def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ batch = x.size()[0] """ sample iw z's for z_i in sample: find p(z_i, all x) find q(z_i, x) average """ phi_m, phi_v = self.enc.encode(x) # (batch, z_dim) phi_m, phi_v = ut.duplicate(phi_m, iw), ut.duplicate(phi_v, iw) # (batch*iw, z_dim) x_iw = ut.duplicate(x, iw) z_hat = ut.sample_gaussian(phi_m, phi_v) # (batch*iw, z_dim) log_q_zx = ut.log_normal(z_hat, phi_m, phi_v) # (batch*iw) log_p_z = ut.log_normal(z_hat, *self.z_prior) # (batch*iw) log_p_xz = ut.log_bernoulli_with_logits( x_iw, self.dec.decode(z_hat)) # (batch*iw) f = lambda x: x.reshape(iw, batch).transpose(1, 0) log_p_xz, log_q_zx, log_p_z = f(log_p_xz), f(log_q_zx), f(log_p_z) iwae = ut.log_mean_exp(log_p_xz - log_q_zx + log_p_z, -1) iwae = iwae.mean(0) niwae = -iwae kl = ut.log_mean_exp(log_q_zx - log_p_z, -1) kl = kl.mean(0) rec = ut.log_mean_exp(log_p_xz, -1) rec = -rec.mean(0) ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ q_m, q_v = self.enc.encode(x) q_m_, q_v_ = ut.duplicate(q_m, rep=iw), ut.duplicate(q_v, rep=iw) z_given_x = ut.sample_gaussian(q_m_, q_v_) decoded_bernoulli_logits = self.dec.decode(z_given_x) #duplicate x x_dup = ut.duplicate(x, rep=iw) rec = ut.log_bernoulli_with_logits(x_dup, decoded_bernoulli_logits) #compute kl p_m, p_v = torch.zeros(q_m.shape), torch.ones(q_v.shape) p_m_, p_v_ = ut.duplicate(p_m, iw), ut.duplicate(p_v, iw) #print("p_m", p_m.shape) log_q_phi = ut.log_normal(z_given_x, q_m_, q_v_) #encoded distribution log_p = ut.log_normal(z_given_x, p_m_, p_v_) #prior distribution kl = log_q_phi - log_p niwae = rec - kl #reshape to size (iw, bs) and then sum niwae = ut.log_mean_exp(niwae.reshape(iw, -1), dim=0) rec = ut.log_mean_exp(rec, dim=0) kl = ut.log_mean_exp(kl, dim=0) niwae = -torch.mean(niwae) kl = torch.mean(kl) rec = torch.mean(kl) ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def get_nll(self, outputs, targets): """ :return: negative log-likelihood of a minibatch """ if not self.constant_var: mean, var = ut.gaussian_parameters_ff(outputs, dim=0) return -torch.mean(ut.log_normal(targets, mean, var)) else: var = self.pred_var * torch.ones_like(outputs) return -torch.mean(ut.log_normal(targets, outputs, var))
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior pm, pv = ut.gaussian_parameters(self.z_pre, dim=1) # # Generate samples. qm, qv = self.enc.encode(x) niwaes = [] recs = [] kls = [] for i in range(iw): z_sample = ut.sample_gaussian(qm, qv).view(-1, qm.shape[1]) rec = self.dec.decode(z_sample) logptheta_x_g_z = ut.log_bernoulli_with_logits(x, rec) logptheta_z = ut.log_normal_mixture(z_sample, pm, pv) logqphi_z_g_x = ut.log_normal(z_sample, qm, qv) niwae = logptheta_x_g_z + logptheta_z - logqphi_z_g_x # # Normal variables. rec = -ut.log_bernoulli_with_logits(x, rec) kl = ut.log_normal(z_sample, qm, qv) - ut.log_normal_mixture( z_sample, pm, pv) niwaes.append(niwae) recs.append(rec) kls.append(kl) niwaes = torch.stack(niwaes, -1) niwae = ut.log_mean_exp(niwaes, -1) kl = torch.stack(kls, -1) rec = torch.stack(recs, -1) ################################################################################ # End of code modification ################################################################################ return -niwae.mean(), kl.mean(), rec.mean()
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ X_dupl = ut.duplicate(x, iw) # Input "x" is duplicated "iw" times (m, v) = self.enc.encode(X_dupl) # compute the encoder outut z = ut.sample_gaussian( m, v) # sample a point from the multivariate Gaussian logits = self.dec.decode(z) # pass the sampled "Z" through the decoder # Calculate log Prob of the output x_hat given latent z ln_P_x_z = ut.log_bernoulli_with_logits(X_dupl, logits) # Calculate log(P(z)) #ln_P_z = -torch.sum(z*z, -1)/2.0 ln_P_z = ut.log_normal(z, self.z_prior_m, self.z_prior_v) # Calculate log(Q(z | x)), Conditional Prob of Latent given x #ln_q_z_x = -torch.sum((z-m)*(z-m)/(2.0*v) + torch.log(v), -1) ln_q_z_x = ut.log_normal(z, m, v) exponent = ln_P_x_z + ln_P_z - ln_q_z_x exponent = exponent.reshape(iw, -1) L_m_x = ut.log_mean_exp(exponent, 0) niwae = -torch.mean(L_m_x) kl = torch.tensor(0) rec = torch.tensor(0) ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ m, v = self.enc.encode(x) # m, v -> (batch, dim) # (batch, dim) -> (batch*iw, dim) m = ut.duplicate(m, iw) # (batch, dim) -> (batch*iw, dim) v = ut.duplicate(v, iw) # (batch, dim) -> (batch*iw, dim) x = ut.duplicate(x, iw) # z -> (batch*iw, dim) z = ut.sample_gaussian(m, v) logits = self.dec.decode(z) kl = ut.log_normal(z, m, v) - ut.log_normal(z, self.z_prior_m, self.z_prior_v) rec = -ut.log_bernoulli_with_logits(x, logits) nelbo = kl + rec niwae = -ut.log_mean_exp(-nelbo.reshape(iw, -1), dim=0) niwae, kl, rec = niwae.mean(), kl.mean(), rec.mean() ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def get_nll(self, outputs, targets): """ :return: negative log-likelihood of a minibatch """ if self.likelihood_cost_form == 'mse': # This method is not validated return self.mse_fn(outputs, targets) elif self.likelihood_cost_form == 'gaussian': if not self.constant_var: mean, var = ut.gaussian_parameters(outputs, dim=-1) return -torch.mean(ut.log_normal(targets, mean, var)) else: var = self.pred_var * torch.ones_like(outputs) return -torch.mean(ut.log_normal(targets, outputs, var))
def negative_elbo_bound(self, x, y): ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # Note that we are interested in the ELBO of ln p(x | y) # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ m, v = self.enc.encode(x, y) z = ut.sample_gaussian(m, v) x_m = self.dec.decode(z, y) rec = ut.log_normal(x, x_m, self.x_v.expand(x_m.size())).mean() kl_z = ut.kl_normal(m, v, self.z_prior_m.expand(m.size()), self.z_prior_v.expand(v.size())).mean() nelbo = kl_z - rec ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, rec
def negative_elbo_bound(self, x, y): ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # Note that we are interested in the ELBO of ln p(x | y) # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ # sample z m, v = self.enc.encode(x, y) z = ut.sample_gaussian(m, v) # generate x given z,y x_logits = self.dec.decode(z, y) # kl on q(z) kl_z = ut.kl_normal(m, v, self.z_prior[0], self.z_prior[1]) rec_loss = -ut.log_normal(x, x_logits, 0.1 * torch.ones_like(x_logits)) kl_z, rec_loss = rec_loss.mean(), kl_z.mean() nelbo = rec_loss + kl_z ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, rec_loss
def negative_elbo_bound(self, x): """ Computes the Evidence Lower Bound, KL and, Reconstruction costs Args: x: tensor: (batch, dim): Observations Returns: nelbo: tensor: (): Negative evidence lower bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ print(x) m, v = self.enc.encode(x) z = ut.sample_gaussian(m, v) logits = self.dec.decode(z) batch_size, dim = m.shape # Compute KL term # km = torch.zeros(batch_size,self.k,dim) # kv = torch.ones(batch_size,self.k,dim) km = self.km.repeat(batch_size, 1, 1) kv = self.kv.repeat(batch_size, 1, 1) kl_vec = ut.log_normal(z, m, v) - ut.log_normal_mixture(z, km, kv) kl = torch.mean(kl_vec) # Compute reconstruction loss rec_vec = torch.neg(ut.log_bernoulli_with_logits(x, logits)) rec = torch.mean(rec_vec) # Compute nelbo nelbo = rec + kl return nelbo, kl, rec
def negative_elbo_bound(self, x, y): ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # Note that we are interested in the ELBO of ln p(x | y) # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ q_mu, q_var = self.enc.encode(x, y) z_samp = ut.sample_gaussian(q_mu, q_var) logits = self.dec.decode(z_samp, y) rec = -torch.mean( ut.log_normal(x, logits, 0.1 * torch.ones_like(logits))) kl_z = torch.mean( ut.kl_normal(q_mu, q_var, torch.zeros_like(q_mu), torch.ones_like(q_var))) nelbo = kl_z + rec ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, rec
def kl_elem(self, z, qm, qv): # Compute the mixture of Gaussian prior prior_m, prior_v = ut.gaussian_parameters(self.z_pre, dim=1) log_prob_net = ut.log_normal(z, qm, qv) log_prob_prior = ut.log_normal_mixture(z, prior_m, prior_v) # print("log_prob_net:", log_prob_net.mean(), "log_prob_prior:", log_prob_prior.mean()) kl_elem = log_prob_net - log_prob_prior return kl_elem
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ niwae = 0 for i in range(x.size()[0]): x_i = x[i][:].view(1, x.size()[1]) x_i = ut.duplicate(x_i, iw) m, v = self.enc.encode(x_i) z = ut.sample_gaussian(m, v) x_hat = self.dec.decode(z) exponent = ut.log_bernoulli_with_logits(x_i, x_hat) + \ ut.log_normal(z, self.z_prior_m.expand(m.size()), self.z_prior_v.expand(v.size())) \ - ut.log_normal(z, m, v) niwae += -ut.log_mean_exp(exponent, 0).squeeze() #print(np.std(exponent.data.cpu().numpy())) #print(exponent.data.cpu().numpy().shape) niwae = niwae / x.size()[0] kl = rec = torch.tensor(0) ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior prior = ut.gaussian_parameters(self.z_pre, dim=1) m, v = self.enc.encode(x) dist = Normal(loc=m, scale=torch.sqrt(v)) z_sample = dist.rsample(sample_shape=torch.Size([iw])) log_batch_z_sample_prob = [] kl_batch_z_sample = [] for i in range(iw): recon_logits = self.dec.decode(z_sample[i]) log_batch_z_sample_prob.append( ut.log_bernoulli_with_logits( x, recon_logits)) # [batch, z_sample] kl_batch_z_sample.append( ut.log_normal(z_sample[i], m, v) - ut.log_normal_mixture(z_sample[i], prior[0], prior[1])) log_batch_z_sample_prob = torch.stack(log_batch_z_sample_prob, dim=1) kl_batch_z_sample = torch.stack(kl_batch_z_sample, dim=1) niwae = -ut.log_mean_exp(log_batch_z_sample_prob - kl_batch_z_sample, dim=1).mean(dim=0) rec = -torch.mean(log_batch_z_sample_prob, dim=0) kl = torch.mean(kl_batch_z_sample, dim=0) ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ m, v = self.enc.encode(x) batch_size, dim = m.shape # Duplicate m = ut.duplicate(m, iw) v = ut.duplicate(v, iw) x = ut.duplicate(x, iw) z = ut.sample_gaussian(m, v) logits = self.dec.decode(z) km = self.km.repeat(batch_size, 1, 1) kv = self.kv.repeat(batch_size, 1, 1) km = ut.duplicate(km, iw) kv = ut.duplicate(kv, iw) kl_vec = ut.log_normal(z, m, v) - ut.log_normal_mixture(z, km, kv) kl = torch.mean(kl_vec) # TODO: compute the values below rec_vec = ut.log_bernoulli_with_logits(x, logits) rec = torch.neg(torch.mean(rec_vec)) if iw > 1: iwtensor = torch.zeros(iw) j = 0 while j < iw: i = 0 sum = 0 while i < batch_size: sum += rec_vec[j * batch_size + i] i += 1 iwtensor[j] = sum / batch_size - kl j += 1 niwae = torch.neg(ut.log_mean_exp(iwtensor, 0)) else: niwae = rec + kl return niwae, kl, rec
def negative_elbo_bound(self, x): """ Computes the Evidence Lower Bound, KL and, Reconstruction costs Args: x: tensor: (batch, dim): Observations Returns: nelbo: tensor: (): Negative evidence lower bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # To help you start, we have computed the mixture of Gaussians prior # prior = (m_mixture, v_mixture) for you, where # m_mixture and v_mixture each have shape (1, self.k, self.z_dim) # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior (m, v) = self.enc.encode(x) # compute the encoder output #print(" ***** \n") #print("x xhape ", x.shape) #print("m and v shapes = ", m.shape, v.shape) prior = ut.gaussian_parameters(self.z_pre, dim=1) #print("prior shapes = ", prior[0].shape, prior[1].shape) z = ut.sample_gaussian(m, v) # sample a point from the multivariate Gaussian #print("shape of z = ",z.shape) logits = self.dec.decode(z) # pass the sampled "Z" through the decoder #print("logits shape = ", logits.shape) rec = -torch.mean(ut.log_bernoulli_with_logits(x, logits), -1) # Calculate log Prob of the output log_prob = ut.log_normal(z, m, v) log_prob -= ut.log_normal_mixture(z, prior[0], prior[1]) kl = torch.mean(log_prob) rec = torch.mean(rec) nelbo = kl + rec ################################################################################ # End of code modification ################################################################################ return nelbo, kl, rec
def negative_elbo_bound(self, x): """ Computes the Evidence Lower Bound, KL and, Reconstruction costs Args: x: tensor: (batch, dim): Observations Returns: nelbo: tensor: (): Negative evidence lower bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # To help you start, we have computed the mixture of Gaussians prior # prior = (m_mixture, v_mixture) for you, where # m_mixture and v_mixture each have shape (1, self.k, self.z_dim) # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior prior = ut.gaussian_parameters(self.z_pre, dim=1) q_m, q_v = self.enc.encode(x) #print("q_m", q_m.size()) z_given_x = ut.sample_gaussian(q_m, q_v) decoded_bernoulli_logits = self.dec.decode(z_given_x) rec = -ut.log_bernoulli_with_logits(x, decoded_bernoulli_logits) #rec = -torch.mean(rec) #terms for KL divergence log_q_phi = ut.log_normal(z_given_x, q_m, q_v) #print("log_q_phi", log_q_phi.size()) log_p_theta = ut.log_normal_mixture(z_given_x, prior[0], prior[1]) #print("log_p_theta", log_p_theta.size()) kl = log_q_phi - log_p_theta #print("kl", kl.size()) nelbo = torch.mean(kl + rec) rec = torch.mean(rec) kl = torch.mean(kl) ################################################################################ # End of code modification ################################################################################ return nelbo, kl, rec
def negative_elbo_bound(self, x): """ Computes the Evidence Lower Bound, KL and, Reconstruction costs Args: x: tensor: (batch, dim): Observations Returns: nelbo: tensor: (): Negative evidence lower bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # To help you start, we have computed the mixture of Gaussians prior # prior = (m_mixture, v_mixture) for you, where # m_mixture and v_mixture each have shape (1, self.k, self.z_dim) # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior prior = ut.gaussian_parameters(self.z_pre, dim=1) prior_m, prior_v = prior batch = x.shape[0] qm, qv = self.enc.encode(x) # Now draw Zs from the posterior qm/qv z = ut.sample_gaussian(qm, qv) l_posterior = ut.log_normal(z, qm, qv) multi_m = prior_m.expand(batch, *prior_m.shape[1:]) multi_v = prior_v.expand(batch, *prior_v.shape[1:]) l_prior = ut.log_normal_mixture(z, multi_m, multi_v) kls = l_posterior - l_prior kl = torch.mean(kls) probs = self.dec.decode(z) recs = ut.log_bernoulli_with_logits(x, probs) rec = -1.0 * torch.mean(recs) nelbo = kl + rec ################################################################################ # End of code modification ################################################################################ return nelbo, kl, rec
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior prior = ut.gaussian_parameters(self.z_pre, dim=1) q_m, q_v = self.enc.encode(x) q_m_, q_v_ = ut.duplicate(q_m, rep=iw), ut.duplicate(q_v, rep=iw) z_given_x = ut.sample_gaussian(q_m_, q_v_) decoded_bernoulli_logits = self.dec.decode(z_given_x) #duplicate x x_dup = ut.duplicate(x, rep=iw) rec = ut.log_bernoulli_with_logits(x_dup, decoded_bernoulli_logits) log_p_theta = ut.log_normal_mixture(z_given_x, prior[0], prior[1]) log_q_phi = ut.log_normal(z_given_x, q_m_, q_v_) kl = log_q_phi - log_p_theta niwae = rec - kl niwae = ut.log_mean_exp(niwae.reshape(iw, -1), dim=0) niwae = -torch.mean(niwae) #yay! ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior prior = ut.gaussian_parameters(self.z_pre, dim=1) N_batches, dims = x.size() x = ut.duplicate(x, iw) q_mu, q_var = self.enc.encode(x) z_samp = ut.sample_gaussian(q_mu, q_var) logits = self.dec.decode(z_samp) probs = ut.log_bernoulli_with_logits(x, logits) kl_vals = -ut.log_normal(z_samp, q_mu, q_var) + ut.log_normal_mixture(z_samp, *prior) probs = probs + kl_vals niwae = torch.mean(-ut.log_mean_exp(probs.reshape(N_batches, iw), 1)) kl = torch.tensor(0) rec = torch.tensor(0) ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def negative_elbo_bound(self, x): """ Computes the Evidence Lower Bound, KL and, Reconstruction costs Args: x: tensor: (batch, dim): Observations Returns: nelbo: tensor: (): Negative evidence lower bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # To help you start, we have computed the mixture of Gaussians prior # prior = (m_mixture, v_mixture) for you, where # m_mixture and v_mixture each have shape (1, self.k, self.z_dim) # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ # # Compute the mixture of Gaussian prior pm, pv = ut.gaussian_parameters(self.z_pre, dim=1) # # Generate samples. qm, qv = self.enc.encode(x) z_sample = ut.sample_gaussian(qm, qv) rec = self.dec.decode(z_sample) # # Compute loss. # KL divergence between the latent distribution and the prior. rec = -ut.log_bernoulli_with_logits(x, rec) # kl = ut.kl_normal(qm, qv, pm, pv) kl = ut.log_normal(z_sample, qm, qv) - ut.log_normal_mixture( z_sample, pm, pv) # # The liklihood of reproducing the sample image given the parameters. # Would need to take the average of this otherwise. nelbo = (kl + rec).mean() # NELBO: 89.24684143066406. KL: 10.346451759338379. Rec: 78.90038299560547 ################################################################################ # End of code modification ################################################################################ return nelbo, kl.mean(), rec.mean()
def negative_elbo_bound(self, x): """ Computes the Evidence Lower Bound, KL and, Reconstruction costs Args: x: tensor: (batch, dim): Observations Returns: nelbo: tensor: (): Negative evidence lower bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # To help you start, we have computed the mixture of Gaussians prior # prior = (m_mixture, v_mixture) for you, where # m_mixture and v_mixture each have shape (1, self.k, self.z_dim) # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior prior = ut.gaussian_parameters(self.z_pre, dim=1) N_samp, dim = x.size() q_mu, q_var = self.enc.encode(x) z_samp = ut.sample_gaussian(q_mu, q_var) logits = self.dec.decode(z_samp) rec = -torch.mean(ut.log_bernoulli_with_logits(x, logits)) kl = torch.mean(ut.log_normal(z_samp, q_mu, q_var) - ut.log_normal_mixture(z_samp, *prior)) nelbo = kl + rec ################################################################################ # End of code modification ################################################################################ return nelbo, kl, rec
def negative_elbo_bound(self, x): """ Computes the Evidence Lower Bound, KL and, Reconstruction costs Args: x: tensor: (batch, dim): Observations Returns: nelbo: tensor: (): Negative evidence lower bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute negative Evidence Lower Bound and its KL and Rec decomposition # # Note that nelbo = kl + rec # # Outputs should all be scalar ################################################################################ m, v = self.enc.encode(x) eps = ut.sample_gaussian(self.z_prior_m.expand(m.size()), self.z_prior_v.expand(v.size())) z_eps = m + eps.mul(v.pow(0.5)) x_hat = self.dec.decode(z_eps) rec = ut.log_bernoulli_with_logits(x, x_hat).mean() #kl = ut.kl_normal(m, v, self.z_prior_m.expand(m.size()), # self.z_prior_v.expand(v.size())).mean() hq = ut.log_normal(z_eps, m, v).mean() #hz = ut.log_normal(z_eps, self.z_prior_m.expand(m.size()), self.z_prior_v.expand(v.size())).mean() kl = hq nelbo = kl - rec ################################################################################ # End of code modification ################################################################################ return nelbo, kl, rec
def nelbo(self, x, epoch=None): """ Computes the Evidence Lower Bound, KL and, Reconstruction costs Args: x: tensor: (batch, dim): Observations Returns: nelbo: tensor: (): Negative evidence lower bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ # get dimensions z_dim = self.z_dim z_num = self.z_num b_size = x.size(0) # sample c and determine parents c = self.mu.sample() mask = torch.zeros((z_num, z_num)) mask[torch.tril(torch.ones((z_num, z_num)), -1) == 1] = c p_num = (mask != 0).sum(dim=0) # get data encoding hx = self.gl_enc.encode(x) # compute log prior and log posterior # sample z from posterior logq = torch.zeros(b_size) logp = torch.zeros(b_size) z = torch.zeros((b_size, z_dim, z_num)) for n in range(1, z_num + 1): # if no parents, sample unit gaussian # else, sample encoded gaussian if p_num[-n] == 0: m_n = torch.zeros((b_size, z_dim), requires_grad=False) v_n = torch.ones((b_size, z_dim), requires_grad=False) z[:, :, -n] = ut.sample_gaussian(m_n, v_n) else: # get parents of z_n p_n = z.transpose(1, 2).reshape(-1, z_dim * z_num) # get bottom-up and top-down encoded gaussian parameters bu_psi_n = self.bu_enc[-n].encode(hx) td_psi_n = self.td_enc[-n].encode(p_n) # compute precision-weighted fusion of encoded gaussian parameters psi_n = self.gaussian_params_fusion(bu_psi_n, td_psi_n) # sample z_n from posterior z_n = ut.sample_gaussian(psi_n[0], psi_n[1]) z[:, :, -n] = z_n # add to log prior and log posterior logp += ut.log_normal(z_n, td_psi_n[0], td_psi_n[1]) logq += ut.log_normal(z_n, psi_n[0], psi_n[1]) # compute log conditional logits = self.dec.decode(hx) # logits = self.dec.decode(z.transpose(1,2).reshape(-1,z_dim*z_num)) logp_cond = ut.log_bernoulli_with_logits(x, logits) # compute rec and kl terms rec = -logp_cond.mean() kl = (logq - logp).mean() nelbo = rec + kl # print(nelbo.data, kl.data, rec.data) # print(c) return nelbo, kl, rec
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ # Compute the mixture of Gaussian prior prior = ut.gaussian_parameters(self.z_pre, dim=1) prior_m, prior_v = prior batch = x.shape[0] multi_x = ut.duplicate(x, iw) qm, qv = self.enc.encode(x) multi_qm = ut.duplicate(qm, iw) multi_qv = ut.duplicate(qv, iw) # z will be (batch*iw x z_dim) # with sampled z's for a given x non-contiguous! z = ut.sample_gaussian(multi_qm, multi_qv) probs = self.dec.decode(z) recs = ut.log_bernoulli_with_logits(multi_x, probs) rec = -1.0 * torch.mean(recs) multi_m = prior_m.expand(batch * iw, *prior_m.shape[1:]) multi_v = prior_v.expand(batch * iw, *prior_v.shape[1:]) z_priors = ut.log_normal_mixture(z, multi_m, multi_v) x_posteriors = recs z_posteriors = ut.log_normal(z, multi_qm, multi_qv) kls = z_posteriors - z_priors kl = torch.mean(kls) log_ratios = z_priors + x_posteriors - z_posteriors # Should be (batch*iw, z_dim), batch ratios non contiguous unflat_log_ratios = log_ratios.reshape(iw, batch) niwaes = ut.log_mean_exp(unflat_log_ratios, 0) niwae = -1.0 * torch.mean(niwaes) ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec
def negative_iwae_bound(self, x, iw): """ Computes the Importance Weighted Autoencoder Bound Additionally, we also compute the ELBO KL and reconstruction terms Args: x: tensor: (batch, dim): Observations iw: int: (): Number of importance weighted samples Returns: niwae: tensor: (): Negative IWAE bound kl: tensor: (): ELBO KL divergence to prior rec: tensor: (): ELBO Reconstruction term """ ################################################################################ # TODO: Modify/complete the code here # Compute niwae (negative IWAE) with iw importance samples, and the KL # and Rec decomposition of the Evidence Lower Bound # # Outputs should all be scalar ################################################################################ ## E_{z(1),...z(n)} {log p(x|z) + log p(z) - log q(z|x)} m, v = self.enc.encode(x) batch_m = m.unsqueeze(1) batch_m = batch_m.repeat(1, iw, 1) # dimension (batch, iw, 10) batch_v = v.unsqueeze(1) batch_v = batch_v.repeat(1, iw, 1) batch_x = x.unsqueeze(1) batch_x = batch_x.repeat(1, iw, 1) # log p(x|z) zs = ut.sample_gaussian(batch_m, batch_v) logits = self.dec.decode(zs) raw_probs = ut.log_bernoulli_with_logits(batch_x, logits) pxz = torch.mean(ut.log_mean_exp(raw_probs, dim=-1)) # log p(z) batch_size = batch_m.shape[0] batch_z_prior_m = self.z_prior_m.view(1, 1, -1) batch_z_prior_m = batch_z_prior_m.repeat(batch_size, iw, 1) batch_z_prior_v = self.z_prior_v.view(1, 1, -1) batch_z_prior_v = batch_z_prior_v.repeat(batch_size, iw, 1) pz = ut.log_normal(zs, batch_z_prior_m, batch_z_prior_v) # (batch, iw) pz = torch.mean(ut.log_mean_exp(pz, dim=-1)) # log q(z|x) qzx = ut.log_normal(zs, batch_m, batch_v) qzx = torch.mean(ut.log_mean_exp(qzx, dim=-1)) # print(pxz, pz, qzx) niwae = -1 * (pxz + pz - qzx) rec = pxz - pz kl = pz - qzx ################################################################################ # End of code modification ################################################################################ return niwae, kl, rec