreteRPM_softmaxForm(torch.nn.Module):
"""
Recognition-Parametrized Model (RPM) with discrete latent variables.
Explicitly utilizes the Softmax-form for p(xj^n|Z) = Softmax(log f(Z|xj^n) ).
"""
def __init__(self, rec_models, latent_prior, pxjs, full_N_for_Fj=True):
super().__init__()
self.J = len(rec_models)
assert len(pxjs) == self.J
self.rec_models = torch.nn.ModuleList(rec_models)
self.latent_prior = latent_prior
self.pxjs = pxjs
self.full_N_for_Fj = full_N_for_Fj
def log_probs(self, idx_n):
xjis = [self.pxjs[j].x for j in range(self.J)] # N - D
if self.full_N_for_Fj:
gji = [m.affine_all_z(xj) for m,xj in zip(self.rec_models, xjis)] # N - K x J
log_Zj = [torch.logsumexp(gji[j],axis=0).unsqueeze(0) for j in range(self.J)] # 1 - K x J
log_aji = [gji[j][idx_n] - log_Zj[j] for j in range(J) ] # b - K x J
else: # compute Fj(Z) only over minimatch
gji = [m.affine_all_z(xj[idx_n]) for m,xj in zip(self.rec_models, xjis)] # N - K x J
log_Zj = [torch.logsumexp(gji[j],axis=0).unsqueeze(0) for j in range(self.J)] # 1 - K x J
log_aji = [gji[j] - log_Zj[j] for j in range(self.J) ] # b - K x J
log_joint = self.latent_prior.log_probs() + sum(log_aji) # b - K
return torch.logsumexp(log_joint,axis=-1) # b
def eval(self, idx_n):
xjis = [self.pxjs[j].x for j in range(self.J)] # N - D
if self.full_N_for_Fj:
gji = [m.affine_all_z(xj) for m,xj in zip(self.rec_models, xjis)] # N - K x J
log_Zj = [torch.logsumexp(gji[j],axis=0).unsqueeze(0) for j in range(self.J)] # 1 - K x J
log_aji = [gji[j][idx_n] - log_Zj[j] for j in range(self.J) ] # b - K x J
else: # compute Fj(Z) only over minimatch
gji = [m.affine_all_z(xj[idx_n]) for m,xj in zip(self.rec_models, xjis)] # N - K x J
log_Zj = [torch.logsumexp(gji[j],axis=0).unsqueeze(0) for j in range(self.J)] # 1 - K x J
log_aji = [gji[j] - log_Zj[j] for j in range(self.J) ] # b - K x J
log_joint = self.latent_prior.log_probs() + sum(log_aji) # b - K
log_w = torch.logsumexp(log_joint,axis=-1) # b
posterior = torch.exp(log_joint - log_w.unsqueeze(-1)) # b - K
return log_w[:,0], posterior[:,0]
def training_step(self, idx_n, batch_idx):
# score matching loss
loss = - self.log_probs(idx_n).mean() # average negative log(w(x))
return loss.sum()
class discreteRPM_localLatents(torch.nn.Module):
"""
Recognition-Parametrized Model (RPM) with local latents.
This variant was written purely for testing purposes.
"""
def __init__(self, rec_models, latent_prior_g, latent_priors_j, px_alljs):
super().__init__()
self.J = len(rec_models)
assert len(px_alljs.pxjs) == self.J
self.rec_models = torch.nn.ModuleList(rec_models)
self.latent_prior_g = latent_prior_g
self.latent_priors_j = torch.nn.ModuleList(latent_priors_j)
self.K_j = [len(prior_j.param_) for prior_j in latent_priors_j]
self.px_alljs = px_alljs
def log_probs(self, xjs, idx_n):
J = self.J
assert len(xjs) == J
N = xjs[0].shape[0]
assert all([xjs[j].shape[0] == N for j in range(self.J)])
log_fnji = [m.log_probs(xj) for m,xj in zip(self.rec_models, xjs)] # N-Kj-K x J
log_hnj = [ pxj.model.log_probs_unnormalized(idx_n) for pxj in self.px_alljs.pxjs] # N-Kj x J
log_pxnji = [ log_fnji[j] + log_hnj[j].unsqueeze(-1) for j in range(J) ] # N-Kj-K x J
log_Fji = [torch.logsumexp(log_pxnji[j],axis=0) for j in range(J) ] # Kj-K x J
log_pj = [self.latent_priors_j[j].log_probs() for j in range(J)] # Kj x J
log_pxzj_zg = [log_pxnji[j]+(log_pj[j].unsqueeze(-1)-log_Fji[j]).unsqueeze(0) for j in range(J)] # N-Kj-K x J
log_px_zg = sum([torch.logsumexp(log_pxzj_zg[j],axis=1) for j in range(J)]) # N - K
log_px = torch.logsumexp(self.latent_prior_g.log_probs().unsqueeze(0) + log_px_zg,axis=1) # N
return log_px
def eval(self, xjs, idx_n):
J = self.J
assert len(xjs) == J
N = xjs[0].shape[0]
assert all([xjs[j].shape[0] == N for j in range(self.J)])
log_fnji = [m.log_probs(xj) for m,xj in zip(self.rec_models, xjs)] # N-Kj-K x J
log_hnj = [ pxj.model.log_probs()[idx_n,0] for pxj in self.px_alljs.pxjs] # N-Kj x J
log_pxnji = [ log_fnji[j] + log_hnj[j].unsqueeze(-1) for j in range(J) ] # N-Kj-K x J
log_Fji = [torch.logsumexp(log_pxnji[j],axis=0) for j in range(J) ] # Kj-K x J
log_pj = [self.latent_priors_j[j].log_probs() for j in range(J)] # Kj x J
log_pxzj_zg = [log_pxnji[j]+(log_pj[j].unsqueeze(-1)-log_Fji[j]).unsqueeze(0) for j in range(J)] # N-Kj-K x J
log_px_zg_j = [torch.logsumexp(log_pxzj_zg[j],axis=1) for j in range(J)] # N - K x J
log_px_zg = sum(log_px_zg_j) # N - K
log_pg = self.latent_prior_g.log_probs() # K
log_pzgx = log_pg.unsqueeze(0) + log_px_zg # N - K
log_px = torch.logsumexp(log_pzgx,axis=1) # N
log_pzg_x = log_pzgx - log_px.unsqueeze(1) # posterior p(zg | x)
log_pzj_xs = [] # posteriors p(zj | x)
for j in range(J):
i_not_j = [i for i in range(J) if i != j]
log_pzinotj_x = sum([log_px_zg_j[i] for i in i_not_j]) # N - K
log_pzjzg_x = log_pxzj_zg[j]+(log_pzinotj_x+log_pg.unsqueeze(0)).unsqueeze(1) # N-Kj-K
log_pzj_x = torch.logsumexp(log_pzjzg_x,axis=-1) - log_px.unsqueeze(1) # N-Kj
log_pzj_xs.append(log_pzj_x)
return log_pzj_xs, log_pzg_x, log_px
def training_step(self, batch, batch_idx):
# score matching loss
xjs = batch[0]
idx_n = batch[1]
loss = - self.log_probs(xjs, idx_n).mean() # average negative log(w(x))
return loss.sum()
def eval_sum(self, xjs):
return self.eval(xjs).sum(axis=0)
def eval_tensor(self, txjs):
assert txjs.shape[1] == self.J
xjs = [txjs[:,j] for j in range(self.J)]
return self.eval(xjs)
def forward(self, xjs):
return [self.rec_models[j](xjs[j])+self.latent_prior.param for j in range(self.J)]
class discreteRPM(torch.nn.Module):
"""
Recognition-Parametrized Model (RPM) with discrete latent variables.
Implements a particular way of expressing the marginal log p(x) = log w(x) + const.
as a weighted sum of posterior expectations. Works, but uses more computations
than strictly necessary.
"""
def __init__(self, rec_models, latent_prior, pxjs):
super().__init__()
self.J = len(rec_models)
assert len(pxjs) == self.J
self.rec_models = torch.nn.ModuleList(rec_models)
self.latent_prior = latent_prior
self.pxjs = pxjs
def eval(self, xjs):
J = self.J
assert len(xjs) == J
N = xjs[0].shape[0]
assert all([xjs[j].shape[0] == N for j in range(self.J)])
log_fnji = torch.stack([m.log_probs(xj)for m,xj in zip(self.rec_models, xjs)], axis=1) # N-J-K
Fji = torch.exp(log_fnji).mean(axis=0) # J-K
log_prod_Fj = torch.log(Fji).sum(axis=0).reshape(1,-1) # 1 - K
log_prod_fj = log_fnji.sum(axis=1) # N - K
log_prod_frac = log_prod_fj - log_prod_Fj # N - K
log_joint_factor = self.latent_prior.log_probs() + log_prod_frac # N - K
logw = torch.log(torch.exp(log_joint_factor).sum(axis=-1)) # N
posterior = torch.exp(log_joint_factor - logw.reshape(-1,1)) # N - K
log_prior_tilda = torch.log(posterior.mean(axis=0)).reshape(1,-1) # 1 - K
log_joint_tilda = log_prior_tilda + log_prod_frac # N - K
w_tilda = torch.exp(log_joint_tilda).sum(axis=-1) # N
log_joint_tilda_j = log_fnji + (log_prior_tilda - torch.log(Fji)).reshape(1,*Fji.shape) # N-J-K
w_tilda_j = torch.exp(log_joint_tilda_j).sum(axis=-1) # N-J
posterior_tilda_j = torch.exp(log_joint_tilda_j) / w_tilda_j.reshape(-1,J,1) # N-J-K
return logw, posterior, w_tilda_j, posterior_tilda_j #logp0.reshape(N) + logw
def training_step(self, batch, batch_idx):
# score matching loss
xjs = batch
loss = - self.eval(xjs)[0].mean() # average negative log(w(x))
return loss.sum()
def eval_sum(self, xjs):
return self.eval(xjs).sum(axis=0)
def eval_tensor(self, txjs):
assert txjs.shape[1] == self.J
xjs = [txjs[:,j] for j in range(self.J)]
return self.eval(xjs)
def forward(self, xjs):
return [self.rec_models[j](xjs[j])+self.latent_prior.param for j in range(self.J)]
class discreteRPVAE(torch.nn.Module):
"""
Variational auto-encoder for recognition-Parametrized Model (RPM) with discrete latents.
Model written for testing purposes - discrete RPMs do not need variational posteriors.
Implements the re-parametrization of a variational posterior q(Z|X) under the assumption
that Fj(Z)=p(Z) for all j to quickly test the idea in the simpler setup with discrete Z.
"""
def __init__(self, rec_models, latent_prior, pxjs):
super().__init__()
self.J = len(rec_models)
assert len(pxjs) == self.J
self.rec_models = torch.nn.ModuleList(rec_models)
self.latent_prior = latent_prior
self.pxjs = pxjs
def eval(self, xjs):
J = self.J
assert len(xjs) == J
N = xjs[0].shape[0]
assert all([xjs[j].shape[0] == N for j in range(self.J)])
log_fnji = torch.stack([m.log_probs(xj)for m,xj in zip(self.rec_models, xjs)], axis=1) # N-J-K
Fji = torch.exp(log_fnji).mean(axis=0) # J-K
log_prod_Fj = torch.log(Fji).sum(axis=0).reshape(1,-1) # 1 - K
log_prod_fj = log_fnji.sum(axis=1) # N - K
log_prod_frac = log_prod_fj - log_prod_Fj # N - K
log_joint_factor = self.latent_prior.log_probs() + log_prod_frac # N - K
logw = torch.log(torch.exp(log_joint_factor).sum(axis=-1)) # N
posterior = torch.exp(log_joint_factor - logw.reshape(-1,1)) # N - K
#log_prior_tilda = torch.log(posterior.mean(axis=0)).reshape(1,-1) # 1 - K
#log_joint_tilda = log_prior_tilda + log_prod_frac # N - K
#w_tilda = torch.exp(log_joint_tilda).sum(axis=-1) # N
#log_joint_tilda_j = log_fnji + (log_prior_tilda - torch.log(Fji)).reshape(1,*Fji.shape) # N-J-K
#w_tilda_j = torch.exp(log_joint_tilda_j).sum(axis=-1) # N-J
#posterior_tilda_j = torch.exp(log_joint_tilda_j) / w_tilda_j.reshape(-1,J,1) # N-J-K
return logw, posterior
def elbo(self, xjs):
J = self.J
assert len(xjs) == J
N = xjs[0].shape[0]
assert all([xjs[j].shape[0] == N for j in range(self.J)])
log_fnji = torch.stack([m.log_probs(xj)for m,xj in zip(self.rec_models, xjs)], axis=1) # N-J-K
Fji = torch.exp(log_fnji).mean(axis=0) # J-K
log_prod_Fj = torch.log(Fji).sum(axis=0).reshape(1,-1) # 1 - K
log_prod_fj = log_fnji.sum(axis=1) # N - K
log_q = (1-J) * self.latent_prior.log_probs() + log_prod_fj # N - K
lognorm_q = torch.logsumexp(log_q, axis=1).unsqueeze(-1) # N - 1
log_q = log_q - lognorm_q # N - K
log_ratio = lognorm_q + (J * self.latent_prior.log_probs() - log_prod_Fj) # N - K
elbo = (torch.exp(log_q) * log_ratio).sum(axis=1) # N
return elbo
def training_step(self, batch, batch_idx):
# score matching loss
xjs = batch
loss = - self.elbo(xjs).mean()
return loss.sum()
class discretenonCondIndRPM(torch.nn.Module):
"""
Recognition-Parametrized Model (RPM) without conditional independence assumption.
Model written for testing purposes.
An RPM variant without conditional independence, inspired by
Infonce is a variational autoencoder, Laurence Aitchison & Stoil Ganev (2021)
which explicitly operates on the full N^J-dimensional grid (!).
"""
def __init__(self, rec_model, latent_prior, pxjs, full_F=True):
super().__init__()
self.rec_model = rec_model
self.latent_prior = latent_prior
self.pxjs = pxjs
self.J = pxjs.J
self.full_F = full_F
def eval(self, xs):
# xs be of shape batchsize-J-D
# xs = torch.stack(xjs, axis=1)
J = self.J
if self.full_F: # compute normalizer across all N datapoints
all_xjs = [pxj.x for pxj in self.pxjs.pxjs]
N = all_xjs[0].shape[0]
assert all([N == xj.shape[0] for xj in all_xjs])
else: # compute normalizer only across datapoints in current minibatch
all_xjs = [xs[:,j] for j in range(J)] # hard assumes that j=1,,.,J instances are stacked in axis=1
N = all_xjs[0].shape[0] # N = batchsize from here on !
shuffle_ids = torch.cartesian_prod(*[torch.arange(N,dtype=torch.long) for j in range(J)])
xshuffled = torch.stack([all_xjs[j][shuffle_ids[:,j]] for j in range(J)], axis=1) # N^J-J-K !!!!
m = self.rec_model
log_fni = m.log_probs(xs) # batchsize - K
log_prior = self.latent_prior.log_probs().reshape(1,-1) # 1 - K
log_fxs = m.log_probs(xshuffled) # N^J - K
denom = torch.logsumexp(log_fxs,dim=0).reshape(1,-1) - np.log(N**J) # 1 - K
log_px = torch.logsumexp(log_fni + log_prior - denom, dim=-1) # batchsize - 1
return log_px
def training_step(self, batch, batch_idx):
# score matching loss
xs = batch
loss = - self.eval(xs).mean() # average negative log(w(x))
return loss.sum()
def forward(self, xs):
return self.rec_model(xs)+self.latent_prior.param
class Prior_discrete(torch.nn.Module):
"""
Discrete distribution for use as RPM prior.
"""
def __init__(self, param, activation_out=None):
super().__init__()
if activation_out is None:
def activation_out(x):
assert x.ndim == 1
return torch.nn.LogSoftmax(dim=0)(x)
self.activation_out = activation_out
self.param_ = torch.nn.Parameter(param)
def log_probs(self, x=None):
return self.activation_out(self.param_)
class RecognitionFactor_discrete(torch.nn.Module):
"""
Discrete conditional distribution
"""
def __init__(self, model):
super().__init__()
self.model = model # model up to softmax layer
def log_probs(self, x):
assert x.ndim >= 2 # N-by-K, where K is number of choices, or N-by-something-by-K
return torch.nn.LogSoftmax(dim=-1)(self.model(x))
def forward(self, x):
return self.log_probs(x) # categorical distribution: eta(xj) = P(Z|xj) in vector form
class RecognitionFunction_discrete(torch.nn.Module):
"""
Discrete recognition function g(xj, Z) *without* any normalization constraints on \int e^g(xj,Z) dZ
"""
def __init__(self, model):
super().__init__()
self.model = model # model up to softmax layer
def affine_all_z(self, x):
assert x.ndim >= 2 # N-by-K, where K is number of choices, or N-by-something-by-K
out_all = self.model(x) # N-by-...-by-K+1
return out_all[...,:-1] + out_all[...,-1:]
def forward(self, x):
return self.affine_all_z(x) # categorical distribution: eta(xj) = P(Z|xj) in vector form
class RecognitionFunction_discrete_norm(torch.nn.Module):
"""
Discrete recognition function g(xj, Z) with normalization constraint \int e^g(xj,Z) dZ = 1
"""
def __init__(self, model):
super().__init__()
self.model = model # model up to softmax layer
def affine_all_z(self, x):
assert x.ndim >= 2 # N-by-K, where K is number of choices, or N-by-something-by-K
return torch.nn.LogSoftmax(dim=-1)(self.model(x)[...,:-1])
def forward(self, x):
return self.affine_all_z(x) # categorical distribution: eta(xj) = P(Z|xj) in vector form
class RecognitionFactor_scaled_discrete(torch.nn.Module):
"""
Scaled discrete conditional distribution
"""
def __init__(self, model):
super().__init__()
self.model = model # model up to softmax layer
def log_probs(self, x):
assert x.ndim >= 2 # N-by-K, where K is number of choices, or N-by-something-by-K
return torch.nn.LogSoftmax(dim=-1)(self.model(x)[:,:-1]) + self.model(x)[:,-1:]
def forward(self, x):
return self.log_probs(x) # categorical distribution: eta(xj) = P(Z|xj) in vector form
class RecognitionFactor_zj_discrete(torch.nn.Module):
"""
Discrete conditional distribution
conditioned on both a continuous x and a categorical z : model now needs to return K log-odds
per x and z=[1,..,K] indexes which one gets used.
"""
def __init__(self, model, K):
super().__init__()
self.model = model # model up to softmax layer
self.K = K # number of possible values for categorical (local) latent variable z
def log_probs(self, x, z=None):
assert x.ndim >= 2 # N-by-K, where K is number of choices, or N-by-something-by-K
if z is None:
return torch.nn.LogSoftmax(dim=-1)(self.model(x).reshape(x.shape[0],self.K,-1) )
else:
assert len(x) == len(z)
assert max(z) <= self.K-1
return torch.nn.LogSoftmax(dim=-1)(self.model(x).reshape(x.shape[0],self.K,-1) )[torch.arange(len(z)),z]
def forward(self, x, z=None):
return self.log_probs(x, z) # categorical distribution: eta(xj) = P(Z|xj) in vector form
class WeightedEmpiricalDistribution(torch.nn.Module):
"""
Rudimentary representation of a weighted mixture distribution of Dirac delta peaks.
"""
def __init__(self, x, model):
super().__init__()
self.x = x
self.N = x.shape[0]
self.model = model
def log_probs(self, n, z): # n is index of data point x[n,:] - otherwise log-prob = - inf !
return self.model.log_probs(z)[n]
def eval(self, n, z):
return self.log_probs(n, z)
def sample(self,z):
i = np.random.choice(self.N, size=1, p=torch.exp(self.model.log_probs(z)).detach().numpy())
return self.x[i]
class EmpWeightModel_RPM(torch.nn.Module):
"""
Discrete conditional distribution
"""
def __init__(self, model, x):
super().__init__()
self.x = x
self.model = model # model up to softmax layer
def log_probs(self):
log_alpha = torch.nn.LogSoftmax(dim=-1)(self.model(self.x)) # alpha(zj | xj) for all zj, xj pairs with xj in xx
return log_alpha - torch.logsumexp(log_alpha, axis=0).unsqueeze(0)
def log_probs_unnormalized(self,idx_n):
log_alpha = torch.nn.LogSoftmax(dim=-1)(self.model(self.x[idx_n])) # alpha(zj | xj) for all zj, xj pairs with xj in minibatch
return log_alpha
def forward(self):
return self.log_probs() # categorical distribution: eta(xj) = P(Z|xj) in vector form
class WeightModel(torch.nn.Module):
"""
Saturated conditional categorical distribution
conditioned on discrete latent variable z.
"""
def __init__(self, M):
super().__init__()
self.M = M
self.K = M.shape[0]
self.N = M.shape[1]
def log_probs(self, z=None):
if z is None:
return torch.nn.LogSoftmax(dim=-1)(self.M)
else:
return torch.nn.LogSoftmax(dim=-1)(self.M)[z]
def forward(self, z=None):
return self.log_probs(z)
class RPMWeightedEmpiricalMarginals(torch.nn.Module):
"""
Placeholder object to represent all marginal data distribution pj(xj), j=1,...,J
used among others to define a recognition-parametrized model.
"""
def __init__(self, pxjs):
super().__init__()
self.J = len(pxjs)
self.N = pxjs[0].x.shape[0]
assert all([self.N == pxjs[j].x.shape[0] for j in range(self.J)])
self.pxjs = torch.nn.ModuleList(pxjs) #[EmpiricalDistribution(x=xj) for xj in xjs]