{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "3403d231", "metadata": {}, "outputs": [], "source": [ "import tqdm\n", "import math\n", "import torch\n", "import qpytorch\n", "from matplotlib import pyplot as plt\n", "\n", "# Make plots inline\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "dd5cad91", "metadata": {}, "source": [ "## SVQEP Model Updating\n", "\n", "In this notebook, we will be describing a \"fantasy model\" strategy for stochastic variational QEPs (SVQEPs) analogous to fantasy modelling for exact QEPs. \n", "\n", "To understand what a \"fantasy model\" is, we first think about exact QEPs. Imagine, we have trained a QEP on some data $\\mathcal{D} := \\{x_i, y_i\\}_{i=1}^N$, which is the same as saying that $\\mathbf{y} \\sim \\mathcal{QEP}(\\mu(\\mathbf{x}), K(\\mathbf{x}, \\mathbf{x}'))$. \n", "\n", "If we observe some new data $\\mathcal{D}^*:= \\{x_j, y_j\\}_{j=1}^{N^*}$, then that data is easily incorporated into our QEP model as $(\\mathbf{y}, \\mathbf{y}^*) \\sim \\mathcal{QEP}(\\mu([\\mathbf{x}, \\mathbf{x}^*]), K([\\mathbf{x}, \\mathbf{x}^*], [\\mathbf{x}, \\mathbf{x}^*]')$.\n", "To compute predictions with this new model (conditional on the same hyper-parameters), we could use the following piece of code for an exact QEP:\n", "\n", "```python\n", "updated_model = deepcopy(model)\n", "updated_model.set_train_data(torch.cat((train_x, new_x)), torch.cat((train_y, new_y)), strict=False)\n", "```\n", "\n", "or we could take advantage of linear algebraic identies to efficiently produce the same model, which is the `get_fantasy_model` function for exact QEPs in QPyTorch:\n", "```python\n", "updated_model = model.get_fantasy_model(new_x, new_y)\n", "```\n", "\n", "The second approach is significantly more computationally efficient, costing $\\mathcal{O}((N^*)^2 N)$ time versus $\\mathcal{O}((N + N^*)^3)$ time.\n", "\n", "In this tutorial notebook, we describe the **online variational conditioning** (OVC) approach of [Maddox et al, '21](https://arxiv.org/abs/2110.15172) which provides a closed form method for updating SVQEPs in the same manner as exact QEPs are updated with respect ot new data, via the usage of the `get_fantasy_model` method." ] }, { "cell_type": "markdown", "id": "6bc1b924", "metadata": {}, "source": [ "### Training Data\n", "\n", "First, we construct some training data, here $250$ data points from a noisy sine wave." ] }, { "cell_type": "code", "execution_count": 2, "id": "81daa65c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "train_x = torch.linspace(0, 3, 250).view(-1, 1).contiguous()\n", "train_y = torch.sin(6. * train_x) + 0.3 * torch.randn_like(train_x)\n", "\n", "plt.scatter(train_x, train_y, marker = \"*\", color = \"black\")\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")" ] }, { "cell_type": "markdown", "id": "a1d8b8f0", "metadata": {}, "source": [ "### Model definition\n", "\n", "Next, we define our model class definition. The only difference from a standard approximate QEP is that we require the likelihood object to be a) Gaussian (for now) and b) to be stored inside of the `ApproximateQEP` object." ] }, { "cell_type": "code", "execution_count": 3, "id": "50f30949", "metadata": {}, "outputs": [], "source": [ "from qpytorch.models import ApproximateQEP\n", "from qpytorch.variational import CholeskyVariationalDistribution\n", "from qpytorch.variational import VariationalStrategy\n", "POWER = 1.0\n", "\n", "class QEPModel(ApproximateQEP):\n", " def __init__(self, inducing_points, likelihood):\n", " self.power = torch.tensor(POWER)\n", " variational_distribution = CholeskyVariationalDistribution(inducing_points.size(0), power=self.power)\n", " variational_strategy = VariationalStrategy(self, inducing_points, variational_distribution, learn_inducing_locations=True)\n", " super(QEPModel, self).__init__(variational_strategy)\n", " self.mean_module = qpytorch.means.ConstantMean()\n", " self.covar_module = qpytorch.kernels.ScaleKernel(qpytorch.kernels.RBFKernel())\n", " self.likelihood = likelihood\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)" ] }, { "cell_type": "markdown", "id": "9c19020b", "metadata": {}, "source": [ "We initialize the SVQEP with $25$ inducing points." ] }, { "cell_type": "code", "execution_count": 4, "id": "9cfef053", "metadata": {}, "outputs": [], "source": [ "likelihood = qpytorch.likelihoods.QExponentialLikelihood(power=torch.tensor(POWER))\n", "model = QEPModel(torch.randn(25, 1) + 2., likelihood)\n" ] }, { "cell_type": "markdown", "id": "11113b9d", "metadata": {}, "source": [ "### Model Training\n", "\n", "As we don't have a lot of data, we train the model with full-batch (although this isn't a restriction) and for $500$ iterations (b/c our choice of inducing points may not have been very good)." ] }, { "cell_type": "code", "execution_count": 28, "id": "990fae51", "metadata": {}, "outputs": [], "source": [ "model.train()\n", "likelihood.train()\n", "\n", "optimizer = torch.optim.Adam([\n", " {'params': model.parameters()},\n", " # {'params': likelihood.parameters()},\n", "], lr=0.1)\n", "\n", "# Our loss object. We're using the VariationalELBO\n", "mll = qpytorch.mlls.VariationalELBO(likelihood, model, num_data=train_y.size(0))" ] }, { "cell_type": "code", "execution_count": 29, "id": "25e5394a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration: 0 \t Loss: 0.7646129131317139\n", "Iteration: 50 \t Loss: 0.7336000800132751\n", "Iteration: 100 \t Loss: 0.718480110168457\n", "Iteration: 150 \t Loss: 0.7089231014251709\n", "Iteration: 200 \t Loss: 0.7016969323158264\n", "Iteration: 250 \t Loss: 0.6985439658164978\n", "Iteration: 300 \t Loss: 0.6927851438522339\n", "Iteration: 350 \t Loss: 0.69287109375\n", "Iteration: 400 \t Loss: 0.7060893774032593\n", "Iteration: 450 \t Loss: 0.6896464824676514\n", "Iteration: 500 \t Loss: 0.6860941648483276\n" ] } ], "source": [ "iters = 500 + 1\n", "\n", "for i in range(iters):\n", " optimizer.zero_grad()\n", " output = model(train_x)\n", " loss = -mll(output, train_y.squeeze())\n", " loss.backward()\n", " optimizer.step()\n", " if i % 50 == 0:\n", " print(\"Iteration: \", i, \"\\t Loss:\", loss.item())" ] }, { "cell_type": "markdown", "id": "20163340", "metadata": {}, "source": [ "### Model Evaluation\n", "\n", "Now, that we've trained our SVQEP, we choose some data to evaluate it on -- here $250$ data points from $[0, 8]$ to illustrate the performance both for interpolation (on $[0,3]$) and extrapolation (on $[3, 8]$)." ] }, { "cell_type": "code", "execution_count": 32, "id": "874a34f0", "metadata": {}, "outputs": [], "source": [ "model.eval()\n", "likelihood.eval()\n", "\n", "test_x = torch.linspace(0, 8, 250).view(-1,1)\n", "with torch.no_grad():\n", " posterior = likelihood(model(test_x))" ] }, { "cell_type": "markdown", "id": "9e2093f8", "metadata": {}, "source": [ "As expected, the posterior model fits the training data well but reverts to a zero mean and high prediction outside of the region of the training data." ] }, { "cell_type": "code", "execution_count": 33, "id": "d56cc9f1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(test_x, posterior.mean, color = \"blue\", label = \"Post Mean\")\n", "plt.fill_between(test_x.squeeze(), *posterior.confidence_region(), color = \"blue\", alpha = 0.3, label = \"Post Conf Region\")\n", "plt.scatter(train_x, train_y, color = \"black\", marker = \"*\", alpha = 0.5, label = \"Training Data\")\n", "plt.legend()\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")" ] }, { "cell_type": "markdown", "id": "d3f79b90", "metadata": {}, "source": [ "### Model Updating\n", "\n", "Now, we choose $25$ points to condition the model on -- imagining that these data points have just been acquired, perhaps from an active learning or Bayesian optimization loop." ] }, { "cell_type": "code", "execution_count": 34, "id": "0896fe69", "metadata": {}, "outputs": [], "source": [ "val_x = torch.linspace(3, 5, 25).view(-1,1)\n", "val_y = torch.sin(6. * val_x) + 0.3 * torch.randn_like(val_x)" ] }, { "cell_type": "code", "execution_count": 35, "id": "2bbfaf5f", "metadata": {}, "outputs": [], "source": [ "cond_model = model.variational_strategy.get_fantasy_model(inputs=val_x, targets=val_y.squeeze())" ] }, { "cell_type": "markdown", "id": "fb931dc8", "metadata": {}, "source": [ "Note that the updated model returned is an ExactQEP class rather than a SVQEP." ] }, { "cell_type": "code", "execution_count": 36, "id": "ac5e171c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "_BaseExactQEP(\n", " (likelihood): QExponentialLikelihood(\n", " (noise_covar): HomoskedasticNoise(\n", " (raw_noise_constraint): GreaterThan(1.000E-04)\n", " )\n", " )\n", " (mean_module): ConstantMean()\n", " (covar_module): ScaleKernel(\n", " (base_kernel): RBFKernel(\n", " (raw_lengthscale_constraint): Positive()\n", " )\n", " (raw_outputscale_constraint): Positive()\n", " )\n", ")" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cond_model" ] }, { "cell_type": "markdown", "id": "4f929bf8", "metadata": {}, "source": [ "We compute its posterior distribution on the same testing dataset as before." ] }, { "cell_type": "code", "execution_count": 37, "id": "f67ed240", "metadata": {}, "outputs": [], "source": [ "with torch.no_grad():\n", " updated_posterior = cond_model.likelihood(cond_model(test_x))" ] }, { "cell_type": "markdown", "id": "52238773", "metadata": {}, "source": [ "Finally, we plot the updated model, showing that the model has been updated to the newly observed data (grey) without forgetting the previous training data (black)." ] }, { "cell_type": "code", "execution_count": 38, "id": "a914fd04", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'y')" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(test_x, posterior.mean, color = \"blue\", label = \"Post Mean\")\n", "plt.fill_between(test_x.squeeze(), *posterior.confidence_region(), color = \"blue\", alpha = 0.3, label = \"Post Conf Region\")\n", "plt.scatter(train_x, train_y, color = \"black\", marker = \"*\", alpha = 0.5, label = \"Training Data\")\n", "\n", "plt.plot(test_x, updated_posterior.mean, color = \"orange\", label = \"Fant Mean\")\n", "plt.fill_between(test_x.squeeze(), *updated_posterior.confidence_region(), color = \"orange\", alpha = 0.3, label = \"Fant Conf Region\")\n", "\n", "plt.scatter(val_x, val_y, color = \"grey\", marker = \"*\", alpha = 0.5, label = \"New Data\")\n", "plt.legend()\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")" ] } ], "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": "3.10.18" } }, "nbformat": 4, "nbformat_minor": 5 }