From 871dbb4d9066b8cb582354cf449b107faf2413e5 Mon Sep 17 00:00:00 2001 From: Elizaveta Semenova Date: Sat, 6 Apr 2024 17:47:38 +0200 Subject: [PATCH] rm odl file --- 19_spatial_statistics.ipynb | 1000 ----------------------------------- 1 file changed, 1000 deletions(-) delete mode 100644 19_spatial_statistics.ipynb diff --git a/19_spatial_statistics.ipynb b/19_spatial_statistics.ipynb deleted file mode 100644 index 428bd66..0000000 --- a/19_spatial_statistics.ipynb +++ /dev/null @@ -1,1000 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Spatial Statstitics, geostatistics and kriging\n", - "\n", - "Spatial statistics is a branch of statistics that deals with the analysis and interpretation of data that has spatial or geographical components, considering how neighboring locations influence each other. It involves techniques for exploring, modelling, and understanding the patterns and relationships within spatial data." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Three types of spatial data\n", - "\n", - "There is three types of spatial data - areal, geostatistical, and point pattern. \n", - "\n", - "\n", - "Selection of the spatial statistical method is determined by the type of the available information about the data. There are three types of spatial data and corresponding models: point-level (or geostatistical data, areal (or lattice) data and spatial point patterns. \n", - "\n", - "Geostatistical data is a collection of random observations at fixed locations. Spatial proximity is defined via a function of distance between pairs of locations.The goal of geostatistical modelling is to identify the effect of covariates that determine disease risk and to predict the outcome at unsampled locations within the study area (referred to as kriging). \n", - "\n", - "Areal data are individual-level or aggregated data typically consisting of counts or rates with geographical information available over a set of regions with common borders. These areas may correspond to administrative units such as states, districts or counties or a regular grid - lattice. Spatial correlation between areas is implemented based on the neighbouring structure. Analysis of areal data aims to identify trends and spatial patterns and to assess large-scale associations between the disease risk and its predictors. \n", - "\n", - "Point pattern data consists of random locations of events. Dependence between case locations is modelled via a Gaussian process. This type of models are particularly appealing for datasets with precisely known locations of events due to their ability to capture disease clusters and identify factors associated with them. Events of a point pattern, tagged with an additional discrete coordinate, constitute marked point pattern data. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Geostatistics and kriging\n", - "\n", - "Geostatistics is the subarea of spatial statstistics which works with geostatstitical data. It finds applications in various fields such as natural resource exploration (e.g., oil and gas reserves estimation), environmental monitoring (e.g., air and water quality assessment), agriculture (e.g., soil fertility mapping), and urban planning (e.g., land use analysis) and, of course, epidemiology (e.g., disease mapping). It offers powerful tools for spatial data analysis, decision-making, and resource management in both scientific research and practical applications.\n", - "\n", - " Kriging is a statistical interpolation technique used primarily in geostatistics. It is named after South African mining engineer DanielG. Krige, who developed the method in the 1950s. Kriging is employed to estimate the value of a variable at an unmeasured locationbased on the values observed at nearby locations.\n", - "\n", - "The basic idea behind kriging is to model the spatial correlation or spatial autocorrelation of the variable being studied. This means that kriging considers the spatial structure of the data. It assumes that nearby points are more similar than those farther away and uses this information to make predictions.\n", - "\n", - "Kriging provides not only the predicted value at an unmeasured location but also an estimate of the uncertainty associated with that prediction. This is valuable because it allows users to assess the reliability of the interpolated values.\n", - "\n", - "As you might have guessed, kriging can be performed using Gaussian Processes! GPs are appropriate for kriging due to their flexibility in modeling complex spatial correlations, ability to quantify uncertainty and flexibility in kernel selection; i.e. GPs tick all the boxes required for kriging.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "import pickle\n", - "\n", - "import numpy as np\n", - "\n", - "from sklearn.gaussian_process import GaussianProcessRegressor\n", - "from sklearn.gaussian_process.kernels import RBF\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib.colors as mcolors\n", - "import matplotlib.patches as mpatches\n", - "from matplotlib.colors import ListedColormap\n", - "\n", - "import jax\n", - "import jax.numpy as jnp\n", - "\n", - "import numpyro\n", - "import numpyro.distributions as dist\n", - "from numpyro.infer import init_to_median, Predictive, MCMC, NUTS\n", - "from numpyro.diagnostics import hpdi\n", - "\n", - "numpyro.set_host_device_count(4) # Set the device count to enable parallel sampling" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Kriging: synthetic visualisation in 2d \n", - "\n", - "Let us visualise schematically how kriging looks like." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "# Generate synthetic data\n", - "np.random.seed(0)\n", - "\n", - "x_train = np.random.uniform(0, 10, (10, 2)) # Training points - x\n", - "y_train = np.sin(x_train[:, 0]) * np.cos(x_train[:, 1]) # Training targets - y" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Plotting\n", - "plt.figure(figsize=(8, 6))\n", - "plt.scatter(x_train[:, 0], x_train[:, 1], s=150, c='none', edgecolor='red', linewidth=2, label='Training data')\n", - "plt.scatter(x_train[:, 0], x_train[:, 1], s=100, c=y_train, cmap='viridis')\n", - "plt.title('Kriging visualization in 2d')\n", - "plt.colorbar(label='y')\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.xlim(0,10)\n", - "plt.ylim(0,10)\n", - "plt.xlabel('x1')\n", - "plt.ylabel('x2')\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our goal now is, given these points, to reconstruct the entire continuous surface over the region $(0,10) \\times (0,10)$ assuming the GP model. Let's do it in a non-Bayesian way first, for illustrative purpuses." - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Generate grid points for visualization\n", - "x_min, x_max = 0, 10\n", - "y_min, y_max = 0, 10\n", - "xx, yy = np.meshgrid(np.linspace(x_min, x_max, 100), np.linspace(y_min, y_max, 100))\n", - "x_grid = np.c_[xx.ravel(), yy.ravel()] # 2D grid points\n", - "\n", - "# fit Gaussian process model\n", - "kernel = RBF(length_scale=1.0)\n", - "gp = GaussianProcessRegressor(kernel=kernel, alpha=0.1, n_restarts_optimizer=10)\n", - "gp.fit(x_train, y_train)\n", - "\n", - "# Predict values for grid points\n", - "y_pred, sigma = gp.predict(x_grid, return_std=True)\n", - "\n", - "# Plot the results\n", - "plt.figure(figsize=(8, 6))\n", - "#plt.contourf(xx, yy, y_pred.reshape(xx.shape), cmap='viridis')\n", - "plt.scatter(xx, yy, s=100, c=y_pred.reshape(xx.shape), cmap='viridis')\n", - "plt.scatter(x_train[:, 0], x_train[:, 1], color='red', label='Training data', s=100)\n", - "plt.colorbar(label='predicted $y$')\n", - "plt.title('Kriging visualization in 2d')\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.xlim(0,10)\n", - "plt.ylim(0,10)\n", - "plt.xlabel('x1')\n", - "plt.ylabel('x2')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The command above `GaussianProcessRegressor` worked out very well. However, if we want to work with non-Gaussian likelihoods, and more complex models overall, such striaghtforward tools won't be available to us. Hence, we need to understand now to implement such models in Numpyro." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 1d example" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Generate data" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": {}, - "outputs": [], - "source": [ - "# synthetic data\n", - "n_points = 50\n", - "x = np.linspace(0, 2*np.pi, n_points)\n", - "f_true = np.sin(x)\n", - "\n", - "# noisy observations\n", - "y_true = f_true + np.random.normal(0, 0.2, size=n_points)\n", - "\n", - "# inidices to skip (and where to make predictions)\n", - "skip_idx = np.array([4, 5, 10, 15, 20, 21, 22, 25, 30, 35,36, 38, 40, 45])\n", - "\n", - "# indices of observed locations excluding skip_idx\n", - "obs_idx = np.delete(np.arange(n_points), skip_idx)\n", - "y_obs = y_true[obs_idx]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Visualise" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(8, 6))\n", - "plt.plot(x, f_true, color='orange', label='f(x)')\n", - "plt.scatter(x[obs_idx], y_obs, color='red', label='y observed')\n", - "\n", - "# unobserved locations\n", - "plt.scatter(x[skip_idx], f_true[skip_idx], color='green', label='unobserved locations', s=50, marker='D')\n", - "\n", - "for idx in skip_idx:\n", - " plt.axvline(x=x[idx], color='gray', linestyle='--', linewidth=1)\n", - "\n", - "plt.legend(loc='upper right')\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Infer" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{margin}\n", - "You might have noticed - this is the exact same kernel and code as in the previous notebook, i.e. we are being repetitive. The code is redundant but the aim is for each notebook to be self-sufficient.\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [], - "source": [ - "def rbf_kernel(x1, x2, lengthscale=1.0, sigma=1.0):\n", - " \"\"\"\n", - " Compute the Radial Basis Function (RBF) kernel matrix between two sets of points.\n", - "\n", - " Args:\n", - " - x1 (array): Array of shape (n1, d) representing the first set of points.\n", - " - x2 (array): Array of shape (n2, d) representing the second set of points.\n", - " - sigma (float): Variance parameter.\n", - " - length_scale (float): Length-scale parameter.\n", - " - jitter (float): Small positive value added to the diagonal elements.\n", - "\n", - " Returns:\n", - " - K (array): Kernel matrix of shape (n1, n2).\n", - " \"\"\"\n", - " sq_dist = jnp.sum(x1**2, axis=1).reshape(-1, 1) + jnp.sum(x2**2, axis=1) - 2 * jnp.dot(x1, x2.T)\n", - " K = sigma**2 * jnp.exp(-0.5 / lengthscale**2 * sq_dist)\n", - " return K" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": {}, - "outputs": [], - "source": [ - "def model(x, obs_idx, y_obs=None, kernel_func=rbf_kernel, lengthcsale=0.2, jitter=1e-5): \n", - "\n", - " n = x.shape[0]\n", - "\n", - " K = kernel_func(x, x, lengthcsale) + jitter*jnp.eye(n)\n", - "\n", - " f = numpyro.sample(\"f\", dist.MultivariateNormal(jnp.zeros(n), covariance_matrix=K))\n", - "\n", - " sigma = numpyro.sample(\"sigma\", dist.HalfNormal(1))\n", - " \n", - " if y_obs is None:\n", - " numpyro.sample(\"y\", dist.Normal(f[obs_idx], sigma))\n", - " else: \n", - " numpyro.sample(\"y\", dist.Normal(f[obs_idx], sigma), obs=y_obs)" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [], - "source": [ - "x = jnp.linspace(0, 1, n_points).reshape(-1, 1)\n", - "\n", - "nuts_kernel = NUTS(model)\n", - "mcmc = MCMC(nuts_kernel, num_samples=10000, num_warmup=2000, num_chains=2, chain_method='parallel', progress_bar=False)\n", - "mcmc.run(jax.random.PRNGKey(42), jnp.array(x), jnp.array(obs_idx), jnp.array(y_obs))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Diagnose" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - " mean std median 5.0% 95.0% n_eff r_hat\n", - " f[0] -0.04 0.13 -0.04 -0.25 0.18 3979.83 1.00\n", - " f[1] 0.07 0.11 0.07 -0.10 0.25 3566.61 1.00\n", - " f[2] 0.20 0.09 0.20 0.05 0.35 3293.72 1.00\n", - " f[3] 0.33 0.09 0.32 0.18 0.47 3178.84 1.00\n", - " f[4] 0.46 0.09 0.46 0.31 0.60 3154.44 1.00\n", - " f[5] 0.58 0.09 0.58 0.44 0.73 3141.05 1.00\n", - " f[6] 0.71 0.09 0.71 0.56 0.84 3114.71 1.00\n", - " f[7] 0.82 0.08 0.82 0.68 0.96 3066.47 1.00\n", - " f[8] 0.92 0.08 0.92 0.78 1.05 3008.90 1.00\n", - " f[9] 1.01 0.08 1.01 0.87 1.13 2941.45 1.00\n", - " f[10] 1.07 0.08 1.07 0.94 1.20 2890.57 1.00\n", - " f[11] 1.12 0.08 1.12 0.99 1.25 2864.15 1.00\n", - " f[12] 1.14 0.08 1.14 1.01 1.26 2857.70 1.00\n", - " f[13] 1.13 0.08 1.14 1.01 1.26 2836.59 1.00\n", - " f[14] 1.11 0.08 1.11 0.98 1.23 2823.41 1.00\n", - " f[15] 1.06 0.08 1.06 0.92 1.18 2800.32 1.00\n", - " f[16] 0.99 0.08 0.99 0.85 1.11 2766.24 1.00\n", - " f[17] 0.90 0.08 0.90 0.77 1.03 2724.85 1.00\n", - " f[18] 0.80 0.08 0.80 0.67 0.94 2679.08 1.00\n", - " f[19] 0.68 0.08 0.68 0.54 0.82 2632.42 1.00\n", - " f[20] 0.56 0.09 0.56 0.42 0.70 2603.55 1.00\n", - " f[21] 0.43 0.09 0.43 0.29 0.57 2599.15 1.00\n", - " f[22] 0.30 0.09 0.30 0.15 0.44 2613.92 1.00\n", - " f[23] 0.17 0.09 0.17 0.03 0.31 2657.35 1.00\n", - " f[24] 0.04 0.08 0.04 -0.10 0.17 2701.72 1.00\n", - " f[25] -0.08 0.08 -0.08 -0.21 0.05 2708.66 1.00\n", - " f[26] -0.20 0.08 -0.20 -0.33 -0.07 2696.06 1.00\n", - " f[27] -0.31 0.08 -0.31 -0.44 -0.18 2628.51 1.00\n", - " f[28] -0.42 0.08 -0.42 -0.54 -0.29 2543.16 1.00\n", - " f[29] -0.51 0.08 -0.51 -0.64 -0.39 2463.68 1.00\n", - " f[30] -0.60 0.08 -0.60 -0.73 -0.48 2396.10 1.00\n", - " f[31] -0.68 0.08 -0.68 -0.81 -0.55 2447.38 1.00\n", - " f[32] -0.76 0.08 -0.76 -0.89 -0.62 2391.86 1.00\n", - " f[33] -0.82 0.08 -0.82 -0.96 -0.68 2364.34 1.00\n", - " f[34] -0.88 0.09 -0.88 -1.02 -0.74 2356.31 1.00\n", - " f[35] -0.92 0.09 -0.92 -1.06 -0.77 2368.16 1.00\n", - " f[36] -0.96 0.09 -0.96 -1.10 -0.81 2397.29 1.00\n", - " f[37] -0.98 0.09 -0.98 -1.12 -0.82 2447.42 1.00\n", - " f[38] -0.98 0.09 -0.98 -1.13 -0.84 2511.17 1.00\n", - " f[39] -0.97 0.09 -0.97 -1.11 -0.83 2586.29 1.00\n", - " f[40] -0.95 0.09 -0.95 -1.09 -0.81 2672.91 1.00\n", - " f[41] -0.90 0.08 -0.90 -1.05 -0.77 2750.37 1.00\n", - " f[42] -0.84 0.08 -0.84 -0.99 -0.71 2777.15 1.00\n", - " f[43] -0.76 0.08 -0.77 -0.90 -0.63 2758.81 1.00\n", - " f[44] -0.67 0.08 -0.67 -0.81 -0.54 2738.02 1.00\n", - " f[45] -0.56 0.08 -0.56 -0.69 -0.42 2730.79 1.00\n", - " f[46] -0.44 0.08 -0.44 -0.57 -0.30 2841.45 1.00\n", - " f[47] -0.31 0.09 -0.31 -0.46 -0.17 3202.96 1.00\n", - " f[48] -0.18 0.11 -0.18 -0.36 -0.01 3569.98 1.00\n", - " f[49] -0.05 0.13 -0.05 -0.27 0.17 3985.41 1.00\n", - " sigma 0.20 0.03 0.20 0.16 0.24 4073.37 1.00\n", - "\n", - "Number of divergences: 0\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "mcmc.print_summary()\n", - "\n", - "posterior_samples = mcmc.get_samples()\n", - "f_posterior = posterior_samples['f']\n", - "\n", - "f_mean = jnp.mean(f_posterior, axis=0)\n", - "f_hpdi = hpdi(f_posterior, 0.90)\n", - "\n", - "plt.figure(figsize=(8, 6))\n", - "plt.plot(x, f_true, color='orange', label='f(x)')\n", - "plt.scatter(x[obs_idx], y_obs, color='red', label='y observed')\n", - "\n", - "plt.plot(x, f_mean, label='Estimated mean')\n", - "plt.fill_between(x.squeeze(), f_hpdi[0], f_hpdi[1], color='lightblue', alpha=0.3, label='HPDI') # Uncertainty bounds\n", - "plt.scatter(x[skip_idx], f_mean[skip_idx], color='purple', label='predicted f', s=50, marker='D')\n", - "\n", - "plt.legend()\n", - "plt.show()\n" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "metadata": {}, - "outputs": [ - { - "ename": "TypeError", - "evalue": "Using a non-tuple sequence for multidimensional indexing is not allowed; use `arr[tuple(seq)]` instead of `arr[seq]`. See https://github.com/google/jax/issues/4564 for more information.", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[76], line 10\u001b[0m\n\u001b[1;32m 7\u001b[0m plt\u001b[38;5;241m.\u001b[39mfigure(figsize\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m4\u001b[39m, \u001b[38;5;241m4\u001b[39m))\n\u001b[1;32m 9\u001b[0m \u001b[38;5;66;03m# Plot observed data\u001b[39;00m\n\u001b[0;32m---> 10\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(\u001b[43mf_true\u001b[49m\u001b[43m[\u001b[49m\u001b[43mskip_idx\u001b[49m\u001b[43m]\u001b[49m, f_mean[skip_idx], \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mo\u001b[39m\u001b[38;5;124m'\u001b[39m, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mObtained results\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 12\u001b[0m \u001b[38;5;66;03m# Plot diagonal line\u001b[39;00m\n\u001b[1;32m 13\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot([xmin, xmax], [ymin, ymax], color\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mred\u001b[39m\u001b[38;5;124m'\u001b[39m, linestyle\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m--\u001b[39m\u001b[38;5;124m'\u001b[39m, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mIdeal prediction\u001b[39m\u001b[38;5;124m'\u001b[39m)\n", - "File \u001b[0;32m/opt/anaconda3/envs/aims/lib/python3.9/site-packages/jax/_src/array.py:336\u001b[0m, in \u001b[0;36mArrayImpl.__getitem__\u001b[0;34m(self, idx)\u001b[0m\n\u001b[1;32m 334\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m lax_numpy\u001b[38;5;241m.\u001b[39m_rewriting_take(\u001b[38;5;28mself\u001b[39m, idx)\n\u001b[1;32m 335\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 336\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mlax_numpy\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_rewriting_take\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43midx\u001b[49m\u001b[43m)\u001b[49m\n", - "File \u001b[0;32m/opt/anaconda3/envs/aims/lib/python3.9/site-packages/jax/_src/numpy/lax_numpy.py:4493\u001b[0m, in \u001b[0;36m_rewriting_take\u001b[0;34m(arr, idx, indices_are_sorted, unique_indices, mode, fill_value)\u001b[0m\n\u001b[1;32m 4487\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m (\u001b[38;5;28misinstance\u001b[39m(aval, core\u001b[38;5;241m.\u001b[39mDShapedArray) \u001b[38;5;129;01mand\u001b[39;00m aval\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m==\u001b[39m () \u001b[38;5;129;01mand\u001b[39;00m\n\u001b[1;32m 4488\u001b[0m dtypes\u001b[38;5;241m.\u001b[39missubdtype(aval\u001b[38;5;241m.\u001b[39mdtype, np\u001b[38;5;241m.\u001b[39minteger) \u001b[38;5;129;01mand\u001b[39;00m\n\u001b[1;32m 4489\u001b[0m \u001b[38;5;129;01mnot\u001b[39;00m dtypes\u001b[38;5;241m.\u001b[39missubdtype(aval\u001b[38;5;241m.\u001b[39mdtype, dtypes\u001b[38;5;241m.\u001b[39mbool_) \u001b[38;5;129;01mand\u001b[39;00m\n\u001b[1;32m 4490\u001b[0m \u001b[38;5;28misinstance\u001b[39m(arr\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m0\u001b[39m], \u001b[38;5;28mint\u001b[39m)):\n\u001b[1;32m 4491\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m lax\u001b[38;5;241m.\u001b[39mdynamic_index_in_dim(arr, idx, keepdims\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m)\n\u001b[0;32m-> 4493\u001b[0m treedef, static_idx, dynamic_idx \u001b[38;5;241m=\u001b[39m \u001b[43m_split_index_for_jit\u001b[49m\u001b[43m(\u001b[49m\u001b[43midx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43marr\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshape\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 4494\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m _gather(arr, treedef, static_idx, dynamic_idx, indices_are_sorted,\n\u001b[1;32m 4495\u001b[0m unique_indices, mode, fill_value)\n", - "File \u001b[0;32m/opt/anaconda3/envs/aims/lib/python3.9/site-packages/jax/_src/numpy/lax_numpy.py:4565\u001b[0m, in \u001b[0;36m_split_index_for_jit\u001b[0;34m(idx, shape)\u001b[0m\n\u001b[1;32m 4560\u001b[0m \u001b[38;5;250m\u001b[39m\u001b[38;5;124;03m\"\"\"Splits indices into necessarily-static and dynamic parts.\u001b[39;00m\n\u001b[1;32m 4561\u001b[0m \n\u001b[1;32m 4562\u001b[0m \u001b[38;5;124;03mUsed to pass indices into `jit`-ted function.\u001b[39;00m\n\u001b[1;32m 4563\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 4564\u001b[0m \u001b[38;5;66;03m# Convert list indices to tuples in cases (deprecated by NumPy.)\u001b[39;00m\n\u001b[0;32m-> 4565\u001b[0m idx \u001b[38;5;241m=\u001b[39m \u001b[43m_eliminate_deprecated_list_indexing\u001b[49m\u001b[43m(\u001b[49m\u001b[43midx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 4566\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28many\u001b[39m(\u001b[38;5;28misinstance\u001b[39m(i, \u001b[38;5;28mstr\u001b[39m) \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m idx):\n\u001b[1;32m 4567\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mJAX does not support string indexing; got \u001b[39m\u001b[38;5;132;01m{\u001b[39;00midx\u001b[38;5;132;01m=}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m)\n", - "File \u001b[0;32m/opt/anaconda3/envs/aims/lib/python3.9/site-packages/jax/_src/numpy/lax_numpy.py:4820\u001b[0m, in \u001b[0;36m_eliminate_deprecated_list_indexing\u001b[0;34m(idx)\u001b[0m\n\u001b[1;32m 4816\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 4817\u001b[0m msg \u001b[38;5;241m=\u001b[39m (\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mUsing a non-tuple sequence for multidimensional indexing is not allowed; \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 4818\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124muse `arr[array(seq)]` instead of `arr[seq]`. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 4819\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mSee https://github.com/google/jax/issues/4564 for more information.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m-> 4820\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(msg)\n\u001b[1;32m 4821\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 4822\u001b[0m idx \u001b[38;5;241m=\u001b[39m (idx,)\n", - "\u001b[0;31mTypeError\u001b[0m: Using a non-tuple sequence for multidimensional indexing is not allowed; use `arr[tuple(seq)]` instead of `arr[seq]`. See https://github.com/google/jax/issues/4564 for more information." - ] - }, - { - "data": { - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "xmin = np.min([np.min(f_true), np.min(f_mean)])\n", - "xmax = np.max([np.max(f_true), np.max(f_mean)])\n", - "\n", - "ymin = xmin\n", - "ymax = xmax\n", - "\n", - "plt.figure(figsize=(4, 4))\n", - "\n", - "# Plot observed data\n", - "plt.plot(f_true[skip_idx], f_mean[skip_idx], 'o', label='Obtained results')\n", - "\n", - "# Plot diagonal line\n", - "plt.plot([xmin, xmax], [ymin, ymax], color='red', linestyle='--', label='Ideal prediction')\n", - "\n", - "plt.xlabel('True $f$ at unobserved locations')\n", - "plt.ylabel('Predicted $f$ at unobserved locations')\n", - "\n", - "plt.xlim(xmin, xmax) \n", - "plt.ylim(ymin, ymax) \n", - "\n", - "plt.title('Comparison of True and Predicted $f$')\n", - "\n", - "plt.legend()\n", - "\n", - "plt.grid(True)\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 2d example" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Generate data" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": {}, - "outputs": [], - "source": [ - "n_points_x = 10\n", - "n_points_y = 8\n", - "\n", - "x = jnp.linspace(0, 2*jnp.pi, n_points_x)\n", - "y = jnp.linspace(0, 2*jnp.pi, n_points_y)\n", - "xx, yy = jnp.meshgrid(x, y)\n", - "x_2d = jnp.column_stack([xx.ravel(), yy.ravel()])\n", - "\n", - "skip_idx = [(0, 1), (2, 4), (3, 1), (5,6)]\n", - "\n", - "obs_idx = np.delete(np.arange(n_points_x * n_points_y), [i * n_points_x + j for i, j in skip_idx])\n", - "\n", - "f_true = jnp.sin(xx/1.2) * jnp.cos(yy)\n", - "noise = np.random.normal(0, 0.1, size=(n_points_y, n_points_x))\n", - "\n", - "y_true = (f_true + noise)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Visualise" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - ":2: MatplotlibDeprecationWarning: You are modifying the state of a globally registered colormap. This has been deprecated since 3.3 and in 3.6, you will not be able to modify a registered colormap in-place. To remove this warning, you can make a copy of the colormap first. cmap = mpl.cm.get_cmap(\"viridis\").copy()\n", - " cmap.set_bad(color='red')\n", - ":27: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n", - " plt.tight_layout()\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "cmap = plt.cm.viridis\n", - "cmap.set_bad(color='red')\n", - "\n", - "fig, axes = plt.subplots(1, 2, figsize=(10, 6))\n", - "\n", - "im1 = axes[0].imshow(f_true, extent=(0, 2*np.pi, 0, 2*np.pi), origin='lower', cmap='viridis')\n", - "axes[0].set_title('True Function $f(\\cdot)$')\n", - "axes[0].set_xlabel('x')\n", - "axes[0].set_ylabel('y')\n", - "\n", - "masked_data = np.ma.masked_where(np.zeros_like(y_true, dtype=bool), y_true)\n", - "for idx in skip_idx:\n", - " masked_data[idx] = np.ma.masked\n", - "\n", - "im2 = axes[1].imshow(masked_data, extent=(0, 2*np.pi, 0, 2*np.pi), origin='lower', cmap=cmap) \n", - "axes[1].set_title('Observed Data')\n", - "axes[1].set_xlabel('x')\n", - "axes[1].set_ylabel('y')\n", - "\n", - "legend_handles = [mpatches.Patch(color='red', label='Missing Values')]\n", - "axes[1].legend(handles=legend_handles)\n", - "\n", - "cax = fig.add_axes([1.02, 0.15, 0.02, 0.7]) # [left, bottom, width, height]\n", - "cbar = fig.colorbar(im1, cax=cax)\n", - "cbar.set_label('Value')\n", - "\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Infer" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{margin}\n", - "Note: we are using here exactly same code for the `rbf_kernel` and `model` as we did in the one-dimensional case! This is all possible because GP only needs pair-wise distances between locations, which we can compute agnostically in any dimension.\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(8, 10)\n", - "(8, 10)\n", - "(80, 2)\n", - "(76,)\n", - "(76,)\n" - ] - } - ], - "source": [ - "y_true_flat = y_true.ravel()\n", - "y_obs = y_true_flat[obs_idx] \n", - "\n", - "print(y_true.shape)\n", - "print(y_true.shape)\n", - "\n", - "# check the shapes\n", - "print(x_2d.shape)\n", - "print(obs_idx.shape)\n", - "print(y_obs.shape)" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "metadata": {}, - "outputs": [], - "source": [ - "# ATTENTION: this cell might take a while to run\n", - "\n", - "nuts_kernel = NUTS(model)\n", - "mcmc = MCMC(nuts_kernel, num_samples=10000, num_warmup=2000, num_chains=2, chain_method='parallel', progress_bar=False)\n", - "mcmc.run(jax.random.PRNGKey(42), jnp.array(x_2d), jnp.array(obs_idx), jnp.array(y_obs))" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - " mean std median 5.0% 95.0% n_eff r_hat\n", - " f[0] 0.15 0.15 0.15 -0.10 0.39 32584.83 1.00\n", - " f[1] 0.00 1.01 0.00 -1.59 1.70 6907.62 1.00\n", - " f[2] 0.94 0.16 0.95 0.69 1.19 11258.85 1.00\n", - " f[3] 1.03 0.16 1.04 0.78 1.28 10690.39 1.00\n", - " f[4] 0.65 0.15 0.66 0.40 0.90 25035.72 1.00\n", - " f[5] 0.19 0.15 0.19 -0.07 0.43 32985.96 1.00\n", - " f[6] -0.35 0.15 -0.35 -0.59 -0.11 29510.27 1.00\n", - " f[7] -0.81 0.15 -0.82 -1.05 -0.56 14717.12 1.00\n", - " f[8] -1.01 0.15 -1.02 -1.24 -0.75 11261.67 1.00\n", - " f[9] -1.01 0.16 -1.03 -1.25 -0.75 10566.52 1.00\n", - " f[10] 0.11 0.15 0.11 -0.14 0.34 36135.02 1.00\n", - " f[11] 0.44 0.15 0.45 0.19 0.67 25094.06 1.00\n", - " f[12] 0.48 0.15 0.48 0.24 0.72 23113.46 1.00\n", - " f[13] 0.46 0.15 0.46 0.23 0.71 30338.47 1.00\n", - " f[14] 0.49 0.15 0.50 0.23 0.73 27469.22 1.00\n", - " f[15] 0.08 0.15 0.09 -0.16 0.33 29743.03 1.00\n", - " f[16] -0.19 0.15 -0.20 -0.44 0.04 40055.06 1.00\n", - " f[17] -0.52 0.15 -0.53 -0.75 -0.27 30751.14 1.00\n", - " f[18] -0.54 0.15 -0.55 -0.79 -0.30 29521.20 1.00\n", - " f[19] -0.46 0.15 -0.47 -0.71 -0.22 26636.26 1.00\n", - " f[20] -0.07 0.15 -0.07 -0.31 0.18 39225.09 1.00\n", - " f[21] -0.25 0.15 -0.26 -0.50 -0.02 32267.94 1.00\n", - " f[22] -0.35 0.15 -0.36 -0.60 -0.10 34446.27 1.00\n", - " f[23] -0.16 0.15 -0.16 -0.39 0.11 32918.78 1.00\n", - " f[24] -0.01 1.01 -0.02 -1.62 1.66 7028.75 1.00\n", - " f[25] -0.10 0.15 -0.10 -0.34 0.15 35071.50 1.00\n", - " f[26] 0.02 0.15 0.02 -0.24 0.26 39643.94 1.00\n", - " f[27] 0.17 0.15 0.17 -0.08 0.41 31856.74 1.00\n", - " f[28] 0.03 0.15 0.03 -0.22 0.27 34276.77 1.00\n", - " f[29] 0.21 0.15 0.21 -0.03 0.46 33888.83 1.00\n", - " f[30] 0.05 0.15 0.05 -0.19 0.29 31526.28 1.00\n", - " f[31] 0.01 1.00 0.02 -1.68 1.59 7172.84 1.00\n", - " f[32] -0.84 0.15 -0.85 -1.07 -0.58 13524.87 1.00\n", - " f[33] -0.86 0.15 -0.87 -1.10 -0.61 15389.42 1.00\n", - " f[34] -0.60 0.15 -0.61 -0.84 -0.35 25721.78 1.00\n", - " f[35] -0.47 0.16 -0.48 -0.72 -0.22 27048.74 1.00\n", - " f[36] 0.49 0.15 0.50 0.24 0.73 27578.80 1.00\n", - " f[37] 0.74 0.15 0.75 0.48 0.98 20028.63 1.00\n", - " f[38] 0.81 0.15 0.83 0.56 1.05 12168.17 1.00\n", - " f[39] 0.72 0.15 0.73 0.47 0.96 22746.64 1.00\n", - " f[40] 0.05 0.15 0.05 -0.21 0.28 29918.52 1.00\n", - " f[41] -0.49 0.15 -0.50 -0.73 -0.24 28745.04 1.00\n", - " f[42] -1.01 0.15 -1.02 -1.24 -0.75 14079.85 1.00\n", - " f[43] -0.67 0.15 -0.68 -0.91 -0.42 23933.35 1.00\n", - " f[44] -0.65 0.15 -0.66 -0.89 -0.39 28212.91 1.00\n", - " f[45] -0.10 0.15 -0.10 -0.36 0.12 32547.22 1.00\n", - " f[46] 0.23 0.15 0.24 -0.02 0.47 32790.00 1.00\n", - " f[47] 0.86 0.15 0.87 0.59 1.08 16817.49 1.00\n", - " f[48] 0.91 0.15 0.92 0.65 1.15 12240.54 1.00\n", - " f[49] 0.82 0.15 0.83 0.58 1.07 16213.13 1.00\n", - " f[50] -0.10 0.15 -0.10 -0.34 0.14 30460.56 1.00\n", - " f[51] -0.00 0.15 -0.00 -0.25 0.25 35372.16 1.00\n", - " f[52] -0.13 0.15 -0.13 -0.37 0.11 31048.59 1.00\n", - " f[53] -0.09 0.15 -0.09 -0.33 0.15 32079.46 1.00\n", - " f[54] -0.22 0.15 -0.22 -0.47 0.02 31513.16 1.00\n", - " f[55] -0.10 0.15 -0.10 -0.34 0.16 32019.40 1.00\n", - " f[56] 0.01 1.00 0.00 -1.67 1.61 6409.01 1.00\n", - " f[57] 0.07 0.15 0.07 -0.18 0.32 29304.94 1.00\n", - " f[58] 0.20 0.15 0.21 -0.03 0.46 35834.64 1.00\n", - " f[59] 0.30 0.15 0.30 0.04 0.54 30566.78 1.00\n", - " f[60] 0.01 0.15 0.01 -0.25 0.24 30510.84 1.00\n", - " f[61] 0.39 0.15 0.40 0.14 0.63 30677.52 1.00\n", - " f[62] 0.52 0.15 0.53 0.28 0.76 30472.45 1.00\n", - " f[63] 0.64 0.15 0.65 0.40 0.88 22447.78 1.00\n", - " f[64] 0.31 0.15 0.32 0.07 0.55 31415.57 1.00\n", - " f[65] 0.30 0.15 0.31 0.05 0.54 31651.38 1.00\n", - " f[66] -0.22 0.15 -0.22 -0.47 0.02 35365.73 1.00\n", - " f[67] -0.56 0.15 -0.56 -0.79 -0.30 29786.74 1.00\n", - " f[68] -0.54 0.15 -0.55 -0.76 -0.27 28140.08 1.00\n", - " f[69] -0.57 0.15 -0.58 -0.81 -0.32 23322.23 1.00\n", - " f[70] -0.13 0.15 -0.13 -0.36 0.11 38111.65 1.00\n", - " f[71] 0.41 0.15 0.41 0.15 0.64 31459.59 1.00\n", - " f[72] 0.97 0.16 0.98 0.72 1.21 18922.24 1.00\n", - " f[73] 0.95 0.16 0.96 0.70 1.19 10489.85 1.00\n", - " f[74] 0.70 0.15 0.71 0.45 0.95 23947.26 1.00\n", - " f[75] 0.33 0.15 0.34 0.09 0.57 32274.61 1.00\n", - " f[76] -0.44 0.15 -0.45 -0.68 -0.19 26372.97 1.00\n", - " f[77] -0.85 0.15 -0.87 -1.09 -0.61 13062.70 1.00\n", - " f[78] -1.01 0.16 -1.03 -1.26 -0.77 12567.06 1.00\n", - " f[79] -0.84 0.15 -0.85 -1.07 -0.59 17354.89 1.00\n", - " sigma 0.13 0.08 0.12 0.01 0.25 232.34 1.03\n", - "\n", - "Number of divergences: 0\n" - ] - } - ], - "source": [ - "# Print summary statistics of posterior\n", - "mcmc.print_summary()\n", - "\n", - "# Get the posterior samples\n", - "posterior_samples = mcmc.get_samples()\n", - "f_posterior = posterior_samples['f']\n", - "\n", - "# Calculate mean and standard deviation\n", - "f_mean = jnp.mean(f_posterior, axis=0)\n", - "f_std = jnp.std(f_posterior, axis=0)" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "f_mean_2d = f_mean.reshape(xx.shape)\n", - "f_std_2d = f_std.reshape(xx.shape)\n", - "\n", - "plt.figure(figsize=(20, 6))\n", - "\n", - "plt.subplot(1, 3, 1)\n", - "plt.imshow(f_true, extent=(0, 2*np.pi, 0, 2*np.pi), origin='lower', cmap='viridis')\n", - "plt.colorbar()\n", - "plt.title('True Function')\n", - "\n", - "plt.subplot(1, 3, 2)\n", - "plt.imshow(f_mean_2d, extent=(0, 2*np.pi, 0, 2*np.pi), origin='lower', cmap='viridis')\n", - "plt.colorbar()\n", - "plt.title('Mean Prediction')\n", - "\n", - "plt.subplot(1, 3, 3)\n", - "plt.imshow(f_std_2d, extent=(0, 2*np.pi, 0, 2*np.pi), origin='lower', cmap='viridis')\n", - "plt.colorbar()\n", - "plt.title('Std')\n", - "\n", - "plt.suptitle('Kriging 2d with Numpyro')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 72, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "f_true_flat = f_true.flatten()\n", - "xmin = np.min([np.min(f_true_flat), np.min(f_mean)])\n", - "xmax = np.max([np.max(f_true_flat), np.max(f_mean)])\n", - "ymin = xmin\n", - "ymax = xmax\n", - "\n", - "plt.figure(figsize=(4, 4)) \n", - "skip_idx_1d = np.array([i * n_points_x + j for i, j in skip_idx])\n", - "plt.plot(f_true_flat[skip_idx_1d], f_mean[skip_idx_1d], 'o', label='Obtained results')\n", - "plt.plot([xmin, xmax], [ymin, ymax], color='red', linestyle='--', label='Ideal prediction')\n", - "plt.xlabel('True $f$ at unobserved locations')\n", - "plt.ylabel('Predicted $f$ at unobserved locations')\n", - "plt.xlim(xmin, xmax) \n", - "plt.ylim(ymin, ymax) \n", - "plt.title('Comparison of True and Predicted $f$')\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Group Task \n", - ":class: tip\n", - "\n", - "It does not look like the model has done a good job estimating unobserved values.\n", - "\n", - "What could have gone wrong?\n", - "\n", - "`````" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# ATTENTION: this cell might take a while to run\n", - "\n", - "# fit the model\n", - "nuts_kernel = NUTS(model)\n", - "mcmc = MCMC(nuts_kernel, num_samples=10000, num_warmup=2000, num_chains=2, chain_method='parallel', progress_bar=False)\n", - "mcmc.run(jax.random.PRNGKey(42), jnp.array(x_2d), jnp.array(obs_idx), jnp.array(y_obs), kernel_func=rbf_kernel, lengthcsale=1.0)\n", - "\n", - "# exatrct posterior\n", - "posterior_samples = mcmc.get_samples()\n", - "f_posterior = posterior_samples['f']\n", - "\n", - "f_mean = jnp.mean(f_posterior, axis=0)\n", - "f_std = jnp.std(f_posterior, axis=0)\n", - "\n", - "f_mean_2d = f_mean.reshape(xx.shape)\n", - "f_std_2d = f_std.reshape(xx.shape)\n", - "\n", - "# plot results\n", - "plt.figure(figsize=(20, 5))\n", - "\n", - "plt.subplot(1, 3, 1)\n", - "plt.imshow(f_true, extent=(0, 2*np.pi, 0, 2*np.pi), origin='lower', cmap='viridis')\n", - "plt.colorbar()\n", - "plt.title('True Function')\n", - "\n", - "plt.subplot(1, 3, 2)\n", - "plt.imshow(f_mean_2d, extent=(0, 2*np.pi, 0, 2*np.pi), origin='lower', cmap='viridis')\n", - "plt.colorbar()\n", - "plt.title('Mean Prediction')\n", - "\n", - "plt.subplot(1, 3, 3)\n", - "plt.imshow(f_std_2d, extent=(0, 2*np.pi, 0, 2*np.pi), origin='lower', cmap='viridis')\n", - "plt.colorbar()\n", - "plt.title('Std')\n", - "\n", - "plt.suptitle('Kriging Prediction')\n", - "plt.show()\n", - "\n", - "# plot results\n", - "xmin = np.min([np.min(f_true_flat), np.min(f_mean)])\n", - "xmax = np.max([np.max(f_true_flat), np.max(f_mean)])\n", - "ymin = xmin\n", - "ymax = xmax\n", - "plt.figure(figsize=(5, 5)) \n", - "plt.plot(f_true_flat[skip_idx_1d], f_mean[skip_idx_1d], 'o', label='Obtained results')\n", - "plt.plot([xmin, xmax], [ymin, ymax], color='red', linestyle='--', label='Ideal prediction')\n", - "plt.xlabel('True $f$ at unobserved locations')\n", - "plt.ylabel('Predicted $f$ at unobserved locations')\n", - "plt.xlim(xmin, xmax) \n", - "plt.ylim(ymin, ymax) \n", - "plt.title('Comparison of True and Predicted $f$')\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3", - "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": "3.9.18" - } - }, - "nbformat": 4, - "nbformat_minor": 0 -}