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 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_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 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 sample_clipped_x(self, batch): z = self.sample_z(batch) z = ut.duplicate(z, 10) y = np.arange(10) y = z.new(np.repeat(np.eye(10)[y], batch, 0)) x_m = self.compute_mean_given(z, y) return x_m
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 """ y_logits = self.cls.classify(x) # Duplicate y based on x's batch size. Then duplicate x y = np.repeat(np.arange(self.y_dim), x.size(0)) y = x.new(np.eye(self.y_dim)[y]) x = ut.duplicate(x, self.y_dim) m, v = self.enc.encode(x, y) z = ut.sample_gaussian(m, v) x_logits = self.dec.decode(z, y) # TODO: compute the values below nelbo, kl_z, kl_y, rec = 0, 0, 0, 0 return nelbo, kl_z, kl_y, 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_Z, KL_Y and Rec decomposition # # To assist you in the vectorization of the summation over y, we have # the computation of q(y | x) and some tensor tiling code for you. # # Note that nelbo = kl_z + kl_y + rec # # Outputs should all be scalar ################################################################################ y_logits = self.cls.classify(x) y_logprob = F.log_softmax(y_logits, dim=1) y_prob = torch.softmax(y_logits, dim=1) # (batch, y_dim) p_y = 1 / 10 * torch.ones_like(y_prob) kl_y = torch.mean(ut.kl_cat(y_prob, y_logprob, torch.log(p_y)), dim=0) batch_size = x.shape[0] # Duplicate y based on x's batch size. Then duplicate x # This enumerates all possible combination of x with labels (0, 1, ..., 9) y = np.repeat(np.arange(self.y_dim), x.size(0)) y = x.new(np.eye(self.y_dim)[y]) x = ut.duplicate(x, self.y_dim) qm, qv = self.enc.encode(x, y) z = ut.sample_gaussian(qm, qv) recon_logits = self.dec.decode(z, y) p_x_given_yz = ut.log_bernoulli_with_logits(x, recon_logits) p_x_given_yz = p_x_given_yz.reshape(self.y_dim, batch_size).transpose( 0, 1) #[batch, 10] rec = -torch.mean(torch.sum(p_x_given_yz * y_prob, dim=1), dim=0) kl_z_over_xy = ut.kl_normal(qm, qv, self.z_prior_m, self.z_prior_v) kl_z_over_xy = kl_z_over_xy.reshape(self.y_dim, batch_size).transpose(0, 1) kl_z = torch.mean(torch.sum(kl_z_over_xy * y_prob, dim=1), dim=0) nelbo = rec + kl_y + kl_z ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, kl_y, 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_Z, KL_Y and Rec decomposition # # To assist you in the vectorization of the summation over y, we have # the computation of q(y | x) and some tensor tiling code for you. # # Note that nelbo = kl_z + kl_y + rec # # Outputs should all be scalar ################################################################################ y_logits = self.cls.classify(x) y_logprob = F.log_softmax(y_logits, dim=1) y_prob = torch.softmax(y_logits, dim=1) # Duplicate y based on x's batch size. Then duplicate x # This enumerates all possible combination of x with labels (0, 1, ..., 9) y = np.repeat(np.arange(self.y_dim), x.size(0)) y = x.new(np.eye(self.y_dim)[y]) x = ut.duplicate(x, self.y_dim) # sample z from x and y qm, qv = self.enc.encode(x, y) z = ut.sample_gaussian(qm, qv) # compute kl x_logits = self.dec.decode(z, y) kl_y = ut.kl_cat(y_prob, y_logprob, np.log(1.0 / self.y_dim)) kl_z = ut.kl_normal(qm, qv, self.z_prior[0], self.z_prior[1]) rec_loss = -ut.log_bernoulli_with_logits(x, x_logits) # (y_dim * batch) # Compute the expected reconstruction and kl base on the distribution q(y|x), q(y,z|x) rec_loss_y = (y_prob.t() * rec_loss.reshape(self.y_dim, -1)).sum(0) kl_z_y = (y_prob.t() * kl_z.reshape(self.y_dim, -1)).sum(0) # Reduce to means kl_y, kl_z, rec = kl_y.mean(), kl_z_y.mean(), rec_loss_y.mean() nelbo = rec + kl_z + kl_y ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, kl_y, 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_Z, KL_Y and Rec decomposition # # To assist you in the vectorization of the summation over y, we have # the computation of q(y | x) and some tensor tiling code for you. # # Note that nelbo = kl_z + kl_y + rec # # Outputs should all be scalar ################################################################################ y_logits = self.cls.classify(x) y_logprob = F.log_softmax(y_logits, dim=1) y_prob = torch.softmax(y_logprob, dim=1) # (batch, y_dim) # Duplicate y based on x's batch size. Then duplicate x # This enumerates all possible combination of x with labels (0, 1, ..., 9) y = np.repeat(np.arange(self.y_dim), x.size(0)) y = x.new(np.eye(self.y_dim)[y]) x = ut.duplicate(x, self.y_dim) # # Generate samples. qm, qv = self.enc.encode(x, y) z_sample = ut.sample_gaussian(qm, qv) xprime = self.dec.decode(z_sample, y) # # Compute loss. y_prior = torch.ones_like(y_logprob) / self.y_dim kl_y = ut.kl_cat(y_prob, y_logprob, y_prior) # # Data is duplicated in a way to make the batch dimension second. kl_z = ut.kl_normal(qm, qv, self.z_prior_m, self.z_prior_v).view(self.y_dim, -1) rec = -ut.log_bernoulli_with_logits(x, xprime).view(self.y_dim, -1) # # Swap axis where the probabilitiees are to match the new batch dimensions. nelbo = kl_y + (y_prob.t() * (kl_z + rec)).sum(0) nelbo = nelbo.mean() # Test set classification accuracy: 0.8104000091552734 ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, kl_y, 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 ################################################################################ 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 """ m, v = self.enc.encode(x) # 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) # TODO: compute the values below # Get KL and Rec of elbo again pm = torch.zeros((m.shape)) pv = torch.ones((v.shape)) kl = ut.kl_normal(m, v, pm, pv) rec = ut.log_bernoulli_with_logits(x, logits) # Now get the log mean of the exp of the KL divergence and subtact the # reconstuction from all of the weighted samples niwae = ut.log_mean_exp(ut.kl_normal(m, v, pm, pv), dim=0) - torch.mean( ut.log_bernoulli_with_logits(x, logits)) 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 ################################################################################ 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) log_vals = -ut.kl_normal(q_mu, q_var, torch.zeros_like(q_mu), torch.ones_like(q_var)) # log_vals = ut.log_normal(z_samp, torch.zeros_like(q_mu), torch.ones_like(q_var)) - ut.log_normal(z_samp, q_mu, q_var) probs = probs + log_vals niwae = torch.mean(-ut.log_mean_exp(probs.reshape(N_batches, iw), 1)) kl = torch.tensor(0) rec = torch.tensor(0) # niwae = kl + rec ################################################################################ # 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 ################################################################################ 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_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_Z, KL_Y and Rec decomposition # # To assist you in the vectorization of the summation over y, we have # the computation of q(y | x) and some tensor tiling code for you. # # Note that nelbo = kl_z + kl_y + rec # # Outputs should all be scalar ################################################################################ y_logits = self.cls.classify(x) y_logprob = F.log_softmax(y_logits, dim=1) y_prob = torch.softmax(y_logprob, dim=1) # (batch, y_dim) # Duplicate y based on x's batch size. Then duplicate x # This enumerates all possible combination of x with labels (0, 1, ..., 9) y = np.repeat(np.arange(self.y_dim), x.size(0)) y = x.new(np.eye(self.y_dim)[y]) x = ut.duplicate(x, self.y_dim) ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, kl_y, 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_Z, KL_Y and Rec decomposition # # To assist you in the vectorization of the summation over y, we have # the computation of q(y | x) and some tensor tiling code for you. # # Note that nelbo = kl_z + kl_y + rec # # Outputs should all be scalar ################################################################################ device = torch.device('cuda' if torch.cuda.is_available() else 'cpu') y_logits = self.cls.classify(x) y_logprob = F.log_softmax(y_logits, dim=1) y_prob = torch.softmax(y_logprob, dim=1) # (batch, y_dim) # Duplicate y based on x's batch size. Then duplicate x # This enumerates all possible combination of x with labels (0, 1, ..., 9) y = np.repeat(np.arange(self.y_dim), x.size(0)) y = x.new(np.eye(self.y_dim)[y]) #1000,10. 0,100,200 dupe x = ut.duplicate(x, self.y_dim) #1000,784. 0,100,200 dupe #100x10 y_prior = torch.tensor([0.1]).expand_as(y_prob).to(device) y_logprior = torch.log(y_prior) #(batch size,) kl_ys = ut.kl_cat(y_prob, y_logprob, y_logprior) kl_y = torch.mean(kl_ys) #1000 x 64. Still 0,100,200 corresponding... zqm, zqv = self.enc.encode(x, y) zpm = self.z_prior_m.expand_as(zqm) zpv = self.z_prior_v.expand_as(zqv) #so the zpm, zpv go as x quickly, y slowly #equivalent to y being the 0th dimension #(batch_size * y_dim,) kl_zs_flat = ut.kl_normal(zqm, zqv, zpm, zpv) kl_zs = kl_zs_flat.reshape(10,100).t() kl_zs_weighted = kl_zs * y_prob batch_kl_zs = kl_zs_weighted.sum(1) kl_z = batch_kl_zs.mean() #1000 x 64 z = ut.sample_gaussian(zqm, zqv) #1000 x 784 probs = self.dec.decode(z, y) #(batch_size * y_dim,) recs_flat = -1.0 * ut.log_bernoulli_with_logits(x, probs) recs = recs_flat.reshape(10,100).t() recs_weighted = recs * y_prob batch_recs = recs_weighted.sum(1) rec = batch_recs.mean() nelbos = kl_ys + batch_kl_zs + batch_recs nelbo = torch.mean(nelbos) ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, kl_y, 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_Z, KL_Y and Rec decomposition # # To assist you in the vectorization of the summation over y, we have # the computation of q(y | x) and some tensor tiling code for you. # # Note that nelbo = kl_z + kl_y + rec # # Outputs should all be scalar ################################################################################ N_batches, dims = x.size() y_logits = self.cls.classify(x) y_logprob = F.log_softmax(y_logits, dim=1) y_prob = torch.softmax(y_logprob, dim=1) # (batch, y_dim) # Duplicate y based on x's batch size. Then duplicate x # This enumerates all possible combination of x with labels (0, 1, ..., 9) y = np.repeat(np.arange(self.y_dim), x.size(0)) y = x.new(np.eye(self.y_dim)[y]) x = ut.duplicate(x, self.y_dim) 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_ls = -ut.log_bernoulli_with_logits(x, logits) rec = torch.mean( torch.sum(y_prob * rec_ls.reshape(N_batches, -1), dim=1)) kl_y = torch.mean( ut.kl_cat(y_prob, y_logprob, torch.log(torch.ones_like(y_prob) / self.y_dim))) kl_z_ls = ut.kl_normal(q_mu, q_var, torch.zeros_like(q_mu), torch.ones_like(q_var)) kl_z = torch.mean( torch.sum(y_prob * kl_z_ls.reshape(N_batches, -1), dim=1)) nelbo = kl_z + kl_y + rec ################################################################################ # End of code modification ################################################################################ return nelbo, kl_z, kl_y, 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