From b43f7d07dc0923dcece64813ac1c39d277056451 Mon Sep 17 00:00:00 2001 From: Eduardo Adame Date: Tue, 23 Apr 2024 22:19:26 -0300 Subject: [PATCH] Initial implementation for #3 and results on current datasets --- .../S2OCGP_ScaleRBFKernel_adaptive_test.png | Bin 0 -> 465560 bytes ...S2OCGP_ScaleRBFKernel_adaptive_HC_test.png | Bin 0 -> 285572 bytes ...2OCGP_ScaleRBFKernel_adaptive_HC2_test.png | Bin 0 -> 244330 bytes ...2OCGP_ScaleRBFKernel_adaptive_HC3_test.png | Bin 0 -> 217099 bytes .../S2OCGP_ScaleRBFKernel_uniform_test.png | Bin 0 -> 361598 bytes .../S2OCGP_ScaleRBFKernel_uniform_HC_test.png | Bin 0 -> 223472 bytes ...S2OCGP_ScaleRBFKernel_uniform_HC2_test.png | Bin 0 -> 244528 bytes ...S2OCGP_ScaleRBFKernel_uniform_HC3_test.png | Bin 0 -> 224155 bytes .../gpytorch-scgp-second-order-only.py | 175 ++++++++++++++++++ src/scgp/__init__.py | 0 src/scgp/kernels.py | 144 ++++++++++++++ 11 files changed, 319 insertions(+) create mode 100644 results/adaptive/s2ocgp/S2OCGP_ScaleRBFKernel_adaptive_test.png create mode 100644 results/adaptive_HC/s2ocgp/S2OCGP_ScaleRBFKernel_adaptive_HC_test.png create mode 100644 results/adaptive_HC2/s2ocgp/S2OCGP_ScaleRBFKernel_adaptive_HC2_test.png create mode 100644 results/adaptive_HC3/s2ocgp/S2OCGP_ScaleRBFKernel_adaptive_HC3_test.png create mode 100644 results/uniform/s2ocgp/S2OCGP_ScaleRBFKernel_uniform_test.png create mode 100644 results/uniform_HC/s2ocgp/S2OCGP_ScaleRBFKernel_uniform_HC_test.png create mode 100644 results/uniform_HC2/s2ocgp/S2OCGP_ScaleRBFKernel_uniform_HC2_test.png create mode 100644 results/uniform_HC3/s2ocgp/S2OCGP_ScaleRBFKernel_uniform_HC3_test.png create mode 100644 src/prototypes/gpytorch-scgp-second-order-only.py create mode 100644 src/scgp/__init__.py create mode 100644 src/scgp/kernels.py diff --git a/results/adaptive/s2ocgp/S2OCGP_ScaleRBFKernel_adaptive_test.png b/results/adaptive/s2ocgp/S2OCGP_ScaleRBFKernel_adaptive_test.png new file mode 100644 index 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z`yZjX|Lu>=Kl~d_VjBL9CW$Qk8%<&o{*5Lv3I7@eOv1lL0h92rQ6Q7>|H&w{k5k-1 W*FB<~%Oc1%c5K tuple: + data = np.loadtxt(path, delimiter=",", skiprows=1, dtype=np.float32) + x_train = torch.from_numpy(data[:, 0]) + y_train = torch.stack( + [torch.from_numpy(data[:, 1]), torch.from_numpy(data[:, 3])], -1 + ).squeeze(1) + return x_train, y_train + + +# Read http://www.gaussianprocess.org/gpml/chapters/RW9.pdf +class SCGP(gpytorch.models.ExactGP): + def __init__(self, train_x, train_y, likelihood, kernel): + super(SCGP, self).__init__(train_x, train_y, likelihood) + self.mean_module = gpytorch.means.ConstantMeanGrad() + self.base_kernel = kernel + self.covar_module = gpytorch.kernels.ScaleKernel(self.base_kernel) + + def forward(self, x): + mean_x = self.mean_module(x) + covar_x = self.covar_module(x) + return gpytorch.distributions.MultitaskMultivariateNormal(mean_x, + covar_x) + + +def scgp_fit(path: str, iters: int, kernel: gpytorch.kernels.Kernel) -> tuple: + train_x, train_y = load_data(path) + + likelihood = gpytorch.likelihoods.MultitaskGaussianLikelihood( + num_tasks=2 + ) # y and y_second_prime + model = SCGP(train_x, train_y, likelihood, kernel) + + # Optimizing hyperparameters via marginal log likelihood + model.train() + likelihood.train() + + optimizer = torch.optim.Adam(model.parameters(), lr=0.1) + mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model) + + for i in trange(iters): + optimizer.zero_grad() + output = model(train_x) + loss = -mll(output, train_y) + loss.backward() + if LOGGING: + tqdm.write( + f"Iter {i + 1}/{iters} - Loss: {loss.item():.3f}" + "noise: {model.likelihood.noise.item():.3f}" + ) + optimizer.step() + + return train_x, train_y, model, likelihood + + +def save_plot_scpg( + train_x: torch.Tensor, + train_y: torch.Tensor, + model: SCGP, + likelihood: gpytorch.likelihoods.MultitaskGaussianLikelihood, + ker_name: str, + dataset_name: str +) -> None: + + # Name of the plot + name = f"S2OCGP_Scale{ker_name}_{dataset_name}_test" + + # Evaluation mode + model.train() + model.eval() + likelihood.eval() + + # Initialize plots + f, (y_ax, y_prime_ax) = plt.subplots(1, 2, + figsize=(10, 4), tight_layout=True) + + # Make predictions + with torch.no_grad(), gpytorch.settings.max_cg_iterations(100): + test_x = torch.linspace(0, 1, 100) + predictions = likelihood(model(test_x)) + mean = predictions.mean + lower, upper = predictions.confidence_region() + + # Plotting predictions for f + y_ax.plot(train_x.detach().numpy(), train_y[:, 0].detach().numpy(), "k*") + y_ax.plot(test_x.numpy(), mean[:, 0].numpy(), "b") + y_ax.fill_between( + test_x.numpy(), lower[:, 0].numpy(), upper[:, 0].numpy(), alpha=0.5 + ) + y_ax.legend(["Observed Values", "Mean", "Confidence"]) + y_ax.set_title("Function values") + y_ax.set_xlim([0, 1]) + # y_ax.set_ylim([-7.5, 12.5]) + y_ax.set_xlabel(r"$\alpha$") + y_ax.set_ylabel(r"$f_{\boldsymbol{z}}(\alpha)$") + + # Plotting predictions for f' + y_prime_ax.plot(train_x.detach().numpy(), train_y[:, 1].detach().numpy(), + "k*") + y_prime_ax.plot(test_x.numpy(), mean[:, 1].numpy(), "b") + y_prime_ax.fill_between( + test_x.numpy(), lower[:, 1].numpy(), upper[:, 1].numpy(), alpha=0.5 + ) + y_prime_ax.legend(["Observed Derivatives", "Mean", "Confidence"]) + y_prime_ax.set_title(r"Second Order Derivatives with respect to $\alpha$") + y_prime_ax.set_xlim([0, 1]) + + y_prime_ax.set_xlabel(r"$\alpha$") + y_prime_ax.set_ylabel(r"$\frac{\mathrm{d}^2}{\mathrm{d}\alpha^2}f_{\boldsymbol{z}}(\alpha)$") + + save_path = PATH / "results" / str(dataset_name) / 's2ocgp' + save_path.mkdir(parents=True, exist_ok=True) + + f.savefig(save_path / (name + ".png"), dpi=600, bbox_inches="tight") + plt.close(f) + + +if __name__ == "__main__": + datasets = { + "uniform": DATA_PATH / "Gaussian_logCA0_uniform_J=20.csv", + "adaptive": DATA_PATH / "Gaussian_logCA0_adaptive_J=20.csv", + "uniform_HC": DATA_PATH / "Gaussian_HC_logCA0_uniform_J=20.csv", + "adaptive_HC": DATA_PATH / "Gaussian_HC_logCA0_adaptive_J=20.csv", + "uniform_HC2": DATA_PATH / "Gaussian_HC_logCA0_uniform_J=20_HC2.csv", + "adaptive_HC2": DATA_PATH / "Gaussian_HC_logCA0_adaptive_J=20_HC2.csv", + "uniform_HC3": DATA_PATH / "Gaussian_HC_logCA0_uniform_J=20_HC3.csv", + "adaptive_HC3": DATA_PATH / "Gaussian_HC_logCA0_adaptive_J=20_HC3.csv", + } + + kernels = {"RBFKernel": RBFKernelSecondGrad(),} + + for ker_name, kernel in kernels.items(): + print(f"Running {ker_name}") + + for dataset_name, dataset_path in datasets.items(): + start_time = time.time() + try: + train_x, train_y, data_scgp, data_likelihood = scgp_fit( + dataset_path, 100, kernel=kernel + ) + save_plot_scpg( + train_x, + train_y, + data_scgp, + data_likelihood, + ker_name, + dataset_name + ) + final_time = time.time() - start_time + print( + f"Finished {ker_name} on {dataset_name} took {final_time:.2f}s" + ) + except Exception as e: + print(f"Error on {ker_name} on {dataset_name} took {e}") + continue \ No newline at end of file diff --git a/src/scgp/__init__.py b/src/scgp/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/src/scgp/kernels.py b/src/scgp/kernels.py new file mode 100644 index 0000000..8d68be7 --- /dev/null +++ b/src/scgp/kernels.py @@ -0,0 +1,144 @@ +import torch +from linear_operator.operators import KroneckerProductLinearOperator +from gpytorch.kernels.rbf_kernel import postprocess_rbf, RBFKernel + + +class RBFKernelSecondGrad(RBFKernel): + def forward(self, x1, x2, diag=False, **params): + batch_shape = x1.shape[:-2] + n_batch_dims = len(batch_shape) + n1, d = x1.shape[-2:] + n2 = x2.shape[-2] + + K = torch.zeros( + *batch_shape, + n1 * (2 * d + 1), + n2 * (2 * d + 1), + device=x1.device, + dtype=x1.dtype + ) + final_K = torch.zeros( + *batch_shape, n1 * (d + 1), n2 * (d + 1), device=x1.device, dtype=x1.dtype + ) + + # Scale the inputs by the lengthscale (for stability) + x1_ = x1.div(self.lengthscale) + x2_ = x2.div(self.lengthscale) + + # Form all possible rank-1 products for the gradient and Hessian blocks + outer = x1_.view(*batch_shape, n1, 1, d) - x2_.view(*batch_shape, 1, n2, d) + outer = outer / self.lengthscale.unsqueeze(-2) + outer = torch.transpose(outer, -1, -2).contiguous() + + # 1) Kernel block + diff = self.covar_dist(x1_, x2_, square_dist=True, **params) + K_11 = postprocess_rbf(diff) + K[..., :n1, :n2] = K_11 + final_K[..., :n1, :n2] = K_11 + + # 2) First gradient block + outer1 = outer.view(*batch_shape, n1, n2 * d) + K[..., :n1, n2 : (n2 * (d + 1))] = outer1 * K_11.repeat( + [*([1] * (n_batch_dims + 1)), d] + ) + + # 3) Second gradient block + outer2 = outer.transpose(-1, -3).reshape(*batch_shape, n2, n1 * d) + outer2 = outer2.transpose(-1, -2) + K[..., n1 : (n1 * (d + 1)), :n2] = -outer2 * K_11.repeat( + [*([1] * n_batch_dims), d, 1] + ) + + # 4) Hessian block + outer3 = outer1.repeat([*([1] * n_batch_dims), d, 1]) * outer2.repeat( + [*([1] * (n_batch_dims + 1)), d] + ) + kp = KroneckerProductLinearOperator( + torch.eye(d, d, device=x1.device, dtype=x1.dtype).repeat(*batch_shape, 1, 1) + / self.lengthscale.pow(2), + torch.ones(n1, n2, device=x1.device, dtype=x1.dtype).repeat( + *batch_shape, 1, 1 + ), + ) + chain_rule = kp.to_dense() - outer3 + K[..., n1 : (n1 * (d + 1)), n2 : (n2 * (d + 1))] = chain_rule * K_11.repeat( + [*([1] * n_batch_dims), d, d] + ) + + # 5) 1-3 block + douter1dx2 = KroneckerProductLinearOperator( + torch.ones(1, d, device=x1.device, dtype=x1.dtype).repeat( + *batch_shape, 1, 1 + ) + / self.lengthscale.pow(2), + torch.ones(n1, n2, device=x1.device, dtype=x1.dtype).repeat( + *batch_shape, 1, 1 + ), + ).to_dense() + + K_13 = (-douter1dx2 + outer1 * outer1) * K_11.repeat( + [*([1] * (n_batch_dims + 1)), d] + ) # verified for n1=n2=1 case + K[..., :n1, (n2 * (d + 1)) :] = K_13 + final_K[..., :n1, n2:] = K_13 + + K_31 = (-douter1dx2.transpose(-1, -2) + outer2 * outer2) * K_11.repeat( + [*([1] * n_batch_dims), d, 1] + ) # verified for n1=n2=1 case + K[..., (n1 * (d + 1)) :, :n2] = K_31 + final_K[..., n1:, :n2] = K_31 + + # rest of the blocks are all of size (n1*d,n2*d) + outer1 = outer1.repeat([*([1] * n_batch_dims), d, 1]) + outer2 = outer2.repeat([*([1] * (n_batch_dims + 1)), d]) + # II = (torch.eye(d,d,device=x1.device,dtype=x1.dtype)/lengthscale.pow(2)).repeat(*batch_shape,n1,n2) + kp2 = KroneckerProductLinearOperator( + torch.ones(d, d, device=x1.device, dtype=x1.dtype).repeat( + *batch_shape, 1, 1 + ) + / self.lengthscale.pow(2), + torch.ones(n1, n2, device=x1.device, dtype=x1.dtype).repeat( + *batch_shape, 1, 1 + ), + ).to_dense() + + # II may not be the correct thing to use. It might be more appropriate to use kp instead?? + II = kp.to_dense() + K_11dd = K_11.repeat([*([1] * (n_batch_dims)), d, d]) + + K_23 = ( + (-kp2 + outer1 * outer1) * (-outer2) + 2.0 * II * outer1 + ) * K_11dd # verified for n1=n2=1 case + + K[..., n1 : (n1 * (d + 1)), (n2 * (d + 1)) :] = K_23 + + K_32 = ( + (-kp2.transpose(-1, -2) + outer2 * outer2) * outer1 - 2.0 * II * outer2 + ) * K_11dd # verified for n1=n2=1 case + + K[..., (n1 * (d + 1)) :, n2 : (n2 * (d + 1))] = K_32 + + K_33 = ( + (-kp2.transpose(-1, -2) + outer2 * outer2) * (-kp2) + - 2.0 * II * outer2 * outer1 + + 2.0 * (II) ** 2 + ) * K_11dd + ( + (-kp2.transpose(-1, -2) + outer2 * outer2) * outer1 - 2.0 * II * outer2 + ) * outer1 * K_11dd # verified for n1=n2=1 case + + K[..., (n1 * (d + 1)) :, (n2 * (d + 1)) :] = K_33 + final_K[..., n1:, n2:] = K_33 + + # Symmetrize for stability + if n1 == n2 and torch.eq(x1, x2).all(): + final_K = 0.5 * (final_K.transpose(-1, -2) + final_K) + + # Apply a perfect shuffle permutation to match the MutiTask ordering + pi1 = torch.arange(n1 * (d + 1)).view(d + 1, n1).t().reshape((n1 * (d + 1))) + pi2 = torch.arange(n2 * (d + 1)).view(d + 1, n2).t().reshape((n2 * (d + 1))) + final_K = final_K[..., pi1, :][..., :, pi2] + + return final_K + + def num_outputs_per_input(self, x1, x2): + return x1.size(-1) + 1