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bcolloran/sklearn-vs-gpytorch-likelihood-v2.ipynb

Created June 22, 2021 19:10
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sklearn-vs-gpytorch-likelihood-v2.ipynb
{
"cells": [
{
"source": [
"# Computing log likelihoods in sklearn and gpytorch\n",
"---\n",
"**Note**: see previous notebook where the computations differed for background: https://gist.github.com/bcolloran/289215b4637faa7b9f69a2b7c844c6fd\n",
"\n",
"**TL;DR** Sklearn gives you access to a kernel matrix which includes the likelihood noise, whereas gpytorch does not.\n",
"\n",
"---\n",
"\n",
"\n",
"This notebook is an attempt to reproduce log likelihood computations from sklearn in gpytorch.\n",
"\n",
"I define a simple sklearn model and a close equivalent a gpytorch, verify that the model output is (approximately) the same in both cases, and attempt to compute the log likelihood for each using the texbook formula from Rasmussen and Williams (eq 5.8, p 113).\n",
"\n",
"I find that, as expected, computing the log likelihood long-hand using that formula results in the same value as sklearn's built in functionality for computing the log likelihood. However, attempting to do the same for gpytorch gives quite different values. I suspect that I've incorrectly accessed the Kernel matrix for the gpytorch model (or its Cholesky decomposition to be more precise), though the matrices I get from gpytorch and sklearn are eerily similar.\n"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import torch\n",
"import gpytorch\n",
"from gpytorch.kernels import Kernel, PeriodicKernel, LinearKernel, RBFKernel, RQKernel, ScaleKernel, ProductKernel, AdditiveKernel\n",
"from matplotlib import pyplot as plt\n",
"from sklearn.preprocessing import MinMaxScaler, StandardScaler\n",
"from sklearn.gaussian_process import GaussianProcessRegressor\n",
"from sklearn.gaussian_process.kernels \\\n",
" import RBF, WhiteKernel, RationalQuadratic, ExpSineSquared, ConstantKernel\n",
"import numpy as np\n",
"import gc\n",
"from typing import Union\n",
"from multimethod import multimethod\n",
"\n",
"from sklearn.datasets import fetch_openml\n",
"\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def load_mauna_loa_atmospheric_co2():\n",
" ml_data = fetch_openml(data_id=41187, as_frame=False)\n",
" months = []\n",
" ppmv_sums = []\n",
" counts = []\n",
"\n",
" y = ml_data.data[:, 0]\n",
" m = ml_data.data[:, 1]\n",
" month_float = y + (m - 1) / 12\n",
" ppmvs = ml_data.target\n",
"\n",
" for month, ppmv in zip(month_float, ppmvs):\n",
" if not months or month != months[-1]:\n",
" months.append(month)\n",
" ppmv_sums.append(ppmv)\n",
" counts.append(1)\n",
" else:\n",
" # aggregate monthly sum to produce average\n",
" ppmv_sums[-1] += ppmv\n",
" counts[-1] += 1\n",
" \n",
" months = np.array(months).reshape(-1, 1)\n",
" avg_ppmvs = np.array(ppmv_sums) / counts\n",
" return months, avg_ppmvs\n",
"\n",
"def to_torch_cuda(V):\n",
" return torch.tensor(V).flatten().double().cuda()\n",
"\n",
"X_raw, Y_raw = load_mauna_loa_atmospheric_co2()\n",
"\n",
"X_test = np.linspace(X_raw.min(), X_raw.max() + 30, 1000)[:, np.newaxis]\n",
"\n",
"# f, ax = plt.subplots(1, 1, figsize=(14, 4))\n",
"# ax.plot(X_raw, Y_raw)\n",
"\n",
"X_torch = to_torch_cuda(X_raw)\n",
"Y_torch = to_torch_cuda(Y_raw)\n",
"X_test_torch = to_torch_cuda(X_test)"
]
},
{
"source": [
"### simple sklearn model"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"\nLearned kernel:\n50**2 * RBF(length_scale=50) + 2**2 * RBF(length_scale=100) * ExpSineSquared(length_scale=1, periodicity=1) + WhiteKernel(noise_level=0.01)\nLog-marginal-likelihood: -6639.702\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.collections.LineCollection at 0x7f2cd2581940>"
]
},
"metadata": {},
"execution_count": 3
},
{
"output_type": "display_data",
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"k1 = ConstantKernel(constant_value=50.0**2, constant_value_bounds = \"fixed\") \\\n",
" * RBF(length_scale=50.0,length_scale_bounds=\"fixed\")\n",
"\n",
"k2 = ConstantKernel(constant_value=2.0**2, constant_value_bounds = \"fixed\")\\\n",
" * RBF(length_scale=100.0, length_scale_bounds=\"fixed\") \\\n",
" * ExpSineSquared(length_scale=1.0, periodicity=1.0,\n",
" length_scale_bounds=\"fixed\",\n",
" periodicity_bounds=\"fixed\") # seasonal component\n",
"\n",
"knoise = WhiteKernel(noise_level=0.1**2, noise_level_bounds=\"fixed\") # noise terms\n",
"\n",
"kernel = k1 + k2 + knoise\n",
"\n",
"\n",
"gp = GaussianProcessRegressor(kernel=kernel, alpha=0, normalize_y=False)\n",
"gp.fit(X_raw, Y_raw)\n",
"\n",
"print(\"\\nLearned kernel:\\n%s\" % gp.kernel_)\n",
"print(\"Log-marginal-likelihood: %.3f\"\n",
" % gp.log_marginal_likelihood(gp.kernel_.theta))\n",
"\n",
"X_test = np.linspace(X_raw.min(), X_raw.max() + 30, 1000)[:, np.newaxis]\n",
"y_pred, y_std = gp.predict(X_test, return_std=True)\n",
"\n",
"# Illustration\n",
"f, ax = plt.subplots(1, 1, figsize=(14, 6))\n",
"ax.plot(X_raw, Y_raw, 'k.', markersize=4)\n",
"ax.plot(X_test, y_pred,\"-\", color=\"steelblue\")\n",
"ax.fill_between(X_test[:, 0], y_pred - 2*y_std, y_pred + 2*y_std, alpha=0.3, color='k')\n",
"ax.vlines(max(X_raw), min(Y_raw), max(y_pred + 2*y_std), \"k\", linewidth=.5, alpha=.3)\n"
]
},
{
"source": [
"## approximately equivalent gpytorch model"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# machinery for printing gpytorch kernel info, for comparison to sklearn results\n",
"\n",
"def kernel_details_str(k: Kernel) -> str:\n",
" if isinstance(k, RBFKernel):\n",
" return f\"RBF(length_scale={k.lengthscale.item():.3f})\"\n",
"\n",
" elif isinstance(k, PeriodicKernel):\n",
" return f\"ExpSineSquared(length_scale={k.lengthscale.item():.3f}, periodcity={k.period_length.item():.3f},)\"\n",
"\n",
" elif isinstance(k, RQKernel):\n",
" return f\"RationalQuadratic(α={k.alpha.item():.3f},length_scale={k.lengthscale.item():.3f})\"\n",
"\n",
" elif isinstance(k, AdditiveKernel):\n",
" return f\"+\"\n",
"\n",
" elif isinstance(k, ProductKernel):\n",
" return f\"*\"\n",
"\n",
" else:\n",
" raise TypeError(\"Invalid kernel type\")\n",
"\n",
"@multimethod\n",
"def print_kernel(leaf: Union[RBFKernel,PeriodicKernel,RQKernel]) -> str:\n",
" return kernel_details_str(leaf)\n",
"\n",
"\n",
"@print_kernel.register\n",
"def print_kernel_scale(node: ScaleKernel) -> str:\n",
" scale = node.outputscale.item()\n",
" return f\"{np.sqrt(scale):.2f}**2 * {print_kernel(node.base_kernel)}\"\n",
"\n",
"\n",
"@print_kernel.register\n",
"def print_kernel_op_node(node: Union[AdditiveKernel, ProductKernel]) -> str:\n",
" children = f\" {kernel_details_str(node)} \".join([print_kernel(k) for k in node.kernels])\n",
" return f\"({children})\"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"def trend_seasonal_kernel_fn():\n",
" #### long term\n",
" k_long_term_RBF = RBFKernel()\n",
" k_long_term_RBF.lengthscale = 50\n",
"\n",
" k_long_term = ScaleKernel(k_long_term_RBF)\n",
" k_long_term.outputscale = 50**2\n",
"\n",
" #### seasonal\n",
" k_seasonal_RBF = RBFKernel()\n",
" k_seasonal_RBF.lengthscale = 100\n",
"\n",
" k_seasonal_periodic = PeriodicKernel()\n",
" k_seasonal_periodic.period_length = 1\n",
" # this must be squared, see https://github.com/cornellius-gp/gpytorch/issues/1020\n",
" k_seasonal_periodic.lengthscale = 1\n",
"\n",
" k_seasonal = ScaleKernel(k_seasonal_RBF * k_seasonal_periodic)\n",
" k_seasonal.outputscale = 2.0**2\n",
"\n",
" return k_long_term + k_seasonal "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"data": {
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191.837966 \nL 523.057033 191.335999 \nL 523.767926 192.4106 \nL 524.478819 194.843916 \nL 525.189711 198.18175 \nL 525.900604 201.49846 \nL 526.611497 202.533924 \nL 527.322389 200.693406 \nL 528.033282 197.990231 \nL 528.744175 195.669571 \nL 529.455068 193.954313 \nL 530.16596 192.745206 \nL 530.876853 191.308905 \nL 531.587746 189.280524 \nL 532.298638 187.946284 \nL 533.009531 188.172126 \nL 533.720424 189.900291 \nL 534.431317 192.794883 \nL 535.142209 196.317431 \nL 535.853102 198.870554 \nL 536.563995 198.414613 \nL 537.274887 195.894189 \nL 537.98578 193.283103 \nL 538.696673 191.220598 \nL 539.407566 189.782171 \nL 540.118458 188.603881 \nL 540.829351 186.842195 \nL 541.540244 184.940762 \nL 542.251136 184.291917 \nL 542.962029 185.216129 \nL 543.672922 187.522559 \nL 544.383814 190.78235 \nL 545.094707 194.162138 \nL 545.8056 195.437555 \nL 546.516493 193.726314 \nL 547.227385 190.976492 \nL 547.938278 188.573538 \nL 548.649171 186.795902 \nL 549.360063 185.57704 \nL 550.070956 184.221944 \nL 550.781849 182.230904 \nL 551.492742 180.782414 \nL 552.203634 180.854883 \nL 552.914527 182.435819 \nL 553.62542 185.220769 \nL 554.336312 188.706258 \nL 555.047205 191.421787 \nL 555.758098 191.190278 \nL 556.468991 188.701254 \nL 557.179883 186.012092 \nL 557.890776 183.870548 \nL 558.601669 182.38527 \nL 559.312561 181.23972 \nL 560.023454 179.567454 \nL 560.734347 177.629455 \nL 561.44524 176.83491 \nL 562.156132 177.60435 \nL 562.867025 179.774924 \nL 563.577918 182.944302 \nL 564.28881 186.363076 \nL 564.999703 187.869734 \nL 565.710596 186.303412 \nL 566.421489 183.512571 \nL 567.132381 181.022736 \nL 567.843274 179.174871 \nL 568.554167 177.936856 \nL 569.265059 176.657217 \nL 569.975952 174.717185 \nL 570.686845 173.164494 \nL 571.397738 173.081076 \nL 572.10863 174.50864 \nL 572.819523 177.173899 \nL 573.530416 180.604649 \nL 574.241308 183.459624 \nL 574.952201 183.458402 \nL 575.663094 181.014167 \nL 576.373986 178.246375 \nL 577.084879 176.019101 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166.880734 \nL 605.520588 164.204958 \nL 606.23148 162.192494 \nL 606.942373 160.885941 \nL 607.653266 159.733515 \nL 608.364158 157.93014 \nL 609.075051 156.206045 \nL 609.785944 155.806511 \nL 610.496837 156.910713 \nL 611.207729 159.307248 \nL 611.918622 162.579567 \nL 612.629515 165.638875 \nL 613.340407 166.104382 \nL 614.0513 163.793356 \nL 614.762193 160.870369 \nL 615.473086 158.453253 \nL 616.183978 156.774876 \nL 616.894871 155.664213 \nL 617.605764 154.26774 \nL 618.316656 152.317848 \nL 619.027549 151.108947 \nL 619.738442 151.391451 \nL 620.449335 153.105092 \nL 621.160227 155.934732 \nL 621.87112 159.330214 \nL 622.582013 161.446249 \nL 623.292905 160.399266 \nL 624.003798 157.530655 \nL 624.714691 154.757293 \nL 625.425584 152.651195 \nL 626.136476 151.294964 \nL 626.847369 150.191814 \nL 627.558262 148.470508 \nL 628.269154 146.682429 \nL 628.980047 146.125101 \nL 629.69094 147.060664 \nL 630.401833 149.309113 \nL 631.112725 152.480246 \nL 631.823618 155.603101 \nL 632.534511 156.299171 \nL 633.245403 154.078115 \nL 633.956296 151.080959 \nL 634.667189 148.561062 \nL 635.378081 146.800643 \nL 636.088974 145.678841 \nL 636.799867 144.369691 \nL 637.51076 142.448087 \nL 638.221652 141.115256 \nL 638.932545 141.230274 \nL 639.643438 142.777569 \nL 640.35433 145.473361 \nL 641.065223 148.817714 \nL 641.776116 151.099682 \nL 642.487009 150.249755 \nL 643.197901 147.375212 \nL 643.908794 144.502446 \nL 644.619687 142.29599 \nL 645.330579 140.879934 \nL 646.041472 139.815303 \nL 646.752365 138.182652 \nL 647.463258 136.346925 \nL 648.17415 135.634126 \nL 648.885043 136.397562 \nL 649.595936 138.489712 \nL 650.306828 141.546829 \nL 651.017721 144.70749 \nL 651.728614 145.628274 \nL 652.439507 143.513502 \nL 653.150399 140.44637 \nL 653.861292 137.819526 \nL 654.572185 135.968767 \nL 655.283077 134.824209 \nL 655.99397 133.59705 \nL 656.704863 131.718963 \nL 657.415756 130.272956 \nL 658.126648 130.219616 \nL 658.837541 131.595119 \nL 659.548434 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687.273249 112.345772 \nL 687.984142 114.1044 \nL 688.695035 116.900563 \nL 689.405928 120.06255 \nL 690.11682 121.403617 \nL 690.827713 119.551014 \nL 691.538606 116.363283 \nL 692.249498 113.513876 \nL 692.960391 111.460217 \nL 693.671284 110.23605 \nL 694.382176 109.151175 \nL 695.093069 107.401588 \nL 695.803962 105.770235 \nL 696.514855 105.383187 \nL 697.225747 106.403369 \nL 697.93664 108.646919 \nL 698.647533 111.72997 \nL 699.358425 114.372079 \nL 700.069318 114.159829 \nL 700.780211 111.350388 \nL 701.491104 108.180283 \nL 702.201996 105.641106 \nL 702.912889 103.988425 \nL 703.623782 102.970077 \nL 704.334674 101.623033 \nL 705.045567 99.75154 \nL 705.75646 98.606692 \nL 706.467353 98.843731 \nL 707.178245 100.427344 \nL 707.889138 103.079333 \nL 708.600031 106.207379 \nL 709.310923 107.738647 \nL 710.021816 106.041477 \nL 710.732709 102.8069 \nL 711.443602 99.844035 \nL 712.154494 97.679629 \nL 712.865387 96.399397 \nL 713.57628 95.372588 \nL 714.287172 93.705248 \nL 714.998065 92.00579 \nL 715.708958 91.456759 \nL 716.419851 92.295974 \nL 717.130743 94.375013 \nL 717.841636 97.341412 \nL 718.552529 100.054776 \nL 719.263421 100.062903 \nL 719.974314 97.308026 \nL 720.685207 94.043779 \nL 721.3961 91.386637 \nL 722.106992 89.63814 \nL 722.817885 88.61169 \nL 723.528778 87.360052 \nL 724.23967 85.513753 \nL 724.950563 84.243996 \nL 725.661456 84.306539 \nL 726.372348 85.711326 \nL 727.083241 88.211827 \nL 727.794134 91.285161 \nL 728.505027 92.990206 \nL 729.215919 91.463826 \nL 729.926812 88.194092 \nL 730.637705 85.117917 \nL 731.348597 82.838056 \nL 732.05949 81.491715 \nL 732.770383 80.513195 \nL 733.481276 78.937959 \nL 734.192168 77.18914 \nL 734.903061 76.483966 \nL 735.613954 77.141883 \nL 736.324846 79.051324 \nL 737.035739 81.889676 \nL 737.746632 84.649767 \nL 738.457525 84.877917 \nL 739.168417 82.19628 \nL 739.87931 78.843114 \nL 740.590203 76.066453 \nL 741.301095 74.215177 \nL 742.011988 73.16917 \nL 742.722881 72.010174 \nL 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759.073413 45.747957 \nL 758.36252 49.293839 \nL 757.651628 51.988501 \nL 756.940735 51.647734 \nL 756.229842 48.968631 \nL 755.51895 46.371416 \nL 754.808057 44.738955 \nL 754.097164 44.363665 \nL 753.386271 45.319113 \nL 752.675379 47.200355 \nL 751.964486 48.781565 \nL 751.253593 49.836428 \nL 750.542701 51.389622 \nL 749.831808 53.919761 \nL 749.120915 57.219166 \nL 748.410023 60.611177 \nL 747.69913 62.050851 \nL 746.988237 60.287702 \nL 746.277344 57.384703 \nL 745.566452 55.138623 \nL 744.855559 54.011415 \nL 744.144666 54.215946 \nL 743.433774 55.692796 \nL 742.722881 57.593168 \nL 742.011988 58.853849 \nL 741.301095 60.014542 \nL 740.590203 61.993901 \nL 739.87931 64.885924 \nL 739.168417 68.337113 \nL 738.457525 71.111545 \nL 737.746632 70.97461 \nL 737.035739 68.305183 \nL 736.324846 65.55728 \nL 735.613954 63.738204 \nL 734.903061 63.169727 \nL 734.192168 63.963904 \nL 733.481276 65.802509 \nL 732.770383 67.469984 \nL 732.05949 68.547601 \nL 731.348597 70.009672 \nL 730.637705 72.407966 \nL 729.926812 75.583395 \nL 729.215919 78.941327 \nL 728.505027 80.553255 \nL 727.794134 78.932712 \nL 727.083241 75.94344 \nL 726.372348 73.527045 \nL 725.661456 72.205941 \nL 724.950563 72.226316 \nL 724.23967 73.579035 \nL 723.528778 75.509759 \nL 722.817885 76.849094 \nL 722.106992 77.974684 \nL 721.3961 79.836958 \nL 720.685207 82.59766 \nL 719.974314 85.947858 \nL 719.263421 88.783175 \nL 718.552529 88.853905 \nL 717.841636 86.21879 \nL 717.130743 83.330358 \nL 716.419851 81.329297 \nL 715.708958 80.567235 \nL 714.998065 81.192945 \nL 714.287172 82.969622 \nL 713.57628 84.716216 \nL 712.865387 85.827891 \nL 712.154494 87.208789 \nL 711.443602 89.479196 \nL 710.732709 92.529974 \nL 710.021816 95.840806 \nL 709.310923 97.611551 \nL 708.600031 96.152771 \nL 707.889138 93.096766 \nL 707.178245 90.516868 \nL 706.467353 89.005094 \nL 705.75646 88.83915 \nL 705.045567 90.055013 \nL 704.334674 91.998627 \nL 703.623782 93.420393 \nL 702.912889 94.523318 \nL 702.201996 96.276039 \nL 701.491104 98.907696 \nL 700.780211 102.152551 \nL 700.069318 105.030914 \nL 699.358425 105.31052 \nL 698.647533 102.735095 \nL 697.93664 99.718384 \nL 697.225747 97.541253 \nL 696.514855 96.586787 \nL 695.803962 97.039061 \nL 695.093069 98.736002 \nL 694.382176 100.55285 \nL 693.671284 101.709468 \nL 692.960391 103.020045 \nL 692.249498 105.16785 \nL 691.538606 108.094655 \nL 690.827713 111.347551 \nL 690.11682 113.262621 \nL 689.405928 111.982917 \nL 688.695035 108.88186 \nL 687.984142 106.146669 \nL 687.273249 104.448911 \nL 686.562357 104.096103 \nL 685.851464 105.164856 \nL 685.140571 107.103641 \nL 684.429679 108.610007 \nL 683.718786 109.703083 \nL 683.007893 111.354861 \nL 682.297 113.861002 \nL 681.586108 116.99793 \nL 680.875215 119.902793 \nL 680.164322 120.38989 \nL 679.45343 117.89975 \nL 678.742537 114.769098 \nL 678.031644 112.422989 \nL 677.320751 111.278773 \nL 676.609859 111.554685 \nL 675.898966 113.155832 \nL 675.188073 115.032446 \nL 674.477181 116.244193 \nL 673.766288 117.496021 \nL 673.055395 119.527685 \nL 672.344502 122.332436 \nL 671.63361 125.518669 \nL 670.922717 127.562865 \nL 670.211824 126.477323 \nL 669.500932 123.354738 \nL 668.790039 120.473858 \nL 668.079146 118.596125 \nL 667.368253 118.057358 \nL 666.657361 118.971175 \nL 665.946468 120.887496 \nL 665.235575 122.478852 \nL 664.524683 123.575048 \nL 663.81379 125.135374 \nL 663.102897 127.520687 \nL 662.392005 130.548679 \nL 661.681112 133.46496 \nL 660.970219 134.155672 \nL 660.259326 131.77608 \nL 659.548434 128.54787 \nL 658.837541 126.040935 \nL 658.126648 124.710994 \nL 657.415756 124.809437 \nL 656.704863 126.300692 \nL 655.99397 128.225108 \nL 655.283077 129.501184 \nL 654.572185 130.706366 \nL 653.861292 132.629344 \nL 653.150399 135.315087 \nL 652.439507 138.427914 \nL 651.728614 140.585668 \nL 651.017721 139.706823 \nL 650.306828 136.587712 \nL 649.595936 133.57213 \nL 648.885043 131.521601 \nL 648.17415 130.799071 \nL 647.463258 131.552436 \nL 646.752365 133.429089 \nL 646.041472 135.103909 \nL 645.330579 136.216113 \nL 644.619687 137.695151 \nL 643.908794 139.965347 \nL 643.197901 142.884776 \nL 642.487009 145.798966 \nL 641.776116 146.687083 \nL 641.065223 144.442426 \nL 640.35433 141.134994 \nL 639.643438 138.476344 \nL 638.932545 136.965946 \nL 638.221652 136.88739 \nL 637.51076 138.256757 \nL 636.799867 140.215725 \nL 636.088974 141.564058 \nL 635.378081 142.735036 \nL 634.667189 144.557576 \nL 633.956296 147.128359 \nL 633.245403 150.162862 \nL 632.534511 152.418549 \nL 631.823618 151.756138 \nL 631.112725 148.66655 \nL 630.401833 145.528618 \nL 629.69094 143.313481 \nL 628.980047 142.410518 \nL 628.269154 143.000055 \nL 627.558262 144.82059 \nL 626.847369 146.575354 \nL 626.136476 147.716109 \nL 625.425584 149.124488 \nL 624.714691 151.286135 \nL 624.003798 154.098562 \nL 623.292905 156.998771 \nL 622.582013 158.075968 \nL 621.87112 155.989224 \nL 621.160227 152.622707 \nL 620.449335 149.822316 \nL 619.738442 148.137844 \nL 619.027549 147.884088 \nL 618.316656 149.121732 \nL 617.605764 151.100956 \nL 616.894871 152.527929 \nL 616.183978 153.677295 \nL 615.473086 155.408205 \nL 614.762193 157.86895 \nL 614.0513 160.821846 \nL 613.340407 163.160057 \nL 612.629515 162.72085 \nL 611.918622 159.687401 \nL 611.207729 156.440811 \nL 610.496837 154.070095 \nL 609.785944 152.991021 \nL 609.075051 153.415275 \nL 608.364158 155.164299 \nL 607.653266 156.993458 \nL 606.942373 158.174702 \nL 606.23148 159.523305 \nL 605.520588 161.58362 \nL 604.809695 164.291601 \nL 604.098802 167.167547 \nL 603.38791 168.423635 \nL 602.677017 166.515883 \nL 601.966124 163.112024 \nL 601.255231 160.180641 \nL 600.544339 158.329453 \nL 599.833446 157.903375 \nL 599.122553 159.001618 \nL 598.411661 160.986027 \nL 597.700768 162.496235 \nL 596.989875 163.636539 \nL 596.278982 165.284956 \nL 595.56809 167.641296 \nL 594.857197 170.510735 \nL 594.146304 172.916514 \nL 593.435412 172.704221 \nL 592.724519 169.753582 \nL 592.013626 166.413325 \nL 591.302733 163.896746 \nL 590.591841 162.646749 \nL 589.880948 162.905936 \nL 589.170055 164.569382 \nL 588.459163 166.465393 \nL 587.74827 167.698177 \nL 587.037377 168.997944 \nL 586.326484 170.964554 \nL 585.615592 173.571453 \nL 584.904699 176.414409 \nL 584.193806 177.837636 \nL 583.482914 176.127626 \nL 582.772021 172.709519 \nL 582.061128 169.658605 \nL 581.350235 167.648882 \nL 580.639343 167.054212 \nL 579.92845 168.007457 \nL 579.217557 169.981521 \nL 578.506665 171.577573 \nL 577.795772 172.721155 \nL 577.084879 174.296318 \nL 576.373986 176.55442 \nL 575.663094 179.339773 \nL 574.952201 181.798805 \nL 574.241308 181.814083 \nL 573.530416 178.972457 \nL 572.819523 175.554786 \nL 572.10863 172.902613 \nL 571.397738 171.487653 \nL 570.686845 171.583411 \nL 569.975952 173.148767 \nL 569.265059 175.102192 \nL 568.554167 176.396417 \nL 567.843274 177.658191 \nL 567.132381 179.538877 \nL 566.421489 182.048707 \nL 565.710596 184.85144 \nL 564.999703 186.428827 \nL 564.28881 184.932633 \nL 563.577918 181.524441 \nL 562.867025 178.366124 \nL 562.156132 176.206733 \nL 561.44524 175.447863 \nL 560.734347 176.252496 \nL 560.023454 178.200592 \nL 559.312561 179.882995 \nL 558.601669 181.041857 \nL 557.890776 182.55294 \nL 557.179883 184.71932 \nL 556.468991 187.420997 \nL 555.758098 189.919777 \nL 555.047205 190.160333 \nL 554.336312 187.452981 \nL 553.62542 183.975392 \nL 552.914527 181.198377 \nL 552.203634 179.625143 \nL 551.492742 179.560297 \nL 550.781849 181.016803 \nL 550.070956 183.016494 \nL 549.360063 184.380688 \nL 548.649171 185.615152 \nL 547.938278 187.417693 \nL 547.227385 189.835022 \nL 546.516493 192.591769 \nL 545.8056 194.309492 \nL 545.094707 193.040277 \nL 544.383814 189.666918 \nL 543.672922 186.413988 \nL 542.962029 184.114381 \nL 542.251136 183.196254 \nL 541.540244 183.850546 \nL 540.829351 185.757393 \nL 540.118458 187.524541 \nL 539.407566 188.710267 \nL 538.696673 190.166362 \nL 537.98578 192.24778 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199.86649 \nL 509.550072 201.536501 \nL 508.839179 203.784939 \nL 508.128286 206.437969 \nL 507.417394 208.393171 \nL 506.706501 207.604762 \nL 505.995608 204.376871 \nL 505.284715 200.97567 \nL 504.573823 198.425856 \nL 503.86293 197.205906 \nL 503.152037 197.561058 \nL 502.441145 199.342795 \nL 501.730252 201.266083 \nL 501.019359 202.537594 \nL 500.308466 203.910836 \nL 499.597574 205.843652 \nL 498.886681 208.305173 \nL 498.175788 210.852398 \nL 497.464896 211.729277 \nL 496.754003 209.560699 \nL 496.04311 206.020143 \nL 495.332217 202.937165 \nL 494.621325 200.935518 \nL 493.910432 200.413716 \nL 493.199539 201.497772 \nL 492.488647 203.556164 \nL 491.777754 205.164676 \nL 491.066861 206.380049 \nL 490.355968 207.995869 \nL 489.645076 210.168848 \nL 488.934183 212.766198 \nL 488.22329 214.817952 \nL 487.512398 214.276427 \nL 486.801505 211.158319 \nL 486.090612 207.704473 \nL 485.379719 205.045104 \nL 484.668827 203.683059 \nL 483.957934 203.891792 \nL 483.247041 205.591601 \nL 482.536149 207.581647 \nL 481.825256 208.909606 \nL 481.114363 210.254198 \nL 480.403471 212.123461 \nL 479.692578 214.510523 \nL 478.981685 217.053661 \nL 478.270792 218.121952 \nL 477.5599 216.170537 \nL 476.849007 212.650524 \nL 476.138114 209.488711 \nL 475.427222 207.360696 \nL 474.716329 206.695635 \nL 474.005436 207.645854 \nL 473.294543 209.693866 \nL 472.583651 211.388348 \nL 471.872758 212.616726 \nL 471.161865 214.185752 \nL 470.450973 216.289275 \nL 469.74008 218.829162 \nL 469.029187 220.962374 \nL 468.318294 220.667247 \nL 467.607402 217.682164 \nL 466.896509 214.190494 \nL 466.185616 211.431853 \nL 465.474724 209.933572 \nL 464.763831 209.998816 \nL 464.052938 211.605166 \nL 463.342045 213.651288 \nL 462.631153 215.042479 \nL 461.92026 216.365742 \nL 461.209367 218.17803 \nL 460.498475 220.493874 \nL 459.787582 223.024206 \nL 459.076689 224.270269 \nL 458.365796 222.549692 \nL 457.654904 219.07138 \nL 456.944011 215.841973 \nL 456.233118 213.595813 \nL 455.522226 212.791752 \nL 454.811333 213.605704 \nL 454.10044 215.627481 \nL 453.389548 217.406215 \nL 452.678655 218.655699 \nL 451.967762 220.184266 \nL 451.256869 222.223976 \nL 450.545977 224.705016 \nL 449.835084 226.904643 \nL 449.124191 226.852045 \nL 448.413299 224.021678 \nL 447.702406 220.507386 \nL 446.991513 217.659573 \nL 446.28062 216.030852 \nL 445.569728 215.955808 \nL 444.858835 217.458437 \nL 444.147942 219.54792 \nL 443.43705 221.007327 \nL 442.726157 222.315562 \nL 442.015264 224.076668 \nL 441.304371 226.324637 \nL 440.593479 228.834239 \nL 439.882586 230.242947 \nL 439.171693 228.763462 \nL 438.460801 225.347886 \nL 437.749908 222.061969 \nL 437.039015 219.705888 \nL 436.328122 218.766865 \nL 435.61723 219.443421 \nL 434.906337 221.423214 \nL 434.195444 223.282075 \nL 433.484552 224.559695 \nL 432.773659 226.052961 \nL 432.062766 228.034016 \nL 431.351873 230.455225 \nL 430.640981 232.706552 \nL 429.930088 232.889558 \nL 429.219195 230.233746 \nL 428.508303 226.712438 \nL 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240.879046 \nL 400.072594 237.650496 \nL 399.361701 234.284713 \nL 398.650809 231.733613 \nL 397.939916 230.536092 \nL 397.229023 230.938884 \nL 396.518131 232.789891 \nL 395.807238 234.787431 \nL 395.096345 236.138196 \nL 394.385452 237.571781 \nL 393.67456 239.448639 \nL 392.963667 241.748804 \nL 392.252774 244.061728 \nL 391.541882 244.684686 \nL 390.830989 242.428609 \nL 390.120096 238.941509 \nL 389.409204 235.884653 \nL 388.698311 233.899421 \nL 387.987418 233.422916 \nL 387.276525 234.567931 \nL 386.565633 236.696948 \nL 385.85474 238.372801 \nL 385.143847 239.665447 \nL 384.432955 241.29845 \nL 383.722062 243.362924 \nL 383.011169 245.770521 \nL 382.300276 247.56703 \nL 381.589384 246.837661 \nL 380.878491 243.731981 \nL 380.167598 240.343027 \nL 379.456706 237.706893 \nL 378.745813 236.385584 \nL 378.03492 236.653646 \nL 377.324027 238.419878 \nL 376.613135 240.471695 \nL 375.902242 241.86529 \nL 375.191349 243.272442 \nL 374.480457 245.10236 \nL 373.769564 247.34205 \nL 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284.006824 \nL 257.894052 282.347504 \nL 259.315837 278.276397 \nL 260.02673 276.71064 \nL 260.737623 275.455444 \nL 261.448516 273.791551 \nL 262.159408 271.7171 \nL 262.870301 270.650208 \nL 263.581194 271.146329 \nL 264.292086 273.133502 \nL 265.713872 279.38783 \nL 266.424765 281.430457 \nL 267.135657 280.816347 \nL 268.557443 276.619387 \nL 269.268335 274.856777 \nL 270.690121 272.119638 \nL 272.111906 268.346421 \nL 272.822799 267.992144 \nL 273.533692 269.203726 \nL 274.244584 271.735649 \nL 275.66637 277.964136 \nL 276.377262 278.815904 \nL 277.088155 277.249617 \nL 278.509941 273.07763 \nL 279.220833 271.464939 \nL 279.931726 270.18359 \nL 280.642619 268.560313 \nL 281.353511 266.450266 \nL 282.064404 265.252918 \nL 282.775297 265.626492 \nL 283.48619 267.512688 \nL 285.618868 276.02836 \nL 286.32976 275.606971 \nL 288.462439 269.552953 \nL 289.884224 266.783708 \nL 291.306009 262.947022 \nL 292.016902 262.461803 \nL 292.727795 263.555756 \nL 293.438688 266.013482 \nL 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245.75356 \nL 366.660637 244.458053 \nL 367.371529 242.712005 \nL 368.082422 240.602529 \nL 368.793315 239.587183 \nL 369.504208 240.192081 \nL 370.2151 242.284778 \nL 371.636886 248.838094 \nL 372.347778 250.873751 \nL 373.058671 250.050374 \nL 374.480457 245.486164 \nL 375.191349 243.656713 \nL 376.613135 240.856795 \nL 378.03492 237.038621 \nL 378.745813 236.770159 \nL 379.456706 238.09105 \nL 380.167598 240.726996 \nL 381.589384 247.222135 \nL 382.300276 247.951967 \nL 383.011169 246.155783 \nL 384.432955 241.683511 \nL 385.143847 240.050208 \nL 385.85474 238.757183 \nL 386.565633 237.081225 \nL 387.276525 234.952384 \nL 387.987418 233.807796 \nL 388.698311 234.284754 \nL 389.409204 236.270254 \nL 391.541882 245.069493 \nL 392.252774 244.446202 \nL 393.67456 239.833366 \nL 394.385452 237.957129 \nL 395.807238 235.173414 \nL 397.229023 231.324373 \nL 397.939916 230.921171 \nL 398.650809 232.118424 \nL 399.361701 234.669563 \nL 400.783487 241.264688 \nL 401.49438 242.245538 \nL 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154.398766 \nL 610.496837 155.490404 \nL 611.207729 157.874029 \nL 612.629515 164.179862 \nL 613.340407 164.63222 \nL 614.0513 162.307601 \nL 614.762193 159.36966 \nL 615.473086 156.930729 \nL 616.183978 155.226085 \nL 616.894871 154.096071 \nL 617.605764 152.684348 \nL 618.316656 150.71979 \nL 619.027549 149.496517 \nL 619.738442 149.764647 \nL 620.449335 151.463704 \nL 621.160227 154.27872 \nL 621.87112 157.659719 \nL 622.582013 159.761108 \nL 623.292905 158.699019 \nL 624.714691 153.021714 \nL 625.425584 150.887842 \nL 626.136476 149.505537 \nL 626.847369 148.383584 \nL 628.269154 144.841242 \nL 628.980047 144.267809 \nL 629.69094 145.187072 \nL 630.401833 147.418866 \nL 631.823618 153.67962 \nL 632.534511 154.35886 \nL 633.245403 152.120488 \nL 634.667189 146.559319 \nL 635.378081 144.76784 \nL 636.799867 142.292708 \nL 637.51076 140.352422 \nL 638.221652 139.001323 \nL 638.932545 139.09811 \nL 639.643438 140.626957 \nL 640.35433 143.304178 \nL 641.065223 146.63007 \nL 641.776116 148.893383 \nL 642.487009 148.024361 \nL 643.908794 142.233896 \nL 644.619687 139.99557 \nL 645.330579 138.548023 \nL 646.041472 137.459606 \nL 647.463258 133.94968 \nL 648.17415 133.216598 \nL 648.885043 133.959581 \nL 649.595936 136.030921 \nL 651.017721 142.207157 \nL 651.728614 143.106971 \nL 652.439507 140.970708 \nL 653.861292 135.224435 \nL 654.572185 133.337566 \nL 655.99397 130.911079 \nL 656.704863 129.009828 \nL 657.415756 127.541197 \nL 658.126648 127.465305 \nL 658.837541 128.818027 \nL 659.548434 131.34795 \nL 660.259326 134.599059 \nL 660.970219 137.001756 \nL 661.681112 136.334555 \nL 663.81379 128.093079 \nL 664.524683 126.570046 \nL 665.235575 125.503219 \nL 665.946468 123.937836 \nL 666.657361 122.046693 \nL 667.368253 121.157782 \nL 668.079146 121.721589 \nL 668.790039 123.624721 \nL 670.211824 129.67896 \nL 670.922717 130.790088 \nL 671.63361 128.772023 \nL 673.055395 122.842387 \nL 673.766288 120.852167 \nL 675.188073 118.454994 \nL 676.609859 115.032839 \nL 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"likelihood = gpytorch.likelihoods.GaussianLikelihood()\n",
"likelihood.initialize(noise=0.1**2) \n",
"\n",
"likelihood.cuda()\n",
"\n",
"class ExactGPModel(gpytorch.models.ExactGP):\n",
" def __init__(self, train_x, train_y, likelihood, kernel):\n",
" super(ExactGPModel, self).__init__(train_x, train_y, likelihood)\n",
" self.mean_module = gpytorch.means.ConstantMean()\n",
" self.covar_module = kernel\n",
" \n",
" def forward(self, x):\n",
" mean_x = self.mean_module(x)\n",
" covar_x = self.covar_module(x)\n",
" return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)\n",
"\n",
"model = ExactGPModel(X_torch, Y_torch, likelihood, trend_seasonal_kernel_fn())\n",
"model.cuda()\n",
"\n",
"model.eval()\n",
"likelihood.eval()\n",
"\n",
"with torch.no_grad(), gpytorch.settings.fast_pred_var():\n",
" observed_pred = likelihood(model(X_test_torch))\n",
" # bigger plot of the last model\n",
" f, ax = plt.subplots(1, 1, figsize=(14, 6))\n",
" # Get upper and lower confidence bounds\n",
" lower, upper = observed_pred.confidence_region()\n",
" # Plot training data as black stars\n",
" ax.plot(X_torch.cpu().numpy(), Y_torch.cpu().numpy(), 'k.', markersize=3)\n",
" ax.vlines(max(X_raw), min(Y_raw), max(upper.cpu().numpy()), \"k\", linewidth=.5, alpha=.3)\n",
" # Plot predictive means as blue line\n",
" ax.plot(X_test_torch.cpu().numpy(), observed_pred.mean.cpu().numpy(), \"-\", color=\"steelblue\")\n",
" # Shade between the lower and upper confidence bounds\n",
" ax.fill_between(X_test_torch.cpu().numpy(), lower.cpu().numpy(), upper.cpu().numpy(), alpha=0.3)"
]
},
{
"source": [
"## Making sure the model outputs are the same\n",
"\n",
"Sklearn automatically updates model parameters when you `.fit` a model unless you hold the parameters `fixed`, so let's make sure the kernel specs remain the same, and then let's verify that the model outputs are the same by (1) plot the predictions from both models on the same set of axes, and (2) plotting the differences between the model outputs.\n",
"\n",
"First the kernels, which are indeed the same:"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"sklearn kernel:\n 50**2 * RBF(length_scale=50) + 2**2 * RBF(length_scale=100) * ExpSineSquared(length_scale=1, periodicity=1) + WhiteKernel(noise_level=0.01) \n\ngpytorch kernel:\n (50.00**2 * RBF(length_scale=50.000) + 2.00**2 * (RBF(length_scale=100.000) * ExpSineSquared(length_scale=1.000, periodcity=1.000,))) \n\ngpytorch mean: 0.0\n"
]
}
],
"source": [
"print(\"sklearn kernel:\\n\", gp.kernel, \"\\n\")\n",
"\n",
"print(\"gpytorch kernel:\\n\", print_kernel(model.covar_module), \"\\n\")\n",
"\n",
"print(\"gpytorch mean:\", model.mean_module.constant.item())"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'prediction intervals')"
]
},
"metadata": {},
"execution_count": 8
},
{
"output_type": "display_data",
"data": {
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\n"
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 1008x288 with 1 Axes>",
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152.019091 \nL 495.332217 153.354198 \nL 496.04311 155.409854 \nL 496.754003 157.770187 \nL 497.464896 159.215667 \nL 498.175788 158.631135 \nL 498.886681 156.933375 \nL 499.597574 155.294017 \nL 500.308466 154.011316 \nL 501.019359 153.099795 \nL 501.730252 152.253152 \nL 502.441145 150.971488 \nL 503.152037 149.783874 \nL 503.86293 149.547136 \nL 504.573823 150.360766 \nL 505.284715 152.06144 \nL 505.995608 154.330061 \nL 506.706501 156.483156 \nL 507.417394 157.009919 \nL 508.128286 155.707449 \nL 508.839179 153.939556 \nL 509.550072 152.44424 \nL 510.260964 151.33765 \nL 510.971857 150.53236 \nL 511.68275 149.518134 \nL 512.393643 148.15094 \nL 513.104535 147.343112 \nL 513.815428 147.593906 \nL 514.526321 148.83984 \nL 515.237213 150.835945 \nL 515.948106 153.196709 \nL 516.658999 154.77663 \nL 517.369891 154.32875 \nL 518.080784 152.635878 \nL 518.791677 150.946409 \nL 519.50257 149.619657 \nL 520.213462 148.686734 \nL 520.924355 147.873338 \nL 521.635248 146.642764 \nL 522.34614 145.410105 \nL 523.057033 145.075461 \nL 523.767926 145.791861 \nL 524.478819 147.414072 \nL 525.189711 149.639294 \nL 525.900604 151.850435 \nL 526.611497 152.540744 \nL 527.322389 151.313732 \nL 528.033282 149.511616 \nL 528.744175 147.964508 \nL 529.455068 146.821003 \nL 530.16596 146.014932 \nL 530.876853 145.057398 \nL 531.587746 143.705144 \nL 532.298638 142.815651 \nL 533.009531 142.966212 \nL 533.720424 144.118322 \nL 534.431317 146.04805 \nL 535.142209 148.396415 \nL 535.853102 150.098498 \nL 536.563995 149.794537 \nL 537.274887 148.114254 \nL 537.98578 146.37353 \nL 538.696673 144.998527 \nL 539.407566 144.039575 \nL 540.118458 143.254049 \nL 540.829351 142.079592 \nL 541.540244 140.81197 \nL 542.251136 140.379406 \nL 542.962029 140.995547 \nL 543.672922 142.533168 \nL 544.383814 144.706361 \nL 545.094707 146.959554 \nL 545.8056 147.809832 \nL 546.516493 146.669004 \nL 547.227385 144.83579 \nL 547.938278 143.23382 \nL 548.649171 142.048729 \nL 549.360063 141.236155 \nL 550.070956 140.332758 \nL 550.781849 139.005398 \nL 551.492742 138.039738 \nL 552.203634 138.08805 \nL 552.914527 139.142008 \nL 553.62542 140.998641 \nL 554.336312 143.3223 \nL 555.047205 145.132653 \nL 555.758098 144.978313 \nL 556.468991 143.318964 \nL 557.179883 141.52619 \nL 557.890776 140.098494 \nL 558.601669 139.108308 \nL 559.312561 138.344608 \nL 560.023454 137.229765 \nL 560.734347 135.937765 \nL 561.44524 135.408068 \nL 562.156132 135.921028 \nL 562.867025 137.368078 \nL 563.577918 139.480996 \nL 564.28881 141.760179 \nL 564.999703 142.764618 \nL 565.710596 141.720403 \nL 566.421489 139.859842 \nL 567.132381 138.199952 \nL 567.843274 136.968042 \nL 568.554167 136.142699 \nL 569.265059 135.289607 \nL 569.975952 133.996252 \nL 570.686845 132.961125 \nL 571.397738 132.905513 \nL 572.10863 133.857222 \nL 572.819523 135.634061 \nL 573.530416 137.921228 \nL 574.241308 139.824544 \nL 574.952201 139.82373 \nL 575.663094 138.19424 \nL 576.373986 136.349045 \nL 577.084879 134.864196 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128.771951 \nL 605.520588 126.988101 \nL 606.23148 125.646458 \nL 606.942373 124.775423 \nL 607.653266 124.007139 \nL 608.364158 122.804889 \nL 609.075051 121.655492 \nL 609.785944 121.389136 \nL 610.496837 122.125271 \nL 611.207729 123.722961 \nL 611.918622 125.904507 \nL 612.629515 127.944045 \nL 613.340407 128.254383 \nL 614.0513 126.7137 \nL 614.762193 124.765042 \nL 615.473086 123.153631 \nL 616.183978 122.034713 \nL 616.894871 121.294271 \nL 617.605764 120.363289 \nL 618.316656 119.063361 \nL 619.027549 118.257427 \nL 619.738442 118.445763 \nL 620.449335 119.58819 \nL 621.160227 121.474617 \nL 621.87112 123.738272 \nL 622.582013 125.148962 \nL 623.292905 124.450973 \nL 624.003798 122.538566 \nL 624.714691 120.689658 \nL 625.425584 119.285593 \nL 626.136476 118.381439 \nL 626.847369 117.646005 \nL 627.558262 116.498468 \nL 628.269154 115.306415 \nL 628.980047 114.934863 \nL 629.69094 115.558572 \nL 630.401833 117.057538 \nL 631.112725 119.171627 \nL 631.823618 121.25353 \nL 632.534511 121.717576 \nL 633.245403 120.236872 \nL 633.956296 118.238768 \nL 634.667189 116.558837 \nL 635.378081 115.385225 \nL 636.088974 114.637356 \nL 636.799867 113.76459 \nL 637.51076 112.48352 \nL 638.221652 111.594967 \nL 638.932545 111.671645 \nL 639.643438 112.703175 \nL 640.35433 114.50037 \nL 641.065223 116.729938 \nL 641.776116 118.25125 \nL 642.487009 117.684633 \nL 643.197901 115.768271 \nL 643.908794 113.853093 \nL 644.619687 112.382123 \nL 645.330579 111.438085 \nL 646.041472 110.728332 \nL 646.752365 109.639897 \nL 647.463258 108.416079 \nL 648.17415 107.94088 \nL 648.885043 108.449837 \nL 649.595936 109.844604 \nL 650.306828 111.882682 \nL 651.017721 113.989789 \nL 651.728614 114.603646 \nL 652.439507 113.193797 \nL 653.150399 111.149043 \nL 653.861292 109.397814 \nL 654.572185 108.163974 \nL 655.283077 107.400936 \nL 655.99397 106.58283 \nL 656.704863 105.330772 \nL 657.415756 104.366767 \nL 658.126648 104.331207 \nL 658.837541 105.248209 \nL 659.548434 106.950149 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687.984142 93.58773 \nL 688.695035 95.451838 \nL 689.405928 97.55983 \nL 690.11682 98.453875 \nL 690.827713 97.218806 \nL 691.538606 95.093652 \nL 692.249498 93.194047 \nL 692.960391 91.824941 \nL 693.671284 91.00883 \nL 694.382176 90.28558 \nL 695.093069 89.119189 \nL 695.803962 88.03162 \nL 696.514855 87.773589 \nL 697.225747 88.45371 \nL 697.93664 89.949409 \nL 698.647533 92.004777 \nL 699.358425 93.766183 \nL 700.069318 93.624682 \nL 700.780211 91.751722 \nL 701.491104 89.638319 \nL 702.201996 87.945535 \nL 702.912889 86.843747 \nL 703.623782 86.164848 \nL 704.334674 85.266819 \nL 705.045567 84.019157 \nL 705.75646 83.255925 \nL 706.467353 83.413951 \nL 707.178245 84.469693 \nL 707.889138 86.237686 \nL 708.600031 88.32305 \nL 709.310923 89.343895 \nL 710.021816 88.212449 \nL 710.732709 86.056064 \nL 711.443602 84.08082 \nL 712.154494 82.637883 \nL 712.865387 81.784395 \nL 713.57628 81.099856 \nL 714.287172 79.988296 \nL 714.998065 78.855324 \nL 715.708958 78.489303 \nL 716.419851 79.04878 \nL 717.130743 80.434806 \nL 717.841636 82.412405 \nL 718.552529 84.221314 \nL 719.263421 84.226733 \nL 719.974314 82.390148 \nL 720.685207 80.213983 \nL 721.3961 78.442555 \nL 722.106992 77.27689 \nL 722.817885 76.592591 \nL 723.528778 75.758165 \nL 724.23967 74.5273 \nL 724.950563 73.680795 \nL 725.661456 73.72249 \nL 726.372348 74.659015 \nL 727.083241 76.326015 \nL 727.794134 78.374904 \nL 728.505027 79.511602 \nL 729.215919 78.494014 \nL 729.926812 76.314192 \nL 730.637705 74.263409 \nL 731.348597 72.743501 \nL 732.05949 71.845941 \nL 732.770383 71.193594 \nL 733.481276 70.143437 \nL 734.192168 68.977558 \nL 734.903061 68.507442 \nL 735.613954 68.946053 \nL 736.324846 70.219014 \nL 737.035739 72.111248 \nL 737.746632 73.951309 \nL 738.457525 74.103409 \nL 739.168417 72.315651 \nL 739.87931 70.080207 \nL 740.590203 68.2291 \nL 741.301095 66.994916 \nL 742.011988 66.297578 \nL 742.722881 65.524914 \nL 743.433774 64.323088 \nL 744.144666 63.402368 \nL 744.855559 63.329728 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774.00216 46.643012 \nL 774.713053 47.683001 \nL 775.423946 49.387102 \nL 776.134838 51.242563 \nL 776.845731 51.680191 \nL 777.556624 50.02986 \nL 778.267516 47.691423 \nL 778.978409 45.681274 \nL 778.978409 32.201769 \nL 778.978409 32.201769 \nL 778.267516 34.305863 \nL 777.556624 36.727306 \nL 776.845731 38.457483 \nL 776.134838 38.098692 \nL 775.423946 36.321779 \nL 774.713053 34.696162 \nL 774.00216 33.734421 \nL 773.291267 33.611643 \nL 772.580375 34.349735 \nL 771.869482 35.618693 \nL 771.158589 36.611733 \nL 770.447697 37.307444 \nL 769.736804 38.409569 \nL 769.025911 40.185906 \nL 768.315018 42.466731 \nL 767.604126 44.740641 \nL 766.893233 45.577563 \nL 766.18234 44.32077 \nL 765.471448 42.454404 \nL 764.760555 41.074162 \nL 764.049662 40.453054 \nL 763.338769 40.709551 \nL 762.627877 41.766759 \nL 761.916984 43.00219 \nL 761.206091 43.793664 \nL 760.495199 44.598762 \nL 759.784306 46.000574 \nL 759.073413 48.01677 \nL 758.36252 50.380691 \nL 757.651628 52.177132 \nL 756.940735 51.949954 \nL 756.229842 50.163886 \nL 755.51895 48.432409 \nL 754.808057 47.344102 \nL 754.097164 47.093909 \nL 753.386271 47.730874 \nL 752.675379 48.985035 \nL 751.964486 50.039175 \nL 751.253593 50.742417 \nL 750.542701 51.777879 \nL 749.831808 53.464639 \nL 749.120915 55.664242 \nL 748.410023 57.925583 \nL 747.69913 58.885365 \nL 746.988237 57.709933 \nL 746.277344 55.7746 \nL 745.566452 54.277213 \nL 744.855559 53.525742 \nL 744.144666 53.662096 \nL 743.433774 54.646662 \nL 742.722881 55.913577 \nL 742.011988 56.754031 \nL 741.301095 57.527826 \nL 740.590203 58.847398 \nL 739.87931 60.775414 \nL 739.168417 63.076207 \nL 738.457525 64.925828 \nL 737.746632 64.834538 \nL 737.035739 63.05492 \nL 736.324846 61.222985 \nL 735.613954 60.010267 \nL 734.903061 59.631283 \nL 734.192168 60.160734 \nL 733.481276 61.386471 \nL 732.770383 62.498121 \nL 732.05949 63.216532 \nL 731.348597 64.191246 \nL 730.637705 65.790108 \nL 729.926812 67.907061 \nL 729.215919 70.145683 \nL 728.505027 71.220301 \nL 727.794134 70.139939 \nL 727.083241 68.147091 \nL 726.372348 66.536161 \nL 725.661456 65.655425 \nL 724.950563 65.669008 \nL 724.23967 66.570821 \nL 723.528778 67.85797 \nL 722.817885 68.75086 \nL 722.106992 69.501254 \nL 721.3961 70.74277 \nL 720.685207 72.583238 \nL 719.974314 74.816703 \nL 719.263421 76.706914 \nL 718.552529 76.754067 \nL 717.841636 74.997324 \nL 717.130743 73.071703 \nL 716.419851 71.737662 \nL 715.708958 71.229621 \nL 714.998065 71.646761 \nL 714.287172 72.831212 \nL 713.57628 73.995608 \nL 712.865387 74.736725 \nL 712.154494 75.657323 \nL 711.443602 77.170928 \nL 710.732709 79.20478 \nL 710.021816 81.412002 \nL 709.310923 82.592498 \nL 708.600031 81.619978 \nL 707.889138 79.582641 \nL 707.178245 77.862709 \nL 706.467353 76.85486 \nL 705.75646 76.744231 \nL 705.045567 77.554806 \nL 704.334674 78.850548 \nL 703.623782 79.798392 \nL 702.912889 80.533676 \nL 702.201996 81.702157 \nL 701.491104 83.456594 \nL 700.780211 85.619831 \nL 700.069318 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128.495058 \nL 587.74827 129.316913 \nL 587.037377 130.183425 \nL 586.326484 131.494498 \nL 585.615592 133.232431 \nL 584.904699 135.127734 \nL 584.193806 136.076553 \nL 583.482914 134.936546 \nL 582.772021 132.657808 \nL 582.061128 130.623865 \nL 581.350235 129.28405 \nL 580.639343 128.887603 \nL 579.92845 129.5231 \nL 579.217557 130.839143 \nL 578.506665 131.903177 \nL 577.795772 132.665565 \nL 577.084879 133.715674 \nL 576.373986 135.221075 \nL 575.663094 137.077977 \nL 574.952201 138.717332 \nL 574.241308 138.727517 \nL 573.530416 136.8331 \nL 572.819523 134.554652 \nL 572.10863 132.786537 \nL 571.397738 131.843231 \nL 570.686845 131.90707 \nL 569.975952 132.95064 \nL 569.265059 134.252923 \nL 568.554167 135.11574 \nL 567.843274 135.956922 \nL 567.132381 137.210713 \nL 566.421489 138.883933 \nL 565.710596 140.752422 \nL 564.999703 141.804013 \nL 564.28881 140.80655 \nL 563.577918 138.534422 \nL 562.867025 136.428878 \nL 562.156132 134.989284 \nL 561.44524 134.48337 \nL 560.734347 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533.009531 142.298969 \nL 532.298638 142.151195 \nL 531.587746 143.043718 \nL 530.876853 144.399296 \nL 530.16596 145.360052 \nL 529.455068 146.171885 \nL 528.744175 147.326712 \nL 528.033282 148.880043 \nL 527.322389 150.684332 \nL 526.611497 151.913505 \nL 525.900604 151.225391 \nL 525.189711 149.016579 \nL 524.478819 146.793855 \nL 523.767926 145.173945 \nL 523.057033 144.459318 \nL 522.34614 144.795308 \nL 521.635248 146.029356 \nL 520.924355 147.261481 \nL 520.213462 148.077216 \nL 519.50257 149.017349 \nL 518.791677 150.353008 \nL 518.080784 152.04571 \nL 517.369891 153.740247 \nL 516.658999 154.189371 \nL 515.948106 152.610174 \nL 515.237213 150.250163 \nL 514.526321 148.255062 \nL 513.815428 147.01039 \nL 513.104535 146.761025 \nL 512.393643 147.570407 \nL 511.68275 148.93925 \nL 510.971857 149.954765 \nL 510.260964 150.762455 \nL 509.550072 151.875796 \nL 508.839179 153.374754 \nL 508.128286 155.143441 \nL 507.417394 156.446909 \nL 506.706501 155.921302 \nL 505.995608 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169.623433 \nL 422.821161 170.76665 \nL 422.110268 172.222307 \nL 421.399376 173.876799 \nL 420.688483 174.913546 \nL 419.97759 174.092465 \nL 419.266697 171.871045 \nL 418.555805 169.650117 \nL 417.844912 168.011622 \nL 417.134019 167.298204 \nL 416.423127 167.657662 \nL 415.712234 168.939382 \nL 415.001341 170.227739 \nL 414.290448 171.102229 \nL 413.579556 172.076873 \nL 412.868663 173.361533 \nL 412.15777 174.935393 \nL 411.446878 176.461298 \nL 410.735985 176.733951 \nL 410.025092 175.091571 \nL 409.314199 172.750012 \nL 408.603307 170.752224 \nL 407.892414 169.504066 \nL 407.181521 169.273539 \nL 406.470629 170.120452 \nL 405.759736 171.541737 \nL 405.048843 172.610789 \nL 404.33795 173.47321 \nL 403.627058 174.588191 \nL 402.916165 176.003101 \nL 402.205272 177.634769 \nL 401.49438 178.757793 \nL 400.783487 178.104157 \nL 400.072594 175.951791 \nL 399.361701 173.707936 \nL 398.650809 172.007202 \nL 397.939916 171.208855 \nL 397.229023 171.477383 \nL 396.518131 172.711388 \nL 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"f, ax = plt.subplots(1, 1, figsize=(14, 4))\n",
"ax.plot(X_test_torch.cpu().numpy(),observed_pred.mean.cpu().numpy(), \"-\", color=\"steelblue\")\n",
"ax.plot(X_test, y_pred,\"--\", color=\"pink\")\n",
"ax.vlines(max(X_raw), min(Y_raw), max(upper.cpu().numpy()), \"k\", linewidth=.5, alpha=.3)\n",
"ax.legend([\"gpytorch\", \"sklearn\"])\n",
"ax.set_title(\"mean prediction\")\n",
"\n",
"# NOTE: gpytorch's built in confidence regions use 2 std devs from the mean.\n",
"# https://docs.gpytorch.ai/en/v1.1.1/_modules/gpytorch/distributions/multivariate_normal.html#MultivariateNormal.confidence_region\n",
"y_lower_sklearn = (y_pred - 2* y_std)\n",
"y_upper_sklearn = (y_pred + 2* y_std)\n",
"\n",
"f, ax = plt.subplots(1, 1, figsize=(14, 4))\n",
"ax.fill_between(X_test_torch.cpu().numpy(), lower.cpu().numpy(), upper.cpu().numpy(), alpha=0.5)\n",
"ax.fill_between(X_test[:, 0], y_lower_sklearn, y_upper_sklearn, alpha=0.2, color='red')\n",
"ax.vlines(max(X_raw), min(Y_raw), max(upper.cpu().numpy()), \"k\", linewidth=.5, alpha=.3)\n",
"ax.legend([\"gpytorch\", \"sklearn\"],loc=\"upper left\")\n",
"ax.set_title(\"prediction intervals\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Text(0.5, 1.0, 'difference in upper and lower confidence regions (gpytorch - sklearn)')"
]
},
"metadata": {},
"execution_count": 9
},
{
"output_type": "display_data",
"data": {
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\n"
},
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}
},
{
"output_type": "display_data",
"data": {
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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"f, ax = plt.subplots(1, 1, figsize=(14, 4))\n",
"ax.plot(observed_pred.mean.cpu().numpy() - y_pred, \"-\", color=\"steelblue\")\n",
"ax.set_title(\"difference in mean prediction (gpytorch - sklearn)\")\n",
"ax.vlines(len(X_raw), min(observed_pred.mean.cpu().numpy() - y_pred), max(observed_pred.mean.cpu().numpy() - y_pred), \"k\", linewidth=.5, alpha=.3)\n",
"\n",
"\n",
"\n",
"f, ax = plt.subplots(1, 1, figsize=(14, 4))\n",
"ax.plot(upper.cpu().numpy() - y_upper_sklearn, alpha=0.7, color='blue')\n",
"ax.plot(lower.cpu().numpy() - y_lower_sklearn, alpha=0.7, color='red')\n",
"ax.vlines(len(X_raw), min(lower.cpu().numpy() - y_lower_sklearn), max(lower.cpu().numpy() - y_lower_sklearn), \"k\", linewidth=.5, alpha=.3)\n",
"\n",
"ax.legend([\"upper\", \"lower\"],loc=\"upper left\")\n",
"ax.set_title(\"difference in upper and lower confidence regions (gpytorch - sklearn)\")"
]
},
{
"source": [
"From the first pair of plots above, the predictions are manifestly the same (the line for the gpytorch prediction, which is dashed blue, is directly on top of the pine line for the sklearn projections). Looking at the differences between the outputs, we see that they only reach order of 1e-6 predicting far past the end of the training data (vertical grey line), and that the differences are basically zero within the training data, so the agreement appears near exact.\n"
],
"cell_type": "markdown",
"metadata": {}
},
{
"source": [
"## Reproducing log likelihood calculations\n",
"\n",
"Having confirmed that the model specifications are the same and that the model outputs are in close agreement, at this point we would hope to be able to produce very similar log likelihoods for the models on the training data.\n",
"\n",
"Using Eq 5.8 from Rassmussen and Williams, to compute the log likelihood we'll need access to the kernel matrix (or an equivalent decomposition).\n",
"\n",
"Sklearn makes the Cholesky decomposition available straight away, and using that we can see that the long-hand computation of the log likelihoods from Rassmussen and Muller (eq 5.8) matches sklearn's built in functionality to very high precision:"
],
"cell_type": "markdown",
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{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"def compute_log_likelihood(Y, L, log_det_K, N):\n",
" # Rassmussen and Williams (eq 5.8)\n",
" L_inv = np.linalg.inv(L)\n",
" return -0.5 * (Y.T @ L_inv.T @ L_inv @ Y + log_det_K + N*np.log(2* np.pi))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"log_det_K = 2 * logdet(L): -2229.3291128356495\nlogdet(L @ L.T): -2229.3291128256783\nlog_likelihood (sklearn, long hand): -6639.7017791596\nlog_likelihood (sklearn, built in): -6639.701779160753\n"
]
}
],
"source": [
"L_sklearn = gp.L_ # the cholesky decomposition of the sklearn kernel\n",
"\n",
"sign, log_det_L = np.linalg.slogdet(L_sklearn)\n",
"log_det_K = 2 * log_det_L\n",
"print(\"log_det_K = 2 * logdet(L): \",log_det_K)\n",
"print(\"logdet(L @ L.T): \",np.linalg.slogdet(L_sklearn @ L_sklearn.T)[1])\n",
"\n",
"N = Y_raw.shape[0]\n",
"\n",
"print(\"log_likelihood (sklearn, long hand): \", compute_log_likelihood(Y_raw, L_sklearn, log_det_K, N))\n",
"print(\"log_likelihood (sklearn, built in): \", gp.log_marginal_likelihood(gp.kernel_.theta))"
]
},
{
"source": [
"In gpytorch, it turns out the Cholesky factor of kernel matrix available through the API does not include the likelihood noise that should be present on the diagonal of the full kernel. \n",
"\n",
"(see https://github.com/cornellius-gp/gpytorch/discussions/1661#discussioncomment-895330)\n",
"\n",
"That is, if the full kernel for the model is $K$, then sklearn makes the Cholesky factor $L$ of the full kernel available: $L L^T = K$.\n",
"\n",
"Gpytorch factorizes a slightly different matrix $\\grave{K} = K - \\sigma^2 I$, where $K$ is the full kernel matrix and $\\sigma^2$ is the likelihood noise (`model.likelihood.noise` in gpytorch, or `noise_level` in a `WhiteKernel` in sklearn).\n",
"\n",
"Therefore, `model.covar_module(...).cholesky()` returns a different matrix than what is available from sklearn -- $\\grave{L}$ such that $\\grave{K} = \\grave{L}\\grave{L}^T$, and therefore to recover the full matrix $K$ required to compute the likelihood, we need to materialize $K = \\grave{L}\\grave{L}^T + \\sigma^2 I$, and also $K^{-1}$\n",
"\n",
"Note: from a couple hours of searching there does not, unfortunately, seem to be a great way of updating $L$ to $\\grave{L}$ directly. I thought there might be some promising leads in the literature around rank-one updates (see e.g. [A More Efficient Rank-one Covariance Matrix Update forEvolution Strategies](https://christian-igel.github.io/paper/AMERCMAUfES.pdf), but I haven't been able to find a recipe for updating a Cholesky factor when adding a full diagonal matrix to the unfactorized matrix. Thus, the full matrix needs to be materialized and inverted :-( \n"
],
"cell_type": "markdown",
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"log_det_K: -2229.328537762464\n",
"log_likelihood (gpytorch, long hand): -6639.693895326409 \n",
"\n",
"/home/bc/miniconda3/lib/python3.9/site-packages/gpytorch/utils/cholesky.py:83: NumericalWarning: A not p.d., added jitter of 1.0e-08 to the diagonal\n",
" warnings.warn(f\"A not p.d., added jitter of {jitter_new:.1e} to the diagonal\", NumericalWarning)\n"
]
}
],
"source": [
"L_gptorch = model.covar_module(X_torch).cpu().detach().cholesky().numpy()\n",
"L_inv = np.linalg.inv(L_gptorch)\n",
"\n",
"N = Y_raw.shape[0]\n",
"sigma2 = model.likelihood.noise.item()\n",
"\n",
"K = L_gptorch @ L_gptorch.T + sigma2 * np.eye(N)\n",
"K_inv = np.linalg.inv(K)\n",
"\n",
"sign, log_det_K = np.linalg.slogdet(K)\n",
"\n",
"print(\"log_det_K:\", log_det_K)\n",
"\n",
"print(\n",
" \"log_likelihood (gpytorch, long hand): \",\n",
" -0.5 * (\n",
" Y_raw.T @ K_inv @ Y_raw\n",
" + log_det_K\n",
" + N*np.log(2* np.pi)\n",
" ),\n",
" \"\\n\"\n",
")"
]
},
{
"source": [
"Above, a log likelihood value that is certainly close enough to the value we get from sklearn to call it a success. Huzzah."
],
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