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W1D2_Tutorial3
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| { | |
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| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "view-in-github", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "<a href=\"https://colab.research.google.com/gist/xanderladd/f062a8571bc7bc1267fedd4e24a157f8/w1d2_tutorial3.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
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| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "w3ov5M9L4xNd" | |
| }, | |
| "source": [ | |
| "# Tutorial 3: Confidence intervals and bootstrapping\n", | |
| "\n", | |
| "**Week 1, Day 2: Model Fitting**\n", | |
| "\n", | |
| "**By Neuromatch Academy**\n", | |
| "\n", | |
| "**Content creators**: Pierre-Étienne Fiquet, Anqi Wu, Alex Hyafil with help from Byron Galbraith\n", | |
| "\n", | |
| "**Content reviewers**: Lina Teichmann, Saeed Salehi, Patrick Mineault, Ella Batty, Michael Waskom" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "gyZFJFkf4xNg" | |
| }, | |
| "source": [ | |
| "<p align='center'><img src='https://github.com/NeuromatchAcademy/widgets/blob/master/sponsors.png?raw=True'/></p>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "XU6F-oOM4xNg" | |
| }, | |
| "source": [ | |
| "# Tutorial Objectives\n", | |
| "\n", | |
| "*Estimated timing of tutorial: 23 minutes*\n", | |
| "\n", | |
| "This is Tutorial 3 of a series on fitting models to data. We start with simple linear regression, using least squares optimization (Tutorial 1) and Maximum Likelihood Estimation (Tutorial 2). We will use bootstrapping to build confidence intervals around the inferred linear model parameters (Tutorial 3). We'll finish our exploration of regression models by generalizing to multiple linear regression and polynomial regression (Tutorial 4). We end by learning how to choose between these various models. We discuss the bias-variance trade-off (Tutorial 5) and Cross Validation for model selection (Tutorial 6).\n", | |
| "\n", | |
| "In this tutorial, we will discuss how to gauge how good our estimated model parameters are. \n", | |
| "- Learn how to use bootstrapping to generate new sample datasets\n", | |
| "- Estimate our model parameter on these new sample datasets\n", | |
| "- Quantify the variance of our estimate using confidence intervals" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "form", | |
| "execution": {}, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 501 | |
| }, | |
| "id": "3Rmozr-m4xNh", | |
| "outputId": "dd50f6bc-69c0-4307-aafd-1ceff5c71c51" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "<IPython.lib.display.IFrame at 0x7f1422f68590>" | |
| ], | |
| "text/html": [ | |
| "\n", | |
| " <iframe\n", | |
| " width=\"854\"\n", | |
| " height=\"480\"\n", | |
| " src=\"https://mfr.ca-1.osf.io/render?url=https://osf.io/2mkq4/?direct%26mode=render%26action=download%26mode=render\"\n", | |
| " frameborder=\"0\"\n", | |
| " allowfullscreen\n", | |
| " ></iframe>\n", | |
| " " | |
| ] | |
| }, | |
| "metadata": {}, | |
| "execution_count": 1 | |
| } | |
| ], | |
| "source": [ | |
| "# @title Tutorial slides\n", | |
| "\n", | |
| "# @markdown These are the slides for the videos in all tutorials today\n", | |
| "from IPython.display import IFrame\n", | |
| "IFrame(src=f\"https://mfr.ca-1.osf.io/render?url=https://osf.io/2mkq4/?direct%26mode=render%26action=download%26mode=render\", width=854, height=480)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "form", | |
| "execution": {}, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 581, | |
| "referenced_widgets": [ | |
| "b0c7353b26e44f3da6d0e7ff07ead131", | |
| "fb78c971a65d449bb6caa94013494eee", | |
| "aab0dda20728421cb80ad15917d7b769", | |
| "e84c30becce24898b4843519c260981b", | |
| "b6d414c465f44f5c9de00e808c64d8f9", | |
| "c01b5d558919442d842c51a65ff63e0b" | |
| ] | |
| }, | |
| "id": "qBze9tvd4xNi", | |
| "outputId": "b333ee94-b6d9-4973-e25f-141e0ad11d9d" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "Tab(children=(Output(), Output()), _titles={'0': 'Youtube', '1': 'Bilibili'})" | |
| ], | |
| "application/vnd.jupyter.widget-view+json": { | |
| "version_major": 2, | |
| "version_minor": 0, | |
| "model_id": "b0c7353b26e44f3da6d0e7ff07ead131" | |
| } | |
| }, | |
| "metadata": {} | |
| } | |
| ], | |
| "source": [ | |
| "# @title Video 1: Confidence Intervals & Bootstrapping\n", | |
| "from ipywidgets import widgets\n", | |
| "\n", | |
| "out2 = widgets.Output()\n", | |
| "with out2:\n", | |
| " from IPython.display import IFrame\n", | |
| " class BiliVideo(IFrame):\n", | |
| " def __init__(self, id, page=1, width=400, height=300, **kwargs):\n", | |
| " self.id=id\n", | |
| " src = 'https://player.bilibili.com/player.html?bvid={0}&page={1}'.format(id, page)\n", | |
| " super(BiliVideo, self).__init__(src, width, height, **kwargs)\n", | |
| "\n", | |
| " video = BiliVideo(id=\"BV1vK4y1s7py\", width=854, height=480, fs=1)\n", | |
| " print('Video available at https://www.bilibili.com/video/{0}'.format(video.id))\n", | |
| " display(video)\n", | |
| "\n", | |
| "out1 = widgets.Output()\n", | |
| "with out1:\n", | |
| " from IPython.display import YouTubeVideo\n", | |
| " video = YouTubeVideo(id=\"hs6bVGQNSIs\", width=854, height=480, fs=1, rel=0)\n", | |
| " print('Video available at https://youtube.com/watch?v=' + video.id)\n", | |
| " display(video)\n", | |
| "\n", | |
| "out = widgets.Tab([out1, out2])\n", | |
| "out.set_title(0, 'Youtube')\n", | |
| "out.set_title(1, 'Bilibili')\n", | |
| "\n", | |
| "display(out)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "ZBim9_kd4xNj" | |
| }, | |
| "source": [ | |
| "Up to this point we have been finding ways to estimate model parameters to fit some observed data. Our approach has been to optimize some criterion, either minimize the mean squared error or maximize the likelihood while using the entire dataset. How good is our estimate really? How confident are we that it will generalize to describe new data we haven't seen yet?\n", | |
| "\n", | |
| "One solution to this is to just collect more data and check the MSE on this new dataset with the previously estimated parameters. However this is not always feasible and still leaves open the question of how quantifiably confident we are in the accuracy of our model.\n", | |
| "\n", | |
| "In Section 1, we will explore how to implement bootstrapping. In Section 2, we will build confidence intervals of our estimates using the bootstrapping method." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "L0oRcYR54xNk" | |
| }, | |
| "source": [ | |
| "---\n", | |
| "# Setup" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "both", | |
| "execution": {}, | |
| "id": "ORhko3Vq4xNl" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# Imports\n", | |
| "import numpy as np\n", | |
| "import matplotlib.pyplot as plt" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "form", | |
| "execution": {}, | |
| "id": "SyvaWez74xNl" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "#@title Figure Settings\n", | |
| "%config InlineBackend.figure_format = 'retina'\n", | |
| "plt.style.use(\"https://raw.githubusercontent.com/NeuromatchAcademy/course-content/main/nma.mplstyle\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "form", | |
| "execution": {}, | |
| "id": "mp8dSOVu4xNm" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# @title Plotting Functions\n", | |
| "\n", | |
| "def plot_original_and_resample(x, y, x_, y_):\n", | |
| " \"\"\" Plot the original sample and the resampled points from this sample.\n", | |
| "\n", | |
| " Args:\n", | |
| " x (ndarray): An array of shape (samples,) that contains the input values.\n", | |
| " y (ndarray): An array of shape (samples,) that contains the corresponding\n", | |
| " measurement values to the inputs.\n", | |
| " x_ (ndarray): An array of shape (samples,) with a subset of input values from x\n", | |
| " y_ (ndarray): An array of shape (samples,) with a the corresponding subset\n", | |
| " of measurement values as x_ from y\n", | |
| "\n", | |
| " \"\"\"\n", | |
| " fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(12, 5))\n", | |
| " ax1.scatter(x, y)\n", | |
| " ax1.set(title='Original', xlabel='x', ylabel='y')\n", | |
| "\n", | |
| " ax2.scatter(x_, y_, color='c')\n", | |
| "\n", | |
| " ax2.set(title='Resampled', xlabel='x', ylabel='y',\n", | |
| " xlim=ax1.get_xlim(), ylim=ax1.get_ylim());" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "vTnx1AW74xNn" | |
| }, | |
| "source": [ | |
| "---\n", | |
| "# Section 1: Bootstrapping\n", | |
| "\n", | |
| "*Estimated timing to here from start of tutorial: 7 min*\n", | |
| "\n", | |
| "[Bootstrapping](https://en.wikipedia.org/wiki/Bootstrapping_(statistics)) is a widely applicable method to assess confidence/uncertainty about estimated parameters, it was originally [proposed](https://projecteuclid.org/euclid.aos/1176344552) by [Bradley Efron](https://en.wikipedia.org/wiki/Bradley_Efron). The idea is to generate many new synthetic datasets from the initial true dataset by randomly sampling from it, then finding estimators for each one of these new datasets, and finally looking at the distribution of all these estimators to quantify our confidence.\n", | |
| "\n", | |
| "Note that each new resampled datasets will be the same size as our original one, with the new data points sampled with replacement i.e. we can repeat the same data point multiple times. Also note that in practice we need a lot of resampled datasets, here we use 2000.\n", | |
| "\n", | |
| "To explore this idea, we will start again with our noisy samples along the line $y_i = 1.2x_i + \\epsilon_i$, but this time, we only use half the data points as last time (15 instead of 30)." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "form", | |
| "execution": {}, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 430 | |
| }, | |
| "id": "P37yxuyN4xNn", | |
| "outputId": "2cb97bcb-42a5-4fb6-d037-04857e719cb4" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "<Figure size 576x432 with 1 Axes>" | |
| ], | |
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EFgAAAICGxBYAAACAhsQWAAAAgIbEFgAAAICGxBYAAACAhsQWAAAAgIbEFgAAAICGxBYAAACAhsQWAAAAgIbGRz0AAADAYbG8vpXF1Y3cuHkrE6fG0+t2Mjc9OeqxgCNGbAEAAE68xdWNXFpYybW1zXuOnZmZysX52fS6nRFMBhxFlhEBAAAn2ovXX835K0v3DS1Jcm1tM+evLOWl668NeTLgqBJbAACAE2txdSPPXX0l2/XB523X5NmrL2dxdWM4gwFHmtgCAACcWJcWVvYMLXds1+TywspgBwKOBbEFAAA4kZbXt3ZdOrSbpbXNLK9vDWgi4LgQWwAAgBPpoEuCLCUC9iK2AAAAJ9KNm7eGeh1wcogtAADAiTRxanyo1wEnh9gCAACcSL1uZ6jXASeH2AIAAJxIc9OTOTMz9VDXnJ2Zytz05IAmAo4LsQUAADixLs7PZqzs79yxklyYnx3sQMCxILYAAAAnVq/byfPnntwzuIyV5IVzT1lCBOyLnZ0AAIAT7Zmnn8jjj53O5YWVLK1t3nP87MxULszPCi3AvoktAADAidfrdtLrdrK8vpXF1Y3cuHkrE6fG0+t27NECPDSxBQAAoG9uelJcAR6ZPVsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaGh/1AAAAABwfy+tbWVzdyI2btzJxajy9bidz05OjHguGSmwBAADgkS2ubuTSwkqurW3ec+zMzFQuzs+m1+2MYDIYPsuIAAAAeCQvXn81568s3Te0JMm1tc2cv7KUl66/NuTJYDTEFgAAAA5scXUjz119Jdv1wedt1+TZqy9ncXVjOIPBCIktAAAAHNilhZU9Q8sd2zW5vLAy2IHgEBBbAAAAOJDl9a1dlw7tZmltM8vrWwOaCA4HsQUAAIADOeiSIEuJOO7EFgAAAA7kxs1bQ70OjgqxBQAAgAOZODU+1OvgqBBbAAAAOJBetzPU6+CoEFsAAAA4kLnpyZyZmXqoa87OTGVuenJAE8HhILYAAABwYBfnZzNW9nfuWEkuzM8OdiA4BMQWAAAADqzX7eT5c0/uGVzGSvLCuacsIeJEsCsRAAAAj+SZp5/I44+dzuWFlSytbd5z/OzMVC7MzwotnBhiCwAAAI+s1+2k1+1keX0ri6sbuXHzViZOjafX7dijhRNHbAEAAKCZuelJcYUTz54tAAAAAA2JLQAAAAANiS0AAAAADYktAAAAAA2JLXsopfy5UspLpZT3l1JullI+XEr5tVLKu0spf3rU8wEAAACHi9iyi3Lbdyf5mSRfnOSJJNtJapKZJF+e5F+WUv7+6KYEAAAADhuxZXd/OcnX99//aJK5WuvpWuvpJG9J8uP9Y+8spXzhCOYDAAAADiGxZXdf1f9zNcmX1VpX7hyotf5Kbt/t8mv9j75kyLMBAAAAh5TYsrtP6//5/9Rab919sNb6+0l+of/jxNCmAgAAAA41sWV3d+5a+eOllPG7D5ZSPiHJv9//8eeGNhUAAABwqN0TEfgD/2OStyfpJnlPKeW5WutqkpRSPjPJC0k+I8mvJvkHe31ZKeV9+/idbzn4uAAAAMBhILbsotb6E6WUdyb5u0m+KMkXlVI+3D/8iUn+bW4HmW+ptf7OiMYEABiZ5fWtLK5u5MbNW5k4NZ5et5O56clRjwUAIye2PECt9V2llJUkP5DkDbkdWe54fW7v1fIpSTb38V1v2+uc/t0vbz3YtAAAw7G4upFLCyu5tnbvvwKdmZnKxfnZ9LqdEUwGAIeDPVt2UUo5XUp5Mck/SfJqks9L8of7r89L8ktJzie5Vkp5amSDAgAM0YvXX835K0v3DS1Jcm1tM+evLOWl668NeTIAODzElt19e24/0vlXkvzJWus/r7Vu9F//PMmfSrKcpJPku0Y4JwDAUCyubuS5q69kuz74vO2aPHv15SyubgxnMAA4ZMSW+yilTCb5uv6P31VrvXn3ObXWDyf5zv6Pn1NKecOw5gMAGIVLCyt7hpY7tmtyeWFlsAMBwCElttzfXD62n82vPuC8nf8GMTO4cQAARmt5fWvXpUO7WVrbzPL61oAmAoDDS2y5v+0d79/0gPOmd7z3bxIAwLF10CVBlhIBcBKJLff3y0nuPOb5a0op9zy1qZTyunxsqdFv5fbeLgAAx9KNm7eGeh0AHGViy33092P5/v6Pb03yE6WUJ0spY/3XU0l+Ksmf6J/zrlrrR0cxKwDAMEycuuf/exrodQBwlPlvv919U5LZJJ+/4/V7/WN/aMd570nybcMdDQBguHrdzlCvA4CjzJ0tu+jf3fIXknxxkh9P8utJSv/wa0n+5yTvqLV+ubtaAIDjbm56Mmdmph7qmrMzU5mbnhzQRABweLmz5QFqrTXJj/ZfAAAn2sX52Zy/srSvxz+PleTC/OzghwKAQ8idLQAA7Euv28nz557MWHnweWMleeHcU5YQAXBiubMFAIB9e+bpJ/L4Y6dzeWElS2ub9xw/OzOVC/OzQgsAJ5rYAgDAQ+l1O+l1O1le38ri6kZu3LyViVPj6XU79mgBgIgtAAAc0Nz0pLgCAPchtgAAPAJ3dwAAdxNbAAAOYHF1I5cWVnLtPvuWnJmZykX7lgDAieVpRAAAD+nF66/m/JWl+4aWJLm2tpnzV5by0vXXhjwZAHAYiC0AAA9hcXUjz119Jdv1wedt1+TZqy9ncXVjOIMBAIeG2AIA8BAuLazsGVru2K7J5YWVwQ4EABw6YgsAwD4tr2/tunRoN0trm1le3xrQRADAYSS2AADs00GXBFlKBAAni9gCALBPN27eGup1AMDRJLYAAOzTxKnxoV4HABxNYgsAwD71up2hXgcAHE1iCwDAPs1NT+bMzNRDXXN2Zipz05MDmggAOIzEFgCAh3BxfjZjZX/njpXkwvzsYAcCAA4dsQUA4CH0up08f+7JPYPLWEleOPeUJUQAcALZrQ0A4CE98/QTefyx07m8sJKltc17jp+dmcqF+VmhBQBOKLEFAOAAet1Oet1Olte3sri6kRs3b2Xi1Hh63Y49WgDghBNbAAAewdz0pLgCAHwce7YAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADTUPLaUUt5TSvnc1t8LAAAAcBQM4s6WZ5IslFJWSil/o5TyhgH8DgAAAIBDaVDLiEqSz0jyfJLXSinvLaX8+QH9LgAAAIBDYxCx5W1JvifJVm5Hl09Ici7JT5VS1kop31JKeeMAfi8AAADAyDWPLbXWn6+1fkOST0vy1Un+z9yOLiXJm5L8rSRrpZQfL6W8o5Rik14AAADg2BhY6Ki1frjW+oO11s9J8tlJLiX5zdyOLuNJ3pHkx5O8Wkr5b0spbxrULAAAAADDMpS7Smqt/7rW+s4kb0zy5Un+1/6hkuSPJPmbSX61lPJPSynnSinjw5gLAAAAoLWhLuGptX6k1vojtdb/MEk3tzfQ/f9yO7qMJflzSd6b5NdLKX+nlPLpw5wPAAAA4FGNbL+UWutakn+R5P++81E+trfLG5J8U5LVUsp3l1L+ndFMCQAAAPBwhh5bSimfVkr55lLKapJ/luQL7hxK8q+TfEeS1/KxJxl9bZKfK6X84WHPCgAAAPCwhhJbym3vKKX8WJL3J/nbST4jt4PKR5L8cJI/XWv97FrrxSRvTvKXkvxc/5yZJP/1MGYFAAAAeBQD3Yi2/4Shr07yV3J7I9zkdjxJktUk35vkB2utv7nzulprTfITpZSfTPLTub2Xy9sHOSsAAABAC81jS/9JQl+Q28t/5vOxfViS5FZuP+75u2utC3t9V611u5TyP+V2bHmi9awAAAAArQ3izpYPJOn039+JLO9P8n1JrtRa1x/y+zb7f76uwWwAAAAAAzWI2HJnI9uPJvmpJN+d5J/2lwYdxAeS/MMWgwEAAAAM2qDubLmS5PtqrR941C+rtf5ibu/5MjKllE9O8g25vWnvbJJPTvIbSVaS/G9J3lVr/bejmxAAAAA4LAYRW95Ua90ewPeORCnlzyR5T5Lp/kcfSfKhJG/svz43yY8l+YVRzAcAAAAcLs0f/XzMQksvyU/mdmi5muTpJKdqrY8l+aQkZ5J8W5LfHtmQAAAAwKEy0Ec/H2WllNNJfijJJyb5jlrrhZ3Ha60fSnK9/wIAAABIMoA7W46R80k+I8kHk/yNEc8CAAAAHBFiy+6+qv/ne2utN0c6CQAAAHBkiC33UUr5Q0n+g/6P7yulPFFK+d5SymullI+UUtZLKT9RSvmLo5wTAAAAOHzs2XJ/b07y+v77z0jyHUkmc/tJRL+b5A1J3pHkHaWU70/ydbXW+qAvLKW8bx+/9y0HHRgAAAA4HNzZcn+P7Xj/LUl+P8kXJ5noP4noTUne2z/+NUneOdzxAAAAgMPKnS33N3bX+6+utf7YnQ9qra+WUr40yVySP57km0spl2utt3b7wlrr2/b6pf27X9568LEBAACAUXNny/1t7Xi/sjO03FFr3U7y9/o/fmqSPWMKAAAAcPyJLff3gR3vf/kB5/3SjvdvGtAsAAAAwBEittxHrXUzHx9cdlN2XjagcQAAAIAjRGzZ3c/0//yjDzjns3a8XxvgLAAAAMARIbbs7gf7f3ZLKV9w98FSyliSv9b/8QNJ/tWwBgMAAAAOL7FlF7XWn03yo/0fv7+U8h+XUsaTpJTyRJL3JHmqf/xv9jfMBQAAAE44j35+sL+c5A1J/lRuh5ffK6V8KMljO875W7XWfziC2QAAAIBDyJ0tD1Br/d0kfybJ1yb535P8bpKJ3F429CNJerXWbx3ZgAAAAMCh486WPfSXB31//wUAAADwQO5sAQAAAGhIbAEAAABoSGwBAAAAaEhsAQAAAGhIbAEAAABoSGwBAAAAaEhsAQAAAGhIbAEAAABoSGwBAAAAaEhsAQAAAGhIbAEAAABoSGwBAAAAaEhsAQAAAGhIbAEAAABoSGwBAAAAaEhsAQAAAGhIbAEAAABoaHzUAwAAh8Py+lYWVzdy4+atTJwaT6/bydz05KjHAgA4csQWADjhFlc3cmlhJdfWNu85dmZmKhfnZ9PrdkYwGQDA0WQZEQCcYC9efzXnryzdN7QkybW1zZy/spSXrr825MkAAI4usQUATqjF1Y08d/WVbNcHn7ddk2evvpzF1Y3hDAYAcMSJLQBwQl1aWNkztNyxXZPLCyuDHQgA4JgQWwDgBFpe39p16dBultY2s7y+NaCJAACOD7EFAE6ggy4JspQIAGBvYgsAnEA3bt4a6nUAACeJ2AIAJ9DEqfGhXgcAcJKILQBwAvW6naFeBwBwkogtAHACzU1P5szM1ENdc3ZmKnPTkwOaCADg+BBbAOCEujg/m7Gyv3PHSnJhfnawAwEAHBNiCwCcUL1uJ8+fe3LP4DJWkhfOPWUJEQDAPtnlDgBOsGeefiKPP3Y6lxdWsrS2ec/xszNTuTA/K7QAADwEsQUATrhet5Net5Pl9a0srm7kxs1bmTg1nl63Y48WAIADEFsAgCS3N80VV3W2ewkAACAASURBVAAAHp09WwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaGh/1AADA6Cyvb2VxdSM3bt7KxKnx9LqdzE1PjnosAIAjTWwBgBNocXUjlxZWcm1t855jZ2amcnF+Nr1uZwSTAQAcfZYRAcAJ8+L1V3P+ytJ9Q0uSXFvbzPkrS3np+mtDngwA4HgQWwDgBFlc3chzV1/Jdn3weds1efbqy1lc3RjOYAAAx4jYAgAnyKWFlT1Dyx3bNbm8sDLYgQAAjiGxBQBOiOX1rV2XDu1maW0zy+tbA5oIAOB4ElsA4IQ46JIgS4kAAB6O2AIAJ8SNm7eGeh0AwEkltgDACTFxanyo1wEAnFRiCwCcEL1uZ6jXAQCcVGILAJwQc9OTOTMz9VDXnJ2Zytz05IAmAgA4nsQWADhBLs7PZqzs79yxklyYnx3sQAAAx5DYAgAnSK/byfPnntwzuIyV5IVzT1lCBABwAHa8A4AT5pmnn8jjj53O5YWVLK1t3nP87MxULszPCi0AAAcktgDACdTrdtLrdrK8vpXF1Y3cuHkrE6fG0+t27NECAPCIxBYAOMHmpifFFQCAxuzZAgAAANCQ2AIAAADQkNgCAAAA0JDYAgAAANCQ2AIAAADQkNgCAAAA0JDYAgAAANCQ2AIAAADQkNgCAAAA0JDYAgAAANCQ2AIAAADQkNgCAAAA0JDY8pBKKc+WUuqd16jnAQAAAA4XseUhlFI+M8l/M+o5AAAAgMNLbNmnUspYkh9IcirJ/zXicQAAAIBDSmzZv/8yyZ9I8u4kPzPiWQAAAIBDSmzZh1LKTJJvS/KbSd454nEAAACAQ2x81AMcEd+X5JOSfGOt9TdKKaOeBwAAADikxJY9lFK+Nsl8kv+l1vpDj/A979vHaW856PcDAAAAh4NlRA9QSnljkm9P8uEkXz/icQAAAIAjwJ0tD/Y9ST4lyTfVWn/tUb6o1vq2vc7p3/3y1kf5PcDxtby+lcXVjdy4eSsTp8bT63YyNz056rEAAIC7iC27KKV8ZZK/mOQXkvz9EY8DnGCLqxu5tLCSa2ub9xw7MzOVi/Oz6XU7I5gMAAC4H8uI7qOUMp3kXUk+muRra623RjwScEK9eP3VnL+ydN/QkiTX1jZz/spSXrr+2pAnAwAAdiO23N8LST41yfcm+eVSysTOV5LX3zlxx+ev3+3LAA5icXUjz119Jdv1wedt1+TZqy9ncXVjOIMBAAAPJLbc30z/z29IsnWf13M7zr3z2X83zAGB4+/SwsqeoeWO7ZpcXlgZ7EAAAMC+iC0Ah9Dy+tauS4d2s7S2meX1rQFNBAAA7JfYch+11s+ttZbdXkn+1o5z73z+V0c4MnDMHHRJkKVEAAAwemILwCF04+bB9uU+6HUAAEA7YgvAITRxanyo1wEAAO2ILQCHUK/bGep1AABAO2LLAdRav3XH/i0Azc1NT+bMzNRDXXN2Zipz05MDmggAANgvsQXgkLo4P5uxfSbdsZJcmJ8d7EAAAMC+iC0Ah1Sv28nz557cM7iMleSFc09ZQgQAAIeEnRQBDrFnnn4ijz92OpcXVrK0tnnP8bMzU7kwPyu0AADAISK2ABxyvW4nvW4ny+tbWVzdyI2btzJxajy9bsceLQAAcAiJLQBHxNz0pLgCAABHgD1bAAAAABoSWwAAAAAaElsAAAAAGhJbAAAAABoSWwAAAAAaElsAAAAAGvLoZ4BdLK9vZXF1Izdu3srEqfH0uh2PXgYAAPYktgDcZXF1I5cWVnJtbfOeY2dmpnJxfja9bmcEkwEAAEeBZUQAO7x4/dWcv7J039CSJNfWNnP+ylJeuv7akCcDAACOCrEFoG9xdSPPXX0l2/XB523X5NmrL2dxdWM4gwEAAEeK2ALQd2lhZc/Qcsd2TS4vrAx2IAAA4EgSWwByezPc3ZYO7WZpbTPL61sDmggAADiqxBaA5MBLgiwlAgAA7ia2ACS5cfPWUK8DAACOL7EFIMnEqfGhXgcAABxfYgtAkl63M9TrAACA40tsAUgyNz2ZMzNTD3XN2ZmpzE1PDmgiAADgqBJbAPouzs9mrOzv3LGSXJifHexAAADAkSS2APT1up08f+7JPYPLWEleOPeUJUQAAMB92dkRYIdnnn4ijz92OpcXVrK0tnnP8bMzU7kwPyu0AAAAuxJbAO7S63bS63ayvL6VxdWN3Lh5KxOnxtPrduzRAgAA7ElsAdjF3PSkuAIAADw0e7YAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQktgAAAAA0JLYAAAAANCS2AAAAADQ0PuoBAE6S5fWtLK5u5MbNW5k4NZ5et5O56clRjwUAADQktgAMweLqRi4trOTa2uY9x87MTOXi/Gx63c4IJgMAAFqzjAhgwF68/mrOX1m6b2hJkmtrmzl/ZSkvXX9tyJMBAACDILYADNDi6kaeu/pKtuuDz9uuybNXX87i6sZwBgMAAAZGbAEYoEsLK3uGlju2a3J5YWWwAwEAAAMntgAMyPL61q5Lh3aztLaZ5fWtAU0EAAAMgw1ygQPzZJ0HO+iSoMXVDf8cAQDgCBNbgIfmyTr7c+PmraFeBwAAHA6WEQEPxZN19m/i1MF69kGvAwAADgexBdg3T9Z5OAe9u8ddQQAAcLSJLcC+ebLOw5mbnsyZmamHuubszJT9WgAA4IgTW4B98WSdg7k4P5uxsr9zx0pyYX52sAMBAAADJ7YA+/IoT9Y5yXrdTp4/9+SewWWsJC+ce8oSIgAAOAbswsgj8ejfk8OTdQ7umaefyOOPnc7lhZUs3efuoLMzU7ngCU4AAHBsiC0ciEf/njyerPNoet1Oet2OQAkAACeA/xXEQ3vx+qsPfCLNnUf/vnDuqXzJ058+3OEYGE/WaWNuelJcAQCAY86eLTwUj/49uTxZBwAAYH/EFh6KR/+ebJ6sAwAAsDexhX3z6F88WQcAAGBvYgv75tG/JLefrPOPvvpszu6ypOjszFT+0VeftV8PAABwYtkgl33z6F/u8GQdAACA3Ykt7JtH/3I3T9YBAAC4l2VE7JtH/wIAAMDexBb2zaN/AQAAYG9iCw/Fo38BAADgwcQWHopH/wIAAMCD2bmUh/bM00/k8cdO5/LCSpbWNu85fnZmKhfmZ4UWAAAATiSxhQPx6F8AAAC4P7GFR+LRvwAAAPDx7NkCAAAA0JDYAgAAANCQ2AIAAADQkNiyi1LKp5ZS/kop5R+XUn6plPK7pZTfK6X8einlx0opXzjqGQEAAIDDxwa5u/tgPv6fz80kv5/kjf3XXyql/HSSL6q1fmgE8wEAAACHkDtbdjee5FqSb0zy79VaP7HWOpFkJsmV/jlvT/I9I5oPAAAAOITc2bK7P1tr/Rd3f1hr/X+TfE0p5VaSr0/ylaWUb661vjbsAQEA4P9v796DrSvr+4B/f4AIr7xekAajrYJBIomXKipOqAkMVWPiOK0JqUqMaaPNWB2NSkxonRGTSWMFqyZ1bLx1vF+iTjImMRoZ0hhq0eINxyAQId6CFWUURFTg1z/2OvNuT8857+05e5/3nM9nZs9+nrWefc5vYL3nrPU9z3oWAFuPmS3rWCtoWeUNc+2HbWYtAAAAwKFD2HLgbplrH760KgAAAIAtxW1EB+6MufblextcVZftw9e8/wFXAwAAAGwJZrYcgKq6a5Lzpu5Huvvzy6wHAAAA2DrMbNlPVXVYkrck+dHMbiV69r58rrtP3YevfVmShx5UgQAAAMBSmdmy/16V5PFT+1nd/ZllFgMAAABsLcKW/VBVF2bPTJbndfcbl1kPAAAAsPUIW/ZRVb0syQum7rnd/cpl1gMAAABsTdZs2QdVdUGSc6fuC7v75cusBwAAANi6hC17Md06tDKj5YXdfcEy6wEAAAC2NmHLBlYFLeea0QIAAADsjbBlHavWaHl+d79imfUAAAAAhwYL5K6hqu6d5Den7u1Jfquqrtvgde4GXw4AAADYQcxsWdthq9rH72X8MZtYCwAAAHAIEbasobuvTVLLrgMAAAA49LiNCAAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMKWvaiq3VV1flVdXlU3VdW3qurjVfWCqjpy2fUBAAAAW8sRyy5gK6uq+yT56yQnTJtuTnLHJA+bXudU1VndfcNSCgQAAAC2HDNb1lFVRyR5f2ZByz8meXR33ynJriRPSnJjkockeeuyagQAAAC2HmHL+p6W5IFT+xe6+8NJ0t23d/e7kvz6tO/nquqsZRQIAAAAbD3ClvU9bXq/uLs/usb+dya5Zmr/ymJKAgAAALY6YcsaqmpXktOn7gfWGtPdneQvp+5jFlEXAAAAsPUJW9Z2Svb8t/nsBuNW9t2jqo7d3JIAAACAQ4GnEa3tnnPtr2wwbn7fPZN8c72BVXXZPnzf++/DGAAAAGALE7asbfdc++YNxs3v273uKDgIV37txlxy9fW56ZZbc8xRR+T0k47Lycc73AAAALYqYcuCdPepexszzX556ALK4RBwydXX51UXXZWPXfP/T5h6xInH5rln3S+nn3TcEioDAABgI9ZsWduNc+1dG4yb33fjuqNgP73r41/MU99w6ZpBS5J87Jpv5qlvuDTv/viXFlwZAAAAeyNsWdtX59r32mDc/L6vrjsK9sMlV1+f8953eW7vjcfd3slvv+8zueTq6xdTGAAAAPtE2LK2v0ty+9R+wAbjVvZd193rLo4L++NVF12116Blxe2d/MFFV21uQQAAAOwXYcsauvvmJJdM3Z9da0xVVZLHTt0PLaIutr8rv3bjurcOrefSa76ZK7/mLjYAAICtQtiyvjdN72dW1Wlr7D87yX2n9psXUxLb3YHeEuRWIgAAgK1D2LK+NyW5PEkleW9VnZUkVXVYVZ2d5HXTuA9090VLqpFt5qZbbl3o5wAAABjPo5/X0d23VtUTklyc5IQkH66qmzMLqI6ahn0yyTnLqZDt6JijDuyf5IF+DgAAgPHMbNlAd1+b5EFJfifJZ5N0kh8kuSzJuUke2d03LK1Atp3TTzpuoZ8DAABgPH8O34vuvjHJi6cXbKqTj9+dR5x47H4tknvaicfm5ON3b2JVAAAA7A8zW2CLee5Z98thtW9jD6vkOWfdb3MLAgAAYL8IW2CLOf2k4/L7T3zgXgOXwyp56RMf5BYiAACALcZtRLAF/ZuH3zv/9G678gcXXZVL17il6LQTj81zzrqfoAUAAGALErbAFnX6Scfl9JOOy5VfuzGXXH19brrl1hxz1BE5/aTjrNECAACwhQlbYIs7+fjdwhUAAIBDiDVbAAAAAAYStgAAAAAMJGwBAAAAGEjYAgAAADCQsAUAAABgIGELAAAAwEDCFgAAAICBhC0AAAAAAwlbAAAAAAYStgAAAAAMJGwBAAAAGEjYAgAAADCQsAUAAABgIGELAAAAwEDCFgAAAICBhC0AAAAAAwlbAAAAAAYStgAAAAAMJGwBAAAAGEjYAgAAADCQsAUAAABgIGELAAAAwEDCFgAAAICBqruXXQOTqvrG0Ucffewpp5yy7FIAAABgx/vEJz7x9u4+Z38/J2zZQqrqmiR3TnLtgr7l/af3Kxb0/WArcfyzUzn22ckc/+xUjn12soM9/q8QtrBfquqyJOnuU5ddCyya45+dyrHPTub4Z6dy7LOTLev4t2YLAAAAwEDCFgAAAICBhC0AAAAAAwlbAAAAAAYStgAAAAAMJGwBAAAAGEjYAgAAADCQsAUAAABgoOruZdcAAAAAsG2Y2QIAAAAwkLAFAAAAYCBhCwAAAMBAwhYAAACAgYQtAAAAAAMJWwAAAAAGErYAAAAADCRsAQAAABhI2LIDVdXuqjq/qi6vqpuq6ltV9fGqekFVHbns+mAzVNXdq+rfVtVbq+pzVfWdqvpeVX25qv6kqv71smuERamq366qXnktux7YbFV156r6rar6X1X19bmf/xdP50R3XXaNsBmq6tFV9e6q+oequqWqvltVX6iqt1XVzyy7PjgQVbWrqh5XVS+qqvdNx/fKec35+/g1jq+ql1fV56d/F9+sqo9U1dOrqobU2e0cayepqvsk+eskJ0ybbk5yeJI7Tv1PJjmru29YeHGwiarqB0mOmNt0S5LbktxpbtsHkvxid9+8yNpgkarqx5N8KslRK9u6e8hJBWxFVXVmknckOX7a9P3Mzn/mA5aHdPenFl0bbJbpYvE1SX59bvN3p/ej57a9orufv7DCYICqOiPJxevsfkl3n7+Xz5+a5INJ7j5tuimz86KVa4UPJnlCd3//YOo0s2UHqaojkrw/s6DlH5M8urvvlGRXkicluTHJQ5K8dVk1wiY6IsnHkvyHJD/W3Ud39zFJTkzyhmnM45L80ZLqg01XVYcleWNmJxQfXXI5sOmq6vQkf55Z0PK+JA9PclR33y2zsP0RSX4vybeWViRsjl/NnqDlPUlO7u5d3b0ryf2T/Om073lm93KIuiHJRUkuSPLkJNfty4eq6i5J/iyzoOWKJA/v7t2Z/U54dpIfJHlsklcebIFmtuwgVfVrSV4/dX+quz+6av+Tk7x96v7L7r5okfXBZqqqM7t7vQQ8VfXfs+ek5N7d/aXFVAaLU1XPzezk4W1Jrk7y4sTMFranqtqV5PIk903yh939nCWXBAtTVRcnOSOzn/WndPetq/bfIbMLzfsmeWd3P3nhRcIBqqrDu/u2VduuTXKf7GVmS1X9bpIXZTbT6ye7+5pV+89L8p8zmwH/E9195YHWaWbLzvK06f3i1UHL5J1JVg62X1lMSbAYGwUtkzfMtR+2mbXAMlTViZn9Bf8bSZ635HJgEZ6a2YXkdUleuORaYNF+dHr/9OqgJUm6+weZ3VKaJMcsrCoYYHXQsp9WrnPfuTpomfxhZrcVHZ7knIP4PsKWnWL6687pU/cDa43p2TSnv5y6j1lEXbCF3DLXPnxpVcDmeV1mU2Sf391fX3YxsAArJ9R/3N23bDgStp8vTO8PnpYS+CHTzJZ/PnX/z8KqgiWa1q2799Rd75r4piQfmboHdU0sbNk5Tsme/9+f3WDcyr57VNWxm1sSbClnzLUvX1YRsBmq6hlJzkry4e5+87Lrgc1WVXfMnlmKl1XVvavqtVX1par6flV9rareX1U/v8w6YRO9Zno/Kck7quqklR3TBee7M5v59fdJXrH48mApHjDX3pdr4p84mG8mbNk57jnX/soG4+b33XPdUbCNTI/8PG/qfqS7P7/MemCkqrpXZovHfTc//FQK2M5OSHLk1L5vZifOz0jyI0m+M70/PsmfVdXrRj3mE7aK7n5/ZreMfj/JLya5qqpurqqbM1ur5YzMAplHdPe3l1YoLNb+XhPfuaoO+DY7YcvOsXuuvdFjbef37V53FGwT09NZ3pLZvc23ZLYKOWwnf5TkLknO7+4v7G0wbBN3m2u/KLOnS5yd5JjpSUT3SfLH0/6nxzpGbEPd/cokT0zyf6dNR2fPY5+PzGytlrssoTRYloVeEwtbgJ3uVZn9dTNJntXdn1lmMTBSVf1ykp/PbBHE/7rkcmCRDlvV/rXufs+0KGi6+4tJnpTk09OY/7jWuhZwqKqqXVX1rswecfvFzNae+CfT6zFJPpfZItIfq6oHLa1Q2MaELTvHjXPtXRuMm99347qjYBuoqguzZybL87r7jcusB0aqquMze8zzbUmesdbTKGAbmz+Huaq7/2T1gO6+PcmFU/fuSU5dRGGwIBck+aUkn0/yqO7+q+6+fnr9VZKfTnJlkuOSvHqJdcIiLfSaWNiyc3x1rn2vDcbN7/vquqPgEFdVL0vygql77jTVFraTl2Z2AfnaJFdU1THzr+xZzyJz249c74vBIWb+XvwrNhj3ubn2fTapFlioqtqd5N9P3Vev9TSu7v5ukv82df9FVf3IouqDJdrfa+JvT08nOiDClp3j75LcPrUfsMG4lX3Xdfc3N7ckWI6quiDJb07dF3b3y5dZD2ySE6f3Z2b2V5nVr/Pmxq5se9kiC4TNMp3DbLT44Yr5hXF7k8qBRTs5ycptcX+/wbir5tonrjsKto/5JxDtyzXx5zYYs1fClh2iu29OcsnU/dm1xkwr8T926n5oEXXBok23Dp07dV/Y3Rcssx4ANs3KucwpG4yZf6znNZtYCyzS7XPtjWZsHT/XtnwAO8GVma1hlKx/TXynJI+augd1TSxs2VneNL2fWVWnrbH/7Mwej5gkb15MSbA4U9Ayf+uQoIVtq7vP6O5a75XkJXNjV7b/xhJLhtH+x/R+UlX9q9U7p6fRrYTvX0nyiUUVBpvsiiTfndpPX2vx56o6PHtuNbohs7VdYFvr7s6e69wnVdUJawx7VmZP6rotydsO5vsJW3aWNyW5PLMps++tqrOS2clGVZ2d5HXTuA9090VLqhE2xao1Wp7v1iGA7a27P5LkPVP39VX1CysXnVV17yTvSLLyFJb/NC2YC4e8aT2W10/dhyZ5f1U9cDrnP2x6+tBfJPmpacwru/u2ZdQKB6qq7lZVx628sifb2DW/fVqnbt6FSa7LbBHcP6+qU6evd2RVPTPJ707jXtvdVx5UjbNwh51iSu8uTnLCtOnmzA7Mo6b+J5Oc1d03LLo22CzTSfU/TN3bk3x9Lx+5sLsv3MsYOKRV1flJXpzMZrYstxrYHNN08L/I7MkrSfK9zM597jY37CXdff6CS4NNVVVHJ3lffvhWie9N73ec2/aOJE8VtnCoqaprs28Lm7+pu3911WdPTfLBzB4kkMxuozsqyR2m/oeSPKG7v5eDYGbLDtPd12b2V5zfyWyBoE7ygySXZTaV9pGCFrahw1a1j9/La3UCDsAhqLu/k+TMJM9I8jdJvpPZz/ivJHlnktMFLWxH0+yWn8tsmYA/TfLl7FkQ+ktJ3pvk8d39FEELO013X5bkJ5O8IrOFou+Q2e+Hv83s98XjDjZoScxsAQAAABjKzBYAAACAgYQtAAAAAAMJWwAAAAAGErYAAAAADCRsAQAAABhI2AIAAAAwkLAFAAAAYCBhCwAAAMBAwhYAAACAgYQtAAAAAAMJWwAAAAAGErYAAAAADCRsAQAAABhI2AIAAAAwkLAFAAAAYCBhCwAAAMBAwhYAAACAgYQtAAAAAAMJWwAADlBV/UxV3VZVXVVfrKq7bjD2xKr61jT2pqr68UXWCgAsjrAFAOAAdff/TPLSqfvPkrx2rXFVdUSStye587TpN7r785tfIQCwDMIWAICD8+Ikl07ts6vq360z5pFT+73d/fqFVAYALEV197JrAAA4pFXVfZN8KsnuJN9J8pDuvmra96gkFyc5PMmXkjy4u29YVq0AwOYzswUA4CB19xeSPGvq3inJ26vqDtMaLm/NLGi5PckvC1oAYPszswUAYJCqeluSp0zd/5LkxCS/NPV/r7tftJTCAICFErYAAAxSVXfO7HaiE1ft+t9JHtXdty6+KgBg0dxGBAAwSHd/O8k5SeZDlW8nOUfQAgA7h7AFAGCsL2e2SO6Ky6Y1XQCAHULYAgAwSFUdltmCuHeZ23xmVT1zSSUBAEsgbAEAGOe8JD89tS9K8q2p/fKqOmU5JQEAi2aBXACAAarqtCR/m+SIJF9N8qAkj0ny9mnIp5Oc1t3fW06FAMCimNkCAHCQqmp3krdlFrR0kqd19ze6+x1J3jINe3CSly6pRABggYQtAAAH79VJfmxqv7y7Pzy371lJVhbIfW5VPXahlQEAC+c2IgCAg1BVT86eW4U+meSR3f39VWPmbzG6LsmDuvvrCy0UAFgYM1sAAA5QVZ2Q5DVT9+YkT1kdtCRJd1+a5Pype48kb1xAeQDAkghbAAAOQFUdnh9+zPPzu/uKDT7y+0n+Zmo/vqqevZn1AQDL4zYiAAAAgIHMbAEAHgVvigAAAINJREFUAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMJCwBQAAAGAgYQsAAADAQMIWAAAAgIGELQAAAAADCVsAAAAABhK2AAAAAAwkbAEAAAAYSNgCAAAAMND/A66PZUMZpkY1AAAAAElFTkSuQmCC\n" | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 557, | |
| "height": 413 | |
| }, | |
| "needs_background": "light" | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "#@title\n", | |
| "\n", | |
| "#@markdown Execute this cell to simulate some data\n", | |
| "\n", | |
| "# setting a fixed seed to our random number generator ensures we will always\n", | |
| "# get the same psuedorandom number sequence\n", | |
| "np.random.seed(121)\n", | |
| "\n", | |
| "# Let's set some parameters\n", | |
| "theta = 1.2\n", | |
| "n_samples = 15\n", | |
| "\n", | |
| "# Draw x and then calculate y\n", | |
| "x = 10 * np.random.rand(n_samples) # sample from a uniform distribution over [0,10)\n", | |
| "noise = np.random.randn(n_samples) # sample from a standard normal distribution\n", | |
| "y = theta * x + noise\n", | |
| "\n", | |
| "fig, ax = plt.subplots()\n", | |
| "ax.scatter(x, y) # produces a scatter plot\n", | |
| "ax.set(xlabel='x', ylabel='y');" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "ll4MlIG64xNn" | |
| }, | |
| "source": [ | |
| "## Coding Exercise 1: Resample Dataset with Replacement\n", | |
| "\n", | |
| "In this exercise you will implement a method to resample a dataset with replacement. The method accepts $\\mathbf{x}$ and $\\mathbf{y}$ arrays. It should return a new set of $\\mathbf{x}'$ and $\\mathbf{y}'$ arrays that are created by randomly sampling from the originals.\n", | |
| "\n", | |
| "We will then compare the original dataset to a resampled dataset.\n", | |
| "\n", | |
| "**Hint:** The [numpy.random.choice](https://numpy.org/doc/stable/reference/random/generated/numpy.random.choice.html) method would be useful here." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "both", | |
| "execution": {}, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 358 | |
| }, | |
| "id": "cE0KrUE74xNo", | |
| "outputId": "9fef160a-9325-4777-f7cf-5b91eb41bdc2" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "<Figure size 864x360 with 2 Axes>" | |
| ], | |
| "image/png": 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| |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 845, | |
| "height": 341 | |
| }, | |
| "needs_background": "light" | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "def resample_with_replacement(x, y):\n", | |
| " \"\"\"Resample data points with replacement from the dataset of `x` inputs and\n", | |
| " `y` measurements.\n", | |
| "\n", | |
| " Args:\n", | |
| " x (ndarray): An array of shape (samples,) that contains the input values.\n", | |
| " y (ndarray): An array of shape (samples,) that contains the corresponding\n", | |
| " measurement values to the inputs.\n", | |
| "\n", | |
| " Returns:\n", | |
| " ndarray, ndarray: The newly resampled `x` and `y` data points.\n", | |
| " \"\"\"\n", | |
| " #######################################################\n", | |
| " ## TODO for students: resample dataset with replacement\n", | |
| " # Fill out function and remove\n", | |
| " #######################################################\n", | |
| "\n", | |
| " # Get array of indices for resampled points\n", | |
| " sample_idx = np.random.choice(np.arange(len(x)), size=len(x), replace=True)\n", | |
| "\n", | |
| " # Sample from x and y according to sample_idx\n", | |
| " x_ = x[sample_idx]\n", | |
| " y_ = y[sample_idx]\n", | |
| "\n", | |
| " return x_, y_\n", | |
| "\n", | |
| "x_, y_ = resample_with_replacement(x, y)\n", | |
| "\n", | |
| "plot_original_and_resample(x, y, x_, y_)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "cellView": "both", | |
| "execution": {}, | |
| "id": "bFbuE8c44xNo" | |
| }, | |
| "source": [ | |
| "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/main//tutorials/W1D2_ModelFitting/solutions/W1D2_Tutorial3_Solution_81af3bd6.py)\n", | |
| "\n", | |
| "*Example output:*\n", | |
| "\n", | |
| "<img alt='Solution hint' align='left' width=1711.0 height=705.0 src=https://raw.githubusercontent.com/NeuromatchAcademy/course-content/main/tutorials/W1D2_ModelFitting/static/W1D2_Tutorial3_Solution_81af3bd6_0.png>\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "bmde9pmL4xNo" | |
| }, | |
| "source": [ | |
| "In the resampled plot on the right, the actual number of points is the same, but some have been repeated so they only display once.\n", | |
| "\n", | |
| "Now that we have a way to resample the data, we can use that in the full bootstrapping process." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "UyvgQ8lH4xNp" | |
| }, | |
| "source": [ | |
| "## Coding Exercise 2: Bootstrap Estimates\n", | |
| "\n", | |
| "In this exercise you will implement a method to run the bootstrap process of generating a set of $\\hat\\theta$ values from a dataset of inputs ($\\mathbf{x}$) and measurements ($\\mathbf{y}$). You should use `resample_with_replacement` here, and you may also invoke the helper function `solve_normal_eqn` from Tutorial 1 to produce the MSE-based estimator.\n", | |
| "\n", | |
| "We will then use this function to look at the theta_hat from different samples.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "form", | |
| "execution": {}, | |
| "id": "rGOLUcAk4xNp" | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# @markdown Execute this cell for helper function `solve_normal_eqn`\n", | |
| "def solve_normal_eqn(x, y):\n", | |
| " \"\"\"Solve the normal equations to produce the value of theta_hat that minimizes\n", | |
| " MSE.\n", | |
| "\n", | |
| " Args:\n", | |
| " x (ndarray): An array of shape (samples,) that contains the input values.\n", | |
| " y (ndarray): An array of shape (samples,) that contains the corresponding\n", | |
| " measurement values to the inputs.\n", | |
| " thata_hat (float): An estimate of the slope parameter.\n", | |
| "\n", | |
| " Returns:\n", | |
| " float: the value for theta_hat arrived from minimizing MSE\n", | |
| " \"\"\"\n", | |
| " theta_hat = (x.T @ y) / (x.T @ x)\n", | |
| " return theta_hat" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "execution": {}, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "5afCa7604xNp", | |
| "outputId": "3a18aced-fb7e-434a-a7a5-60fd268e90fa" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "[1.27550888 1.17317819 1.18198819 1.25329255 1.20714664]\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "def bootstrap_estimates(x, y, n=2000):\n", | |
| " \"\"\"Generate a set of theta_hat estimates using the bootstrap method.\n", | |
| "\n", | |
| " Args:\n", | |
| " x (ndarray): An array of shape (samples,) that contains the input values.\n", | |
| " y (ndarray): An array of shape (samples,) that contains the corresponding\n", | |
| " measurement values to the inputs.\n", | |
| " n (int): The number of estimates to compute\n", | |
| "\n", | |
| " Returns:\n", | |
| " ndarray: An array of estimated parameters with size (n,)\n", | |
| " \"\"\"\n", | |
| " theta_hats = np.zeros(n)\n", | |
| "\n", | |
| " ##############################################################################\n", | |
| " ## TODO for students: implement bootstrap estimation\n", | |
| " # Fill out function and remove\n", | |
| " ##############################################################################\n", | |
| "\n", | |
| " # Loop over number of estimates\n", | |
| " for i in range(n):\n", | |
| "\n", | |
| " # Resample x and y\n", | |
| " x_, y_ = resample_with_replacement(x,y)\n", | |
| "\n", | |
| " # Compute theta_hat for this sample\n", | |
| " theta_hats[i] = np.dot(x_,y_) / np.dot(x_,x_)\n", | |
| "\n", | |
| " return theta_hats\n", | |
| "\n", | |
| "\n", | |
| "# Set random seed\n", | |
| "np.random.seed(123)\n", | |
| "\n", | |
| "# Get bootstrap estimates\n", | |
| "theta_hats = bootstrap_estimates(x, y, n=2000)\n", | |
| "print(theta_hats[0:5])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "cellView": "both", | |
| "execution": {}, | |
| "id": "uFAgahpp4xNq" | |
| }, | |
| "source": [ | |
| "[*Click for solution*](https://github.com/NeuromatchAcademy/course-content/tree/main//tutorials/W1D2_ModelFitting/solutions/W1D2_Tutorial3_Solution_d73b40e4.py)\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "yfsvUG-z4xNq" | |
| }, | |
| "source": [ | |
| "You should see `[1.27550888 1.17317819 1.18198819 1.25329255 1.20714664]` as the first five estimates." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "38z5CLj24xNr" | |
| }, | |
| "source": [ | |
| "Now that we have our bootstrap estimates, we can visualize all the potential models (models computed with different resampling) together to see how distributed they are." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "execution": {}, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 430 | |
| }, | |
| "id": "BALf9vuA4xNr", | |
| "outputId": "5cae1fa1-d20b-4958-df1e-882b1db74188" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "<Figure size 576x432 with 1 Axes>" | |
| ], | |
| "image/png": 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| |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "width": 557, | |
| "height": 413 | |
| }, | |
| "needs_background": "light" | |
| } | |
| } | |
| ], | |
| "source": [ | |
| "#@title\n", | |
| "#@markdown Execute this cell to visualize all potential models\n", | |
| "\n", | |
| "fig, ax = plt.subplots()\n", | |
| "\n", | |
| "# For each theta_hat, plot model\n", | |
| "theta_hats = bootstrap_estimates(x, y, n=2000)\n", | |
| "for i, theta_hat in enumerate(theta_hats):\n", | |
| " y_hat = theta_hat * x\n", | |
| " ax.plot(x, y_hat, c='r', alpha=0.01, label='Resampled Fits' if i==0 else '')\n", | |
| "\n", | |
| "# Plot observed data\n", | |
| "ax.scatter(x, y, label='Observed')\n", | |
| "\n", | |
| "# Plot true fit data\n", | |
| "y_true = theta * x\n", | |
| "ax.plot(x, y_true, 'g', linewidth=2, label='True Model')\n", | |
| "\n", | |
| "ax.set(\n", | |
| " title='Bootstrapped Slope Estimation',\n", | |
| " xlabel='x',\n", | |
| " ylabel='y'\n", | |
| ")\n", | |
| "\n", | |
| "# Change legend line alpha property\n", | |
| "handles, labels = ax.get_legend_handles_labels()\n", | |
| "handles[0].set_alpha(1)\n", | |
| "\n", | |
| "ax.legend();" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "zq7NQusX4xNr" | |
| }, | |
| "source": [ | |
| "This looks pretty good! The bootstrapped estimates spread around the true model, as we would have hoped. Note that here we have the luxury to know the ground truth value for $\\theta$, but in applications we are trying to guess it from data. Therefore, assessing the quality of estimates based on finite data is a task of fundamental importance in data analysis.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "eowQmw784xNr" | |
| }, | |
| "source": [ | |
| "---\n", | |
| "# Section 2: Confidence Intervals\n", | |
| "\n", | |
| "*Estimated timing to here from start of tutorial: 17 min*\n", | |
| "\n", | |
| "Let us now quantify how uncertain our estimated slope is. We do so by computing [confidence intervals](https://en.wikipedia.org/wiki/Confidence_interval) (CIs) from our bootstrapped estimates. The most direct approach is to compute percentiles from the empirical distribution of bootstrapped estimates. Note that this is widely applicable as we are not assuming that this empirical distribution is Gaussian." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "cellView": "form", | |
| "execution": {}, | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 448 | |
| }, | |
| "id": "T76IYAQi4xNs", | |
| "outputId": "d277ec64-f917-4a5b-88a1-538ccb42fb23" | |
| }, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "name": "stdout", | |
| "text": [ | |
| "mean = 1.24, std = 0.05\n" | |
| ] | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "text/plain": [ | |
| "<Figure size 576x432 with 1 Axes>" | |
| ], | |
| "image/png": 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| |
| }, | |
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| "width": 558, | |
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| ], | |
| "source": [ | |
| "#@title\n", | |
| "\n", | |
| "#@markdown Execute this cell to plot bootstrapped CI\n", | |
| "\n", | |
| "theta_hats = bootstrap_estimates(x, y, n=2000)\n", | |
| "print(f\"mean = {np.mean(theta_hats):.2f}, std = {np.std(theta_hats):.2f}\")\n", | |
| "\n", | |
| "fig, ax = plt.subplots()\n", | |
| "ax.hist(theta_hats, bins=20, facecolor='C1', alpha=0.75)\n", | |
| "ax.axvline(theta, c='g', label=r'True $\\theta$')\n", | |
| "ax.axvline(np.percentile(theta_hats, 50), color='r', label='Median')\n", | |
| "ax.axvline(np.percentile(theta_hats, 2.5), color='b', label='95% CI')\n", | |
| "ax.axvline(np.percentile(theta_hats, 97.5), color='b')\n", | |
| "ax.legend()\n", | |
| "ax.set(\n", | |
| " title='Bootstrapped Confidence Interval',\n", | |
| " xlabel=r'$\\hat{{\\theta}}$',\n", | |
| " ylabel='count',\n", | |
| " xlim=[1.0, 1.5]\n", | |
| ");" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "L8W-ud_f4xNs" | |
| }, | |
| "source": [ | |
| "Looking at the distribution of bootstrapped $\\hat{\\theta}$ values, we see that the true $\\theta$ falls well within the 95% confidence interval, which is reassuring. We also see that the value $\\theta = 1$ does not fall within the confidence interval. From this we would reject the hypothesis that the slope was 1." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "o6SwI0rX4xNs" | |
| }, | |
| "source": [ | |
| "---\n", | |
| "# Summary\n", | |
| "\n", | |
| "*Estimated timing of tutorial: 23 minutes*\n", | |
| "\n", | |
| "- Bootstrapping is a resampling procedure that allows to build confidence intervals around inferred parameter values\n", | |
| "- it is a widely applicable and very practical method that relies on computational power and pseudo-random number generators (as opposed to more classical approaches than depend on analytical derivations)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "IF68YSAz4xNs" | |
| }, | |
| "source": [ | |
| "---\n", | |
| "# Notation\n", | |
| "\n", | |
| "\\begin{align}\n", | |
| "\\theta &\\quad \\text{parameter}\\\\\n", | |
| "\\hat{\\theta} &\\quad \\text{estimated parameter}\\\\\n", | |
| "x &\\quad \\text{input, independent variable}\\\\\n", | |
| "y &\\quad \\text{response measurement, dependent variable}\\\\\n", | |
| "\\mathbf{x} &\\quad \\text{vector of input values}\\\\\n", | |
| "\\mathbf{y} &\\quad \\text{vector of measurements}\\\\\n", | |
| "\\mathbf{x}' &\\quad \\text{vector of resampled input values }\\\\\n", | |
| "\\mathbf{y}' &\\quad \\text{vector of resampled measurement values}\\\\\n", | |
| "\\end{align}" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "execution": {}, | |
| "id": "5U53XMH04xNs" | |
| }, | |
| "source": [ | |
| "**Suggested readings** \n", | |
| "\n", | |
| "Computer Age Statistical Inference: Algorithms, Evidence and Data Science, by Bradley Efron and Trevor Hastie\n" | |
| ] | |
| } | |
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| "Video available at https://youtube.com/watch?v=hs6bVGQNSIs\n" | |
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| } | |
| } | |
| } | |
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| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 0 | |
| } |
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