From f8b1b9bb1a323317775c2c3e41dd2120ec61315c Mon Sep 17 00:00:00 2001 From: Sachinthaka Abeywardana Date: Sun, 3 Sep 2017 00:34:26 +1000 Subject: [PATCH] Redid lesson 0 --- Lesson 0 - LinRegression.ipynb | 392 +++++++++++++++++---------------- 1 file changed, 208 insertions(+), 184 deletions(-) diff --git a/Lesson 0 - LinRegression.ipynb b/Lesson 0 - LinRegression.ipynb index d8d9e54..dc129a7 100644 --- a/Lesson 0 - LinRegression.ipynb +++ b/Lesson 0 - LinRegression.ipynb @@ -4,7 +4,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Linear Regression" + "# Linear Regression\n", + "\n", + "Machine learning is about using data to infer patterns.\n", + "\n", + "Linear regression is the basic unit of Deep Learning. In fact personally I prefer to think of it as stacking linear regression modules.\n", + "\n", + "Deep Learning has proven itself over and over again to be far superior to traditional machine learning techiques. It's strength comes from the fact that it can be scalable to large amounts of data. \n", + "\n", + "Some of the most impressive applications are in voice recognition, self driving cars and in chatbots." ] }, { @@ -27,7 +35,7 @@ " " ], "text/plain": [ - "" + "" ] }, "execution_count": 1, @@ -42,7 +50,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": { "collapsed": true }, @@ -54,16 +62,23 @@ "%matplotlib inline" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the line $y=2x+3$. See below for a light introduction to plotting and numpy arrays. Numpy arrays are really important to understand. If you have experience with Matlab once you take out the `np.` part it should be familiar to the relevant Matlab function." + ] + }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { - "image/png": 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Oc9OmTWPatGm9Lb0sNTenw5e+8x2YNy+dseD4aUkqf/X19dTX15/zXFtbW6/f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\nJCmn/w9vc4Ta3eOSiAAAAABJRU5ErkJggg==\n", 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NNbMsM1sR+jOqnHEjzCzDzDLNbFI4c0aT/MJiHl+4mtHPfc6OA0d44fozeOG/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\nTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -79,9 +94,18 @@ ] }, { - "cell_type": "code", - "execution_count": 39, + "cell_type": "markdown", "metadata": {}, + "source": [ + "This is how you define a function in Python. Remember to return the value." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": true + }, "outputs": [], "source": [ "def f(w,b):\n", @@ -96,19 +120,25 @@ " Note that w and b are the ONLY variables\n", " \"\"\"\n", " e = y - f(w,b)\n", - " return np.sum(np.square(e))" + " return np.mean(np.square(e))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Let us do a grid search over w and b for the smallest loss function value" + "## Find the function\n", + "\n", + "Given the observation $x,y$ the goal is to find the best parameters, $w,b$ that fits the data. Ignore the fact that you can solve this as an equation. Most of the time the data isn't as linear or noiseless as what is being presented here.\n", + "\n", + "The most naiive way of finding $w$ and $b$ is to do a grid search over $w$ and $b$ for the smallest loss function value. In this case the loss function is: $$\\frac{1}{N}\\sum_{i=1}^N \\xi_i^2$$ where, $\\xi_i = y_i - f(x_i|w,b)$ and $f(x_i|w,b)=wx_i+b$.\n", + "\n", + "Another way of stating the above is that we need to find the best fitting function $f(x_i|w,b)$ such that we minimising the __loss function__ by varying $w$ and $b$. An illustration is shown below:" ] }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -141,7 +171,7 @@ " 12.39393939, 12.5959596 , 12.7979798 , 13. ])" ] }, - "execution_count": 40, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -152,7 +182,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -180,7 +210,7 @@ " 4.5959596 , 4.6969697 , 4.7979798 , 4.8989899 , 5. ])" ] }, - "execution_count": 5, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -191,16 +221,16 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "100.0" + "1.0" ] }, - "execution_count": 43, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -211,7 +241,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -220,7 +250,7 @@ "0.0" ] }, - "execution_count": 7, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -231,28 +261,39 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 10, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "w_try, b_try = np.meshgrid(np.linspace(-5,5), np.linspace(-5,5))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", + "array([[-5. , -4.79591837, -4.59183673, ..., 4.59183673,\n", + " 4.79591837, 5. ],\n", + " [-5. , -4.79591837, -4.59183673, ..., 4.59183673,\n", + " 4.79591837, 5. ],\n", + " [-5. , -4.79591837, -4.59183673, ..., 4.59183673,\n", + " 4.79591837, 5. ],\n", " ..., \n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ]])" + " [-5. , -4.79591837, -4.59183673, ..., 4.59183673,\n", + " 4.79591837, 5. ],\n", + " [-5. , -4.79591837, -4.59183673, ..., 4.59183673,\n", + " 4.79591837, 5. ],\n", + " [-5. , -4.79591837, -4.59183673, ..., 4.59183673,\n", + " 4.79591837, 5. ]])" ] }, - "execution_count": 45, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } @@ -263,28 +304,28 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[-4. , -4. , -4. , ..., -4. ,\n", - " -4. , -4. ],\n", - " [-3.91919192, -3.91919192, -3.91919192, ..., -3.91919192,\n", - " -3.91919192, -3.91919192],\n", - " [-3.83838384, -3.83838384, -3.83838384, ..., -3.83838384,\n", - " -3.83838384, -3.83838384],\n", + "array([[-5. , -5. , -5. , ..., -5. ,\n", + " -5. , -5. ],\n", + " [-4.79591837, -4.79591837, -4.79591837, ..., -4.79591837,\n", + " -4.79591837, -4.79591837],\n", + " [-4.59183673, -4.59183673, -4.59183673, ..., -4.59183673,\n", + " -4.59183673, -4.59183673],\n", " ..., \n", - " [ 3.83838384, 3.83838384, 3.83838384, ..., 3.83838384,\n", - " 3.83838384, 3.83838384],\n", - " [ 3.91919192, 3.91919192, 3.91919192, ..., 3.91919192,\n", - " 3.91919192, 3.91919192],\n", - " [ 4. , 4. , 4. , ..., 4. ,\n", - " 4. , 4. ]])" + " [ 4.59183673, 4.59183673, 4.59183673, ..., 4.59183673,\n", + " 4.59183673, 4.59183673],\n", + " [ 4.79591837, 4.79591837, 4.79591837, ..., 4.79591837,\n", + " 4.79591837, 4.79591837],\n", + " [ 5. , 5. , 5. , ..., 5. ,\n", + " 5. , 5. ]])" ] }, - "execution_count": 46, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -295,14 +336,14 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 25, "metadata": {}, "outputs": [ { "data": { - "image/png": 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HFf/efQhq9t3zQax5P89j9iEyAADAxDEYAABg4vbPNEEHUW0L9iEvRBQtTOQN7UenAGpO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\nAABJRU5ErkJggg==\n", 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3XdF8rr8ilDEUIS+/In5e0ixnWf0EHoNZCCSPJ3k5yc+T/BzJ5w0lixBCiGEthAMAXmBm\nnyJ5JICrSF5mZp8fUCYhhNixDLYgmNnNAG5uHn+f5HUAjgWgBaEicWmFjSV0G4Uybi6hfOtMbhXP\n5PaJE+4ZhpkCAAKncstvGseMJubvOJWdaqfJ0Nj4UhW2dXK3hvztv8WWqEixFL8+kicAeCiAj085\ntofkPpL7brl1Iz4shBCiEoM7lUkeAeAvADzfzG6Pj5vZXgB7AeBhpx68el6aGQmVqs21f7fLRbsH\nQl1ncawBjlqqb+4ceWUt4nG5zlHPIdqK3HQcsek+BGh9uUPtnuPYIZxwKseO4/C86BhDp3LCwTx5\nIXjo3LfcBL5FEvcEr8GgFgLJ3ZgsBheb2XuGlEUIIXY6g1kIJAngTwBcZ2avHUoOsR6EGpy3sbhI\nf0VYxM8rNV4jEaml0c8wXWpfOzsE0yl/zVjTb4WJbj20+N7Y9PljC6E1R8dCCJ9Mlw+I3xeKCD+/\nbH9C5ocUF4JM+RpqhbgOaSE8CsDTAZxF8urm74kDyiOEEDuaIaOMrsBM7SrETiDWgPruZ5xDbjMe\nIG5ANPu1Ohqg8/5rJz6VFLeLtepW85xOslgwLiw7EV8sJYbTBKdb4nq6RTOKLYnEpSbnTX9c2wro\nnFcj8imuGJh9nhBCCIEliDISQqQp0TK91o1eBFJJKWyO2pooR1s6pm3G+/pBlFHL4IijpxJ6uxNl\nRDfKaLrs8fMaLS89apch6QNZCEIIIQBoQRBCCNGgLaM1ZNwKwZTfvk9iU7/Pqraew7k07DRF11kc\nPHbGtXsZR1s8Nl1G63xHE28g3u5JdEXrCplXuiJ3O2mWbadVQxaCEEIIADvcQhgH6sLGgF2KRJow\nkWwDeeUkxq0SFOur8+Q6nEcJx3F8zAutbIXTetpyWNwu7msQnhd+lE5eWmruiVDpY+1yFZ52j+Sx\neVkFJ3LM+v5ahBBCzMSOthByGQdqxEZKfRErRzcJbkttDf0wNQoTxxrh2EKNe+sK40hdPlByrRms\n3dz979zSFe2Q1HQxPgtvaqSWtsRw+zc7cgTXDpPRchPRJmIlkttmCOtNjfMIv5eeRddHyWxZCEII\nIQDIQhBiZnIL6Y0K/B+dOZz9/9Q471hnnzy1X59ZBK5z3VbRurxrWazoptR4xwro+BCSpTZmSdpL\njCvw3Ww7dk4fZlwErxRZCEIIIQCsqYWwanv+8+YNxJqIV2p5lWmXk848J/IAbBZq6stIKvfAa6Tj\n7X+nylhMjk0/ZzO+VjCwY420ymEX/C5nsBBG2VFG6WMlrTHzrYd+W2aWRjHJQhBCCAFAC4IQQoiG\ntdwyEmIo2h3ZFrc9VSfccbrjOD7mJqa1eg+05wi3b1myfeSU04j7HCCxxTX2nM/epTP7UnvU6IzX\nN7IQhBBCAJCFUBWVwlgccUeojQq6TSoZrY8ubu3ko63vzchix2YwLjNYYCanciKE1uub4PUhDs/b\niA6GWvxmcEs7vZdTzOAQTsvrOMs7jvT5Es5mCjsNrRgn+Wzc8/+VQS0Ekm8h+S2S1w4phxBCiOEt\nhLcCuAjA2waWQ+wQWhpsBWUrt99ynDhUIzS4pT16vZcdrTJXk26Xcdh6fRx1TLNUSW4Am4GIobSd\nBLakrPFzJ+w0YcV4oaWeteO9XlK6okrf5B4K5A1qIZjZRwB8Z0gZhBBCTBjaQtgWknsA7AGA449d\nn6SieRmyCU5rH9PVUsON4uDVHkpSh5p6SktfNK3InJ5dSqEGXxpx1LKeomOpxLTY0PG08dbQsHR1\n7PIwJ7ktnM8pWheeF1oxnpWR22+6JGqrb2KfWvk8S46Z7TWz083s9KN/ajl+6EIIsY4svYUghifW\nPjbn1CO6EULLt9CPWk122vL1aY10o0q2VNq4TETtBjnhXn6s3VrS19BWuds+heh7EhqTrbkjgRNv\ny7M4RpEvY5woXeFFWbnWiGdZlVgPnc9hesnrUisjLtmSy9JbCEIIIRbD0GGnfwbgYwBOJnkTyWcN\nKY8QQuxkBt0yMrOnzjKe2Eri2VTiV68ssi9xGJJZIxQ0t19BtxJqjYSzvPfSSkQKu6cVBgiUVNyM\nzwvvlVuSIpjfOltL0+eOj3kHUtszuT0avGNuYlpmOGl2aKmzLVRK71VSe51dCCHEyiCn8gA4wZmD\nEafELzqUdUuO+lr7MjCkI72ltTpJYF4/BEtp3J1yD+mQ0XHwUYZhuHFiWnbYqZMgl3Ike051Lxkv\ndc6054uiVpe0kPX4tQkhhJgbWQhiqRkt0JeRCjWNrad2YGVsWc0rQ6R9tkJBN6NjnHosLoJXUk4h\n1tpThe86bZPDa8VRp5vTD8V+k5RVkFtwD0iHnRYnppV0T5uhxIVX0G7W686DLAQhhBAAZCEkCUsS\nL0tEU+1yFe3SCuvah7l+6ersa2c2y/GS4GrjJWZ5vZLTRfCixDQ4iWnB09ACYeF3L1vzdxK9Sqwn\nzw9Rm9g67btshiwEIYQQAHaYhTCKtOoamn97L1T0Sah9lkbp1Ghx6fk1cstajAuss04J7Vwt2DuW\nWXq6XdAunYcQ+gPiCKS03yBPhtgKCImjjML3nPInxM9LSoHEz9v3Oi1TlZyEHv7jyEIQQggBYIdZ\nCCLWsldXH+g2nKk8f6KdZimdZjEJeTsRTQss6+1FwYR7/qFlEmvmYRec2PjYbLWrDIg0/5TFlFue\nenIsMc5tkJMfFVSbGgXt6sghhBBCQAuCEEKIBm0ZibVgVLAVFpvmJYX1vJ7KJYXuZtn6SiWj+Qls\nuQ7RPAd2vJ3W7lQWHQwHh+852jPKLcmQ6vMMpLd7vPIUpfcmtwheyVZQrvO5tP9B53pVZhFCCLHy\nrIWFMIrWtc0lDAAdBxpMriY66jjbCq67JEXrVplYS6uRPDbKDKH1CtOVfJaudut0TEuWtYhEMKat\nh3Zxu8BqyQx99cJOc8tazFKeoqT8dS6xFZRtCWReO7Zcc5GFIIQQAsCaWAhChJT2PG4nrZXpSqnm\nPN2y3tPlKrVGcksr5CbBedpyy5/QCS0N5YiOhfOFByqEncaE4bC598ZL6PNIJZyVNsiJrfrkdVX+\nWgghRF8MaiGQPAfAfwcwBvBmM3v1kPKIurQ1pGES4mqXpwbqJ63llrGINcxxWIDRjWLKK43tWRLJ\ncfG1nHuTW+YlO8ooN6kMmeMKCt1td15yvspWwMqXvyY5BvAGAE8AcAqAp5I8ZSh5hBBip5NlIZA8\nBMBzAPwCJpWorgDwRjP70RzXPgPAl8zsy8013gXgPACfn2NOgbI941Ja+52ZpaY7ERChcsP2OSW5\nATXILUnd3fPfkt/zZeTmHrStkTzrIbYC/PMSkTRx5I/TjD7Ei0AK71RoBViF8tfe/n9uJFFMbvnr\nnHMA3/Jpn5e2n/ooaNeeP4+3AXgwgD8GcBEmGv3b57z2sQBuDJ7f1LzWguQekvtI7vv2rTUMfiGE\nENPI9SE8xMzC7ZzLSS5EkzezvQD2AsDDTz14uKpPQgix5uQuCJ8i+QgzuxIASJ4JYN+c1/46gOOD\n58c1rw3COLJvNxJm4TjKjtnITKrJlyMMW1zOJLJRhfDMXGqEgrbmK+jR7PVUro1XFdXrZeB9V7xt\njM1EWYvccTFeSGpKxNL76W3jpLaJcstTbHdee1w61DTnHA9vm8krV5ErR4y7IJD8LCY7vLsB/D3J\nrzXP7wfg+qIrbvFJACeRvD8mC8FTADxtzjmFEEIUsp2FcG5fFzazAySfC+ADmISdvsXMPtfX9RZN\nrsVR51r9lqcYsi9xSEurim5nSQe13GSxmeZMOJK9QnpeGYtc53YrdNXV7tOF70Lns9tZLbOERCfs\nNPUTyPy6elpvbjjpTN3kEtp5/rh82yc3Ga1v3AXBzG7o8+Jm9j4A7+vzGkIIIfJY+9IV4Z5/7f3+\ndWYVfBkh7eSusjnyy1Xnae0eqd7O3U5weaGmbWskzwqYjJ09nDIc5s3XIREOHWvHqTBUr1RFjcJ0\n7rHMfsj5cxTKkThWWsyuM3+VWYQQQqw8a28hiDy8qJJVo6RZTkxudJMXgZQqdFdK91rBnr9j0XlW\nQCuKyUmCS+6T97D3ndJ1Z9Gcc5PKsiOQMjX/kNwSHJP5p79rLxFNxe2EEEL0hiyEJSC36FfIqu3x\nD4XX4nJZ5PDKWJQc6/ohgnPcksyj5Lj2fNMtEwDZEUMeZa0m8/ILZipdkbgHuTkJ3jEvqqg096A9\nhxrkCCGEmAMtCEIIIQBoy2hHM67gfF01Shy9s3QxG2WWxkiFuMZOxDBRzZMjFYK6/bHp207eVpC7\npRMeWuBOZm7C2SyO4+wKpAt0uCdlqHStnfFfQAghxLbIQhA7ltKSHLkd03J7O6eS1CZzTE/m6sqR\ndvRuOCUp0mUtRs64TG3UG1bZesgNJ52luF3uuJazuHLCmXdOrWS01vWqzyiEEGIlWVkLYRT2k+15\nry73WiXho4tmkeGqLQ3GnLsTihHf3rCDmvVbdtvT1FPk+hdq9HbOLY0dh6d6ZT1acgWfQ+64Yir/\nZEv7HPshqYlksSolLsq6ouX3WFbYqRBCiDlYWQuhBou0MkLGkYaV2zd45Ghwy0DfZbhDOhpQcOmS\nUtjd+adHAW3HvP4Fzwroyji9yF58b7zCd6FO6JXJbumOhZFERX6ITEp6I3fHRUUBM/0LKb9Bp6dy\nwRx9J6LFyEIQQggBYIdbCDuBvovWLbKdZi4tbcuiPf4CGbuNdPLmmDcnAYj2k5mO/ElFHE3mSO//\nJ3MPOl+TRARSx+cTn7cYsi0EJxopd/5S30DudUv8H7VYjl+wEEKIwdGCIIQQAsBAW0YkfxXAKwA8\nCMAZZrZvCDlEGePMrZBlJDdZzKOkY1pu1dVZ+jwny050thzyylp4W0HxNlRSpgrhqSXO59JOZeH7\n98pfhMQO4OQ4t7JsLGNd53Fpj+ahfs3XAvgVAB8Z6PpCCCEiBrEQzOw6ACD78UCNwlC6pU0R257S\nMM7ayWeLDCddJN0CbrNbPh1NLNN6yC2y5yWctcfNfl0AbjJaSo6kgxn99kqYJVQ1XdwuP7Q015Fc\nImNuN7W+E9E681SZpUdI7iG5j+S+b99aoxGhEEKIafRmIZD8EIB7TTl0oZm9N3ceM9sLYC8APPzU\ng5cuHWscWDkbtnTiFdPWTNfDIpiFkjIW3TnqFsHr7DNzelJZ12pBMC4th1fcLp2M5iSwxSSu3Uf/\n5hLtvjvH9KJ1fte59Ou5oaaLTkYL6W1BMLOz+5pbCCFEfZSYlmAcaC0bFRJAas8nFkdHsysostct\ngjf9PP9aeRFHsdbulbVoFR3M1fzd0hWhtdN+j0kNufDnUNLbOLeRTqkcudE9pVFFuVbSShW3I/nL\nJG8C8EgAf0XyA0PIIYQQYouhoowuAXDJENdedkpKaNeIAor3LftsqdnVcsLyDNGhljY6vRR257zU\nOahfFHCW9pohqdLguRFHk/PCFqheA5680hUl+JFE6W9waD2Ua+bzt7X0fA0pv0FpxFHtyKLW3Gqh\nKYQQoiZaEIQQQgDYYU7lcZQIt05hostIe6tiOcpdjJztqdJSFiHp91y3xEX3vPR3OTvUNOlgBlLJ\naHFIcn7pirohkzVKV3glKbwSF+Ma20kFTuZayWghshCEEEIAWDkLgRg3TsKN2KkoZqZ2iYs4lG5Z\n+iPkMurRoomdfrnf3pYmafH9Lej7HL+XlBM4d9wMpSvCBLTqHdO8XucVktSy5QhDUDsWx+zX7qPn\ngX89IYQQAitnIawO8UpbWy9Zlv7Kq1wKO5fO/m4QyjpLv+WQlKY6ix8jaT04ndVqMHaS4EpKV/RB\nrlWQW5LCSz4rsTri71TbsiiwJOKQ2RUrfy2EEGLJkIUwI6Nor32zRlmLYMpSjTOXGkXravseVpmu\n9RA8DiymbJ+BU0471t9yvyteWYvs0hWt9xIU0nOb8eSVrsj9Hs5U/jqhZedGEpXStjjyi9vl0oqK\nUk9lIYQQfbEWFkINrb0PzV/MT7vEQ3Ag2idv76GHr0cTOuUvei3X4RSVK9VLW9aJW9bDe18FeQgJ\nawHYzr8QHOm5dEVKptIS2l6uQQ3Nv5VfgPn8CfMgC0EIIQQALQhCCCEa1mLLaKdQ4sytUQk1Nolr\nhzG2zfjl673MAAAPNUlEQVTFbePEpCqQIjLba4fXulsfmZVQF4mX6OY7nNsja+Jdy09am70khVfF\nNHQke+Up+nYwr1Q/BCGEEMuHLAQxlVCbqa2lx46yVUtoSzpzgaRzO7e4nXvdjtaXcCS7MhU4mIGo\nL3NYgsIJY+3Mnms9zE/KKvAcwn2EcZbgFbDrW8bV+iUKIYTojbW3EEZhqd7qBSTahOW1vdLa42gf\nv3aP5WVJHGsn5oR74Tsvma2j2SX24ZelZGNu7+VO+evgvE5iWub3PA5lnfX8WI7262Vz5Bata1sc\n+eUpFl3ELsVQPZVfQ/J6kteQvITk3YeQQwghxBZDWQiXAbjAzA6Q/CMAFwB48UCybEuo0dfW5j36\nLpAXUqUv84r7BpaB3IgjAOmyFl5iWmbSmhdJ5vVojmZJH3G+G7nacmkzmpC+E876xJM9t+FOzCC/\nWDP7oJkdaJ5eCeC4IeQQQgixxTL4EJ4J4M9TB0nuAbAHAO577DKIK5aBTrORlBYca7BF5S8czTyz\nNMYqNAvKzRsItXvPsvTyV2o3qsm1ArrnlZS/8CKVvHyF6eUpOsd6yC/Ipbf/sCQ/BOBeUw5daGbv\nbcZcCOAAgItT85jZXgB7AeDhpx6y3DacEEKsML0tCGZ2tnec5PkAzgXwODN1uxdCiKEZZA+G5DkA\nXgTgF83sh0PIAOSHiS47o2hbJLeD2ir0RmgngW09XDWHtR/G6SWEZTqZnb4JuUlr3rZWqqdC7Bx2\nE6cWGG2cksPbcsktSbHODPWrugjAkQAuI3k1yTcNJIcQQoiGQSwEMztx3jnGrb62y796hyuvJ+0i\nu6eVUsOyCEkWlUM6SUnUIbcv84alnMX5oaUprb20UGMuuVZBbjmN3KJ1XvJZ51jCkeyVrmifUydk\ndrXsbiGEEL2hOM45CTutLbLLWunefVkJ7bolqWskwS2STlE5pzR2Mqw1smJzw1DbSWAl/gTAS1pL\nfZZeWG/aWsgPLfVCV0soTVLzy2bnlaRYJ2QhCCGEACALIclQmv+6EmpbfSdpjVP74kBRv+U+5E02\nmYk0Xa/EQw1Spbw7ResS4zY6xe3Sv5U+E9NiUnLkWgTeHN61cpPPlhVZCEIIIQCsqYUg7X6L0v36\nGvkFoUZUO2+gu6+/9XAVykTUxovU8nIUUlFirm/AaxAUkGs95EaqlUbOzGIVJOfosf3lZP5U9FC6\ndIVbJmOVitsJIYRYPrQgCCGEALCmW0bLQFgWA8jvoOb1W8hNbhuKvsNJ++zz3AclvZf9yqrpY7nO\n59y+zPH9TSUjxlsu4Xadt1Xjha6WkJ1U5vxySrddUo7kVXAixyz/r0oIIcRC2FEWwih2qBXo2X33\nQ65BWOyupNDd5LxhksW8JLC+y1gkNXo3dDWttQ9VgK/0HibLWKBtMXilS3LDi3M1+lJyncW5CWde\nSYpsmbKdxenSFX0jC0EIIQSAHWYhiPqsQgnt9rXS3dT6TgIrwS1dkUhom6lfcaZFk/LfZIenOuSG\nCZeWoPa7qeX7FJLjEn6DPrT7ZCG96H0UWzFlYgkhhFg3ZCEMQLwKp9bycaTB1i6HXV4gb75oHy8y\npQZe4lScLNUn7WSx6GBmD+gSq8XTTF0rIDOBzfv8c0tXtM6pEDOXq82XWgReSYpccstaD4ksBCGE\nEABWzEIgtiKFSiKEPGbJG0ixDKWwgeUsJ127jEVH01tge82R44foMyqqo0UmchS8zz83AsnLV0hZ\nCzGzWA990rdVUNtv0Efjm+xr9zq7EEKIlWGQBYHkK0le0/RT/iDJ+wwhhxBCiC2G2jJ6jZn9JwAg\n+bsAXgbgt0snG3cch6uXMr4oyjqmDVcxNSQ02/tIUhulnMA9O6a9hDC0kgwLuqwBRSGp8f31HM4h\npdtJJZRU9MzdInKvmzsuM/mslPD9e/2bZ2EQC8HMbg+eHo5uDIYQQogFM5hTmeSrADwDwPcAPHYo\nOXJQf4XhqO6MzizPUIORm1Q2/3VTSWuuFZAZkhprmCmHc/yZ5CYq9t2XODsM1bkfuYXqamj+niN5\nkfRmIZD8EMlrp/ydBwBmdqGZHQ/gYgDPdebZQ3IfyX3fvnWjL3GFEGLH05uFYGZnZw69GMD7ALw8\nMc9eAHsB4PRTD5l5+V0W7T4Ma11kKexRJ9HJGdw6b/aSFDUK5NUIofUSwnpNggOqh7/WKLWR68tx\nNf+EfyHWnFtWRmGI5Gb10tiZhe4y/z/khpbWSD7zSnL3UV57qCijk4Kn5wG4fgg5hBBCbDGUD+HV\nJE/GRLm9AXNEGIlhqdG0Jrdkct9y5MwNoBV1VCPiyGukk2tleUXwQksiNwLJ1fyzo5Ha5FpMJVZB\nbSsgntOzCkrKVXeth/m0/fh9lVoPgywIZvZvhriuEEKINCtVuqI2YcOc0lIYuXv+y84iy1942mcu\nXhRMKan9+tKy2G1fxvyNdLxyHbmRRaXjUv4FT+OexXrok9yyE53zEsdyfQHlEUd5TXv6QKUrhBBC\nANCCIIQQomFHbxktC7khpONWSKMzrucOZPOWvyiVqUaSWu1eCZ3ewDafg9xzYHsO5pGzPeWGmiY+\nl3i7JOVw9j6HWbaT5iXXWVyyRQT42z8ljuTSraAafRk8ZCEIIYQAIAshSW4iWYpRpAEtY8mLRfYy\nLmVeGWs4sLsy1Qi1nR4mOot8uXKUhKTG9zrlcC4NM+1Du01R2yqoHYI6GTufI7lb3E49lYUQQszB\nyloINUJGRR6lJSmKyl9U6LdcQ4OvUTKiNV+hpVKStObt/3tjvQQ2z7+QulZumGmp1VYSxtqHnyA/\nDLWG5q+OaUIIIRbAyloIHuNWaYG61sMifQPj6FqpxLd4Vc8tdpdb6C6XWAPK1c7rRA/N3zwnjBgq\nLUmRKq+da+nMYkmkGut0exnnRSC5iWmZvpzcJLjW3H0UaStsYpMzR52Io3TRulzWpridEEKI5WMt\nLYRlJ4xgAsqimPqmzwik6iWuMcOefIXS2MlWmyizikKt3bNuci2wWSy1ojwER0PO9TV4hNcqnSNF\nH36CtCUR7f9XaNqTlCG6Vic/JnseIYQQAloQhBBCNOyoLaO+HcKLrHxaUsYC6Hf7p+/ktrKSGfP3\nTa4xR2k4bXaZiMwQ39ytoNzEtI68mdtJHjW2iXJDQesnpuU6s8v6N/RdMVYWghBCCAA7zELwGEVr\n41DJbrmF7moziyUxb7/lWXotl3RTGzIENZVI5s3h9U3IdTL7juO8kNTaiWldOYYPnqiRYNY9b/qc\ns3R+q+FIroEsBCGEEABkIYgeKSkhUSOctEZp7KIQVOQnY+VeK1UED2i/z9wSF54/pHZiWkxp57kS\naiSmlcznWQUlfoNcyyEOMy0trz2ohUDyBSSN5NFDyiGEEGJAC4Hk8QAeD+BrQ8mQy7ylsIF2hFPf\npbBz/RC5ZSyWMVKpVCavaF1Jwbl8yyeSN+FTmMVCqhGBlHovNRLTunIMX4SyRtmJGpFEpUXr+vAb\ntOcfjtcBeBE6uZ5CCCGGYBALgeR5AL5uZp8hfc2O5B4Ae5qnPx7f+4vX9i1fBY4GcMvQQmQgOeux\nCjICkrM2qyLnyTmDaD3V0SH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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -320,84 +361,58 @@ " for j in range(100):\n", " e_obs[i,j] = loss_function(w_try[i,j],b_try[i,j])\n", " \n", - "plt.pcolormesh(w_try, b_try, e_obs)\n", + "plt.pcolormesh(w_try, b_try, np.log(e_obs)) #using log here helps visualise better, you may take it out\n", + "plt.xlabel('w')\n", + "plt.ylabel('b')\n", + "plt.title('Mean Squared Error')\n", "plt.show() " ] }, { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], + "cell_type": "markdown", + "metadata": {}, "source": [ - "y = wx+b\n", - "loss = sum((y-wx+b)^2)" + "You can see that the error in the plot is minimised at $w=2$ and $b=3$." ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " ..., \n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ],\n", - " [-4. , -3.91919192, -3.83838384, ..., 3.83838384,\n", - " 3.91919192, 4. ]])" + "355.06060606060601" ] }, - "execution_count": 9, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "w_try" + "e_obs.max()" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[-4. , -4. , -4. , ..., -4. ,\n", - " -4. , -4. ],\n", - " [-3.91919192, -3.91919192, -3.91919192, ..., -3.91919192,\n", - " -3.91919192, -3.91919192],\n", - " [-3.83838384, -3.83838384, -3.83838384, ..., -3.83838384,\n", - " -3.83838384, -3.83838384],\n", - " ..., \n", - " [ 3.83838384, 3.83838384, 3.83838384, ..., 3.83838384,\n", - " 3.83838384, 3.83838384],\n", - " [ 3.91919192, 3.91919192, 3.91919192, ..., 3.91919192,\n", - " 3.91919192, 3.91919192],\n", - " [ 4. , 4. , 4. , ..., 4. ,\n", - " 4. , 4. ]])" + "0.0043879944910451526" ] }, - "execution_count": 10, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "b_try" + "e_obs.min()" ] }, { @@ -424,7 +439,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 29, "metadata": { "collapsed": true }, @@ -433,16 +448,26 @@ "from sklearn.linear_model import LinearRegression" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Scikit learn is another Machine Learning that is quite powerful on itself. However it may not scale to millions of data points same way that DL does.\n", + "\n", + "## Noisy Data\n", + "We see how to find the weights using scikit learn below. However, the data isn't as perfect as before. We add a tiny bit of noise." + ] + }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 30, "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -459,25 +484,25 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[-0.20033541],\n", - " [ 0.99593549],\n", - " [ 0.33620163],\n", - " [ 0.15856806],\n", - " [-1.79497902],\n", - " [ 2.67305261],\n", - " [ 0.28610749],\n", - " [-0.47895651],\n", - " [-0.23491752],\n", - " [ 0.13383936]])" + "array([[-0.53140766],\n", + " [-0.39093887],\n", + " [-1.05119687],\n", + " [ 0.31837372],\n", + " [-0.21698498],\n", + " [-0.10631009],\n", + " [ 0.386783 ],\n", + " [-0.09697643],\n", + " [-0.36057248],\n", + " [-0.47221554]])" ] }, - "execution_count": 13, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -488,37 +513,37 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "LinearRegression(copy_X=True, fit_intercept=False, n_jobs=1, normalize=False)" + "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)" ] }, - "execution_count": 55, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "model = LinearRegression(fit_intercept=False) # \n", + "model = LinearRegression() # \n", "model.fit(x,y)" ] }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[ 2.28342337]])" + "array([[ 1.89343643]])" ] }, - "execution_count": 56, + "execution_count": 38, "metadata": {}, "output_type": "execute_result" } @@ -529,16 +554,16 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.0" + "array([ 2.98122518])" ] }, - "execution_count": 57, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" } @@ -549,16 +574,16 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[ 45.66846743]])" + "array([[ 40.84995375]])" ] }, - "execution_count": 58, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } @@ -567,9 +592,17 @@ "model.predict(20)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Note:\n", + "1. `model.fit(...)` and `model.predict` will be two of the most important functions you will use all throughout. Worth remembering!" + ] + }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 41, "metadata": {}, "outputs": [ { @@ -578,7 +611,7 @@ "43" ] }, - "execution_count": 59, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" } @@ -589,14 +622,14 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 42, "metadata": {}, "outputs": [ { "data": { - "image/png": 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gIqUiJSWFzZs3a/fAokpNhVtvhf/9z9lpcOBAryOSIKSWAREpkT179tC1a3ea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\nBB7tTSAiIhLklAyIiIgEOb9PBowxfzH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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -617,36 +650,32 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## A more complicated function" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - " y = b +w^T X\n", - "X = [x x^2 x^3]\n", - "y = b +wx +w_2 x**2 +w_3 x**3 \n", + "## A more complicated function\n", + "Remember that when we say linear regression it mean linear in the parmaters $w, b$ not $x$! See illustration below:\n", + "\n", + "\\begin{align}\n", + "y = b +w^T X \\\\\n", + "X = [x\\quad x^2\\quad x^3] \\\\\n", + "y = b +wx +w_2 x^2 +w_3 x^3 \\\\\n", + "\\end{align}\n", + "The shapes of the matrices are:\n", + "- X = NxD matrix\n", + "- y = Nx1 vector\n", + "- w = Dx1 vector\n", "\n", - "X = NxD matrix\n", - "y = Nx1 vector\n", - "w = Dx1 vector" + "Note in the example below that there is no $x^2$ term. i.e. it's coefficient is zero!" ] }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 44, "metadata": {}, "outputs": [ { "data": { - "image/png": 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UGEQKjBrlIaF375LH+/b1mQ2ff150bMkS77bIzPQg8N//+piE0h580Lshnnwy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\n0KwZdOkSdSUiIiLbR4EhQfL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T4PdQ+RW1/Obt7dQ1Onlh7X4AfAy8cGOyVoQSkTYp8Huohz5Ow1r4/FenUlHT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\nXkKBLyLiJRT4IiJeQoEvIuIl/h9+RldPsEkAdAAAAABJRU5ErkJggg==\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -663,7 +692,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 45, "metadata": {}, "outputs": [ { @@ -672,7 +701,7 @@ "(100, 1)" ] }, - "execution_count": 62, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } @@ -683,7 +712,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 46, "metadata": {}, "outputs": [ { @@ -692,7 +721,7 @@ "(100, 4)" ] }, - "execution_count": 63, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -704,7 +733,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 47, "metadata": {}, "outputs": [ { @@ -713,7 +742,7 @@ "(100, 1)" ] }, - "execution_count": 32, + "execution_count": 47, "metadata": {}, "output_type": "execute_result" } @@ -724,7 +753,7 @@ }, { "cell_type": "code", - "execution_count": 70, + "execution_count": 49, "metadata": {}, "outputs": [ { @@ -733,28 +762,29 @@ "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)" ] }, - "execution_count": 70, + "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model = LinearRegression()\n", - "model.fit(x_new2,y)" + "model.fit(x_new,y)" ] }, { "cell_type": "code", - "execution_count": 71, + "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([[ 2.2666389 , 0.09331596, 0.29051083, -0.00509105]])" + "array([[ 1.96056458e+00, 6.42083377e-03, 3.17153449e-01,\n", + " 1.19352599e-03]])" ] }, - "execution_count": 71, + "execution_count": 50, "metadata": {}, "output_type": "execute_result" } @@ -763,18 +793,26 @@ "model.coef_" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Note:\n", + "- The coefficient of $x^2$ and $x^4$ is really close to zero." + ] + }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([-0.76351838])" + "array([-1.05542925])" ] }, - "execution_count": 72, + "execution_count": 51, "metadata": {}, "output_type": "execute_result" } @@ -785,14 +823,14 @@ }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 52, "metadata": {}, "outputs": [ { "data": { - "image/png": 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3xMVRD4OIiJQvxsDYsfD++zBnDvTrB+S/t4T2jrg46mEQEZEyLzOJMSCAwPfe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\nSgmDiIiIZPX/gmp1iWZImVYAAAAASUVORK5CYII=\n", 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19UKIss7hA37Yvli6vruBjff049b5i2x++xP639c6W8WO7EMrhCgP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\nDkICvhBCOAgJ+EII4SAk4AshhIP4f4Z7rOWo5fUrAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -810,7 +848,7 @@ }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 53, "metadata": {}, "outputs": [ { @@ -820,7 +858,7 @@ " [ -4.8989899 , 24.00010203, -117.57625742, 576.00489747]])" ] }, - "execution_count": 68, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" } @@ -834,7 +872,7 @@ }, { "cell_type": "code", - "execution_count": 69, + "execution_count": 54, "metadata": {}, "outputs": [ { @@ -843,18 +881,18 @@ "(100, 4)" ] }, - "execution_count": 69, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "x_new2.shape" + "x_new.shape" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 55, "metadata": {}, "outputs": [ { @@ -864,7 +902,7 @@ " [ -4.8989899 , 24.00010203, -117.57625742, 576.00489747]])" ] }, - "execution_count": 21, + "execution_count": 55, "metadata": {}, "output_type": "execute_result" } @@ -873,20 +911,6 @@ "x_new[:2]" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [] - }, { "cell_type": "code", "execution_count": null,