{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Exact QEP Regression on Classification Labels\n", "\n", "In this notebok, we demonstrate how one can convert classification problems into regression problems by performing fixed noise regression on the classification labels. \n", "\n", "We follow the method of [Dirichlet-based Gaussian Processes for Large-Scale Calibrated Classification](https://papers.nips.cc/paper/2018/file/b6617980ce90f637e68c3ebe8b9be745-Paper.pdf) who transform classification targets into regression ones by using an approximate likelihood." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import math\n", "import torch\n", "import numpy as np\n", "import qpytorch\n", "from matplotlib import pyplot as plt\n", "\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generate Data\n", "\n", "Firs, we will generate 500 data points from a smooth underlying latent function and have the inputs be iid Gaussian.\n", "The decision boundaries are given by rounding a latent function:\n", "\n", "$f(x,y) = \\sin(0.15 \\pi u + (x + y)) + 1,$ where $u \\sim \\text{Unif}(0,1).$\n", "Then, $y = \\text{round}(f(x,y)).$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def gen_data(num_data, seed = 2019):\n", " torch.random.manual_seed(seed)\n", " \n", " x = torch.randn(num_data,1)\n", " y = torch.randn(num_data,1)\n", " \n", " u = torch.rand(1)\n", " data_fn = lambda x, y: 1 * torch.sin(0.15 * u * 3.1415 * (x + y)) + 1\n", " latent_fn = data_fn(x, y)\n", " z = torch.round(latent_fn).long().squeeze()\n", " return torch.cat((x,y),dim=1), z, data_fn" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "train_x, train_y, genfn = gen_data(500)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(train_x[:,0].numpy(), train_x[:,1].numpy(), c = train_y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The below plots illustrate the decision boundary. We will predict the class logits and ultimately the predictions across $[-3, 3]^2$ for illustration; this region contains both interpolation and extrapolation." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "test_d1 = np.linspace(-3, 3, 20)\n", "test_d2 = np.linspace(-3, 3, 20)\n", "\n", "test_x_mat, test_y_mat = np.meshgrid(test_d1, test_d2)\n", "test_x_mat, test_y_mat = torch.Tensor(test_x_mat), torch.Tensor(test_y_mat)\n", "\n", "test_x = torch.cat((test_x_mat.view(-1,1), test_y_mat.view(-1,1)),dim=1)\n", "test_labels = torch.round(genfn(test_x_mat, test_y_mat))\n", "test_y = test_labels.view(-1)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.contourf(test_x_mat.numpy(), test_y_mat.numpy(), test_labels.numpy())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setting Up the Model\n", "\n", "The Dirichlet QEP model is an exact QEP model with a couple of caveats. First, it uses a special likelihood: a DirichletClassificationLikelihood, and second, it is natively a multi-output model (for each data point, we need to predict `num_classes`, $C$, outputs) so we need to specify the batch shape for our mean and covariance functions.\n", "\n", "The DirichletClassificationLikelhood is just a special type of `FixedQExponentialNoiseLikelihood` that does the required data transformations into a regression problem for us. Succinctly, we soft one hot encode the labels into $C$ outputs so that $\\alpha_i = \\alpha_\\epsilon$ if $y_c=0$ and $\\alpha_i = 1 + \\alpha_\\epsilon$ if $y_c=1.$\n", "Then, our variances are $\\sigma^2 = \\log(1./\\alpha + 1.)$ and our targets are $\\log(\\alpha) - 0.5 \\sigma^2.$\n", "\n", "That is, rather than a classification problem, we have a regression problem with $C$ outputs.\n", "For more details, please see the original paper." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from qpytorch.models import ExactQEP\n", "from qpytorch.likelihoods import QExponentialDirichletClassificationLikelihood\n", "from qpytorch.means import ConstantMean\n", "from qpytorch.kernels import ScaleKernel, RBFKernel" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# We will use the simplest form of QEP model, exact inference\n", "POWER = 1.0\n", "class DirichletQEPModel(ExactQEP):\n", " def __init__(self, train_x, train_y, likelihood, num_classes):\n", " super(DirichletQEPModel, self).__init__(train_x, train_y, likelihood)\n", " self.power = torch.tensor(POWER)\n", " self.mean_module = ConstantMean(batch_shape=torch.Size((num_classes,)))\n", " self.covar_module = ScaleKernel(\n", " RBFKernel(batch_shape=torch.Size((num_classes,))),\n", " batch_shape=torch.Size((num_classes,)),\n", " )\n", " \n", " def forward(self, x):\n", " mean_x = self.mean_module(x)\n", " covar_x = self.covar_module(x)\n", " return qpytorch.distributions.MultivariateQExponential(mean_x, covar_x, power=self.power)\n", "\n", "# initialize likelihood and model\n", "# we let the QExponentialDirichletClassificationLikelihood compute the targets for us\n", "likelihood = QExponentialDirichletClassificationLikelihood(train_y, learn_additional_noise=True, power=torch.tensor(POWER))\n", "model = DirichletQEPModel(train_x, likelihood.transformed_targets, likelihood, num_classes=likelihood.num_classes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we train and fit the model as we would any other GPyTorch model." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iter 1/50 - Loss: 9.540 lengthscale: 0.693 noise: 0.693\n", "Iter 6/50 - Loss: 9.207 lengthscale: 0.958 noise: 0.475\n", "Iter 11/50 - Loss: 9.062 lengthscale: 1.171 noise: 0.321\n", "Iter 16/50 - Loss: 8.977 lengthscale: 1.239 noise: 0.219\n", "Iter 21/50 - Loss: 8.901 lengthscale: 1.172 noise: 0.153\n", "Iter 26/50 - Loss: 8.831 lengthscale: 1.036 noise: 0.111\n", "Iter 31/50 - Loss: 8.779 lengthscale: 0.887 noise: 0.084\n", "Iter 36/50 - Loss: 8.734 lengthscale: 0.737 noise: 0.066\n", "Iter 41/50 - Loss: 8.668 lengthscale: 0.609 noise: 0.053\n", "Iter 46/50 - Loss: 8.654 lengthscale: 0.570 noise: 0.044\n" ] } ], "source": [ "# this is for running the notebook in our testing framework\n", "import os\n", "smoke_test = ('CI' in os.environ)\n", "training_iter = 2 if smoke_test else 50\n", "\n", "\n", "# Find optimal model hyperparameters\n", "model.train()\n", "likelihood.train()\n", "\n", "# Use the adam optimizer\n", "optimizer = torch.optim.Adam(model.parameters(), lr=0.1) # Includes GaussianLikelihood parameters\n", "\n", "# \"Loss\" for QEPs - the marginal log likelihood\n", "mll = qpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)\n", "\n", "for i in range(training_iter):\n", " # Zero gradients from previous iteration\n", " optimizer.zero_grad()\n", " # Output from model\n", " output = model(train_x)\n", " # Calc loss and backprop gradients\n", " loss = -mll(output, likelihood.transformed_targets).sum()\n", " loss.backward()\n", " if i % 5 == 0:\n", " print('Iter %d/%d - Loss: %.3f lengthscale: %.3f noise: %.3f' % (\n", " i + 1, training_iter, loss.item(),\n", " model.covar_module.base_kernel.lengthscale.mean().item(),\n", " model.likelihood.second_noise_covar.noise.mean().item()\n", " ))\n", " optimizer.step()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model Predictions" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "model.eval()\n", "likelihood.eval()\n", "\n", "with qpytorch.settings.fast_pred_var(), torch.no_grad():\n", " test_dist = model(test_x)\n", " \n", " pred_means = test_dist.loc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We've predicted the logits for each class in the classification problem, and can clearly see that the logits for class 0 are highest in the bottom left, the logits for class 2 are highest in the top right, and the logits for class 1 are highest in the middle." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 3, figsize = (15, 5))\n", "\n", "for i in range(3):\n", " im = ax[i].contourf(\n", " test_x_mat.numpy(), test_y_mat.numpy(), pred_means[i].numpy().reshape((20,20))\n", " )\n", " fig.colorbar(im, ax=ax[i])\n", " ax[i].set_title(\"Logits: Class \" + str(i), fontsize = 20)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unfortunately, we can't get closed form estimates of the probabilities; however, we can approximate them with a lightweight sampling step using $J$ samples from the posterior as:\n", "$$\\mathbb{E}(p(y_i = j)) = \\int \\frac{\\exp\\{f_i^*\\}}{\\sum_k^C \\exp\\{f_i^*\\}} p(f^* | y) df^* \\approx \\frac{1}{J} \\sum_j^J \\frac{\\exp\\{f_{i,j}^*\\}}{\\sum_k^C \\exp\\{f_{i,j}^*\\}}$$\n", "\n", "Here, we draw $256$ samples from the posterior." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/shiweilan/miniconda/envs/qpytorch/lib/python3.10/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning: A not p.d., added jitter of 1.0e-06 to the diagonal\n", " warnings.warn(\n", "/Users/shiweilan/miniconda/envs/qpytorch/lib/python3.10/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning: A not p.d., added jitter of 1.0e-05 to the diagonal\n", " warnings.warn(\n", "/Users/shiweilan/miniconda/envs/qpytorch/lib/python3.10/site-packages/linear_operator/utils/cholesky.py:40: NumericalWarning: A not p.d., added jitter of 1.0e-04 to the diagonal\n", " warnings.warn(\n" ] } ], "source": [ "pred_samples = test_dist.sample(torch.Size((256,))).exp()\n", "probabilities = (pred_samples / pred_samples.sum(-2, keepdim=True)).mean(0)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 3, figsize = (15, 5))\n", "\n", "levels = np.linspace(0, 1.05, 20)\n", "for i in range(3):\n", " im = ax[i].contourf(\n", " test_x_mat.numpy(), test_y_mat.numpy(), probabilities[i].numpy().reshape((20,20)), levels=levels\n", " )\n", " fig.colorbar(im, ax=ax[i])\n", " ax[i].set_title(\"Probabilities: Class \" + str(i), fontsize = 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we plot the decision boundary (on the right) and the true decision boundary on the left. They align pretty closely.\n", "\n", "To get the decision boundary from our model, all we need to do is to compute the elementwise maximium at each test point." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Estimated Response')" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1,2, figsize=(10, 5))\n", "\n", "ax[0].contourf(test_x_mat.numpy(), test_y_mat.numpy(), test_labels.numpy())\n", "ax[0].set_title('True Response', fontsize=20)\n", "\n", "ax[1].contourf(test_x_mat.numpy(), test_y_mat.numpy(), pred_means.max(0)[1].reshape((20,20)))\n", "ax[1].set_title('Estimated Response', fontsize=20)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.12" } }, "nbformat": 4, "nbformat_minor": 4 }