{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Gaussian Processes (GP)\n",
"\n",
"In this notebook we will learn how to use GPy library to deal with gaussian processes. This library provide quite simple and inuitive interfaces for training and inference, and we will try to get familiar with them in a few tasks. For more details about Gaussian Processes see basic_gp.ipynb notebook (with 1-D and 2-D examples).\n",
"\n",
"Additional implementation of GPR models can be found in \n",
"* Scikit-Learn sklearn.gaussian_process library\n",
"* Matlab: gaussian-process-regression-models\n",
"\n",
"Further reading: see [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/chapters/) by Carl Edward Rasmussen and Christopher K. I. Williams.\n",
"\n",
"### Setup:\n",
"\n",
"Install and import the necessary libraries."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"try:\n",
" import google.colab\n",
" IN_COLAB = True\n",
"except:\n",
" IN_COLAB = False\n",
"if IN_COLAB:\n",
" ! pip install GPy"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import GPy\n",
"import matplotlib.pyplot as plt\n",
"import time\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gaussian processes: GPy (documentation)\n",
"\n",
"We will start with a simple regression problem, for which we will try to fit a Gaussian Process with RBF kernel.\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def generate_points(n=25, noise_variance=0.0036):\n",
" #np.random.seed(777)\n",
" X = np.random.uniform(-3., 3., (n, 1))\n",
" y = np.sin(X) + np.random.randn(n, 1) * noise_variance**0.5\n",
" return X, y\n",
" \n",
"def generate_noise(n=25, noise_variance=0.0036):\n",
" #np.random.seed(777)\n",
" X = np.random.uniform(-3., 3., (n, 1))\n",
" y = np.random.randn(n, 1) * noise_variance**0.5\n",
" return X, y"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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JQ8eHXZIkLQuDYYl2bd/Mxg3rWB84a8M6dm3fPOySJGlZLDorSbN2btvE3TfsYuLQcXZt3+wwkqRVy2A4DTu3bTIQJK16DiVp7Dg7TFpe9hg0VpwdJi0/ewwaK84Ok5afwaCx4uwwafk5lKSx4uwwafkZDBo7zg6TlpdDSRp5zkKSVpY9Bo00ZyFJK88eg0aas5CklWcwaKQ5C0laeQ4laaQ5C0laeQaDRp6zkKSV5VCSJKmHwSBJ6tEqGJKcm+T+JE83P1/V30/y1iQHul7/L8nVzbbfS/Kdrm2XtalHktRe2x7DLcCDVbUDeLBZ7lFVD1fVZVV1GfA24EXgy11NfmNue1UdaFmPJKmltsGwB7ireX8XcPUi7d8FfKmqXmx5XEnSMmkbDK+rqmcBmp+vXaT9NcCn5637aJJvJvl4krMX2jHJ3iSTSSaPHTvWrmpJ0oIWDYYkDyR5rM9rz+kcKMn5wN8C7uta/SHgZ4FfAM4Fbl5o/6raV1Wdqups2bLldA4tSToNi97HUFVXLLQtyfeSnF9VzzYf/M+d4lf9MvD5qnq563c/27x9KcnvAh9cYt1jZ+rwCW/SkjQW2t7gth+4Hrit+fmFU7S9ltkewo90hUqYvT7xWMt6RpIPgpM0TtpeY7gNuDLJ08CVzTJJOknumGuU5GLgIuB/zNv/7iSPAo8C5wH/rmU9I8kHwUkaJ616DFV1HHh7n/WTwA1dy/8buKBPu7e1Of64mHsQ3MvTMz4ITtLI81lJK8AHwUkaJwbDCvFBcJLGhc9KkiT1MBgkST0MhiHyS+4ljSKvMQyJ9zZIGlX2GIbEexskjSqDYUj8kntJo8qhpCHx3gZJo8pgGCLvbZA0ihxKkiT1MBjUilNupdXHoSSdMafcSquTPYYxNQp/qTvlVlqd7DGMoVH5S93HiUurk8Ewhvr9pT6MYHDKrbQ6GQxjaJT+UnfKrbT6tLrGkOTdSR5PMpOkc4p2u5M8leRgklu61l+S5GtJnk7ymSQb29SzVsz9pX7TO97gBV9JA9f24vNjwD8C/nihBknWA7cDvwhcClyb5NJm88eAj1fVDuAE8L6W9awZO7dt4gNvfb2hIGngWgVDVT1ZVU8t0uxy4GBVHaqqk8A9wJ4kAd4GfLZpdxdwdZt6JEntrcR01QuAZ7qWjzTrNgMvVNX0vPWSpCFa9OJzkgeAn+6z6cNV9YUlHCN91tUp1i9Ux15gL8DWrVuXcFhJ0plYNBiq6oqWxzgCXNS1fCFwFPg+cE6SDU2vYW79QnXsA/YBdDqdBQNEktTOSgwlPQLsaGYgbQSuAfZXVQEPA+9q2l0PLKUHIklaRm2nq/5SkiPA3wG+mOS+Zv3PJPkjgKY3cCNwH/AkcG9VPd78ipuBm5IcZPaaw6fa1CNJai+zf7iPl06nU5OTk8MuY2xNHT7h3crSGpRkqqoWvOdsjnc+rzGj8pwlSaPLp6uuMT4RVdJiDIY1Zu45S+vDkp+zNAqP+Ja0chxKWmNO94moDj1Ja4/BsAadzhNRR+UR35JWjkNJOqUzGXqSNN7sMeiU/DIeae0xGLQov4xHWlscSpIk9TAYJEk9DAZJUg+DQZLUw2CQJPUwGCRJPcbysdtJjgGH560+j9lvhVtNVts5rbbzgdV3TqvtfGD1nVOb89lWVVsWazSWwdBPksmlPGd8nKy2c1pt5wOr75xW2/nA6junlTgfh5IkST0MBklSj9UUDPuGXcAyWG3ntNrOB1bfOa2284HVd07Lfj6r5hqDJGkwVlOPQZI0AKsqGJL8VpJvJjmQ5MtJfmbYNbWR5LeT/FlzTp9Pcs6wa2orybuTPJ5kJsnYzhRJsjvJU0kOJrll2PW0leTOJM8leWzYtQxCkouSPJzkyea/t18ddk1tJXlNkq8n+UZzTv922Y61moaSkvxUVf1F8/5XgEur6v1DLuuMJXkH8FBVTSf5GEBV3TzkslpJ8kZgBvgk8MGqmhxySactyXrgW8CVwBHgEeDaqnpiqIW1kOQtwA+A36+qvznsetpKcj5wflX9aZK/BkwBV4/5v1GAn6iqHyQ5C/gq8KtVNTHoY62qHsNcKDR+Ahjr1KuqL1fVdLM4AVw4zHoGoaqerKqnhl1HS5cDB6vqUFWdBO4B9gy5plaq6o+B54ddx6BU1bNV9afN+78EngQuGG5V7dSsHzSLZzWvZfmMW1XBAJDko0meAa4DfnPY9QzQvwC+NOwiBMx+wDzTtXyEMf/QWc2SXAy8CfjacCtpL8n6JAeA54D7q2pZzmnsgiHJA0ke6/PaA1BVH66qi4C7gRuHW+3iFjufps2HgWlmz2nkLeWcxlz6rBvr3ulqleQngc8BvzZvRGEsVdUrVXUZs6MHlydZlmG/sftqz6q6YolN/yvwReAjy1hOa4udT5LrgX8IvL3G5ILQafwbjasjwEVdyxcCR4dUixbQjMN/Dri7qv7bsOsZpKp6IclXgN3AwCcMjF2P4VSS7OhavAr4s2HVMghJdgM3A1dV1YvDrkc/8giwI8klSTYC1wD7h1yTujQXaj8FPFlV/3HY9QxCki1zMxOT/BhwBcv0GbfaZiV9DngDs7NeDgPvr6o/H25VZy7JQeBs4HizamKcZ1kBJPkl4D8BW4AXgANV9c7hVnX6kvwD4BPAeuDOqvrokEtqJcmngb/P7JM7vwd8pKo+NdSiWkjyd4H/CTzK7OcBwL+uqj8aXlXtJPl54C5m/5tbB9xbVbcuy7FWUzBIktpbVUNJkqT2DAZJUg+DQZLUw2CQJPUwGCRJPQwGSVIPg0GS1MNgkCT1+P9LuK3H4Lz9sAAAAABJRU5ErkJggg==\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Create data points\n",
"X, y = generate_points()\n",
"plt.plot(X, y, '.')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To fit a Gaussian Process, we will need to define a kernel. For Gaussian (RBF) kernel we can use `GPy.kern.RBF` function.\n",
"\n",
"Let's create a RBF kernel, with variance 0.1 and length-scale parameter 1 for 1D samples:\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"kernel = GPy.kern.RBF(input_dim=1, variance=0.1, lengthscale=1.)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can fit GP into generated data using the `GPy.models.GPRegression` class."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"model = GPy.models.GPRegression(X,y,kernel)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can plot the model predictions:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"model.plot()\n",
"plt.rcParams['figure.autolayout']\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the model dodn't fit the data quite well. Is because we didn't fit the model. You can see the current parameters below:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
"Model: GP regression \n",
"Objective: 27.181865497789232 \n",
"Number of Parameters: 3 \n",
"Number of Optimization Parameters: 3 \n",
"Updates: True \n",
"
\n",
"Model: GP regression \n",
"Objective: -22.97711674165552 \n",
"Number of Parameters: 3 \n",
"Number of Optimization Parameters: 3 \n",
"Updates: True \n",
"
\n",
"\n",
"
GP_regression.
value
constraints
priors
\n",
"
rbf.variance
1.1532550301054725
+ve
\n",
"
rbf.lengthscale
1.8316770548092471
+ve
\n",
"
Gaussian_noise.variance
0.002383215091921367
+ve
\n",
"
"
],
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's draw the predictions. The output of the `model.predict(x)` function will be the mean and variance of the GPR fit.\n",
"\n",
"To get predictions for 95% Confedence Level (CL) you should use\n",
"```python\n",
"mu, var = model.predict(x)\n",
"mu_max = mu + 1.96*sqrt(var)\n",
"mu_min = mu - 1.96*sqrt(var)\n",
"```\n"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"
"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x = np.atleast_2d(np.linspace(-4, 4, 200)).T\n",
"#model.plot(plot_density=False) # set density to True for density plot\n",
"y_pred, variance = model.predict(x)\n",
"sigma = np.sqrt(variance)\n",
"fig=plt.figure(figsize=(10,10))\n",
"plt.plot(x, y_pred, 'k', linewidth=4, label='mean predicted')\n",
"plt.fill(np.concatenate([x, x[::-1]]),\n",
" np.concatenate([y_pred - 1.9600 * sigma,\n",
" (y_pred + 1.9600 * sigma)[::-1]]),\n",
" alpha=.5, fc='b', ec='None', label='95% confidence interval') \n",
"plt.plot(x,np.sin(x),'k:',linewidth=4, label=r'$f(x) = \\sin(x)$') \n",
"plt.plot(X, y, 'r.', markersize=10, label='Sampled data')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see, the process generates outputs just right. Let's see if GP can figure out itself when we try to fit it into noise or signal.\n",
"\n",
"Generate two datasets: sinusoid wihout noise and samples from gaussian noise. Optimize kernel parameters and submit optimal values of noise component. Generate data only using ```generate_points(n, noise_variance)``` and ```generate_noise(n, noise_variance)``` function!"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
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