gp pymc3 notebook init
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"WARNING (theano.configdefaults): install mkl with `conda install mkl-service`: No module named 'mkl'\n"
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]
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}
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],
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"source": [
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"import pymc3 as pm\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from pymc3.gp.util import plot_gp_dist\n",
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"\n",
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"#https://docs.pymc.io/notebooks/GP-Marginal.html"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[<matplotlib.lines.Line2D at 0x7fcf4339ec18>]"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": 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truncated
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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}
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],
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"source": [
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"np.random.seed(5)\n",
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"x = np.linspace(0, 10)[:, None]\n",
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"y = np.sin(x)\n",
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"\n",
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"X = np.random.choice(x.flatten(), 7, replace=False)[:, None]\n",
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"Y = np.sin(X)\n",
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"\n",
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"plt.plot(x, y)\n",
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"plt.plot(X, Y, 'o')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 25,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/opt/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
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" result[diagonal_slice] = x\n",
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"Only 100 samples in chain.\n",
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"Sequential sampling (1 chains in 1 job)\n",
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"NUTS: [f*, ls]\n",
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"100%|██████████| 150/150 [03:43<00:00, 1.05it/s]\n",
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"The acceptance probability does not match the target. It is 0.9064175024104284, but should be close to 0.8. Try to increase the number of tuning steps.\n",
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"The chain reached the maximum tree depth. Increase max_treedepth, increase target_accept or reparameterize.\n",
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"Only one chain was sampled, this makes it impossible to run some convergence checks\n"
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]
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}
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],
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"source": [
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"with pm.Model() as model:\n",
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" ls = pm.HalfCauchy('ls', beta=5)\n",
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" \n",
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" # zero mean\n",
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" mean = pm.gp.mean.Constant(0)\n",
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" # input_dim = the total columns of X\n",
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" cov = pm.gp.cov.ExpQuad(input_dim=1, ls=ls)\n",
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" \n",
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" # The GP\n",
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" gp = pm.gp.Marginal(mean , cov)\n",
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" \n",
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" # Observed data\n",
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" f = gp.marginal_likelihood('y_obs', X, Y.flatten(), noise=0)\n",
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" \n",
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" # Conditional GP\n",
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" f_star = gp.conditional('f*', x) \n",
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" step = pm.NUTS()\n",
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"\n",
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" trace = pm.sample(chains=1, step=step, tune=50, draws=100)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 26,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"100%|██████████| 1000/1000 [00:01<00:00, 891.40it/s]\n"
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]
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}
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],
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"source": [
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"with model:\n",
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" pred_samples = pm.sample_ppc(trace, vars=[f_star, f], samples=1000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 27,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[<matplotlib.lines.Line2D at 0x7fcf281c8748>]"
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]
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},
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"execution_count": 27,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"plt.plot(pred_samples['f*'].mean(0))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 28,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"[<matplotlib.lines.Line2D at 0x7fcf28183d68>]"
|
||||
]
|
||||
},
|
||||
"execution_count": 28,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 864x360 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# plot the results\n",
|
||||
"fig = plt.figure(figsize=(12,5))\n",
|
||||
"ax = fig.gca()\n",
|
||||
"\n",
|
||||
"plot_gp_dist(ax, pred_samples[\"f*\"], x)\n",
|
||||
"plt.plot(X, Y, 'o')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 29,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"/opt/miniconda3/lib/python3.7/site-packages/theano/tensor/basic.py:6611: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
|
||||
" result[diagonal_slice] = x\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"with model:\n",
|
||||
" prior_pc = pm.sample_prior_predictive(samples=100)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.7.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 2
|
||||
}
|
||||
Reference in new issue
Block a user