diff --git a/Basic statistics (sol.).ipynb b/0 Basic statistics (sol.).ipynb similarity index 100% rename from Basic statistics (sol.).ipynb rename to 0 Basic statistics (sol.).ipynb diff --git a/Basic statistics.ipynb b/0 Basic statistics.ipynb similarity index 100% rename from Basic statistics.ipynb rename to 0 Basic statistics.ipynb diff --git a/CLT.ipynb b/0 CLT.ipynb similarity index 100% rename from CLT.ipynb rename to 0 CLT.ipynb diff --git a/Representation Learning.ipynb b/2.1 Representation Learning.ipynb similarity index 100% rename from Representation Learning.ipynb rename to 2.1 Representation Learning.ipynb diff --git a/Supervised Regression.ipynb b/3.1 Supervised Regression.ipynb similarity index 100% rename from Supervised Regression.ipynb rename to 3.1 Supervised Regression.ipynb diff --git a/Regression Uncertainties.ipynb b/3.2 Regression Uncetainties.ipynb similarity index 100% rename from Regression Uncertainties.ipynb rename to 3.2 Regression Uncetainties.ipynb diff --git a/Mixture Models.ipynb b/7 Mixture Models.ipynb similarity index 100% rename from Mixture Models.ipynb rename to 7 Mixture Models.ipynb diff --git a/Bayesian fits.ipynb b/Bayesian fits.ipynb deleted file mode 100644 index d0cbfe6..0000000 --- a/Bayesian fits.ipynb +++ /dev/null @@ -1,284 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "1bba0128", - "metadata": {}, - "source": [ - "# Bayesian fits\n", - "\n", - "This is a notebook showing a visualization of a Byesian interpretation for the line fit.\n", - "The idea is that we generate all possible line fits and reject them if they are not compatible with the data.\n", - "Naturally, this is not how most fits are done, but it illustrates the logic behind the Bayes Theorem when applied for fitting lines.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "23feddde", - "metadata": {}, - "outputs": [], - "source": [ - "from typing import Tuple\n", - "\n", - "import pandas as pd\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n" - ] - }, - { - "cell_type": "markdown", - "id": "bb1286f0", - "metadata": {}, - "source": [ - "We start by generating some fake dataset, which is simple enough that we can visualize the results easily. For this reason, the dataset will contain only two variables.\n", - "\n", - "The simulated example data will be $f(x) = 2 x + 1 + \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(\\mu=0, \\sigma=0.5)$.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "aef54435-78af-4b13-aee2-2bc576c773cd", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "true_alpha = 0.3\n", - "true_beta = 0.5\n", - "true_eps = 0.5\n", - "def generate_data(N: int) -> np.ndarray:\n", - " x = 2*np.random.randn(N, 1)\n", - " epsilon = true_eps*np.random.randn(N, 1)\n", - " z = true_beta*x + true_alpha + epsilon\n", - " return np.concatenate((x, z), axis=1).astype(np.float32)\n", - "\n", - "data = generate_data(N=100)" - ] - }, - { - "cell_type": "markdown", - "id": "04432613-39cd-4209-8833-7af585e7eed9", - "metadata": {}, - "source": [ - "Given some parameters $\\alpha$ and $\\beta$, we don't know the true $f(x)$, but we assume it is something like $f(x) = \\beta x + \\alpha$." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "a795239a-03eb-483a-8b07-635e3d9dbc55", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def f(x: np.ndarray, alpha: float, beta: float) -> np.ndarray:\n", - " return beta*x + alpha" - ] - }, - { - "cell_type": "markdown", - "id": "a2fba887-dc1a-4400-ab40-59fec452dc83", - "metadata": {}, - "source": [ - "Let's plot it for reference:" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "id": "fead461d-4d3a-48f2-a525-c518be4f1cf8", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig = plt.figure(figsize=(8, 6))\n", - "plt.scatter(data[:,0], data[:,1], label=r\"Data $\\mathcal{D}$\")\n", - "plt.plot(data[:,0], f(data[:,0], true_alpha, true_beta), c='r', ls='-', alpha=0.5, lw=4, label=r\"True $y=\\beta x + \\alpha$\")\n", - "xs = np.linspace(-2, 2, 10)\n", - "plt.plot(xs, f(xs, true_alpha, true_beta) - 2*true_eps, c='r', ls='--', alpha=0.5, lw=4)\n", - "plt.plot(xs, f(xs, true_alpha, true_beta) + 2*true_eps, c='r', ls='--', alpha=0.5, lw=4)\n", - "xa = 2\n", - "ya = f(xa, true_alpha, true_beta)\n", - "plt.annotate(xy=(xa, ya + 2*true_eps), xytext=(xa, ya - 2*true_eps), arrowprops=dict(arrowstyle='|-|', lw=3, alpha=0.5, color=\"green\"), text=r\"\")\n", - "plt.text(xa+0.5, ya, s=r\"$\\epsilon$ noise\", size=16)\n", - "plt.legend(frameon=False)\n", - "plt.savefig(\"data.png\")" - ] - }, - { - "cell_type": "markdown", - "id": "00e098e8-0082-4451-927a-073cf242787e", - "metadata": {}, - "source": [ - "Let's show several random lines and reject the ones that do not agree with the likelihood:" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "id": "08d9daaf-25c5-4d06-b4a6-6cecaaa35651", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import matplotlib.pylab as pylab\n", - "params = {'legend.fontsize': 'x-large',\n", - " 'figure.figsize': (15, 5),\n", - " 'axes.labelsize': 'x-large',\n", - " 'axes.titlesize':'x-large',\n", - " 'xtick.labelsize':'x-large',\n", - " 'ytick.labelsize':'x-large'}\n", - "pylab.rcParams.update(params)" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "id": "4c7002b2-5cb5-4929-8e01-964144ee60b6", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "def get_log_prior(A, B):\n", - " #return 0.25*A/A/1/5\n", - " return -0.5*A**2/1**2 - 0.5*B**2/1**2 #- (2*np.pi*p_width**2)\n", - "def sample_prior() -> Tuple[float, float]:\n", - " #return (2*np.random.rand() - 1)*1, (2*np.random.rand() - 1)*5\n", - " return 1*np.random.randn(), 1*np.random.randn()\n", - "def get_log_likelihood(x, y, A, B, sigma):\n", - " error = f(x, A, B) - y\n", - " return np.sum(-0.5*error**2/sigma**2, axis=0) # - (2*np.pi*sigma**2)\n", - "def plot(I: int):\n", - " # how many lines to show in last column\n", - " K = 20\n", - " # assumed noise std. dev.\n", - " sigma=0.5\n", - " # region of alpha and beta to plot\n", - " R = 4\n", - " # take a subset of data points\n", - " D = data[:I,:]\n", - " # make plot\n", - " fig, ax = plt.subplots(figsize=(4*5, 4), ncols=4)\n", - " # create alpha and beta grid\n", - " A = np.linspace(-R, R, 50)\n", - " B = np.linspace(-R, R, 50)\n", - " A, B = np.meshgrid(A, B)\n", - " \n", - " # calculate the log prior\n", - " log_prior = get_log_prior(A, B)\n", - " # calculate the log likelihood\n", - " log_likelihood = get_log_likelihood(D[:, 0, np.newaxis, np.newaxis],\n", - " D[:, 1, np.newaxis, np.newaxis],\n", - " A[np.newaxis, ...],\n", - " B[np.newaxis, ...],\n", - " sigma=sigma)\n", - " # the log posterior is, except for a constant factor, just the sum of those\n", - " log_posterior = log_prior + log_likelihood\n", - "\n", - " m=ax[0].imshow(np.exp(log_prior), extent=(-R, R, -R, R), aspect=\"equal\")\n", - " #plt.colorbar(m,ax=ax[0], orientation=\"horizontal\")\n", - " ax[0].set(xlabel=r\"$\\alpha$\", ylabel=r\"$\\beta$\", title=r\"$p(\\alpha, \\beta)$\")\n", - " \n", - " m=ax[1].imshow(np.exp(log_likelihood), extent=(-R, R, -R, R), aspect=\"equal\")\n", - " #plt.colorbar(m,ax=ax[1], orientation=\"horizontal\")\n", - " \n", - " ax[1].set(xlabel=r\"$\\alpha$\", ylabel=r\"$\\beta$\", title=r\"$p(\\mathcal{D}|\\alpha,\\beta)$\")\n", - " m=ax[2].imshow(np.exp(log_posterior), extent=(-R, R, -R, R), aspect=\"equal\")\n", - " #plt.colorbar(m,ax=ax[2], orientation=\"horizontal\")\n", - " ax[2].set(xlabel=r\"$\\alpha$\", ylabel=r\"$\\beta$\", title=r\"$p(\\alpha, \\beta|\\mathcal{D})$\")\n", - "\n", - " if I > 0:\n", - " ax[3].scatter(D[:, 0], D[:,1], label=\"Data\")\n", - " ax[3].set(xlabel=\"x\", ylabel=\"y\", title=\"Data\", xlim=(-5, 5), ylim=(-5, 5))\n", - "\n", - " # sample alpha and beta\n", - " def get_line():\n", - " a, b = sample_prior()\n", - " if len(D) == 0:\n", - " return a, b\n", - " for _ in range(1000):\n", - " ap, bp = a + 0.1*np.random.randn(), b + 0.1*np.random.randn()\n", - " A = min(1, np.exp(get_log_likelihood(D[:, 0], D[:, 1], ap, bp, sigma=sigma) - get_log_likelihood(D[:, 0], D[:, 1], a, b, sigma=sigma) ))\n", - " if np.random.rand() <= A:\n", - " a = ap\n", - " b = bp\n", - " return a, b\n", - " for _ in range(K):\n", - " a, b = get_line()\n", - " ax[3].axline((0, a), slope=b, lw=2, ls='-', c='r', alpha=0.5)\n", - " #plt.legend(frameon=False)\n", - " plt.tight_layout()\n", - " plt.savefig(f\"bayes_reg_{I}.png\")" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "id": "693827d3-c5ac-4b6d-b019-233799cd5d78", - "metadata": { - "tags": [] - }, - "outputs": [ - { - 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plot(I=7)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a1fbd00b-e7f2-4eff-90db-e1d44d104fba", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/Gaussian Processes.ipynb b/Gaussian Processes.ipynb deleted file mode 100644 index e2e5ef5..0000000 --- a/Gaussian Processes.ipynb +++ /dev/null @@ -1,667 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "6a764d92", - "metadata": {}, - "source": [ - "# Gaussian Processes\n", - "\n", - "If one is ready to assume the data available is such that the variable being fit is Gaussian for any pair of samples taken, one can use fit the data and obtain a reliable uncertainty with a very small set of assumptions.\n", - "\n", - "For this example, we will use the dataset collected in Mauna Loa showing the amount of CO2 present in the atmosphere. This data may be downloaded from https://gml.noaa.gov/ccgg/trends/data.html and it should already be available in this repository.\n" - ] - }, - { - "cell_type": "markdown", - "id": "c8131588", - "metadata": {}, - "source": [ - "We can take a quick look at the file to see what is inside:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "07ecc0d3", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "# --------------------------------------------------------------------\n", - "# USE OF NOAA GML DATA\n", - "# \n", - "# These data are made freely available to the public and the\n", - "# scientific community in the belief that their wide dissemination\n", - "# will lead to greater understanding and new scientific insights.\n", - "# The availability of these data does not constitute publication\n", - "# of the data. NOAA relies on the ethics and integrity of the user to\n", - "# ensure that GML receives fair credit for their work. If the data \n", - "# are obtained for potential use in a publication or presentation, \n", - "# GML should be informed at the outset of the nature of this work. \n", - "# If the GML data are essential to the work, or if an important \n", - "# result or conclusion depends on the GML data, co-authorship\n", - "# may be appropriate. This should be discussed at an early stage in\n", - "# the work. Manuscripts using the GML data should be sent to GML\n", - "# for review before they are submitted for publication so we can\n", - "# ensure that the quality and limitations of the data are accurately\n", - "# represented.\n", - "# \n", - "# Contact: Pieter Tans (303 497 6678; pieter.tans@noaa.gov)\n", - "# \n", - "# File Creation: Fri Jan 21 05:00:12 2022\n", - "# \n", - "# RECIPROCITY\n", - "# \n", - "# Use of these data implies an agreement to reciprocate.\n", - "# Laboratories making similar measurements agree to make their\n", - "# own data available to the general public and to the scientific\n", - "# community in an equally complete and easily accessible form.\n", - "# Modelers are encouraged to make available to the community,\n", - "# upon request, their own tools used in the interpretation\n", - "# of the GML data, namely well documented model code, transport\n", - "# fields, and additional information necessary for other\n", - "# scientists to repeat the work and to run modified versions.\n", - "# Model availability includes collaborative support for new\n", - "# users of the models.\n", - "# --------------------------------------------------------------------\n", - "# \n", - "# \n", - "# See www.esrl.noaa.gov/gmd/ccgg/trends/ for additional details.\n", - "# \n", - "# NOTE: DATA FOR THE LAST SEVERAL MONTHS ARE PRELIMINARY, ARE STILL SUBJECT\n", - "# TO QUALITY CONTROL PROCEDURES.\n", - "# NOTE: The week \"1 yr ago\" is exactly 365 days ago, and thus does not run from\n", - "# Sunday through Saturday. 365 also ignores the possibility of a leap year.\n", - "# The week \"10 yr ago\" is exactly 10*365 days +3 days (for leap years) ago.\n", - "# \n", - "# Start of week CO2 molfrac (-999.99 = no data) increase\n", - "# (yr, mon, day, decimal) (ppm) #days 1 yr ago 10 yr ago since 1800\n", - " 1974 5 19 1974.3795 333.37 5 -999.99 -999.99 50.40\n", - " 1974 5 26 1974.3986 332.95 6 -999.99 -999.99 50.06\n", - " 1974 6 2 1974.4178 332.35 5 -999.99 -999.99 49.60\n", - " 1974 6 9 1974.4370 332.20 7 -999.99 -999.99 49.65\n", - " 1974 6 16 1974.4562 332.37 7 -999.99 -999.99 50.06\n", - " 1974 6 23 1974.4753 331.73 5 -999.99 -999.99 49.72\n", - " 1974 6 30 1974.4945 331.68 6 -999.99 -999.99 50.02\n", - " 1974 7 7 1974.5137 331.46 6 -999.99 -999.99 50.20\n", - " 1974 7 14 1974.5329 330.83 5 -999.99 -999.99 50.01\n", - " 1974 7 21 1974.5521 330.76 7 -999.99 -999.99 50.41\n", - " 1974 7 28 1974.5712 329.80 4 -999.99 -999.99 49.97\n", - " 1974 8 4 1974.5904 329.85 5 -999.99 -999.99 50.54\n" - ] - } - ], - "source": [ - "with open(\"co2_weekly_mlo.txt\", \"r\") as f:\n", - " for i, line in enumerate(f.readlines()):\n", - " if i > 60: # let's print only the first 60 lines only\n", - " break\n", - " print(line[:-1])" - ] - }, - { - "cell_type": "markdown", - "id": "fce4d8e8", - "metadata": {}, - "source": [ - "We start by loading the necessary Python modules." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "300cf8d3", - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "import pandas as pd\n", - "import numpy as np\n", - "from sklearn.gaussian_process import GaussianProcessRegressor\n", - "from sklearn.gaussian_process.kernels import RBF, ExpSineSquared, WhiteKernel, RationalQuadratic" - ] - }, - { - "cell_type": "markdown", - "id": "0ecd6a69", - "metadata": {}, - "source": [ - "Let us now load the data downloaded using pandas. If you are not familiar with Pandas, take a look at the documentation for a quick introduction at https://pandas.pydata.org/docs/user_guide/10min.html\n", - "\n", - "We can easily parse the data file using Pandas' read_csv function. It would require some coding to do it manually. As Pandas does not detect the column names, we have to specify it manually in the names parameter below." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "4959a292", - "metadata": {}, - "outputs": [], - "source": [ - "data = pd.read_csv(\"co2_weekly_mlo.txt\",\n", - " delim_whitespace=True,\n", - " comment='#',\n", - " header=None,\n", - " names=[\"year\", \"month\", \"day\", \"decimal\",\n", - " \"co2\",\n", - " \"ndays\",\n", - " \"last_year\", \"last_decade\",\n", - " \"increase\"])" - ] - }, - { - "cell_type": "markdown", - "id": "d8295e8a", - "metadata": {}, - "source": [ - "Let's print out the dataset read first." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "024fb65a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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yearmonthdaydecimalco2ndayslast_yearlast_decadeincrease
019745191974.3795333.375-999.99-999.9950.40
119745261974.3986332.956-999.99-999.9950.06
21974621974.4178332.355-999.99-999.9949.60
31974691974.4370332.207-999.99-999.9949.65
419746161974.4562332.377-999.99-999.9950.06
..............................
2482202112122021.9466416.457414.00392.19137.16
2483202112192021.9658417.496414.86392.54137.93
2484202112262021.9849417.467415.32392.43137.66
24852022122022.0041417.436415.44393.18137.40
24862022192022.0233418.337415.06393.99138.10
\n", - "

2487 rows × 9 columns

\n", - "
" - ], - "text/plain": [ - " year month day decimal co2 ndays last_year last_decade \n", - "0 1974 5 19 1974.3795 333.37 5 -999.99 -999.99 \\\n", - "1 1974 5 26 1974.3986 332.95 6 -999.99 -999.99 \n", - "2 1974 6 2 1974.4178 332.35 5 -999.99 -999.99 \n", - "3 1974 6 9 1974.4370 332.20 7 -999.99 -999.99 \n", - "4 1974 6 16 1974.4562 332.37 7 -999.99 -999.99 \n", - "... ... ... ... ... ... ... ... ... \n", - "2482 2021 12 12 2021.9466 416.45 7 414.00 392.19 \n", - "2483 2021 12 19 2021.9658 417.49 6 414.86 392.54 \n", - "2484 2021 12 26 2021.9849 417.46 7 415.32 392.43 \n", - "2485 2022 1 2 2022.0041 417.43 6 415.44 393.18 \n", - "2486 2022 1 9 2022.0233 418.33 7 415.06 393.99 \n", - "\n", - " increase \n", - "0 50.40 \n", - "1 50.06 \n", - "2 49.60 \n", - "3 49.65 \n", - "4 50.06 \n", - "... ... \n", - "2482 137.16 \n", - "2483 137.93 \n", - "2484 137.66 \n", - "2485 137.40 \n", - "2486 138.10 \n", - "\n", - "[2487 rows x 9 columns]" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "data" - ] - }, - { - "cell_type": "markdown", - "id": "1c178424", - "metadata": {}, - "source": [ - "We can plot this fairly easily using Matplotlib." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "e63b38c5", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(figsize=(8, 8))\n", - "data.plot(x=\"decimal\", y=\"co2\", legend=False, ax=ax)\n", - "ax.set(xlabel=\"Time [years]\", ylabel=r\"CO$_2$ [ppm]\", title=\"Atmospheric CO$_2$ concentration in Mauna Loa\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "efd249fe", - "metadata": {}, - "source": [ - "The spikes are related to missing data. We can clean those up and plot again." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "0837b3ff", - "metadata": {}, - "outputs": [], - "source": [ - "data = data[data.co2 > -999]" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "333581b5", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(figsize=(8, 8))\n", - "data.plot(x=\"decimal\", y=\"co2\", legend=False, ax=ax)\n", - "ax.set(xlabel=\"Time [years]\", ylabel=r\"CO$_2$ [ppm]\", title=\"Atmospheric CO$_2$ concentration in Mauna Loa\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "c62fd7f3", - "metadata": {}, - "source": [ - "That's better.\n", - "\n", - "We can now try to model this behaviour with Gaussian Processes. The key parameter we must choose is the covariance matrix analytic form, which establishes how correlated two points in the time axis are.\n", - "\n", - "One simple assumption would be that two values of the CO2 concentration are highly correlated they happened at close by times. We use a Gaussian-based model (named here \"Radial Basis Function\", as this does not refer to a probability distribution) to establish that if two points are one year apart they are likely to be highly correlated.\n", - "\n", - "Additionally, we assume that there is a correlation between points within certain period, since we know that data from the same season in an year is expected to be correlated to data if that same season in the year (ie: CO$_2$ emissions have a rough periodicity of one year due to the season changes).\n", - "\n", - "Another term of the covariance matrix must be related to the random noise appearing in the data.\n", - "\n", - "All those assumptions can be motivated by an analysis of the covariance matrix of the data. That is, we can take the covariance matrix of all the data points and analyse it to establish whether our assumptions here are valid or not. A very long and detailed explanation on this point can be found in Bishop (2006), which has a very pedagogical chapter on Gaussian Processes. Online resources can be found on: http://www.gaussianprocess.org/\n", - "\n", - "Note that all of those are very strong assumptions, but they are made directly on the covariance matrix of the fit function. The actual numbers used below are taken from an example, but they will be optimized in the fit below (unless explicitly asked not to).\n", - "\n", - "Note: this notebook is a simplified example with extra explanations, with lots of material taken from https://scikit-learn.org/stable/auto_examples/gaussian_process/plot_gpr_co2.html -- take a look at the original example for more details.\n", - "\n", - "We also assume the data within an year from each other is highly correlated and should show a periodicity of 1 year." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "a31d7eca", - "metadata": {}, - "outputs": [], - "source": [ - "# Kernel with parameters given in GPML book\n", - "\n", - "# these hyper parameters are optimised in the GP fit\n", - "# we provide here only a starting value\n", - "\n", - "# Kernel with optimized parameters\n", - "k1 = 50.0 ** 2 * RBF(length_scale=50.0) # long term smooth rising trend\n", - "k2 = (\n", - " 2.0 ** 2\n", - " * RBF(length_scale=100.0)\n", - " * ExpSineSquared(length_scale=1.0, periodicity=1.0, periodicity_bounds=\"fixed\")\n", - ") # seasonal component\n", - "# medium term irregularities\n", - "k3 = 0.5 ** 2 * RationalQuadratic(length_scale=1.0, alpha=1.0)\n", - "k4 = 0.1 ** 2 * RBF(length_scale=0.1) + WhiteKernel(\n", - " noise_level=0.1 ** 2, noise_level_bounds=(1e-5, np.inf)\n", - ") # noise terms\n", - "kernel = k1 + k2 + k3 + k4" - ] - }, - { - "cell_type": "markdown", - "id": "0ad8ddf0", - "metadata": {}, - "source": [ - "The kernel hyper-parameters are:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "032ada0d", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "50**2 * RBF(length_scale=50) + 2**2 * RBF(length_scale=100) * ExpSineSquared(length_scale=1, periodicity=1) + 0.5**2 * RationalQuadratic(alpha=1, length_scale=1) + 0.1**2 * RBF(length_scale=0.1) + WhiteKernel(noise_level=0.01)\n" - ] - } - ], - "source": [ - "print(kernel)" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "4412a9a7", - "metadata": {}, - "outputs": [], - "source": [ - "gp = GaussianProcessRegressor(kernel=kernel, normalize_y=True)\n", - "time = data.decimal.to_numpy()[:, np.newaxis]\n", - "co2 = data.co2.to_numpy()[:, np.newaxis]\n", - "gp = gp.fit(time, co2)" - ] - }, - { - "cell_type": "markdown", - "id": "eb69bb80", - "metadata": {}, - "source": [ - "These are the hyper-parameters after the fit and the log-likelihood given the data:" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "667db862", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "GPML kernel: 3.19**2 * RBF(length_scale=42.7) + 0.114**2 * RBF(length_scale=174) * ExpSineSquared(length_scale=1.31, periodicity=1) + 0.295**2 * RationalQuadratic(alpha=0.000879, length_scale=6.84) + 0.0101**2 * RBF(length_scale=0.0188) + WhiteKernel(noise_level=0.00014)\n", - "Log-marginal-likelihood: 6660.284\n" - ] - } - ], - "source": [ - "print(\"GPML kernel: %s\" % gp.kernel_)\n", - "print(\"Log-marginal-likelihood: %.3f\" % gp.log_marginal_likelihood(gp.kernel_.theta))" - ] - }, - { - "cell_type": "markdown", - "id": "4968439e", - "metadata": {}, - "source": [ - "Now we can use the fit model to predict how the CO2 concentration will evolve at other times." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "ef6b7762", - "metadata": {}, - "outputs": [], - "source": [ - "new_time = np.linspace(time.min(), time.max()+20, 1000)[:, np.newaxis]\n", - "co2_pred, co2_std = gp.predict(new_time, return_std=True)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "5b263358", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(figsize=(8, 8))\n", - "ax.scatter(time, co2, color='red', marker='.', label=\"Data\")\n", - "ax.fill_between(new_time[:,0],\n", - " co2_pred - co2_std,\n", - " co2_pred + co2_std,\n", - " color=\"b\",\n", - " alpha=0.4,\n", - " label=\"Predictions\")\n", - "ax.set(xlabel=\"Time [years]\", ylabel=r\"CO$_2$ [ppm]\", title=\"Atmospheric CO$_2$ concentration in Mauna Loa\")\n", - "ax.legend(frameon=False, loc=\"lower right\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "b625b695", - "metadata": {}, - "source": [ - "Many more details on the kernel selection as well as further details in this example can be seen in the following references:\n", - "\n", - "https://scikit-learn.org/stable/auto_examples/gaussian_process/plot_gpr_co2.html\n", - "\n", - "https://scikit-learn.org/stable/auto_examples/gaussian_process/plot_gpr_noisy_targets.html#sphx-glr-auto-examples-gaussian-process-plot-gpr-noisy-targets-py\n", - "\n", - "To read more on Gaussian Processes:\n", - "\n", - "http://www.gaussianprocess.org/gpml/chapters/RW.pdf" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6d44d78a", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/Line fits (sol.).ipynb b/Line fits (sol.).ipynb deleted file mode 100644 index ed413ab..0000000 --- a/Line fits (sol.).ipynb +++ /dev/null @@ -1,199 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "1bba0128", - "metadata": {}, - "source": [ - "# Simple fits\n", - "\n", - "Here we are fitting a line from scratch.\n", - "In the next notebook, we will do fancier fits with neural networks, but let's start with a basic problem and complicate it as we go along.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "23feddde", - "metadata": {}, - "outputs": [], - "source": [ - "from typing import Tuple\n", - "\n", - "import pandas as pd\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n" - ] - }, - { - "cell_type": "markdown", - "id": "bb1286f0", - "metadata": {}, - "source": [ - "We start by generating some fake dataset, which is simple enough that we can visualize the results easily. For this reason, the dataset will contain only two variables.\n", - "\n", - "The simulated example data will be $f(x) = 3 x + \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(\\mu=0, \\sigma=0.5)$.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "5d457cd8", - "metadata": {}, - "outputs": [], - "source": [ - "def generate_data(N: int) -> np.ndarray:\n", - " x = 2*np.random.randn(N, 1)\n", - " epsilon = 0.5*np.random.randn(N, 1)\n", - " z = 3*x + epsilon\n", - " return np.concatenate((x, z), axis=1).astype(np.float32)\n", - "\n", - "data = generate_data(N=1000)" - ] - }, - { - "cell_type": "markdown", - "id": "48433f6f", - "metadata": {}, - "source": [ - "We can fit this line from scratch, assuming $y = f(x) = \\beta x + \\alpha + \\epsilon$, where $\\epsilon$ is a zero-mean Gaussian noise." - ] - }, - { - "cell_type": "markdown", - "id": "6a170344-34ff-4af6-9a6c-daa44b95408e", - "metadata": {}, - "source": [ - "We can do this in two ways. In both cases, we start assuming the knowledge of $f(x)$ and use the Bayes Theorem:\n", - "\n", - "$ p(\\alpha, \\beta|\\mathcal{D}) \\, \\propto p(\\mathcal{D}|\\alpha, \\beta) \\, p(\\alpha) \\, p(\\beta)$\n", - "\n", - "We assume $p(\\alpha)$ and $p(\\beta)$ are constants, so we just need to maximize the likelihood $p(\\mathcal{D}|\\alpha, \\beta)$.\n", - "That likelihood is a Gaussian distribution, because we assumed $y$ is exactly equals to a line plus some Gaussian noise coming from $\\epsilon$.\n", - "\n", - "$p(\\alpha,\\beta|\\mathcal{D}) \\propto \\prod \\mathcal{N}(y_i|\\text{mean}=f(x_i), \\text{std. dev.}=\\sigma_\\epsilon)$\n", - "\n", - "This leads to minimizing $L = \\sum_i (y_i - \\beta x_i - \\alpha)^2$, as seen in the lecture (simply take $- \\log p$ and to maximize $p$, one has to minimize $-\\log p$).\n", - "\n", - "We can try finding out $\\beta$ and $\\alpha$ by taking the derivative of $L$ and setting it to zero:\n", - "\n", - "$\\frac{d L}{d\\beta} = 2 \\sum_i (y_i - \\beta x_i - \\alpha) x_i = 0$\n", - "\n", - "$\\frac{d L}{d\\alpha} = -2 \\sum_i (y_i - \\beta x_i - \\alpha) = 0$\n", - "\n", - "Re-arranging:\n", - "\n", - "$2 \\sum_i (y_i x_i - \\beta x_i^2 - \\alpha x_i) = 0$\n", - "\n", - "$2 \\sum_i (y_i - \\beta x_i - \\alpha) = 0$\n", - "\n", - "This leads to:\n", - "\n", - "$ \\beta \\sum_i x_i^2 = \\sum_i (y_i - \\alpha) x_i$\n", - "\n", - "$ \\alpha = 1/N \\sum_i y_i - \\beta x_i = \\mathbb{E}[y - \\beta x]$\n", - "\n", - "We can then substitute $\\alpha$ in $\\beta$:\n", - "\n", - "$ \\beta \\sum_i x_i^2 = \\sum_i y_i x_i - 1/N \\sum_i \\sum_j (y_j - \\beta x_j) x_i$\n", - "\n", - "And expand it:\n", - "\n", - "$ \\beta (\\sum_i x_i^2 - 1/N \\sum_i \\sum_j x_i x_j) = \\sum_i y_i x_i - 1/N \\sum_i \\sum_j y_j x_i$\n", - "\n", - "Taking $x_j$ from a sum that does not depend on $j$, we see that the second term is just the square of the sum over $x_i$:\n", - "\n", - "$ \\beta (\\sum_i x_i^2 - 1/N(\\sum_{i} x_i)^2 ) = \\sum_i y_i x_i - 1/N \\sum_i \\sum_j y_j x_i$\n", - "\n", - "Dividing by the number of points $N$, several sums reduce to averages, which make this much easier to interpret if we use some standard identities from statistics.\n", - "For example $1/N \\sum_i x_i^2 - 1/N^2 (\\sum_i x_i)^2$ is a known expression for the variance of $X$. \n", - "\n", - "$ \\beta \\text{var}[X] = \\mathbb{E}[XY] - \\mathbb{E}[X]\\mathbb{E}[Y]$\n", - "\n", - "And the right-hand-side is a known expression for the covariance between $X$ and $Y$:\n", - "\n", - "$ \\beta \\text{var}[X] = \\text{cov}[X,Y]$\n", - "\n", - "This leads to:\n", - "\n", - "$\\beta = \\frac{\\text{cov}[X,Y]}{\\text{var}[X]}$\n", - "\n", - "This, together with the expression from above for $\\alpha$, allows us to easily fit a line in a few lines of code:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "30205402", - "metadata": {}, - "outputs": [], - "source": [ - "cov = np.cov(data[:,0], data[:,1])[0,1]\n", - "varX = np.std(data[:,0])**2\n", - "beta = cov/varX\n", - "alpha = np.mean(data[:,1] - beta*data[:,0])" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "cabdfc12-3033-4a2f-96ed-4ab1ea8312ab", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.scatter(data[:,0], data[:,1])\n", - "plt.axline((0, alpha), slope=beta, c='r', lw=2, ls='--', label=\"Line fit\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a1fbd00b-e7f2-4eff-90db-e1d44d104fba", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/Line fits.ipynb b/Line fits.ipynb deleted file mode 100644 index fe6ac73..0000000 --- a/Line fits.ipynb +++ /dev/null @@ -1,104 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "1bba0128", - "metadata": {}, - "source": [ - "# Simple fits\n", - "\n", - "Here we are fitting a line from scratch.\n", - "In the next notebook, we will do fancier fits with neural networks, but let's start with a basic problem and complicate it as we go along.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "23feddde", - "metadata": {}, - "outputs": [], - "source": [ - "from typing import Tuple\n", - "\n", - "import pandas as pd\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n" - ] - }, - { - "cell_type": "markdown", - "id": "bb1286f0", - "metadata": {}, - "source": [ - "We start by generating some fake dataset, which is simple enough that we can visualize the results easily. For this reason, the dataset will contain only two variables.\n", - "\n", - "The simulated example data will be $f(x) = 3 x + \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(\\mu=0, \\sigma=0.5)$.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "5d457cd8", - "metadata": {}, - "outputs": [], - "source": [ - "def generate_data(N: int) -> np.ndarray:\n", - " x = 2*np.random.randn(N, 1)\n", - " epsilon = 0.5*np.random.randn(N, 1)\n", - " z = 3*x + epsilon\n", - " return np.concatenate((x, z), axis=1).astype(np.float32)\n", - "\n", - "data = generate_data(N=1000)" - ] - }, - { - "cell_type": "markdown", - "id": "48433f6f", - "metadata": {}, - "source": [ - "We can fit this line from scratch, assuming $y = f(x) = \\beta x + \\alpha + \\epsilon$, where $\\epsilon$ is a zero-mean Gaussian noise.\n", - "\n", - "How would you do it? Feel free to use standard Python modules. Look at the solution for a simple mathematical expression for this fit with a full derivation.\n", - "\n", - "Tip: Look for the documentation for `numpy.linalg.lstsq`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "85040eef-3558-4531-9bce-4f29d520f86b", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "5e9170af-ca77-4526-b3d2-e19e77fef44e", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/bayes_reg_0.png b/bayes_reg_0.png deleted file mode 100644 index d32122c..0000000 Binary files a/bayes_reg_0.png and /dev/null differ diff --git a/bayes_reg_1.png b/bayes_reg_1.png deleted file mode 100644 index 7e9c1e2..0000000 Binary files a/bayes_reg_1.png and /dev/null differ diff --git a/bayes_reg_2.png b/bayes_reg_2.png deleted file mode 100644 index 697f673..0000000 Binary files a/bayes_reg_2.png and /dev/null differ diff --git a/bayes_reg_3.png b/bayes_reg_3.png deleted file mode 100644 index ee46352..0000000 Binary files a/bayes_reg_3.png and /dev/null differ diff --git a/data.png b/data.png deleted file mode 100644 index 54f89be..0000000 Binary files a/data.png and /dev/null differ