diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle index 8d3a58e34..5c0673c51 100644 Binary files a/doc/LectureNotes/_build/.doctrees/environment.pickle and b/doc/LectureNotes/_build/.doctrees/environment.pickle differ diff --git a/doc/LectureNotes/_build/.doctrees/project2.doctree b/doc/LectureNotes/_build/.doctrees/project2.doctree index 99edac8ac..23faf0efe 100644 Binary files a/doc/LectureNotes/_build/.doctrees/project2.doctree and b/doc/LectureNotes/_build/.doctrees/project2.doctree differ diff --git a/doc/LectureNotes/_build/.doctrees/week42.doctree b/doc/LectureNotes/_build/.doctrees/week42.doctree index 2d658f359..a93db2b6f 100644 Binary files a/doc/LectureNotes/_build/.doctrees/week42.doctree and b/doc/LectureNotes/_build/.doctrees/week42.doctree differ diff --git a/doc/LectureNotes/_build/html/_sources/project2.ipynb b/doc/LectureNotes/_build/html/_sources/project2.ipynb index b22fbdd58..faf4aee16 100644 --- a/doc/LectureNotes/_build/html/_sources/project2.ipynb +++ b/doc/LectureNotes/_build/html/_sources/project2.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "061af572", + "id": "96e577ca", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "22578683", + "id": "067c02b9", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "61fb162f", + "id": "01f9fedd", "metadata": { "editable": true }, @@ -58,7 +58,7 @@ }, { "cell_type": "markdown", - "id": "104c69e1", + "id": "9f8e4871", "metadata": { "editable": true }, @@ -104,7 +104,7 @@ }, { "cell_type": "markdown", - "id": "0d2c42e3", + "id": "460cc6ea", "metadata": { "editable": true }, @@ -121,7 +121,7 @@ "\n", "* Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be\n", "\n", - " * The simple one-dimensional function Runge function from project 1, that is $f(x) = \\frac{1}{1+25x^2}$. We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", + " * The simple one-dimensional function Runge function from project 1, that is $f(x) = \\frac{1}{1+25x^2}$. We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", "\n", "* Classification.\n", "\n", @@ -132,7 +132,7 @@ }, { "cell_type": "markdown", - "id": "d8baab67", + "id": "d62a07ef", "metadata": { "editable": true }, @@ -162,7 +162,7 @@ }, { "cell_type": "markdown", - "id": "87e7ed71", + "id": "9cd8b8ac", "metadata": { "editable": true }, @@ -189,7 +189,7 @@ }, { "cell_type": "markdown", - "id": "5a26b6ad", + "id": "5931b155", "metadata": { "editable": true }, @@ -205,7 +205,7 @@ }, { "cell_type": "markdown", - "id": "096fe6c4", + "id": "b273fc8a", "metadata": { "editable": true }, @@ -217,7 +217,7 @@ }, { "cell_type": "markdown", - "id": "fd986596", + "id": "e13db1ec", "metadata": { "editable": true }, @@ -252,7 +252,7 @@ }, { "cell_type": "markdown", - "id": "e853d4b6", + "id": "4f864e31", "metadata": { "editable": true }, @@ -270,7 +270,7 @@ }, { "cell_type": "markdown", - "id": "fc2d413b", + "id": "c9faeafd", "metadata": { "editable": true }, @@ -285,7 +285,7 @@ }, { "cell_type": "markdown", - "id": "e6821051", + "id": "d865c22b", "metadata": { "editable": true }, @@ -302,7 +302,7 @@ }, { "cell_type": "markdown", - "id": "cba72d68", + "id": "5270af8f", "metadata": { "editable": true }, @@ -328,7 +328,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "e16fb528", + "id": "4e0e1fea", "metadata": { "collapsed": false, "editable": true @@ -347,7 +347,7 @@ }, { "cell_type": "markdown", - "id": "73599f42", + "id": "8fe85677", "metadata": { "editable": true }, @@ -358,7 +358,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "f1a639ef", + "id": "b28318b2", "metadata": { "collapsed": false, "editable": true @@ -370,7 +370,7 @@ }, { "cell_type": "markdown", - "id": "90fb7b41", + "id": "97e02c71", "metadata": { "editable": true }, @@ -381,7 +381,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "424af629", + "id": "88af355c", "metadata": { "collapsed": false, "editable": true @@ -394,7 +394,7 @@ }, { "cell_type": "markdown", - "id": "3c006080", + "id": "d1f8f0ed", "metadata": { "editable": true }, @@ -407,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "a18ddd54", + "id": "554b3a48", "metadata": { "editable": true }, @@ -419,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "1a1afaf9", + "id": "77bfdd5c", "metadata": { "editable": true }, @@ -434,7 +434,7 @@ "code for classification and pertinent results against a similar code using **Scikit-Learn** or **tensorflow/keras** or **pytorch**.\n", "\n", "If you have time, you can use the functionality of **scikit-learn** and compare your neural network results with those from Logistic regression. This is optional.\n", - "The weblink here compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article. Your neural network code can implement the equivalent of logistic regression by simply setting the number of hidden layers to zero. \n", + "The weblink here compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article. Your neural network code can implement the equivalent of logistic regression by simply setting the number of hidden layers to zero and keeping just the input and the output layers. \n", "\n", "If you wish to compare with say Logisti Regression from **scikit-learn**, the following code uses the above data set" ] @@ -442,7 +442,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "3c37cbaf", + "id": "eaa9e72e", "metadata": { "collapsed": false, "editable": true @@ -464,7 +464,7 @@ }, { "cell_type": "markdown", - "id": "106b9303", + "id": "c7ba883e", "metadata": { "editable": true }, @@ -480,7 +480,88 @@ }, { "cell_type": "markdown", - "id": "55da0d7f", + "id": "595be693", + "metadata": { + "editable": true + }, + "source": [ + "## Summary of methods to implement and analyze\n", + "\n", + "**Required Implementation:**\n", + "1. Reuse the regression code and results from project 1, these will act as a benchmark for seeing how suited a neural network is for this regression task.\n", + "\n", + "2. Implement a neural network with\n", + "\n", + " * A flexible number of layers\n", + "\n", + " * A flexible number of nodes in each layer\n", + "\n", + " * A changeable activation function in each layer (Sigmoid, ReLU, LeakyReLU, as well as Linear and Softmax)\n", + "\n", + " * A changeable cost function, which will be set to MSE for regression and cross-entropy for multiple-classification\n", + "\n", + " * An optional L1 or L2 norm of the weights and biases in the cost function (only used for computing gradients, not interpretable metrics)\n", + "\n", + "3. Implement the back-propagation algorithm to compute the gradient of your neural network\n", + "\n", + "4. Reuse the implementation of Plain and Stochastic Gradient Descent from Project 1 (and adapt the code to work with the your neural network)\n", + "\n", + " * With no optimization algorithm\n", + "\n", + " * With RMS Prop\n", + "\n", + " * With ADAM\n", + "\n", + "5. Implement scaling and train-test splitting of your data, preferably using sklearn\n", + "\n", + "6. Implement and compute metrics like the MSE and Accuracy" + ] + }, + { + "cell_type": "markdown", + "id": "35138b41", + "metadata": { + "editable": true + }, + "source": [ + "### Required Analysis:\n", + "\n", + "1. Briefly show and argue for the advantages and disadvantages of the methods from Project 1.\n", + "\n", + "2. Explore and show the impact of changing the number of layers, nodes per layer, choice of activation function, and inclusion of L1 and L2 norms. Present only the most interesting results from this exploration. 2D Heatmaps will be good for this: Start with finding a well performing set of hyper-parameters, then change two at a time in a range that shows good and bad performance.\n", + "\n", + "3. Show and argue for the advantages and disadvantages of using a neural network for regression on your data\n", + "\n", + "4. Show and argue for the advantages and disadvantages of using a neural network for classification on your data\n", + "\n", + "5. Show and argue for the advantages and disadvantages of the different gradient methods and learning rates when training the neural network" + ] + }, + { + "cell_type": "markdown", + "id": "b18bea03", + "metadata": { + "editable": true + }, + "source": [ + "### Optional (Note that you should include at least two of these in the report):\n", + "\n", + "1. Implement Logistic Regression as simple classification model case (equivalent to a Neural Network with just the output layer)\n", + "\n", + "2. Compute the gradient of the neural network with autograd, to show that it gives the same result as your hand-written backpropagation.\n", + "\n", + "3. Compare your results with results from using a machine-learning library like pytorch (https://docs.pytorch.org/tutorials/beginner/basics/buildmodel_tutorial.html)\n", + "\n", + "4. Use a more complex classification dataset instead, like the fashion MNIST (see )\n", + "\n", + "5. Use a more complex regression dataset instead, like the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", + "\n", + "6. Compute and interpret a confusion matrix of your best classification model (see )" + ] + }, + { + "cell_type": "markdown", + "id": "580d8424", "metadata": { "editable": true }, @@ -496,7 +577,7 @@ }, { "cell_type": "markdown", - "id": "d3731e2c", + "id": "96f5c67e", "metadata": { "editable": true }, @@ -527,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "6c7c5340", + "id": "d1bc28ba", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/_build/html/_sources/week42.ipynb b/doc/LectureNotes/_build/html/_sources/week42.ipynb index af01abbf4..45a126e79 100644 --- a/doc/LectureNotes/_build/html/_sources/week42.ipynb +++ b/doc/LectureNotes/_build/html/_sources/week42.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7dcf8613", + "id": "d231eeee", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "98019924", + "id": "5e782cb1", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "ab0e660a", + "id": "53309290", "metadata": { "editable": true }, @@ -40,32 +40,34 @@ }, { "cell_type": "markdown", - "id": "bcea021f", + "id": "71367514", "metadata": { "editable": true }, "source": [ "## Readings and videos\n", "1. These lecture notes\n", - "\n", - "\n", "\n", - "2. For a more in depth discussion on neural networks we recommend Goodfellow et al chapters 6 and 7. For the optimization part, see chapter 8. \n", + "2. Video of lecture at \n", "\n", - "3. Neural Networks demystified at \n", + "3. Whiteboard notes at \n", "\n", - "4. Building Neural Networks from scratch at \n", + "4. For a more in depth discussion on neural networks we recommend Goodfellow et al chapters 6 and 7. For the optimization part, see chapter 8. \n", "\n", - "5. Video on Neural Networks at \n", + "5. Neural Networks demystified at \n", "\n", - "6. Video on the back propagation algorithm at \n", + "6. Building Neural Networks from scratch at \n", + "\n", + "7. Video on Neural Networks at \n", + "\n", + "8. Video on the back propagation algorithm at \n", "\n", "I also recommend Michael Nielsen's intuitive approach to the neural networks and the universal approximation theorem, see the slides at ." ] }, { "cell_type": "markdown", - "id": "fd77cd6b", + "id": "c7be87be", "metadata": { "editable": true }, @@ -78,7 +80,7 @@ }, { "cell_type": "markdown", - "id": "7d93059a", + "id": "8e0567a2", "metadata": { "editable": true }, @@ -97,7 +99,7 @@ }, { "cell_type": "markdown", - "id": "5156bf60", + "id": "549dcc05", "metadata": { "editable": true }, @@ -113,7 +115,7 @@ }, { "cell_type": "markdown", - "id": "4f5d5b27", + "id": "21203bae", "metadata": { "editable": true }, @@ -124,7 +126,7 @@ }, { "cell_type": "markdown", - "id": "0a490014", + "id": "1c102a30", "metadata": { "editable": true }, @@ -138,7 +140,7 @@ }, { "cell_type": "markdown", - "id": "9fa74383", + "id": "53f11afe", "metadata": { "editable": true }, @@ -153,7 +155,7 @@ }, { "cell_type": "markdown", - "id": "417ce076", + "id": "afa8c42a", "metadata": { "editable": true }, @@ -165,7 +167,7 @@ }, { "cell_type": "markdown", - "id": "07ed6afb", + "id": "cb5c959f", "metadata": { "editable": true }, @@ -179,7 +181,7 @@ }, { "cell_type": "markdown", - "id": "3b926536", + "id": "0083ae15", "metadata": { "editable": true }, @@ -191,7 +193,7 @@ }, { "cell_type": "markdown", - "id": "0e1bd556", + "id": "f4931203", "metadata": { "editable": true }, @@ -207,7 +209,7 @@ }, { "cell_type": "markdown", - "id": "edebc935", + "id": "d3a3754d", "metadata": { "editable": true }, @@ -223,7 +225,7 @@ }, { "cell_type": "markdown", - "id": "3e2794ac", + "id": "bcd5dbab", "metadata": { "editable": true }, @@ -235,7 +237,7 @@ }, { "cell_type": "markdown", - "id": "54f91430", + "id": "2cbc30f1", "metadata": { "editable": true }, @@ -245,7 +247,7 @@ }, { "cell_type": "markdown", - "id": "f1e0a166", + "id": "1a1d803d", "metadata": { "editable": true }, @@ -257,7 +259,7 @@ }, { "cell_type": "markdown", - "id": "ad62ed90", + "id": "776735c7", "metadata": { "editable": true }, @@ -267,7 +269,7 @@ }, { "cell_type": "markdown", - "id": "57dac362", + "id": "c1a2e5af", "metadata": { "editable": true }, @@ -279,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "a4dc4050", + "id": "9e603df9", "metadata": { "editable": true }, @@ -289,7 +291,7 @@ }, { "cell_type": "markdown", - "id": "b223c83d", + "id": "533212cd", "metadata": { "editable": true }, @@ -301,7 +303,7 @@ }, { "cell_type": "markdown", - "id": "a1c9b5e7", + "id": "09d91067", "metadata": { "editable": true }, @@ -317,7 +319,7 @@ }, { "cell_type": "markdown", - "id": "9c3b03c0", + "id": "f767afe7", "metadata": { "editable": true }, @@ -329,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "186485f2", + "id": "f38ded54", "metadata": { "editable": true }, @@ -341,7 +343,7 @@ }, { "cell_type": "markdown", - "id": "c2f1b30b", + "id": "f3f03bc3", "metadata": { "editable": true }, @@ -351,7 +353,7 @@ }, { "cell_type": "markdown", - "id": "13142fad", + "id": "9062730e", "metadata": { "editable": true }, @@ -363,7 +365,7 @@ }, { "cell_type": "markdown", - "id": "b441f95a", + "id": "75bbc32c", "metadata": { "editable": true }, @@ -373,7 +375,7 @@ }, { "cell_type": "markdown", - "id": "46e57fd2", + "id": "fcf02dbf", "metadata": { "editable": true }, @@ -389,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "50158555", + "id": "aa97678f", "metadata": { "editable": true }, @@ -401,7 +403,7 @@ }, { "cell_type": "markdown", - "id": "4174ea9e", + "id": "98f68e27", "metadata": { "editable": true }, @@ -413,7 +415,7 @@ }, { "cell_type": "markdown", - "id": "f7a29d74", + "id": "c4528178", "metadata": { "editable": true }, @@ -425,7 +427,7 @@ }, { "cell_type": "markdown", - "id": "cb1a387b", + "id": "d6304298", "metadata": { "editable": true }, @@ -437,7 +439,7 @@ }, { "cell_type": "markdown", - "id": "125bcb29", + "id": "dfc47ba6", "metadata": { "editable": true }, @@ -449,7 +451,7 @@ }, { "cell_type": "markdown", - "id": "76272ae9", + "id": "8834c3dc", "metadata": { "editable": true }, @@ -459,7 +461,7 @@ }, { "cell_type": "markdown", - "id": "7e0d1157", + "id": "40956770", "metadata": { "editable": true }, @@ -475,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "53dfc3bd", + "id": "69e7fdcf", "metadata": { "editable": true }, @@ -487,7 +489,7 @@ }, { "cell_type": "markdown", - "id": "126420bb", + "id": "726d4c90", "metadata": { "editable": true }, @@ -499,7 +501,7 @@ }, { "cell_type": "markdown", - "id": "2114b4ba", + "id": "0ee83d1c", "metadata": { "editable": true }, @@ -509,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "7d3549bb", + "id": "f5b3b5a5", "metadata": { "editable": true }, @@ -521,7 +523,7 @@ }, { "cell_type": "markdown", - "id": "80265b39", + "id": "b2746792", "metadata": { "editable": true }, @@ -535,7 +537,7 @@ }, { "cell_type": "markdown", - "id": "df2f78ac", + "id": "76e2e41a", "metadata": { "editable": true }, @@ -553,7 +555,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "0ec652bf", + "id": "1c4719c1", "metadata": { "collapsed": false, "editable": true @@ -626,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "c382e2f2", + "id": "debaaadc", "metadata": { "editable": true }, @@ -636,7 +638,7 @@ }, { "cell_type": "markdown", - "id": "1bec2330", + "id": "7d576f19", "metadata": { "editable": true }, @@ -653,7 +655,7 @@ }, { "cell_type": "markdown", - "id": "165fb3f3", + "id": "582b3b43", "metadata": { "editable": true }, @@ -665,7 +667,7 @@ }, { "cell_type": "markdown", - "id": "7ae8de36", + "id": "c8eace47", "metadata": { "editable": true }, @@ -675,7 +677,7 @@ }, { "cell_type": "markdown", - "id": "9a2729ab", + "id": "81ec9945", "metadata": { "editable": true }, @@ -687,7 +689,7 @@ }, { "cell_type": "markdown", - "id": "372f0fac", + "id": "c35e1f69", "metadata": { "editable": true }, @@ -703,7 +705,7 @@ }, { "cell_type": "markdown", - "id": "d4f432cc", + "id": "05b8eea9", "metadata": { "editable": true }, @@ -715,7 +717,7 @@ }, { "cell_type": "markdown", - "id": "064af49b", + "id": "7ef9cb55", "metadata": { "editable": true }, @@ -727,7 +729,7 @@ }, { "cell_type": "markdown", - "id": "91115cc6", + "id": "1eb5c5ac", "metadata": { "editable": true }, @@ -738,7 +740,7 @@ }, { "cell_type": "markdown", - "id": "c38d1990", + "id": "00492358", "metadata": { "editable": true }, @@ -750,7 +752,7 @@ }, { "cell_type": "markdown", - "id": "43de152e", + "id": "45cca5aa", "metadata": { "editable": true }, @@ -763,7 +765,7 @@ }, { "cell_type": "markdown", - "id": "f935912b", + "id": "22cfb40b", "metadata": { "editable": true }, @@ -775,7 +777,7 @@ }, { "cell_type": "markdown", - "id": "15b380de", + "id": "45b30d06", "metadata": { "editable": true }, @@ -785,7 +787,7 @@ }, { "cell_type": "markdown", - "id": "302da250", + "id": "ebd6a7a5", "metadata": { "editable": true }, @@ -797,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "3faf23cf", + "id": "659dd686", "metadata": { "editable": true }, @@ -809,7 +811,7 @@ }, { "cell_type": "markdown", - "id": "4fe83376", + "id": "34a1d4ca", "metadata": { "editable": true }, @@ -821,7 +823,7 @@ }, { "cell_type": "markdown", - "id": "9bee26b1", + "id": "34471712", "metadata": { "editable": true }, @@ -831,7 +833,7 @@ }, { "cell_type": "markdown", - "id": "9affa08f", + "id": "0b3a74fd", "metadata": { "editable": true }, @@ -843,7 +845,7 @@ }, { "cell_type": "markdown", - "id": "1866378d", + "id": "1a5bdab3", "metadata": { "editable": true }, @@ -859,7 +861,7 @@ }, { "cell_type": "markdown", - "id": "e6d27f9d", + "id": "37f19e78", "metadata": { "editable": true }, @@ -871,7 +873,7 @@ }, { "cell_type": "markdown", - "id": "b33dac74", + "id": "5505aab8", "metadata": { "editable": true }, @@ -881,7 +883,7 @@ }, { "cell_type": "markdown", - "id": "27c367b4", + "id": "d55d045c", "metadata": { "editable": true }, @@ -893,7 +895,7 @@ }, { "cell_type": "markdown", - "id": "18898e14", + "id": "04f101e7", "metadata": { "editable": true }, @@ -903,7 +905,7 @@ }, { "cell_type": "markdown", - "id": "31fcc7f9", + "id": "bfab2e91", "metadata": { "editable": true }, @@ -915,7 +917,7 @@ }, { "cell_type": "markdown", - "id": "76219fdd", + "id": "77f35b7e", "metadata": { "editable": true }, @@ -927,7 +929,7 @@ }, { "cell_type": "markdown", - "id": "2cbccf94", + "id": "8cf4a606", "metadata": { "editable": true }, @@ -940,7 +942,7 @@ }, { "cell_type": "markdown", - "id": "ccdb071b", + "id": "86951351", "metadata": { "editable": true }, @@ -950,7 +952,7 @@ }, { "cell_type": "markdown", - "id": "55e4bed1", + "id": "73414e65", "metadata": { "editable": true }, @@ -962,7 +964,7 @@ }, { "cell_type": "markdown", - "id": "c00fd151", + "id": "8f0aaa15", "metadata": { "editable": true }, @@ -972,7 +974,7 @@ }, { "cell_type": "markdown", - "id": "d49ae60d", + "id": "730c5415", "metadata": { "editable": true }, @@ -984,7 +986,7 @@ }, { "cell_type": "markdown", - "id": "920db2dd", + "id": "1afcb5a1", "metadata": { "editable": true }, @@ -995,7 +997,7 @@ }, { "cell_type": "markdown", - "id": "62806f12", + "id": "7f30cb44", "metadata": { "editable": true }, @@ -1007,7 +1009,7 @@ }, { "cell_type": "markdown", - "id": "f1d3e7b6", + "id": "14c045ce", "metadata": { "editable": true }, @@ -1017,7 +1019,7 @@ }, { "cell_type": "markdown", - "id": "51fd0b81", + "id": "0c1a2c68", "metadata": { "editable": true }, @@ -1029,7 +1031,7 @@ }, { "cell_type": "markdown", - "id": "ba9dd4ad", + "id": "a3385222", "metadata": { "editable": true }, @@ -1039,7 +1041,7 @@ }, { "cell_type": "markdown", - "id": "91137440", + "id": "18ee3804", "metadata": { "editable": true }, @@ -1051,7 +1053,7 @@ }, { "cell_type": "markdown", - "id": "8e2ecb8c", + "id": "ad741d56", "metadata": { "editable": true }, @@ -1063,7 +1065,7 @@ }, { "cell_type": "markdown", - "id": "8d91daf9", + "id": "65870a70", "metadata": { "editable": true }, @@ -1075,7 +1077,7 @@ }, { "cell_type": "markdown", - "id": "8450f964", + "id": "f7807fdc", "metadata": { "editable": true }, @@ -1085,7 +1087,7 @@ }, { "cell_type": "markdown", - "id": "1e662a52", + "id": "9af4a759", "metadata": { "editable": true }, @@ -1097,7 +1099,7 @@ }, { "cell_type": "markdown", - "id": "e90d34b5", + "id": "dc548cb7", "metadata": { "editable": true }, @@ -1107,7 +1109,7 @@ }, { "cell_type": "markdown", - "id": "2d4b194d", + "id": "83b75e94", "metadata": { "editable": true }, @@ -1119,7 +1121,7 @@ }, { "cell_type": "markdown", - "id": "8990fe0b", + "id": "1c2be559", "metadata": { "editable": true }, @@ -1131,7 +1133,7 @@ }, { "cell_type": "markdown", - "id": "37e9e142", + "id": "18b85f86", "metadata": { "editable": true }, @@ -1143,7 +1145,7 @@ }, { "cell_type": "markdown", - "id": "5f66c64a", + "id": "63e39eb4", "metadata": { "editable": true }, @@ -1153,7 +1155,7 @@ }, { "cell_type": "markdown", - "id": "03e836ad", + "id": "a55371c1", "metadata": { "editable": true }, @@ -1165,7 +1167,7 @@ }, { "cell_type": "markdown", - "id": "1ea8a6ff", + "id": "fa31a9b3", "metadata": { "editable": true }, @@ -1175,7 +1177,7 @@ }, { "cell_type": "markdown", - "id": "84537cc9", + "id": "580df891", "metadata": { "editable": true }, @@ -1188,7 +1190,7 @@ }, { "cell_type": "markdown", - "id": "2bad6141", + "id": "c10bf2ce", "metadata": { "editable": true }, @@ -1200,7 +1202,7 @@ }, { "cell_type": "markdown", - "id": "5150b413", + "id": "0bae11f8", "metadata": { "editable": true }, @@ -1210,7 +1212,7 @@ }, { "cell_type": "markdown", - "id": "4166af55", + "id": "ed4a8b93", "metadata": { "editable": true }, @@ -1222,7 +1224,7 @@ }, { "cell_type": "markdown", - "id": "e5101f70", + "id": "2d582987", "metadata": { "editable": true }, @@ -1232,7 +1234,7 @@ }, { "cell_type": "markdown", - "id": "0c662571", + "id": "5fa760a1", "metadata": { "editable": true }, @@ -1244,7 +1246,7 @@ }, { "cell_type": "markdown", - "id": "a7e1af99", + "id": "bc9de8bf", "metadata": { "editable": true }, @@ -1254,7 +1256,7 @@ }, { "cell_type": "markdown", - "id": "5a73623e", + "id": "f00e3ace", "metadata": { "editable": true }, @@ -1266,7 +1268,7 @@ }, { "cell_type": "markdown", - "id": "b1d5327b", + "id": "7ac96362", "metadata": { "editable": true }, @@ -1276,7 +1278,7 @@ }, { "cell_type": "markdown", - "id": "5cc5921c", + "id": "9c46f966", "metadata": { "editable": true }, @@ -1293,7 +1295,7 @@ }, { "cell_type": "markdown", - "id": "21633b14", + "id": "ea509b11", "metadata": { "editable": true }, @@ -1305,7 +1307,7 @@ }, { "cell_type": "markdown", - "id": "171782c4", + "id": "e08ff771", "metadata": { "editable": true }, @@ -1317,7 +1319,7 @@ }, { "cell_type": "markdown", - "id": "830e0cc3", + "id": "6f476983", "metadata": { "editable": true }, @@ -1333,7 +1335,7 @@ }, { "cell_type": "markdown", - "id": "3de97402", + "id": "0535d087", "metadata": { "editable": true }, @@ -1350,7 +1352,7 @@ }, { "cell_type": "markdown", - "id": "f4a20e55", + "id": "5e024ec1", "metadata": { "editable": true }, @@ -1362,7 +1364,7 @@ }, { "cell_type": "markdown", - "id": "e373e6cc", + "id": "239fb4c6", "metadata": { "editable": true }, @@ -1375,7 +1377,7 @@ }, { "cell_type": "markdown", - "id": "a9fa6a69", + "id": "7e4fa6c5", "metadata": { "editable": true }, @@ -1387,7 +1389,7 @@ }, { "cell_type": "markdown", - "id": "f1730e5a", + "id": "c47cc3c6", "metadata": { "editable": true }, @@ -1403,7 +1405,7 @@ }, { "cell_type": "markdown", - "id": "59d7d98a", + "id": "4eb89f11", "metadata": { "editable": true }, @@ -1415,7 +1417,7 @@ }, { "cell_type": "markdown", - "id": "5a3d0931", + "id": "92744a90", "metadata": { "editable": true }, @@ -1431,7 +1433,7 @@ }, { "cell_type": "markdown", - "id": "c56d749e", + "id": "35424d45", "metadata": { "editable": true }, @@ -1443,7 +1445,7 @@ }, { "cell_type": "markdown", - "id": "f3dd37e7", + "id": "b8502930", "metadata": { "editable": true }, @@ -1455,7 +1457,7 @@ }, { "cell_type": "markdown", - "id": "7654c47c", + "id": "81ad45a5", "metadata": { "editable": true }, @@ -1465,7 +1467,7 @@ }, { "cell_type": "markdown", - "id": "cb1aa2a9", + "id": "11bb8afb", "metadata": { "editable": true }, @@ -1477,7 +1479,7 @@ }, { "cell_type": "markdown", - "id": "11607454", + "id": "b53ec752", "metadata": { "editable": true }, @@ -1487,7 +1489,7 @@ }, { "cell_type": "markdown", - "id": "29a881cd", + "id": "b7519a84", "metadata": { "editable": true }, @@ -1499,7 +1501,7 @@ }, { "cell_type": "markdown", - "id": "1244c442", + "id": "c57689db", "metadata": { "editable": true }, @@ -1513,7 +1515,7 @@ }, { "cell_type": "markdown", - "id": "7d43f636", + "id": "a9f83b15", "metadata": { "editable": true }, @@ -1525,7 +1527,7 @@ }, { "cell_type": "markdown", - "id": "c23708ab", + "id": "067c2583", "metadata": { "editable": true }, @@ -1535,7 +1537,7 @@ }, { "cell_type": "markdown", - "id": "3a3d49b9", + "id": "43545710", "metadata": { "editable": true }, @@ -1547,7 +1549,7 @@ }, { "cell_type": "markdown", - "id": "31b8b489", + "id": "1eb33717", "metadata": { "editable": true }, @@ -1557,7 +1559,7 @@ }, { "cell_type": "markdown", - "id": "2cb11e87", + "id": "e09a8734", "metadata": { "editable": true }, @@ -1569,7 +1571,7 @@ }, { "cell_type": "markdown", - "id": "85b6783b", + "id": "3dc0f5a3", "metadata": { "editable": true }, @@ -1581,7 +1583,7 @@ }, { "cell_type": "markdown", - "id": "1d9102e8", + "id": "bb58784b", "metadata": { "editable": true }, @@ -1593,7 +1595,7 @@ }, { "cell_type": "markdown", - "id": "92547c80", + "id": "10aea094", "metadata": { "editable": true }, @@ -1603,7 +1605,7 @@ }, { "cell_type": "markdown", - "id": "e06d7f47", + "id": "b7cc2db8", "metadata": { "editable": true }, @@ -1615,7 +1617,7 @@ }, { "cell_type": "markdown", - "id": "a15b2c15", + "id": "6cce9a62", "metadata": { "editable": true }, @@ -1625,7 +1627,7 @@ }, { "cell_type": "markdown", - "id": "69a96bb6", + "id": "43e5a84b", "metadata": { "editable": true }, @@ -1637,7 +1639,7 @@ }, { "cell_type": "markdown", - "id": "6954d50b", + "id": "d5c607a7", "metadata": { "editable": true }, @@ -1655,7 +1657,7 @@ }, { "cell_type": "markdown", - "id": "a8d2b720", + "id": "a51b3b58", "metadata": { "editable": true }, @@ -1673,7 +1675,7 @@ }, { "cell_type": "markdown", - "id": "b40feaea", + "id": "4cd9d058", "metadata": { "editable": true }, @@ -1685,7 +1687,7 @@ }, { "cell_type": "markdown", - "id": "04d0916c", + "id": "c80b630d", "metadata": { "editable": true }, @@ -1695,7 +1697,7 @@ }, { "cell_type": "markdown", - "id": "4067515f", + "id": "dc0c1a06", "metadata": { "editable": true }, @@ -1707,7 +1709,7 @@ }, { "cell_type": "markdown", - "id": "572f5043", + "id": "8f2065b7", "metadata": { "editable": true }, @@ -1719,7 +1721,7 @@ }, { "cell_type": "markdown", - "id": "4272e56c", + "id": "7f89b9d8", "metadata": { "editable": true }, @@ -1731,7 +1733,7 @@ }, { "cell_type": "markdown", - "id": "3ffcc3a4", + "id": "49c2cd3f", "metadata": { "editable": true }, @@ -1741,7 +1743,7 @@ }, { "cell_type": "markdown", - "id": "87dc5557", + "id": "517b1a37", "metadata": { "editable": true }, @@ -1753,7 +1755,7 @@ }, { "cell_type": "markdown", - "id": "36f9508b", + "id": "65c8107f", "metadata": { "editable": true }, @@ -1763,7 +1765,7 @@ }, { "cell_type": "markdown", - "id": "5e7f7ab6", + "id": "2a10f902", "metadata": { "editable": true }, @@ -1775,7 +1777,7 @@ }, { "cell_type": "markdown", - "id": "b5caac62", + "id": "b2ebf9c2", "metadata": { "editable": true }, @@ -1793,7 +1795,7 @@ }, { "cell_type": "markdown", - "id": "beffe853", + "id": "90336322", "metadata": { "editable": true }, @@ -1803,7 +1805,7 @@ }, { "cell_type": "markdown", - "id": "9ff991bb", + "id": "f25ff166", "metadata": { "editable": true }, @@ -1821,7 +1823,7 @@ }, { "cell_type": "markdown", - "id": "5c75d805", + "id": "4cf11d5e", "metadata": { "editable": true }, @@ -1831,7 +1833,7 @@ }, { "cell_type": "markdown", - "id": "df242f2d", + "id": "2670748d", "metadata": { "editable": true }, @@ -1849,7 +1851,7 @@ }, { "cell_type": "markdown", - "id": "18a65420", + "id": "18c29f71", "metadata": { "editable": true }, @@ -1861,7 +1863,7 @@ }, { "cell_type": "markdown", - "id": "04cb64d1", + "id": "c593470c", "metadata": { "editable": true }, @@ -1873,7 +1875,7 @@ }, { "cell_type": "markdown", - "id": "c5320606", + "id": "28e8caef", "metadata": { "editable": true }, @@ -1883,7 +1885,7 @@ }, { "cell_type": "markdown", - "id": "58b67295", + "id": "516de9d7", "metadata": { "editable": true }, @@ -1895,7 +1897,7 @@ }, { "cell_type": "markdown", - "id": "3b7c74a4", + "id": "004c0bf4", "metadata": { "editable": true }, @@ -1907,7 +1909,7 @@ }, { "cell_type": "markdown", - "id": "76ff59e0", + "id": "d62a3b1f", "metadata": { "editable": true }, @@ -1917,7 +1919,7 @@ }, { "cell_type": "markdown", - "id": "60a7be03", + "id": "e9af770e", "metadata": { "editable": true }, @@ -1929,7 +1931,7 @@ }, { "cell_type": "markdown", - "id": "27739d6d", + "id": "eca56f17", "metadata": { "editable": true }, @@ -1939,7 +1941,7 @@ }, { "cell_type": "markdown", - "id": "1efdb6f5", + "id": "bb0e4414", "metadata": { "editable": true }, @@ -1951,7 +1953,7 @@ }, { "cell_type": "markdown", - "id": "b0b04f61", + "id": "a4b190fc", "metadata": { "editable": true }, @@ -1963,7 +1965,7 @@ }, { "cell_type": "markdown", - "id": "e6c4318c", + "id": "ec0f87c0", "metadata": { "editable": true }, @@ -1989,7 +1991,7 @@ }, { "cell_type": "markdown", - "id": "4e58634a", + "id": "2fb45155", "metadata": { "editable": true }, @@ -2012,7 +2014,7 @@ }, { "cell_type": "markdown", - "id": "690eb424", + "id": "3d5c2a0e", "metadata": { "editable": true }, @@ -2024,7 +2026,7 @@ }, { "cell_type": "markdown", - "id": "5f475d02", + "id": "9183bbd0", "metadata": { "editable": true }, @@ -2036,7 +2038,7 @@ }, { "cell_type": "markdown", - "id": "016ce549", + "id": "32ece956", "metadata": { "editable": true }, @@ -2046,7 +2048,7 @@ }, { "cell_type": "markdown", - "id": "51f9ed82", + "id": "466d6bda", "metadata": { "editable": true }, @@ -2058,7 +2060,7 @@ }, { "cell_type": "markdown", - "id": "a8996176", + "id": "9f31b228", "metadata": { "editable": true }, @@ -2072,7 +2074,7 @@ }, { "cell_type": "markdown", - "id": "aaf186a8", + "id": "fbeac005", "metadata": { "editable": true }, @@ -2084,7 +2086,7 @@ }, { "cell_type": "markdown", - "id": "3b8a0a79", + "id": "bc6ae984", "metadata": { "editable": true }, @@ -2096,7 +2098,7 @@ }, { "cell_type": "markdown", - "id": "299cc7bb", + "id": "65f3133d", "metadata": { "editable": true }, @@ -2106,7 +2108,7 @@ }, { "cell_type": "markdown", - "id": "3b10a1a0", + "id": "5d27bbe1", "metadata": { "editable": true }, @@ -2118,7 +2120,7 @@ }, { "cell_type": "markdown", - "id": "0f8769f8", + "id": "5e5d0aa0", "metadata": { "editable": true }, @@ -2130,7 +2132,7 @@ }, { "cell_type": "markdown", - "id": "03860e2f", + "id": "ea32e5bb", "metadata": { "editable": true }, @@ -2140,7 +2142,7 @@ }, { "cell_type": "markdown", - "id": "00cea1da", + "id": "3a9bb5a6", "metadata": { "editable": true }, @@ -2152,7 +2154,7 @@ }, { "cell_type": "markdown", - "id": "fe5bbd2a", + "id": "9008dcf8", "metadata": { "editable": true }, @@ -2164,7 +2166,7 @@ }, { "cell_type": "markdown", - "id": "e791fb56", + "id": "89aba7d6", "metadata": { "editable": true }, @@ -2187,7 +2189,7 @@ }, { "cell_type": "markdown", - "id": "14ed4124", + "id": "ea0cdce2", "metadata": { "editable": true }, @@ -2206,7 +2208,7 @@ }, { "cell_type": "markdown", - "id": "d6b31eb8", + "id": "91342c80", "metadata": { "editable": true }, @@ -2218,7 +2220,7 @@ }, { "cell_type": "markdown", - "id": "2be10af5", + "id": "bd6eb22a", "metadata": { "editable": true }, @@ -2228,7 +2230,7 @@ }, { "cell_type": "markdown", - "id": "f45b9a99", + "id": "4e75b2ab", "metadata": { "editable": true }, @@ -2240,7 +2242,7 @@ }, { "cell_type": "markdown", - "id": "865d802b", + "id": "1626d9b7", "metadata": { "editable": true }, @@ -2257,7 +2259,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "37773874", + "id": "4ac7c23c", "metadata": { "collapsed": false, "editable": true @@ -2341,7 +2343,7 @@ }, { "cell_type": "markdown", - "id": "9cccb9ca", + "id": "6aeb0ee4", "metadata": { "editable": true }, @@ -2363,7 +2365,7 @@ }, { "cell_type": "markdown", - "id": "a42f7226", + "id": "ea47d1d6", "metadata": { "editable": true }, @@ -2381,7 +2383,7 @@ }, { "cell_type": "markdown", - "id": "0f57d23f", + "id": "1947aa95", "metadata": { "editable": true }, @@ -2404,7 +2406,7 @@ }, { "cell_type": "markdown", - "id": "ad459faf", + "id": "d024119f", "metadata": { "editable": true }, @@ -2423,7 +2425,7 @@ }, { "cell_type": "markdown", - "id": "1e307870", + "id": "c9178132", "metadata": { "editable": true }, @@ -2451,7 +2453,7 @@ }, { "cell_type": "markdown", - "id": "06fe5be6", + "id": "756185f5", "metadata": { "editable": true }, @@ -2471,7 +2473,7 @@ }, { "cell_type": "markdown", - "id": "736441f3", + "id": "3d92cad4", "metadata": { "editable": true }, @@ -2492,7 +2494,7 @@ }, { "cell_type": "markdown", - "id": "9ac6f21d", + "id": "cbc6f721", "metadata": { "editable": true }, @@ -2506,7 +2508,7 @@ }, { "cell_type": "markdown", - "id": "80ebd77c", + "id": "9249dc7b", "metadata": { "editable": true }, @@ -2518,7 +2520,7 @@ }, { "cell_type": "markdown", - "id": "2566a903", + "id": "e59de3af", "metadata": { "editable": true }, @@ -2540,7 +2542,7 @@ }, { "cell_type": "markdown", - "id": "382f5fe1", + "id": "e2da998c", "metadata": { "editable": true }, @@ -2562,7 +2564,7 @@ }, { "cell_type": "markdown", - "id": "fed07226", + "id": "e1abf01e", "metadata": { "editable": true }, @@ -2591,7 +2593,7 @@ }, { "cell_type": "markdown", - "id": "9ddc2586", + "id": "a8ded7cd", "metadata": { "editable": true }, @@ -2617,7 +2619,7 @@ }, { "cell_type": "markdown", - "id": "d327b303", + "id": "96da4f48", "metadata": { "editable": true }, @@ -2643,7 +2645,7 @@ }, { "cell_type": "markdown", - "id": "a3f4a57d", + "id": "395346a7", "metadata": { "editable": true }, @@ -2663,7 +2665,7 @@ }, { "cell_type": "markdown", - "id": "da0c8dbe", + "id": "9c712bbb", "metadata": { "editable": true }, @@ -2683,7 +2685,7 @@ }, { "cell_type": "markdown", - "id": "60e3da23", + "id": "2b66ea72", "metadata": { "editable": true }, @@ -2709,7 +2711,7 @@ }, { "cell_type": "markdown", - "id": "17f8f5ed", + "id": "5acbc082", "metadata": { "editable": true }, @@ -2738,7 +2740,7 @@ }, { "cell_type": "markdown", - "id": "06ba3896", + "id": "31825b65", "metadata": { "editable": true }, @@ -2756,7 +2758,7 @@ }, { "cell_type": "markdown", - "id": "72bc99e6", + "id": "c76d9af9", "metadata": { "editable": true }, @@ -2772,7 +2774,7 @@ }, { "cell_type": "markdown", - "id": "d5f452a2", + "id": "bdc93363", "metadata": { "editable": true }, @@ -2784,7 +2786,7 @@ }, { "cell_type": "markdown", - "id": "63889ee1", + "id": "a1d6ff64", "metadata": { "editable": true }, @@ -2798,7 +2800,7 @@ }, { "cell_type": "markdown", - "id": "5f47ef0f", + "id": "0c2e5742", "metadata": { "editable": true }, @@ -2826,7 +2828,7 @@ }, { "cell_type": "markdown", - "id": "b08a7b7e", + "id": "d4da3f02", "metadata": { "editable": true }, @@ -2838,7 +2840,7 @@ }, { "cell_type": "markdown", - "id": "10220190", + "id": "01ea2e0b", "metadata": { "editable": true }, @@ -2848,7 +2850,7 @@ }, { "cell_type": "markdown", - "id": "0fb4d5ad", + "id": "9c1c7bec", "metadata": { "editable": true }, @@ -2860,7 +2862,7 @@ }, { "cell_type": "markdown", - "id": "f8aa1bae", + "id": "9238ff2d", "metadata": { "editable": true }, @@ -2871,7 +2873,7 @@ }, { "cell_type": "markdown", - "id": "17de8e22", + "id": "3be74bd1", "metadata": { "editable": true }, @@ -2883,7 +2885,7 @@ }, { "cell_type": "markdown", - "id": "ca8f4f94", + "id": "2e2fd39c", "metadata": { "editable": true }, @@ -2896,7 +2898,7 @@ }, { "cell_type": "markdown", - "id": "ca998f7f", + "id": "42b1d26b", "metadata": { "editable": true }, @@ -2921,7 +2923,7 @@ }, { "cell_type": "markdown", - "id": "525b0573", + "id": "f740a484", "metadata": { "editable": true }, @@ -2934,7 +2936,7 @@ }, { "cell_type": "markdown", - "id": "a9279995", + "id": "19189bfc", "metadata": { "editable": true }, @@ -2946,7 +2948,7 @@ }, { "cell_type": "markdown", - "id": "e6cef751", + "id": "aeb3ef60", "metadata": { "editable": true }, @@ -2958,7 +2960,7 @@ }, { "cell_type": "markdown", - "id": "0ec11e1d", + "id": "dbf419a1", "metadata": { "editable": true }, @@ -2968,7 +2970,7 @@ }, { "cell_type": "markdown", - "id": "e5d6a067", + "id": "9e345753", "metadata": { "editable": true }, @@ -2980,7 +2982,7 @@ }, { "cell_type": "markdown", - "id": "add6e597", + "id": "3b13095e", "metadata": { "editable": true }, @@ -2992,7 +2994,7 @@ }, { "cell_type": "markdown", - "id": "dc7ca42d", + "id": "96501a91", "metadata": { "editable": true }, @@ -3004,7 +3006,7 @@ }, { "cell_type": "markdown", - "id": "80b56aa5", + "id": "48cf79fe", "metadata": { "editable": true }, @@ -3016,7 +3018,7 @@ }, { "cell_type": "markdown", - "id": "72a87573", + "id": "3243c0b1", "metadata": { "editable": true }, @@ -3026,7 +3028,7 @@ }, { "cell_type": "markdown", - "id": "ff8418ea", + "id": "bb312a09", "metadata": { "editable": true }, @@ -3038,7 +3040,7 @@ }, { "cell_type": "markdown", - "id": "dd978909", + "id": "484cf2b4", "metadata": { "editable": true }, @@ -3048,7 +3050,7 @@ }, { "cell_type": "markdown", - "id": "ce5a0650", + "id": "2b9c5483", "metadata": { "editable": true }, @@ -3060,7 +3062,7 @@ }, { "cell_type": "markdown", - "id": "dce8478b", + "id": "5ca21f09", "metadata": { "editable": true }, @@ -3073,7 +3075,7 @@ }, { "cell_type": "markdown", - "id": "92f7282e", + "id": "4852e4d2", "metadata": { "editable": true }, @@ -3085,7 +3087,7 @@ }, { "cell_type": "markdown", - "id": "e83bc7a2", + "id": "e3b7cbef", "metadata": { "editable": true }, @@ -3095,7 +3097,7 @@ }, { "cell_type": "markdown", - "id": "04f9d7f2", + "id": "0c1e69a1", "metadata": { "editable": true }, @@ -3107,7 +3109,7 @@ }, { "cell_type": "markdown", - "id": "c70ab677", + "id": "e71df7f4", "metadata": { "editable": true }, @@ -3118,7 +3120,7 @@ }, { "cell_type": "markdown", - "id": "801a6bd2", + "id": "50d6fecc", "metadata": { "editable": true }, @@ -3130,7 +3132,7 @@ }, { "cell_type": "markdown", - "id": "38eeee4b", + "id": "e145e461", "metadata": { "editable": true }, @@ -3140,7 +3142,7 @@ }, { "cell_type": "markdown", - "id": "d70ddf11", + "id": "97f13260", "metadata": { "editable": true }, @@ -3152,7 +3154,7 @@ }, { "cell_type": "markdown", - "id": "324ee5e0", + "id": "4361ce3b", "metadata": { "editable": true }, @@ -3162,7 +3164,7 @@ }, { "cell_type": "markdown", - "id": "3366df27", + "id": "52a16654", "metadata": { "editable": true }, @@ -3173,7 +3175,7 @@ }, { "cell_type": "markdown", - "id": "c9a2bd62", + "id": "3bfb321e", "metadata": { "editable": true }, @@ -3186,7 +3188,7 @@ }, { "cell_type": "markdown", - "id": "401183f6", + "id": "eccac6c9", "metadata": { "editable": true }, @@ -3196,7 +3198,7 @@ }, { "cell_type": "markdown", - "id": "d4e6a79e", + "id": "23634198", "metadata": { "editable": true }, @@ -3208,7 +3210,7 @@ }, { "cell_type": "markdown", - "id": "61cfab52", + "id": "7a2e75ba", "metadata": { "editable": true }, @@ -3218,7 +3220,7 @@ }, { "cell_type": "markdown", - "id": "fc5cf891", + "id": "2dad2d14", "metadata": { "editable": true }, @@ -3230,7 +3232,7 @@ }, { "cell_type": "markdown", - "id": "2e7f3950", + "id": "46415917", "metadata": { "editable": true }, @@ -3240,7 +3242,7 @@ }, { "cell_type": "markdown", - "id": "144969f6", + "id": "6adc7c1e", "metadata": { "editable": true }, @@ -3264,7 +3266,7 @@ }, { "cell_type": "markdown", - "id": "b6e503bd", + "id": "4110d83e", "metadata": { "editable": true }, @@ -3314,7 +3316,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "54230ef9", + "id": "070c610d", "metadata": { "collapsed": false, "editable": true @@ -3367,7 +3369,7 @@ }, { "cell_type": "markdown", - "id": "6738e7b4", + "id": "28bb6085", "metadata": { "editable": true }, @@ -3388,7 +3390,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "f369aa9d", + "id": "5a6ae0b0", "metadata": { "collapsed": false, "editable": true @@ -3426,7 +3428,7 @@ }, { "cell_type": "markdown", - "id": "f8bf8d16", + "id": "c26d604d", "metadata": { "editable": true }, @@ -3470,7 +3472,7 @@ }, { "cell_type": "markdown", - "id": "112b8cc3", + "id": "2775283b", "metadata": { "editable": true }, @@ -3510,7 +3512,7 @@ }, { "cell_type": "markdown", - "id": "e4166103", + "id": "f7455c00", "metadata": { "editable": true }, @@ -3531,7 +3533,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "36399cb5", + "id": "20b3c8c0", "metadata": { "collapsed": false, "editable": true @@ -3557,7 +3559,7 @@ }, { "cell_type": "markdown", - "id": "5eaf095b", + "id": "a41d9acd", "metadata": { "editable": true }, @@ -3585,7 +3587,7 @@ }, { "cell_type": "markdown", - "id": "91eec6b8", + "id": "b2f64238", "metadata": { "editable": true }, @@ -3622,7 +3624,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "ef497434", + "id": "1f5589af", "metadata": { "collapsed": false, "editable": true @@ -3668,7 +3670,7 @@ }, { "cell_type": "markdown", - "id": "ab88238a", + "id": "4518e911", "metadata": { "editable": true }, @@ -3699,7 +3701,7 @@ }, { "cell_type": "markdown", - "id": "506145ff", + "id": "d519516b", "metadata": { "editable": true }, @@ -3737,7 +3739,7 @@ }, { "cell_type": "markdown", - "id": "e8138025", + "id": "46b71202", "metadata": { "editable": true }, @@ -3771,7 +3773,7 @@ }, { "cell_type": "markdown", - "id": "25becf76", + "id": "129c39d3", "metadata": { "editable": true }, @@ -3812,7 +3814,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "657c604c", + "id": "8abafb44", "metadata": { "collapsed": false, "editable": true @@ -3891,7 +3893,7 @@ }, { "cell_type": "markdown", - "id": "3c595805", + "id": "e95c7166", "metadata": { "editable": true }, @@ -3912,7 +3914,7 @@ }, { "cell_type": "markdown", - "id": "17d5f534", + "id": "b4365471", "metadata": { "editable": true }, @@ -3926,7 +3928,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "5aeaa0cd", + "id": "5a0357b2", "metadata": { "collapsed": false, "editable": true @@ -4036,7 +4038,7 @@ }, { "cell_type": "markdown", - "id": "77f30e1e", + "id": "a417307d", "metadata": { "editable": true }, @@ -4055,7 +4057,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "c1ab41e1", + "id": "8ee4b306", "metadata": { "collapsed": false, "editable": true @@ -4082,7 +4084,7 @@ }, { "cell_type": "markdown", - "id": "1b2b35c3", + "id": "efcbd954", "metadata": { "editable": true }, @@ -4096,7 +4098,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "ac2ab4a6", + "id": "bb527e6e", "metadata": { "collapsed": false, "editable": true @@ -4127,7 +4129,7 @@ }, { "cell_type": "markdown", - "id": "f3e5dfec", + "id": "d282951d", "metadata": { "editable": true }, @@ -4138,7 +4140,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "6d875555", + "id": "69d3d9c8", "metadata": { "collapsed": false, "editable": true @@ -4182,7 +4184,7 @@ }, { "cell_type": "markdown", - "id": "81c742e3", + "id": "99f5058c", "metadata": { "editable": true }, @@ -4205,7 +4207,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "d21828bb", + "id": "7898d99f", "metadata": { "collapsed": false, "editable": true @@ -4232,7 +4234,7 @@ }, { "cell_type": "markdown", - "id": "4b40579d", + "id": "7ceec918", "metadata": { "editable": true }, @@ -4243,7 +4245,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "bfc97198", + "id": "98abf229", "metadata": { "collapsed": false, "editable": true @@ -4288,7 +4290,7 @@ }, { "cell_type": "markdown", - "id": "550680d5", + "id": "ba07c374", "metadata": { "editable": true }, @@ -4306,7 +4308,7 @@ }, { "cell_type": "markdown", - "id": "bbade60e", + "id": "1cf09819", "metadata": { "editable": true }, @@ -4341,7 +4343,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "e5505ed3", + "id": "2c2c3ec5", "metadata": { "collapsed": false, "editable": true @@ -4353,7 +4355,7 @@ }, { "cell_type": "markdown", - "id": "98d4797a", + "id": "39d013b1", "metadata": { "editable": true }, @@ -4365,7 +4367,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "95b05730", + "id": "fbf36c26", "metadata": { "collapsed": false, "editable": true @@ -4378,7 +4380,7 @@ }, { "cell_type": "markdown", - "id": "94170f18", + "id": "94e66380", "metadata": { "editable": true }, @@ -4389,7 +4391,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "65ae6e69", + "id": "5e72b1d2", "metadata": { "collapsed": false, "editable": true @@ -4402,7 +4404,7 @@ }, { "cell_type": "markdown", - "id": "df39c5c6", + "id": "40470dbd", "metadata": { "editable": true }, @@ -4417,7 +4419,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "d0d627f6", + "id": "f2cd4f41", "metadata": { "collapsed": false, "editable": true @@ -4429,7 +4431,7 @@ }, { "cell_type": "markdown", - "id": "4124b5af", + "id": "636940c6", "metadata": { "editable": true }, @@ -4441,7 +4443,7 @@ }, { "cell_type": "markdown", - "id": "22dc977c", + "id": "d9f47b57", "metadata": { "editable": true }, @@ -4454,7 +4456,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "7df2e4d4", + "id": "1489b5d5", "metadata": { "collapsed": false, "editable": true @@ -4509,7 +4511,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "4f5bff6f", + "id": "672dc5a2", "metadata": { "collapsed": false, "editable": true @@ -4538,7 +4540,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "3ae517ea", + "id": "0513084f", "metadata": { "collapsed": false, "editable": true @@ -4568,7 +4570,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "c880b209", + "id": "02a34777", "metadata": { "collapsed": false, "editable": true @@ -4595,7 +4597,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "cf8cea73", + "id": "52c1d6e2", "metadata": { "collapsed": false, "editable": true @@ -4637,7 +4639,7 @@ }, { "cell_type": "markdown", - "id": "3024761c", + "id": "53f9be79", "metadata": { "editable": true }, @@ -4656,7 +4658,7 @@ }, { "cell_type": "markdown", - "id": "53987675", + "id": "39bd1718", "metadata": { "editable": true }, @@ -4678,7 +4680,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "5ed03631", + "id": "4c1f42f1", "metadata": { "collapsed": false, "editable": true @@ -4819,7 +4821,7 @@ }, { "cell_type": "markdown", - "id": "8b98c385", + "id": "532aecc2", "metadata": { "editable": true }, @@ -4835,7 +4837,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "54298abd", + "id": "b24b4414", "metadata": { "collapsed": false, "editable": true @@ -4848,7 +4850,7 @@ }, { "cell_type": "markdown", - "id": "c03dc1b1", + "id": "32a25c0b", "metadata": { "editable": true }, @@ -4860,7 +4862,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "5a2f7871", + "id": "7a7d273f", "metadata": { "collapsed": false, "editable": true @@ -4882,7 +4884,7 @@ }, { "cell_type": "markdown", - "id": "07fa559a", + "id": "d34cd45c", "metadata": { "editable": true }, @@ -4898,7 +4900,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "718450a2", + "id": "9ad6425d", "metadata": { "collapsed": false, "editable": true @@ -4936,7 +4938,7 @@ }, { "cell_type": "markdown", - "id": "0db28b52", + "id": "baaaff79", "metadata": { "editable": true }, @@ -4949,7 +4951,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "1479de5a", + "id": "78f11b83", "metadata": { "collapsed": false, "editable": true @@ -4970,7 +4972,7 @@ }, { "cell_type": "markdown", - "id": "d42e1ccf", + "id": "05285af5", "metadata": { "editable": true }, @@ -4986,7 +4988,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "2c2a8d32", + "id": "7ac52c84", "metadata": { "collapsed": false, "editable": true @@ -5044,7 +5046,7 @@ }, { "cell_type": "markdown", - "id": "65e7caab", + "id": "873e7caa", "metadata": { "editable": true }, @@ -5059,7 +5061,7 @@ { "cell_type": "code", "execution_count": 29, - "id": "75e9399d", + "id": "bd43ac18", "metadata": { "collapsed": false, "editable": true @@ -5080,7 +5082,7 @@ }, { "cell_type": "markdown", - "id": "0b0b82e8", + "id": "3dc2175e", "metadata": { "editable": true }, @@ -5104,7 +5106,7 @@ { "cell_type": "code", "execution_count": 30, - "id": "5351bfd6", + "id": "5b4b161c", "metadata": { "collapsed": false, "editable": true @@ -5576,7 +5578,7 @@ }, { "cell_type": "markdown", - "id": "2d63ec5b", + "id": "9596ae53", "metadata": { "editable": true }, @@ -5588,7 +5590,7 @@ { "cell_type": "code", "execution_count": 31, - "id": "85a6b185", + "id": "a11f680f", "metadata": { "collapsed": false, "editable": true @@ -5632,7 +5634,7 @@ }, { "cell_type": "markdown", - "id": "f8842209", + "id": "0fc39e40", "metadata": { "editable": true }, @@ -5648,7 +5650,7 @@ { "cell_type": "code", "execution_count": 32, - "id": "b7b14d8f", + "id": "a67ab3a0", "metadata": { "collapsed": false, "editable": true @@ -5663,7 +5665,7 @@ }, { "cell_type": "markdown", - "id": "3e35cc67", + "id": "3add8665", "metadata": { "editable": true }, @@ -5674,7 +5676,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "c2b3e7a3", + "id": "4a4fbc7a", "metadata": { "collapsed": false, "editable": true @@ -5689,7 +5691,7 @@ }, { "cell_type": "markdown", - "id": "9d0eb8b2", + "id": "4dff1871", "metadata": { "editable": true }, @@ -5705,7 +5707,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "19fd68fe", + "id": "ad40e38c", "metadata": { "collapsed": false, "editable": true @@ -5719,7 +5721,7 @@ }, { "cell_type": "markdown", - "id": "ecbc4c88", + "id": "43cd1e22", "metadata": { "editable": true }, @@ -5734,7 +5736,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "c62f0877", + "id": "cde36b38", "metadata": { "collapsed": false, "editable": true @@ -5760,7 +5762,7 @@ { "cell_type": "code", "execution_count": 36, - "id": "5b955b7a", + "id": "2bc572a4", "metadata": { "collapsed": false, "editable": true @@ -5775,7 +5777,7 @@ }, { "cell_type": "markdown", - "id": "e4c3e9cc", + "id": "e3e6fa31", "metadata": { "editable": true }, @@ -5786,7 +5788,7 @@ { "cell_type": "code", "execution_count": 37, - "id": "4e994594", + "id": "575ceb29", "metadata": { "collapsed": false, "editable": true @@ -5801,7 +5803,7 @@ }, { "cell_type": "markdown", - "id": "690debd0", + "id": "622015f0", "metadata": { "editable": true }, @@ -5812,7 +5814,7 @@ { "cell_type": "code", "execution_count": 38, - "id": "ea04ae66", + "id": "9c075b36", "metadata": { "collapsed": false, "editable": true @@ -5832,7 +5834,7 @@ { "cell_type": "code", "execution_count": 39, - "id": "cd892db0", + "id": "44ded771", "metadata": { "collapsed": false, "editable": true @@ -5847,7 +5849,7 @@ }, { "cell_type": "markdown", - "id": "c85e6aa4", + "id": "317e6e5c", "metadata": { "editable": true }, @@ -5862,7 +5864,7 @@ { "cell_type": "code", "execution_count": 40, - "id": "1dc44b4d", + "id": "8911de9d", "metadata": { "collapsed": false, "editable": true @@ -5899,7 +5901,7 @@ }, { "cell_type": "markdown", - "id": "785a6539", + "id": "82d61377", "metadata": { "editable": true }, @@ -5912,7 +5914,7 @@ { "cell_type": "code", "execution_count": 41, - "id": "f2137088", + "id": "2a72a374", "metadata": { "collapsed": false, "editable": true @@ -5935,7 +5937,7 @@ }, { "cell_type": "markdown", - "id": "6caa78c7", + "id": "2d892009", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/_build/html/project2.html b/doc/LectureNotes/_build/html/project2.html index 658681044..299e9417a 100644 --- a/doc/LectureNotes/_build/html/project2.html +++ b/doc/LectureNotes/_build/html/project2.html @@ -424,6 +424,11 @@ document.write(`
  • Part g) Critical evaluation of the various algorithms
    • +
  • Summary of methods to implement and analyze +
  • Background literature
  • Introduction to numerical projects
  • Format for electronic delivery of report and programs
    • @@ -510,7 +515,7 @@ feed-forward neural network (FFNN) code. The exercises from week 41 and 42 (see

    • Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be

        -

      • The simple one-dimensional function Runge function from project 1, that is \(f(x) = \frac{1}{1+25x^2}\). We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the the two-dimensional Runge function \(f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1}\), or even more complicated two-dimensional functions (see the supplementary material of https://www.nature.com/articles/s41467-025-61362-4 for an extensive list of two-dimensional functions).

        • +

      • The simple one-dimensional function Runge function from project 1, that is \(f(x) = \frac{1}{1+25x^2}\). We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the two-dimensional Runge function \(f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1}\), or even more complicated two-dimensional functions (see the supplementary material of https://www.nature.com/articles/s41467-025-61362-4 for an extensive list of two-dimensional functions).

    • Classification.

      • @@ -670,7 +675,7 @@ represents the target and \(y_i\)Again, we strongly recommend that you compare your own neural Network code for classification and pertinent results against a similar code using Scikit-Learn or tensorflow/keras or pytorch.

      If you have time, you can use the functionality of scikit-learn and compare your neural network results with those from Logistic regression. This is optional. -The weblink here https://medium.com/ai-in-plain-english/comparison-between-logistic-regression-and-neural-networks-in-classifying-digits-dc5e85cd93c3compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article. Your neural network code can implement the equivalent of logistic regression by simply setting the number of hidden layers to zero.

      +The weblink here https://medium.com/ai-in-plain-english/comparison-between-logistic-regression-and-neural-networks-in-classifying-digits-dc5e85cd93c3compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article. Your neural network code can implement the equivalent of logistic regression by simply setting the number of hidden layers to zero and keeping just the input and the output layers.

      If you wish to compare with say Logisti Regression from scikit-learn, the following code uses the above data set

      @@ -699,6 +704,55 @@ is best for the classification case. These codes can also be part of your final project 3, but now applied to other data sets.

      +
      +

      Summary of methods to implement and analyze#

      +

      Required Implementation:

      +
        +

      1. Reuse the regression code and results from project 1, these will act as a benchmark for seeing how suited a neural network is for this regression task.

        2. +

      2. Implement a neural network with

        3. +
      +
        +

      • A flexible number of layers

        • +

      • A flexible number of nodes in each layer

        • +

      • A changeable activation function in each layer (Sigmoid, ReLU, LeakyReLU, as well as Linear and Softmax)

        • +

      • A changeable cost function, which will be set to MSE for regression and cross-entropy for multiple-classification

        • +

      • An optional L1 or L2 norm of the weights and biases in the cost function (only used for computing gradients, not interpretable metrics)

        • +
      +
        +

      1. Implement the back-propagation algorithm to compute the gradient of your neural network

        2. +

      2. Reuse the implementation of Plain and Stochastic Gradient Descent from Project 1 (and adapt the code to work with the your neural network)

        3. +
      +
        +

      • With no optimization algorithm

        • +

      • With RMS Prop

        • +

      • With ADAM

        • +
      +
        +

      1. Implement scaling and train-test splitting of your data, preferably using sklearn

        2. +

      2. Implement and compute metrics like the MSE and Accuracy

        3. +
      +
      +

      Required Analysis:#

      +
        +

      1. Briefly show and argue for the advantages and disadvantages of the methods from Project 1.

        2. +

      2. Explore and show the impact of changing the number of layers, nodes per layer, choice of activation function, and inclusion of L1 and L2 norms. Present only the most interesting results from this exploration. 2D Heatmaps will be good for this: Start with finding a well performing set of hyper-parameters, then change two at a time in a range that shows good and bad performance.

        3. +

      3. Show and argue for the advantages and disadvantages of using a neural network for regression on your data

        4. +

      4. Show and argue for the advantages and disadvantages of using a neural network for classification on your data

        5. +

      5. Show and argue for the advantages and disadvantages of the different gradient methods and learning rates when training the neural network

        6. +
      +
      +
      +

      Optional (Note that you should include at least two of these in the report):#

      +
        +

      1. Implement Logistic Regression as simple classification model case (equivalent to a Neural Network with just the output layer)

        2. +

      2. Compute the gradient of the neural network with autograd, to show that it gives the same result as your hand-written backpropagation.

        3. +

      3. Compare your results with results from using a machine-learning library like pytorch (https://docs.pytorch.org/tutorials/beginner/basics/buildmodel_tutorial.html)

        4. +

      4. Use a more complex classification dataset instead, like the fashion MNIST (see https://www.kaggle.com/datasets/zalando-research/fashionmnist)

        5. +

      5. Use a more complex regression dataset instead, like the two-dimensional Runge function \(f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1}\), or even more complicated two-dimensional functions (see the supplementary material of https://www.nature.com/articles/s41467-025-61362-4 for an extensive list of two-dimensional functions).

        6. +

      6. Compute and interpret a confusion matrix of your best classification model (see https://www.researchgate.net/figure/Confusion-matrix-of-MNIST-and-F-MNIST-embeddings_fig5_349758607)

        7. +
      +
      +

      Background literature#

        @@ -807,6 +861,11 @@ we encourage you to collaborate. Optimal working groups consist of
      1. Part g) Critical evaluation of the various algorithms
    +
  • Summary of methods to implement and analyze +
  • Background literature
  • Introduction to numerical projects
  • Format for electronic delivery of report and programs
    • diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js index 444471419..b4bfdece5 100644 --- a/doc/LectureNotes/_build/html/searchindex.js +++ b/doc/LectureNotes/_build/html/searchindex.js @@ -1 +1 @@ -Search.setIndex({"alltitles": {"1a)": [[18, "a"]], "3a)": [[18, "id1"]], "3b)": [[18, "b"]], "4a)": [[18, "id2"]], "4b)": [[18, "id3"]], "A Classification Tree": [[9, "a-classification-tree"]], "A Frequentist approach to data analysis": [[0, "a-frequentist-approach-to-data-analysis"], [31, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[31, "a-first-summary"]], "A more compact expression": [[36, "a-more-compact-expression"], [37, "a-more-compact-expression"]], "A new Cost Function": [[35, "a-new-cost-function"]], "A quick Reminder on Lagrangian Multipliers": [[8, "a-quick-reminder-on-lagrangian-multipliers"]], "A simple example": [[4, "a-simple-example"]], "A soft classifier": [[8, "a-soft-classifier"]], "A top-down perspective on Neural networks": [[1, "a-top-down-perspective-on-neural-networks"], [39, "a-top-down-perspective-on-neural-networks"]], "A way to Read the Bias-Variance Tradeoff": [[35, "a-way-to-read-the-bias-variance-tradeoff"], [36, "a-way-to-read-the-bias-variance-tradeoff"]], "ADAM algorithm, taken from Goodfellow et al": [[34, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[13, "adam-optimizer"], [34, "id2"]], "Accuracy": [[34, "accuracy"]], "Activation functions": [[12, "activation-functions"], [37, "activation-functions"], [39, "activation-functions"], [39, "id3"]], "Activation functions, Logistic and Hyperbolic ones": [[37, "activation-functions-logistic-and-hyperbolic-ones"], [39, "activation-functions-logistic-and-hyperbolic-ones"]], "AdaGrad Properties": [[34, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[34, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[34, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adam Optimizer": [[34, "adam-optimizer"]], "Adam vs. AdaGrad and RMSProp": [[34, "adam-vs-adagrad-and-rmsprop"]], "Adam: Bias Correction": [[34, "adam-bias-correction"]], "Adam: Exponential Moving Averages (Moments)": [[34, "adam-exponential-moving-averages-moments"]], "Adam: Update Rule Derivation": [[34, "adam-update-rule-derivation"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[10, "adaptive-boosting-adaboost-basic-algorithm"]], "Adaptivity Across Dimensions": [[34, "adaptivity-across-dimensions"]], "Adding Neural Networks": [[37, "adding-neural-networks"]], "Adding a hidden layer": [[38, "adding-a-hidden-layer"], [39, "adding-a-hidden-layer"]], "Adding error analysis and training set up": [[31, "adding-error-analysis-and-training-set-up"], [32, "adding-error-analysis-and-training-set-up"]], "Adjust hyperparameters": [[1, "adjust-hyperparameters"], [39, "adjust-hyperparameters"]], "Algorithms and codes for Adagrad, RMSprop and Adam": [[34, "algorithms-and-codes-for-adagrad-rmsprop-and-adam"]], "Algorithms for Setting up Decision Trees": [[9, "algorithms-for-setting-up-decision-trees"]], "An Overview of Ensemble Methods": [[10, "an-overview-of-ensemble-methods"]], "An extrapolation example": [[4, "an-extrapolation-example"]], "An optimization/minimization problem": [[31, "an-optimization-minimization-problem"]], "Analyzing the last results": [[38, "analyzing-the-last-results"], [39, "analyzing-the-last-results"]], "And finally \\boldsymbol{X}\\boldsymbol{X}^T": [[32, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[34, "and-finally-adam"]], "And what about using neural networks?": [[31, "and-what-about-using-neural-networks"]], "Another Example from Scikit-Learn\u2019s Repository": [[35, "another-example-from-scikit-learn-s-repository"], [36, "another-example-from-scikit-learn-s-repository"]], "Another Example, now with a polynomial fit": [[33, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[23, null]], "Artificial neurons": [[37, "artificial-neurons"], [38, "artificial-neurons"]], "Assumptions made": [[35, "assumptions-made"]], "Autocorrelation function": [[28, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"], [38, "automatic-differentiation"]], "Automatic differentiation through examples": [[38, "automatic-differentiation-through-examples"]], "Back to Ridge and LASSO Regression": [[32, "back-to-ridge-and-lasso-regression"], [33, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], "Background literature": [[25, "background-literature"], [26, "background-literature"]], "Bagging": [[10, "bagging"]], "Bagging Examples": [[10, "bagging-examples"]], "Basic Matrix Features": [[24, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[11, null]], "Basic math of the SVD": [[5, "basic-math-of-the-svd"], [32, "basic-math-of-the-svd"], [33, "basic-math-of-the-svd"]], "Basics": [[7, "basics"], [36, "basics"], [37, "basics"]], "Basics of a tree": [[9, "basics-of-a-tree"]], "Basics of an NN": [[38, "basics-of-an-nn"]], "Batch Normalization": [[1, "batch-normalization"], [39, "batch-normalization"]], "Batches and mini-batches": [[34, "batches-and-mini-batches"]], "Bayes\u2019 Theorem and Ridge and Lasso Regression": [[5, "bayes-theorem-and-ridge-and-lasso-regression"]], "Boosting, a Bird\u2019s Eye View": [[10, "boosting-a-bird-s-eye-view"]], "Bootstrap": [[6, "bootstrap"]], "Bringing it together": [[38, "bringing-it-together"], [39, "bringing-it-together"]], "Bringing it together, first back propagation equation": [[12, "bringing-it-together-first-back-propagation-equation"]], "Building a Feed Forward Neural Network": [[1, null]], "Building a neural network code": [[39, "building-a-neural-network-code"]], "Building a tree, regression": [[9, "building-a-tree-regression"]], "Building neural networks in Tensorflow and Keras": [[1, "building-neural-networks-in-tensorflow-and-keras"], [39, "building-neural-networks-in-tensorflow-and-keras"]], "But none of these can compete with Newton\u2019s method": [[34, "but-none-of-these-can-compete-with-newton-s-method"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[3, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Cancer Data again now with Decision Trees and other Methods": [[9, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Chain rule": [[38, "chain-rule"]], "Chain rule, forward and reverse modes": [[38, "chain-rule-forward-and-reverse-modes"]], "Challenge: Choosing a Fixed Learning Rate": [[34, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[1, "choose-cost-function-and-optimizer"], [39, "choose-cost-function-and-optimizer"]], "Class of functions we can approximate": [[38, "class-of-functions-we-can-approximate"]], "Classical PCA Theorem": [[11, "classical-pca-theorem"]], "Classification and Regression, writing our own neural network code": [[26, "classification-and-regression-writing-our-own-neural-network-code"]], "Classification problems": [[36, "classification-problems"], [37, "classification-problems"]], "Clustering and Unsupervised Learning": [[14, null]], "Code Example for Cross-validation and k-fold Cross-validation": [[35, "code-example-for-cross-validation-and-k-fold-cross-validation"], [36, "code-example-for-cross-validation-and-k-fold-cross-validation"]], "Code example": [[38, "code-example"], [39, "code-example"]], "Code example for the Bootstrap method": [[35, "code-example-for-the-bootstrap-method"]], "Code for SVD and Inversion of Matrices": [[5, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[34, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[14, "codes-and-approaches"]], "Codes for the SVD": [[5, "codes-for-the-svd"], [32, "codes-for-the-svd"], [33, "codes-for-the-svd"]], "Coding Setup and Linear Regression": [[15, "coding-setup-and-linear-regression"]], "Collect and pre-process data": [[1, "collect-and-pre-process-data"], [39, "collect-and-pre-process-data"], [39, "id2"]], "Communication channels": [[31, "communication-channels"]], "Compact expressions": [[38, "compact-expressions"], [39, "compact-expressions"]], "Compare Bagging on Trees with Random Forests": [[10, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[2, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[33, "comparison-with-ols"]], "Completing the list": [[38, "completing-the-list"], [39, "completing-the-list"]], "Computation of gradients": [[34, "computation-of-gradients"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[33, "conditions-on-convex-functions"]], "Confidence Intervals": [[35, "confidence-intervals"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convergence rates": [[34, "convergence-rates"]], "Convex function": [[33, "convex-function"]], "Convex functions": [[13, "convex-functions"], [33, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[3, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[3, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[12, "convolutional-neural-network"], [37, "convolutional-neural-network"], [38, "convolutional-neural-network"]], "Convolutional Neural Networks": [[3, null]], "Correlation Function and Design/Feature Matrix": [[32, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [32, "correlation-matrix"]], "Correlation Matrix with Pandas": [[32, "correlation-matrix-with-pandas"]], "Cost functions": [[39, "cost-functions"]], "Counting the number of floating point operations": [[38, "counting-the-number-of-floating-point-operations"]], "Course Format": [[31, "course-format"]], "Course setting": [[27, null]], "Covariance Matrix Examples": [[32, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[32, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Cross-validation in brief": [[35, "cross-validation-in-brief"], [36, "cross-validation-in-brief"]], "Deadlines for projects (tentative)": [[31, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep Neural Networks": [[34, "deep-neural-networks"]], "Deep learning methods": [[31, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"], [39, "define-model-and-architecture"]], "Defining intermediate operations": [[38, "defining-intermediate-operations"]], "Defining the cost function": [[1, "defining-the-cost-function"], [39, "defining-the-cost-function"]], "Definitions": [[19, "definitions"], [38, "definitions"], [39, "definitions"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"], [19, "deliverables"], [20, "deliverables"], [25, "deliverables"], [26, "deliverables"]], "Derivation of the AdaGrad Algorithm": [[34, "derivation-of-the-adagrad-algorithm"]], "Derivative of the cost function": [[38, "derivative-of-the-cost-function"], [39, "derivative-of-the-cost-function"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"], [38, "derivatives-and-the-chain-rule"], [39, "derivatives-and-the-chain-rule"]], "Derivatives in terms of z_j^L": [[38, "derivatives-in-terms-of-z-j-l"], [39, "derivatives-in-terms-of-z-j-l"]], "Derivatives of the hidden layer": [[38, "derivatives-of-the-hidden-layer"], [39, "derivatives-of-the-hidden-layer"]], "Derivatives, example 1": [[32, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"], [35, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the Lasso Regression Equations": [[32, "deriving-the-lasso-regression-equations"], [33, "deriving-the-lasso-regression-equations"], [33, "id6"]], "Deriving the Ridge Regression Equations": [[32, "deriving-the-ridge-regression-equations"], [33, "deriving-the-ridge-regression-equations"], [33, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"], [39, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[8, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[9, "disadvantages"]], "Discriminative Modeling": [[31, "discriminative-modeling"]], "Discussing the correlation data": [[37, "discussing-the-correlation-data"]], "Does Logistic Regression do a better Job?": [[37, "does-logistic-regression-do-a-better-job"]], "Domains and probabilities": [[28, "domains-and-probabilities"]], "Dropout": [[1, "dropout"], [39, "dropout"]], "ELU function": [[39, "elu-function"]], "Economy-size SVD": [[32, "economy-size-svd"], [33, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[28, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[34, "empirical-evidence-convergence-time-and-memory-in-practice"]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[31, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"], [39, "evaluate-model-performance-on-test-data"]], "Example 2": [[32, "example-2"]], "Example 3": [[32, "example-3"]], "Example 4": [[32, "example-4"]], "Example Matrix": [[32, "example-matrix"], [33, "example-matrix"]], "Example code for Bias-Variance tradeoff": [[35, "example-code-for-bias-variance-tradeoff"]], "Example code for Logistic Regression": [[36, "example-code-for-logistic-regression"], [37, "example-code-for-logistic-regression"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[31, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[31, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[32, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[32, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"], [39, "example-binary-classification-problem"]], "Examples": [[31, "examples"]], "Examples of XOR, OR and AND gates": [[37, "examples-of-xor-or-and-and-gates"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Examples of likelihood functions used in logistic regression and nueral networks": [[36, "examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks"]], "Exercise 1": [[21, "exercise-1"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1 - Understand the feed forward pass": [[22, "exercise-1-understand-the-feed-forward-pass"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Creating the report document": [[20, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Including more data": [[38, "exercise-1-including-more-data"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2": [[21, "exercise-2"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Gradient with one layer using autograd": [[22, "exercise-2-gradient-with-one-layer-using-autograd"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Adding good figures": [[20, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: Extended program": [[38, "exercise-2-extended-program"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3": [[21, "exercise-3"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Gradient with one layer writing backpropagation by hand": [[22, "exercise-3-gradient-with-one-layer-writing-backpropagation-by-hand"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[20, "exercise-3-writing-an-abstract-and-introduction"]], "Exercise 4 - Custom activation for each layer": [[21, "exercise-4-custom-activation-for-each-layer"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Gradient with two layers writing backpropagation by hand": [[22, "exercise-4-gradient-with-two-layers-writing-backpropagation-by-hand"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code available and presentable": [[20, "exercise-4-making-the-code-available-and-presentable"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5 - Gradient with any number of layers writing backpropagation by hand": [[22, "exercise-5-gradient-with-any-number-of-layers-writing-backpropagation-by-hand"]], "Exercise 5 - Processing multiple inputs at once": [[21, "exercise-5-processing-multiple-inputs-at-once"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[20, "exercise-5-referencing"]], "Exercise 6 - Batched inputs": [[22, "exercise-6-batched-inputs"]], "Exercise 6 - Predicting on real data": [[21, "exercise-6-predicting-on-real-data"]], "Exercise 7 - Training": [[22, "exercise-7-training"]], "Exercise 7 - Training on real data (Optional)": [[21, "exercise-7-training-on-real-data-optional"]], "Exercise 8 (Optional) - Object orientation": [[22, "exercise-8-optional-object-orientation"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Exercises week 39": [[20, null]], "Exercises week 41": [[21, null]], "Exercises week 42": [[22, null]], "Expectation value and variance": [[35, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\theta}": [[35, "expectation-value-and-variance-for-boldsymbol-theta"]], "Expectation values": [[28, "expectation-values"]], "Explicit derivatives": [[38, "explicit-derivatives"], [39, "explicit-derivatives"]], "Exploding gradients": [[39, "exploding-gradients"]], "Extending to more predictors": [[36, "extending-to-more-predictors"], [37, "extending-to-more-predictors"]], "Extending to more than one variable": [[33, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[31, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"], [37, "feed-forward-neural-networks"], [38, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"], [39, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"], [38, "final-back-propagating-equation"], [39, "final-back-propagating-equation"]], "Final derivatives": [[38, "final-derivatives"]], "Final expression": [[38, "final-expression"], [39, "final-expression"]], "Final expressions for the biases of the hidden layer": [[38, "final-expressions-for-the-biases-of-the-hidden-layer"], [39, "final-expressions-for-the-biases-of-the-hidden-layer"]], "Finding the Limit": [[35, "finding-the-limit"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"], [39, "fine-tuning-neural-network-hyperparameters"]], "First network example, simple percepetron with one input": [[38, "first-network-example-simple-percepetron-with-one-input"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[32, "fixing-the-singularity"], [33, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[25, "format-for-electronic-delivery-of-report-and-programs"], [26, "format-for-electronic-delivery-of-report-and-programs"]], "Forward and reverse modes": [[38, "forward-and-reverse-modes"]], "Frequently used scaling functions": [[32, "frequently-used-scaling-functions"], [34, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[33, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Full object-oriented implementation": [[39, "full-object-oriented-implementation"]], "Functionality in Scikit-Learn": [[32, "functionality-in-scikit-learn"], [34, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [32, "further-properties-important-for-our-analyses-later"], [33, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[24, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[31, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[31, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [31, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[31, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting serious, the back propagation equations for a neural network": [[38, "getting-serious-the-back-propagation-equations-for-a-neural-network"]], "Getting started with project 1": [[20, "getting-started-with-project-1"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"], [39, "gradient-clipping"]], "Gradient Descent Example": [[33, "id1"], [34, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"]], "Gradient descent and Ridge": [[33, "gradient-descent-and-ridge"], [34, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[34, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[33, "gradient-descent-example"], [34, "gradient-descent-example"]], "Gradient expressions": [[38, "gradient-expressions"], [39, "gradient-expressions"]], "Grading": [[29, "grading"], [29, "id2"], [31, "grading"]], "Hidden layers": [[39, "hidden-layers"]], "Homogeneous data": [[39, "homogeneous-data"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Identifying Terms": [[35, "identifying-terms"]], "Illustration of a single perceptron model and a multi-perceptron model": [[37, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"], [38, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"]], "Important Matrix and vector handling packages": [[24, "important-matrix-and-vector-handling-packages"]], "Important observations": [[38, "important-observations"], [39, "important-observations"]], "Important technicalities: More on Rescaling data": [[32, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[34, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"], [39, "improving-performance"]], "In general not this simple": [[38, "in-general-not-this-simple"]], "In summary": [[29, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [34, "including-stochastic-gradient-descent-with-autograd"]], "Including more classes": [[36, "including-more-classes"], [37, "including-more-classes"]], "Incremental PCA": [[11, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[35, "independent-and-identically-distributed-iid"]], "Inputs to the activation function": [[38, "inputs-to-the-activation-function"], [39, "inputs-to-the-activation-function"]], "Insights from the paper by Glorot and Bengio": [[39, "insights-from-the-paper-by-glorot-and-bengio"]], "Installing R, C++, cython or Julia": [[31, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[31, "installing-r-c-cython-numba-etc"]], "Instructor information": [[29, "instructor-information"]], "Interpretations and optimizing our parameters": [[31, "interpretations-and-optimizing-our-parameters"], [31, "id2"], [31, "id3"], [32, "interpretations-and-optimizing-our-parameters"], [32, "id1"], [32, "id2"]], "Interpreting the Ridge results": [[32, "interpreting-the-ridge-results"], [33, "interpreting-the-ridge-results"], [33, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [32, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [23, "introduction"], [24, "introduction"]], "Introduction to Neural networks": [[37, "introduction-to-neural-networks"], [38, "introduction-to-neural-networks"]], "Introduction to numerical projects": [[25, "introduction-to-numerical-projects"], [26, "introduction-to-numerical-projects"]], "Is the Logistic activation function (Sigmoid) our choice?": [[39, "is-the-logistic-activation-function-sigmoid-our-choice"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[24, "lu-decomposition-the-inverse-of-a-matrix"]], "Lab sessions Tuesday and Wednesday": [[37, "lab-sessions-tuesday-and-wednesday"]], "Lab sessions on Tuesday and Wednesday": [[38, "lab-sessions-on-tuesday-and-wednesday"]], "Lab sessions week 39": [[36, "lab-sessions-week-39"]], "Lasso Regression": [[33, "lasso-regression"]], "Lasso case": [[33, "lasso-case"]], "Layers": [[1, "layers"], [39, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Layout of a neural network with three hidden layers": [[38, "layout-of-a-neural-network-with-three-hidden-layers"]], "Layout of a neural network with three hidden layers (last layer = l=L=4, first layer l=0)": [[39, "layout-of-a-neural-network-with-three-hidden-layers-last-layer-l-l-4-first-layer-l-0"]], "Layout of a simple neural network with no hidden layer": [[38, "layout-of-a-simple-neural-network-with-no-hidden-layer"], [39, "layout-of-a-simple-neural-network-with-no-hidden-layer"]], "Layout of a simple neural network with one hidden layer": [[38, "layout-of-a-simple-neural-network-with-one-hidden-layer"], [39, "layout-of-a-simple-neural-network-with-one-hidden-layer"]], "Layout of a simple neural network with two input nodes, one hidden layer and one output node": [[38, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-and-one-output-node"]], "Layout of a simple neural network with two input nodes, one hidden layer with two hidden noeds and one output node": [[39, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-with-two-hidden-noeds-and-one-output-node"]], "Layout of input to first hidden layer l=1 from input layer l=0": [[39, "layout-of-input-to-first-hidden-layer-l-1-from-input-layer-l-0"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"], [20, "learning-goals"]], "Learning outcomes": [[23, "learning-outcomes"], [31, "learning-outcomes"]], "Learning rate methods": [[39, "learning-rate-methods"]], "Lecture Monday October 6": [[38, "lecture-monday-october-6"]], "Lecture Monday September 29, 2025": [[37, "lecture-monday-september-29-2025"]], "Lecture October 13, 2025": [[39, "lecture-october-13-2025"]], "Lecture material": [[36, "lecture-material"]], "Lecture material: Writing a code which implements a feed-forward neural network": [[39, "lecture-material-writing-a-code-which-implements-a-feed-forward-neural-network"]], "Lectures and ComputerLab": [[31, "lectures-and-computerlab"]], "Limitations of NNs": [[39, "limitations-of-nns"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"], [39, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[24, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[32, "linear-regression-problems"], [33, "linear-regression-problems"]], "Linear Regression and the SVD": [[33, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linear classifier": [[36, "linear-classifier"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": 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own test-train splitting": [[32, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[32, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[33, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[33, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[34, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[34, "material-for-the-lab-sessions"], [35, "material-for-the-lab-sessions"]], "Material for the lab sessions on Tuesday and Wednesday": [[39, "material-for-the-lab-sessions-on-tuesday-and-wednesday"]], "Material for the lecture on Monday October 6, 2025": [[38, "material-for-the-lecture-on-monday-october-6-2025"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [32, "mathematical-interpretation-of-ordinary-least-squares"], [33, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical model": [[37, "mathematical-model"], [37, "id1"], [37, "id2"], [37, "id3"], [37, "id4"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of deep learning": [[38, "mathematics-of-deep-learning"], [39, "mathematics-of-deep-learning"]], "Mathematics of deep learning and neural networks": [[38, "mathematics-of-deep-learning-and-neural-networks"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [32, "mathematics-of-the-svd-and-implications"], [33, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[31, "matrices-in-python"]], "Matrix multiplication": [[1, "matrix-multiplication"], [39, "matrix-multiplication"]], "Matrix multiplications": [[39, "matrix-multiplications"]], "Matrix-vector notation": [[37, "matrix-vector-notation"]], "Matrix-vector notation and activation": [[12, "matrix-vector-notation-and-activation"], [37, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[35, "maximum-likelihood-estimation-mle"]], "Maximum likelihood": [[36, "maximum-likelihood"], [37, "maximum-likelihood"]], "Meet the covariance!": [[28, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [32, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[32, "meet-the-hessian-matrix"]], "Meet the Pandas": [[31, "meet-the-pandas"]], "Memory Usage and Scalability": [[34, "memory-usage-and-scalability"]], "Memory constraints": [[34, "memory-constraints"]], "Min-Max Scaling": [[32, "min-max-scaling"]], "Minimizing the cross entropy": [[36, "minimizing-the-cross-entropy"], [37, "minimizing-the-cross-entropy"]], "Momentum based GD": [[13, "momentum-based-gd"], [34, "momentum-based-gd"]], "More classes": [[36, "more-classes"], [37, "more-classes"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More complicated function": [[38, "more-complicated-function"]], "More considerations": [[38, "more-considerations"], [39, "more-considerations"]], "More examples on bootstrap and cross-validation and errors": [[35, "more-examples-on-bootstrap-and-cross-validation-and-errors"], [36, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[32, "more-interpretations"], [33, "more-interpretations"], [33, "id5"]], "More limitations": [[39, "more-limitations"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[33, "more-on-steepest-descent"]], "More on activation functions, output layers": [[39, "more-on-activation-functions-output-layers"]], "More on convex functions": [[33, "more-on-convex-functions"]], "More on the general approximation theorem": [[38, "more-on-the-general-approximation-theorem"]], "More preprocessing": [[32, "more-preprocessing"], [34, "more-preprocessing"]], "More top-down perspectives": [[39, "more-top-down-perspectives"]], "Motivation for Adaptive Step Sizes": [[34, "motivation-for-adaptive-step-sizes"]], "Multiclass classification": [[39, "multiclass-classification"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"], [37, "multilayer-perceptrons"], [38, "multilayer-perceptrons"]], "Multivariable functions": [[38, "multivariable-functions"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural network types": [[37, "neural-network-types"], [38, "neural-network-types"]], "Neural networks": [[12, null]], "New expression for the derivative": [[38, "new-expression-for-the-derivative"]], "Non-Convex Problems": [[34, "non-convex-problems"]], "Note about SVD Calculations": [[32, "note-about-svd-calculations"], [33, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[33, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[28, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[24, "numpy-and-arrays"], [31, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[31, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and Deep learning": [[36, "optimization-and-deep-learning"], [37, "optimization-and-deep-learning"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[33, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null], [36, "optimization-the-central-part-of-any-machine-learning-algortithm"], [37, "optimization-the-central-part-of-any-machine-learning-algortithm"]], "Optimizing our parameters": [[31, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[31, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"], [39, "optimizing-the-cost-function"]], "Optimizing the parameters": [[38, "optimizing-the-parameters"], [39, "optimizing-the-parameters"]], "Organizing our data": [[0, "organizing-our-data"], [31, "organizing-our-data"]], "Other Matrix and Vector Operations": [[24, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning at UiO": [[31, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[31, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other ingredients of a neural network": [[38, "other-ingredients-of-a-neural-network"]], "Other measures in classification studies": [[37, "other-measures-in-classification-studies"]], "Other parameters": [[38, "other-parameters"]], "Other popular texts": [[31, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"], [37, "other-types-of-networks"], [38, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[31, "our-model-for-the-nuclear-binding-energies"]], "Output layer": [[38, "output-layer"], [39, "output-layer"]], "Overarching aims of the exercises this week": [[21, "overarching-aims-of-the-exercises-this-week"], [22, "overarching-aims-of-the-exercises-this-week"]], "Overarching view of a neural network": [[38, "overarching-view-of-a-neural-network"]], "Overview of first week": [[31, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[34, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[31, "own-code-for-ordinary-least-squares"], [32, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[31, "pandas-ai"]], "Parameters of neural networks": [[38, "parameters-of-neural-networks"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[25, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part a): Analytical warm-up": [[26, "part-a-analytical-warm-up"]], "Part b): Writing your own Neural Network code": [[26, "part-b-writing-your-own-neural-network-code"]], "Part b: Adding Ridge regression for the Runge function": [[25, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c): Testing against other software libraries": [[26, "part-c-testing-against-other-software-libraries"]], "Part c: Writing your own gradient descent code": [[25, "part-c-writing-your-own-gradient-descent-code"]], "Part d): Testing different activation functions and depths of the neural network": [[26, "part-d-testing-different-activation-functions-and-depths-of-the-neural-network"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[25, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e): Testing different norms": [[26, "part-e-testing-different-norms"]], "Part e: Writing our own code for Lasso regression": [[25, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f): Classification analysis using neural networks": [[26, "part-f-classification-analysis-using-neural-networks"]], "Part f: Stochastic gradient descent": [[25, "part-f-stochastic-gradient-descent"]], "Part g) Critical evaluation of the various algorithms": [[26, "part-g-critical-evaluation-of-the-various-algorithms"]], "Part g: Bias-variance trade-off and resampling techniques": [[25, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[25, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"]], "Plan for week 39, September 22-26, 2025": [[36, "plan-for-week-39-september-22-26-2025"]], "Plan for week 41, October 6-10": [[38, "plan-for-week-41-october-6-10"]], "Plans for week 35": [[32, "plans-for-week-35"]], "Plans for week 36": [[33, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[34, "plans-for-week-37-lecture-monday"]], "Plans for week 38, lecture Monday September 15": [[35, "plans-for-week-38-lecture-monday-september-15"]], "Plotting the Histogram": [[35, "plotting-the-histogram"]], "Plotting the mean value for each group": [[36, "plotting-the-mean-value-for-each-group"]], "Practical tips": [[13, "practical-tips"], [34, "practical-tips"]], "Practicalities": [[29, "practicalities"], [29, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[25, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"], [26, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[32, "preprocessing-our-data"]], "Prerequisites": [[31, "prerequisites"]], "Prerequisites and background": [[23, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[28, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[33, "program-example-for-gradient-descent-with-ridge-regression"], [34, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[25, null]], "Project 2 on Machine Learning, deadline November 10 (Midnight)": [[26, null]], "Properties of PDFs": [[28, "properties-of-pdfs"]], "Pros and cons": [[34, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[23, "python-installers"], [31, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[34, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[34, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[34, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[28, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[31, "reading-material"]], "Reading recommendations": [[39, "reading-recommendations"]], "Reading recommendations:": [[32, "reading-recommendations"]], "Reading suggestions week 34": [[31, "reading-suggestions-week-34"]], "Readings and Videos": [[35, "readings-and-videos"]], "Readings and Videos, logistic regression": [[36, "readings-and-videos-logistic-regression"]], "Readings and Videos, resampling methods": [[36, "readings-and-videos-resampling-methods"]], "Readings and Videos:": [[34, "readings-and-videos"], [38, "readings-and-videos"]], "Readings and videos": [[39, "readings-and-videos"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"], [37, "recurrent-neural-networks"], [38, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [32, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reducing the number of operations": [[38, "reducing-the-number-of-operations"]], "Reformulating the problem": [[2, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis and resampling methods": [[25, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[31, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[31, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"], [39, "regularization"]], "Relevance": [[37, "relevance"], [39, "relevance"]], "Reminder about the gradient machinery from project 1": [[26, "reminder-about-the-gradient-machinery-from-project-1"]], "Reminder from last week": [[32, "reminder-from-last-week"]], "Reminder from last week: First network example, simple percepetron with one input": [[39, "reminder-from-last-week-first-network-example-simple-percepetron-with-one-input"]], "Reminder on Newton-Raphson\u2019s method": [[33, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on books with hands-on material and codes": [[38, "reminder-on-books-with-hands-on-material-and-codes"], [39, "reminder-on-books-with-hands-on-material-and-codes"]], "Reminder on different scaling methods": [[34, "reminder-on-different-scaling-methods"]], "Reminder on the chain rule and gradients": [[38, "reminder-on-the-chain-rule-and-gradients"]], "Replace or not": [[13, "replace-or-not"], [34, "replace-or-not"]], "Required Technologies": [[23, "required-technologies"]], "Resampling Methods": [[6, null]], "Resampling and the Bias-Variance Trade-off": [[19, "resampling-and-the-bias-variance-trade-off"]], "Resampling approaches can be computationally expensive": [[35, "resampling-approaches-can-be-computationally-expensive"], [36, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[6, "id1"], [35, "resampling-methods"], [35, "id2"], [36, "resampling-methods"], [36, "id1"]], "Resampling methods: Bootstrap": [[35, "resampling-methods-bootstrap"], [36, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[35, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[35, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[35, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[35, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[32, "residual-error"], [33, "residual-error"]], "Resources on differential equations and deep learning": [[2, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[33, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[13, "revisiting-our-linear-regression-solvers"]], "Revisiting our Logistic Regression case": [[36, "revisiting-our-logistic-regression-case"], [37, "revisiting-our-logistic-regression-case"]], "Rewriting the Covariance and/or Correlation Matrix": [[32, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the \\delta-function": [[35, "rewriting-the-delta-function"]], "Rewriting the fitting procedure as a linear algebra problem": [[31, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[31, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[33, "ridge-regression"]], "Ridge and LASSO Regression": [[32, "ridge-and-lasso-regression"], [33, "ridge-and-lasso-regression"], [33, "id2"]], "Ridge and Lasso Regression": [[5, null], [5, "id1"]], "SGD example": [[34, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[34, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[33, "svd-analysis"]], "Same code but now with momentum gradient descent": [[13, "same-code-but-now-with-momentum-gradient-descent"], [34, "same-code-but-now-with-momentum-gradient-descent"], [34, "id3"], [34, "id4"]], "Schedule first week": [[31, "schedule-first-week"]], "Schematic Regression Procedure": [[9, "schematic-regression-procedure"]], "Second moment of the gradient": [[34, "second-moment-of-the-gradient"]], "September 15-19": [[19, "september-15-19"]], "Setting up a Multi-layer perceptron model for classification": [[39, "setting-up-a-multi-layer-perceptron-model-for-classification"]], "Setting up the Back propagation algorithm": [[12, "setting-up-the-back-propagation-algorithm"]], "Setting up the Back propagation algorithm, part 3": [[38, "setting-up-the-back-propagation-algorithm-part-3"], [39, "setting-up-the-back-propagation-algorithm-part-3"]], "Setting up the Matrix to be inverted": [[32, "setting-up-the-matrix-to-be-inverted"], [33, "setting-up-the-matrix-to-be-inverted"]], "Setting up the back propagation algorithm": [[38, "setting-up-the-back-propagation-algorithm"]], "Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations": [[39, "setting-up-the-back-propagation-algorithm-and-algorithm-for-a-feed-forward-nn-initalizations"]], "Setting up the back propagation algorithm, part 1": [[39, "setting-up-the-back-propagation-algorithm-part-1"]], "Setting up the back propagation algorithm, part 2": [[38, "setting-up-the-back-propagation-algorithm-part-2"], [39, "setting-up-the-back-propagation-algorithm-part-2"]], "Setting up the equations for a neural network": [[38, "setting-up-the-equations-for-a-neural-network"], [39, "setting-up-the-equations-for-a-neural-network"]], "Setting up the network using Autograd; The full program": [[2, "setting-up-the-network-using-autograd-the-full-program"]], "Similar (second order function now) problem but now with AdaGrad": [[13, "similar-second-order-function-now-problem-but-now-with-adagrad"], [34, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[9, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple case": [[32, "simple-case"], [33, "simple-case"]], "Simple code for solving the above problem": [[33, "simple-code-for-solving-the-above-problem"]], "Simple example": [[36, "simple-example"], [38, "simple-example"]], "Simple example code": [[34, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[33, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[33, "simple-geometric-interpretation"]], "Simple linear regression model using scikit-learn": [[0, "simple-linear-regression-model-using-scikit-learn"], [31, "simple-linear-regression-model-using-scikit-learn"]], "Simple neural network and the back propagation equations": [[38, "simple-neural-network-and-the-back-propagation-equations"], [39, "simple-neural-network-and-the-back-propagation-equations"]], "Simple one-dimensional second-order polynomial": [[18, "simple-one-dimensional-second-order-polynomial"]], "Simple program": [[33, "simple-program"], [34, "simple-program"]], "Simpler examples first, and automatic differentiation": [[38, "simpler-examples-first-and-automatic-differentiation"]], "Slightly different approach": [[34, "slightly-different-approach"]], "Smarter way of evaluating the above function": [[38, "smarter-way-of-evaluating-the-above-function"]], "Sneaking in automatic differentiation using Autograd": [[34, "sneaking-in-automatic-differentiation-using-autograd"]], "Software and needed installations": [[25, "software-and-needed-installations"], [31, "software-and-needed-installations"]], "Solving Differential Equations with Deep Learning": [[2, null]], "Solving the one dimensional Poisson equation": [[2, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation with Neural Networks": [[2, "solving-the-wave-equation-with-neural-networks"]], "Solving using Newton-Raphson\u2019s method": [[36, "solving-using-newton-raphson-s-method"], [37, "solving-using-newton-raphson-s-method"]], "Some famous Matrices": [[24, "some-famous-matrices"]], "Some parallels from real analysis": [[38, "some-parallels-from-real-analysis"]], "Some selected properties": [[36, "some-selected-properties"]], "Some simple problems": [[13, "some-simple-problems"], [33, "some-simple-problems"]], "Some useful matrix and vector expressions": [[32, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[0, "splitting-our-data-in-training-and-test-data"], [32, "splitting-our-data-in-training-and-test-data"]], "Standard Approach based on the Normal Distribution": [[35, "standard-approach-based-on-the-normal-distribution"]], "Standard steepest descent": [[13, "standard-steepest-descent"]], "Statistical analysis": [[35, "statistical-analysis"], [36, "statistical-analysis"]], "Statistical analysis and optimization of data": [[23, "statistical-analysis-and-optimization-of-data"], [31, "statistical-analysis-and-optimization-of-data"]], "Steepest descent": [[13, "steepest-descent"], [33, "steepest-descent"]], "Stochastic Gradient Descent": [[34, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[13, "stochastic-gradient-descent-sgd"], [34, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[28, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strongly Convex Case": [[34, "strongly-convex-case"]], "Suggested readings and videos": [[37, "suggested-readings-and-videos"]], "Summing up": [[35, "summing-up"], [36, "summing-up"]], "Support Vector Machines, overarching aims": [[8, null]], "Synthetic data generation": [[36, "synthetic-data-generation"], [37, "synthetic-data-generation"]], "Systematic reduction": [[3, "systematic-reduction"]], "Teachers": [[31, "teachers"]], "Teachers and Grading": [[29, null]], "Teaching Assistants Fall semester 2023": [[29, "teaching-assistants-fall-semester-2023"]], "Tensorflow": [[39, "tensorflow"]], "Tentative deadllines for projects": [[29, "tentative-deadllines-for-projects"]], "Testing the Means Squared Error as function of Complexity": [[0, "testing-the-means-squared-error-as-function-of-complexity"], [32, "testing-the-means-squared-error-as-function-of-complexity"]], "Testing the XOR gate and other gates": [[39, "testing-the-xor-gate-and-other-gates"]], "Textbooks": [[30, null]], "The back propagation equations for a neural network": [[39, "the-back-propagation-equations-for-a-neural-network"]], "The Algorithm before theorem": [[11, "the-algorithm-before-theorem"]], "The Breast Cancer Data, now with Keras": [[1, "the-breast-cancer-data-now-with-keras"]], "The CART algorithm for Classification": [[9, "the-cart-algorithm-for-classification"]], "The CART algorithm for Regression": [[9, "the-cart-algorithm-for-regression"]], "The CIFAR01 data set": [[3, "the-cifar01-data-set"]], "The Central Limit Theorem": [[35, "the-central-limit-theorem"]], "The Hessian matrix": [[33, "the-hessian-matrix"], [34, "the-hessian-matrix"]], "The Hessian matrix for Ridge Regression": [[33, "the-hessian-matrix-for-ridge-regression"], [34, "the-hessian-matrix-for-ridge-regression"]], "The Jacobian": [[32, "the-jacobian"]], "The MNIST dataset again": [[3, "the-mnist-dataset-again"]], "The Neural Network": [[39, "the-neural-network"]], "The OLS case": [[33, "the-ols-case"]], "The RELU function family": [[1, "the-relu-function-family"], [39, "the-relu-function-family"]], "The Ridge case": [[33, "the-ridge-case"]], "The SVD, a Fantastic Algorithm": [[32, "the-svd-a-fantastic-algorithm"], [33, "the-svd-a-fantastic-algorithm"]], "The Softmax function": [[1, "the-softmax-function"], [39, "the-softmax-function"]], "The \\chi^2 function": [[0, "the-chi-2-function"], [31, "the-chi-2-function"], [31, "id4"], [31, "id5"], [31, "id6"], [31, "id7"], [31, "id8"]], "The approximation theorem in words": [[38, "the-approximation-theorem-in-words"]], "The bias-variance tradeoff": [[6, "the-bias-variance-tradeoff"], [35, "the-bias-variance-tradeoff"], [36, "the-bias-variance-tradeoff"]], "The code for solving the ODE": [[2, "the-code-for-solving-the-ode"]], "The complete code with a simple data set": [[32, "the-complete-code-with-a-simple-data-set"]], "The cost function rewritten": [[36, "the-cost-function-rewritten"], [37, "the-cost-function-rewritten"]], "The cost/loss function": [[32, "the-cost-loss-function"]], "The course has two central parts": [[23, "the-course-has-two-central-parts"]], "The derivative of the Logistic funtion": [[39, "the-derivative-of-the-logistic-funtion"]], "The derivative of the cost/loss function": [[33, "the-derivative-of-the-cost-loss-function"], [34, "the-derivative-of-the-cost-loss-function"]], "The derivatives": [[38, "the-derivatives"], [39, "the-derivatives"]], "The equations": [[33, "the-equations"]], "The equations for ordinary least squares": [[32, "the-equations-for-ordinary-least-squares"]], "The equations to solve": [[36, "the-equations-to-solve"], [37, "the-equations-to-solve"]], "The first Case": [[33, "the-first-case"]], "The gradient step": [[34, "the-gradient-step"]], "The ideal": [[33, "the-ideal"]], "The logistic function": [[7, "the-logistic-function"], [36, "the-logistic-function"]], "The mean squared error and its derivative": [[32, "the-mean-squared-error-and-its-derivative"]], "The moons example": [[8, "the-moons-example"]], "The multilayer perceptron (MLP)": [[12, "the-multilayer-perceptron-mlp"]], "The network with one input layer, specified number of hidden layers, and one output layer": [[2, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"]], "The optimization problem": [[38, "the-optimization-problem"]], "The ouput layer": [[38, "the-ouput-layer"], [39, "the-ouput-layer"]], "The plethora of machine learning algorithms/methods": [[31, "the-plethora-of-machine-learning-algorithms-methods"]], "The same example but now with cross-validation": [[35, "the-same-example-but-now-with-cross-validation"], [36, "the-same-example-but-now-with-cross-validation"]], "The sensitiveness of the gradient descent": [[33, "the-sensitiveness-of-the-gradient-descent"]], "The singular value decomposition": [[5, "the-singular-value-decomposition"], [32, "the-singular-value-decomposition"], [33, "the-singular-value-decomposition"]], "The training": [[38, "the-training"], [39, "the-training"]], "The two-dimensional case": [[8, "the-two-dimensional-case"]], "Theoretical Convergence Speed and convex optimization": [[34, "theoretical-convergence-speed-and-convex-optimization"]], "Time decay rate": [[34, "time-decay-rate"]], "To our real data: nuclear binding energies. Brief reminder on masses and binding energies": [[31, "to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies"]], "Topics covered in this course: Statistical analysis and optimization of data": [[31, "topics-covered-in-this-course-statistical-analysis-and-optimization-of-data"]], "Towards the PCA theorem": [[11, "towards-the-pca-theorem"]], "Train and test datasets": [[1, "train-and-test-datasets"], [39, "train-and-test-datasets"]], "Two parameters": [[36, "two-parameters"], [37, "two-parameters"]], "Two-dimensional Objects": [[3, "two-dimensional-objects"]], "Type of problem": [[2, "type-of-problem"]], "Types of Machine Learning": [[31, "types-of-machine-learning"]], "Understanding what happens": [[35, "understanding-what-happens"], [36, "understanding-what-happens"]], "Universal approximation theorem": [[38, "universal-approximation-theorem"]], "Updating the gradients": [[38, "updating-the-gradients"], [39, "updating-the-gradients"]], "Usage of the above learning rate schedulers": [[39, "usage-of-the-above-learning-rate-schedulers"]], "Use the books!": [[19, "use-the-books"]], "Useful Python libraries": [[23, "useful-python-libraries"], [31, "useful-python-libraries"]], "Using Autograd": [[13, "using-autograd"]], "Using Keras": [[39, "using-keras"]], "Using Scikit-learn": [[37, "using-scikit-learn"]], "Using forward Euler to solve the ODE": [[2, "using-forward-euler-to-solve-the-ode"]], "Using gradient descent methods, limitations": [[13, "using-gradient-descent-methods-limitations"], [33, "using-gradient-descent-methods-limitations"], [34, "using-gradient-descent-methods-limitations"]], "Using the chain rule and summing over all k entries": [[38, "using-the-chain-rule-and-summing-over-all-k-entries"], [39, "using-the-chain-rule-and-summing-over-all-k-entries"]], "Using the correlation matrix": [[37, "using-the-correlation-matrix"]], "Vanishing gradients": [[39, "vanishing-gradients"]], "Various steps in cross-validation": [[35, "various-steps-in-cross-validation"], [36, "various-steps-in-cross-validation"]], "Visualization": [[1, "visualization"], [1, "id1"], [39, "visualization"], [39, "id1"]], "Visualizing the Tree, Classification": [[9, "visualizing-the-tree-classification"]], "Week 34: Introduction to the course, Logistics and Practicalities": [[31, null]], "Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression": [[32, null]], "Week 36: Linear Regression and Gradient descent": [[33, null]], "Week 37: Gradient descent methods": [[34, null]], "Week 38: Statistical analysis, bias-variance tradeoff and resampling methods": [[35, null]], "Week 39: Resampling methods and logistic regression": [[36, null]], "Week 40: Gradient descent methods (continued) and start Neural networks": [[37, null]], "Week 41 Neural networks and constructing a neural network code": [[38, null]], "Week 42 Constructing a Neural Network code with examples": [[39, null]], "Weights and biases": [[39, "weights-and-biases"]], "What Is Generative Modeling?": [[31, "what-is-generative-modeling"]], "What does it mean?": [[32, "what-does-it-mean"], [33, "what-does-it-mean"]], "What is Machine Learning?": [[0, "what-is-machine-learning"]], "What is a good model?": [[0, "what-is-a-good-model"], [31, "what-is-a-good-model"]], "What is a good model? Can we define it?": [[31, "what-is-a-good-model-can-we-define-it"]], "When do we stop?": [[34, "when-do-we-stop"]], "Which activation function should I use?": [[1, "which-activation-function-should-i-use"]], "Which activation function should we use?": [[39, "which-activation-function-should-we-use"]], "Why Combine Momentum and RMSProp?": [[34, "why-combine-momentum-and-rmsprop"]], "Why Linear Regression (aka Ordinary Least Squares and family)": [[31, "why-linear-regression-aka-ordinary-least-squares-and-family"]], "Why multilayer perceptrons?": [[37, "why-multilayer-perceptrons"], [38, "why-multilayer-perceptrons"]], "Why resampling methods": [[35, "why-resampling-methods"]], "Why resampling methods ?": [[35, "id1"], [36, "why-resampling-methods"]], "Wisconsin Cancer Data": [[7, "wisconsin-cancer-data"]], "With Lasso Regression": [[33, "with-lasso-regression"]], "Wrapping it up": [[35, "wrapping-it-up"]], "Writing Our First Generative Adversarial Network": [[4, 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Newton\u2019s method": [[34, "but-none-of-these-can-compete-with-newton-s-method"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[3, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Cancer Data again now with Decision Trees and other Methods": [[9, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Chain rule": [[38, "chain-rule"]], "Chain rule, forward and reverse modes": [[38, "chain-rule-forward-and-reverse-modes"]], "Challenge: Choosing a Fixed Learning Rate": [[34, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[1, "choose-cost-function-and-optimizer"], [39, "choose-cost-function-and-optimizer"]], "Class of functions we can approximate": [[38, "class-of-functions-we-can-approximate"]], "Classical PCA Theorem": [[11, "classical-pca-theorem"]], "Classification and Regression, writing our own neural network code": [[26, "classification-and-regression-writing-our-own-neural-network-code"]], "Classification problems": [[36, "classification-problems"], [37, "classification-problems"]], "Clustering and Unsupervised Learning": [[14, null]], "Code Example for Cross-validation and k-fold Cross-validation": [[35, "code-example-for-cross-validation-and-k-fold-cross-validation"], [36, "code-example-for-cross-validation-and-k-fold-cross-validation"]], "Code example": [[38, "code-example"], [39, "code-example"]], "Code example for the Bootstrap method": [[35, "code-example-for-the-bootstrap-method"]], "Code for SVD and Inversion of Matrices": [[5, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[34, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[14, "codes-and-approaches"]], "Codes for the SVD": [[5, "codes-for-the-svd"], [32, "codes-for-the-svd"], [33, "codes-for-the-svd"]], "Coding Setup and Linear Regression": [[15, "coding-setup-and-linear-regression"]], "Collect and pre-process data": [[1, "collect-and-pre-process-data"], [39, "collect-and-pre-process-data"], [39, "id2"]], "Communication channels": [[31, "communication-channels"]], "Compact expressions": [[38, "compact-expressions"], [39, "compact-expressions"]], "Compare Bagging on Trees with Random Forests": [[10, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[2, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[33, "comparison-with-ols"]], "Completing the list": [[38, "completing-the-list"], [39, "completing-the-list"]], "Computation of gradients": [[34, "computation-of-gradients"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[33, "conditions-on-convex-functions"]], "Confidence Intervals": [[35, "confidence-intervals"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convergence rates": [[34, "convergence-rates"]], "Convex function": [[33, "convex-function"]], "Convex functions": [[13, "convex-functions"], [33, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[3, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[3, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[12, "convolutional-neural-network"], [37, "convolutional-neural-network"], [38, "convolutional-neural-network"]], "Convolutional Neural Networks": [[3, null]], "Correlation Function and Design/Feature Matrix": [[32, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [32, "correlation-matrix"]], "Correlation Matrix with Pandas": [[32, "correlation-matrix-with-pandas"]], "Cost functions": [[39, "cost-functions"]], "Counting the number of floating point operations": [[38, "counting-the-number-of-floating-point-operations"]], "Course Format": [[31, "course-format"]], "Course setting": [[27, null]], "Covariance Matrix Examples": [[32, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[32, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Cross-validation in brief": [[35, "cross-validation-in-brief"], [36, "cross-validation-in-brief"]], "Deadlines for projects (tentative)": [[31, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep Neural Networks": [[34, "deep-neural-networks"]], "Deep learning methods": [[31, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"], [39, "define-model-and-architecture"]], "Defining intermediate operations": [[38, "defining-intermediate-operations"]], "Defining the cost function": [[1, "defining-the-cost-function"], [39, "defining-the-cost-function"]], "Definitions": [[19, "definitions"], [38, "definitions"], [39, "definitions"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"], [19, "deliverables"], [20, "deliverables"], [25, "deliverables"], [26, "deliverables"]], "Derivation of the AdaGrad Algorithm": [[34, "derivation-of-the-adagrad-algorithm"]], "Derivative of the cost function": [[38, "derivative-of-the-cost-function"], [39, "derivative-of-the-cost-function"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"], [38, "derivatives-and-the-chain-rule"], [39, "derivatives-and-the-chain-rule"]], "Derivatives in terms of z_j^L": [[38, "derivatives-in-terms-of-z-j-l"], [39, "derivatives-in-terms-of-z-j-l"]], "Derivatives of the hidden layer": [[38, "derivatives-of-the-hidden-layer"], [39, "derivatives-of-the-hidden-layer"]], "Derivatives, example 1": [[32, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"], [35, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the Lasso Regression Equations": [[32, "deriving-the-lasso-regression-equations"], [33, "deriving-the-lasso-regression-equations"], [33, "id6"]], "Deriving the Ridge Regression Equations": [[32, "deriving-the-ridge-regression-equations"], [33, "deriving-the-ridge-regression-equations"], [33, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"], [39, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[8, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[9, "disadvantages"]], "Discriminative Modeling": [[31, "discriminative-modeling"]], "Discussing the correlation data": [[37, "discussing-the-correlation-data"]], "Does Logistic Regression do a better Job?": [[37, "does-logistic-regression-do-a-better-job"]], "Domains and probabilities": [[28, "domains-and-probabilities"]], "Dropout": [[1, "dropout"], [39, "dropout"]], "ELU function": [[39, "elu-function"]], "Economy-size SVD": [[32, "economy-size-svd"], [33, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[28, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[34, "empirical-evidence-convergence-time-and-memory-in-practice"]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[31, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"], [39, "evaluate-model-performance-on-test-data"]], "Example 2": [[32, "example-2"]], "Example 3": [[32, "example-3"]], "Example 4": [[32, "example-4"]], "Example Matrix": [[32, "example-matrix"], [33, "example-matrix"]], "Example code for Bias-Variance tradeoff": [[35, "example-code-for-bias-variance-tradeoff"]], "Example code for Logistic Regression": [[36, "example-code-for-logistic-regression"], [37, "example-code-for-logistic-regression"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[31, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[31, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[32, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[32, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"], [39, "example-binary-classification-problem"]], "Examples": [[31, "examples"]], "Examples of XOR, OR and AND gates": [[37, "examples-of-xor-or-and-and-gates"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Examples of likelihood functions used in logistic regression and nueral networks": [[36, "examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks"]], "Exercise 1": [[21, "exercise-1"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1 - Understand the feed forward pass": [[22, "exercise-1-understand-the-feed-forward-pass"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Creating the report document": [[20, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Including more data": [[38, "exercise-1-including-more-data"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2": [[21, "exercise-2"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Gradient with one layer using autograd": [[22, "exercise-2-gradient-with-one-layer-using-autograd"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Adding good figures": [[20, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: Extended program": [[38, "exercise-2-extended-program"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3": [[21, "exercise-3"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Gradient with one layer writing backpropagation by hand": [[22, "exercise-3-gradient-with-one-layer-writing-backpropagation-by-hand"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[20, "exercise-3-writing-an-abstract-and-introduction"]], "Exercise 4 - Custom activation for each layer": [[21, "exercise-4-custom-activation-for-each-layer"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Gradient with two layers writing backpropagation by hand": [[22, "exercise-4-gradient-with-two-layers-writing-backpropagation-by-hand"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code available and presentable": [[20, "exercise-4-making-the-code-available-and-presentable"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5 - Gradient with any number of layers writing backpropagation by hand": [[22, "exercise-5-gradient-with-any-number-of-layers-writing-backpropagation-by-hand"]], "Exercise 5 - Processing multiple inputs at once": [[21, "exercise-5-processing-multiple-inputs-at-once"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[20, "exercise-5-referencing"]], "Exercise 6 - Batched inputs": [[22, "exercise-6-batched-inputs"]], "Exercise 6 - Predicting on real data": [[21, "exercise-6-predicting-on-real-data"]], "Exercise 7 - Training": [[22, "exercise-7-training"]], "Exercise 7 - Training on real data (Optional)": [[21, "exercise-7-training-on-real-data-optional"]], "Exercise 8 (Optional) - Object orientation": [[22, "exercise-8-optional-object-orientation"]], "Exercise: Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Exercises week 39": [[20, null]], "Exercises week 41": [[21, null]], "Exercises week 42": [[22, null]], "Expectation value and variance": [[35, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\theta}": [[35, "expectation-value-and-variance-for-boldsymbol-theta"]], "Expectation values": [[28, "expectation-values"]], "Explicit derivatives": [[38, "explicit-derivatives"], [39, "explicit-derivatives"]], "Exploding gradients": [[39, "exploding-gradients"]], "Extending to more predictors": [[36, "extending-to-more-predictors"], [37, "extending-to-more-predictors"]], "Extending to more than one variable": [[33, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[31, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"], [37, "feed-forward-neural-networks"], [38, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"], [39, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"], [38, "final-back-propagating-equation"], [39, "final-back-propagating-equation"]], "Final derivatives": [[38, "final-derivatives"]], "Final expression": [[38, "final-expression"], [39, "final-expression"]], "Final expressions for the biases of the hidden layer": [[38, "final-expressions-for-the-biases-of-the-hidden-layer"], [39, "final-expressions-for-the-biases-of-the-hidden-layer"]], "Finding the Limit": [[35, "finding-the-limit"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"], [39, "fine-tuning-neural-network-hyperparameters"]], "First network example, simple percepetron with one input": [[38, "first-network-example-simple-percepetron-with-one-input"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[32, "fixing-the-singularity"], [33, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[25, "format-for-electronic-delivery-of-report-and-programs"], [26, "format-for-electronic-delivery-of-report-and-programs"]], "Forward and reverse modes": [[38, "forward-and-reverse-modes"]], "Frequently used scaling functions": [[32, "frequently-used-scaling-functions"], [34, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[33, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Full object-oriented implementation": [[39, "full-object-oriented-implementation"]], "Functionality in Scikit-Learn": [[32, "functionality-in-scikit-learn"], [34, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [32, "further-properties-important-for-our-analyses-later"], [33, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[24, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[31, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[31, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [31, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[31, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting serious, the back propagation equations for a neural network": [[38, "getting-serious-the-back-propagation-equations-for-a-neural-network"]], "Getting started with project 1": [[20, "getting-started-with-project-1"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"], [39, "gradient-clipping"]], "Gradient Descent Example": [[33, "id1"], [34, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"]], "Gradient descent and Ridge": [[33, "gradient-descent-and-ridge"], [34, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[34, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[33, "gradient-descent-example"], [34, "gradient-descent-example"]], "Gradient expressions": [[38, "gradient-expressions"], [39, "gradient-expressions"]], "Grading": [[29, "grading"], [29, "id2"], [31, "grading"]], "Hidden layers": [[39, "hidden-layers"]], "Homogeneous data": [[39, "homogeneous-data"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Identifying Terms": [[35, "identifying-terms"]], "Illustration of a single perceptron model and a multi-perceptron model": [[37, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"], [38, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"]], "Important Matrix and vector handling packages": [[24, "important-matrix-and-vector-handling-packages"]], "Important observations": [[38, "important-observations"], [39, "important-observations"]], "Important technicalities: More on Rescaling data": [[32, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[34, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"], [39, "improving-performance"]], "In general not this simple": [[38, "in-general-not-this-simple"]], "In summary": [[29, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [34, "including-stochastic-gradient-descent-with-autograd"]], "Including more classes": [[36, "including-more-classes"], [37, "including-more-classes"]], "Incremental PCA": [[11, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[35, "independent-and-identically-distributed-iid"]], "Inputs to the activation function": [[38, "inputs-to-the-activation-function"], [39, "inputs-to-the-activation-function"]], "Insights from the paper by Glorot and Bengio": [[39, "insights-from-the-paper-by-glorot-and-bengio"]], "Installing R, C++, cython or Julia": [[31, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[31, "installing-r-c-cython-numba-etc"]], "Instructor information": [[29, "instructor-information"]], "Interpretations and optimizing our parameters": [[31, "interpretations-and-optimizing-our-parameters"], [31, "id2"], [31, "id3"], [32, "interpretations-and-optimizing-our-parameters"], [32, "id1"], [32, "id2"]], "Interpreting the Ridge results": [[32, "interpreting-the-ridge-results"], [33, "interpreting-the-ridge-results"], [33, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [32, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [23, "introduction"], [24, "introduction"]], "Introduction to Neural networks": [[37, "introduction-to-neural-networks"], [38, "introduction-to-neural-networks"]], "Introduction to numerical projects": [[25, "introduction-to-numerical-projects"], [26, "introduction-to-numerical-projects"]], "Is the Logistic activation function (Sigmoid) our choice?": [[39, "is-the-logistic-activation-function-sigmoid-our-choice"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[24, "lu-decomposition-the-inverse-of-a-matrix"]], "Lab sessions Tuesday and Wednesday": [[37, "lab-sessions-tuesday-and-wednesday"]], "Lab sessions on Tuesday and Wednesday": [[38, "lab-sessions-on-tuesday-and-wednesday"]], "Lab sessions week 39": [[36, "lab-sessions-week-39"]], "Lasso Regression": [[33, "lasso-regression"]], "Lasso case": [[33, "lasso-case"]], "Layers": [[1, "layers"], [39, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Layout of a neural network with three hidden layers": [[38, "layout-of-a-neural-network-with-three-hidden-layers"]], "Layout of a neural network with three hidden layers (last layer = l=L=4, first layer l=0)": [[39, "layout-of-a-neural-network-with-three-hidden-layers-last-layer-l-l-4-first-layer-l-0"]], "Layout of a simple neural network with no hidden layer": [[38, "layout-of-a-simple-neural-network-with-no-hidden-layer"], [39, "layout-of-a-simple-neural-network-with-no-hidden-layer"]], "Layout of a simple neural network with one hidden layer": [[38, "layout-of-a-simple-neural-network-with-one-hidden-layer"], [39, "layout-of-a-simple-neural-network-with-one-hidden-layer"]], "Layout of a simple neural network with two input nodes, one hidden layer and one output node": [[38, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-and-one-output-node"]], "Layout of a simple neural network with two input nodes, one hidden layer with two hidden noeds and one output node": [[39, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-with-two-hidden-noeds-and-one-output-node"]], "Layout of input to first hidden layer l=1 from input layer l=0": [[39, "layout-of-input-to-first-hidden-layer-l-1-from-input-layer-l-0"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"], [20, "learning-goals"]], "Learning outcomes": [[23, "learning-outcomes"], [31, "learning-outcomes"]], "Learning rate methods": [[39, "learning-rate-methods"]], "Lecture Monday October 6": [[38, "lecture-monday-october-6"]], "Lecture Monday September 29, 2025": [[37, "lecture-monday-september-29-2025"]], "Lecture October 13, 2025": [[39, "lecture-october-13-2025"]], "Lecture material": [[36, "lecture-material"]], "Lecture material: Writing a code which implements a feed-forward neural network": [[39, "lecture-material-writing-a-code-which-implements-a-feed-forward-neural-network"]], "Lectures and ComputerLab": [[31, "lectures-and-computerlab"]], "Limitations of NNs": [[39, "limitations-of-nns"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"], [39, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[24, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[32, "linear-regression-problems"], [33, "linear-regression-problems"]], "Linear Regression and the SVD": [[33, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linear classifier": [[36, "linear-classifier"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"], [35, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [32, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[30, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"], [36, "logistic-regression"]], "Logistic Regression, from last week": [[37, "logistic-regression-from-last-week"]], "Logistic function as the root of problems": [[39, "logistic-function-as-the-root-of-problems"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[31, "machine-learning"]], "Machine learning": [[23, "machine-learning"]], "Main textbooks": [[31, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[32, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[32, "material-for-exercises-week-35"]], "Material for lab sessions sessions Tuesday and Wednesday": [[33, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[33, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[34, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[34, "material-for-the-lab-sessions"], [35, "material-for-the-lab-sessions"]], "Material for the lab sessions on Tuesday and Wednesday": [[39, "material-for-the-lab-sessions-on-tuesday-and-wednesday"]], "Material for the lecture on Monday October 6, 2025": [[38, "material-for-the-lecture-on-monday-october-6-2025"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [32, "mathematical-interpretation-of-ordinary-least-squares"], [33, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical model": [[37, "mathematical-model"], [37, "id1"], [37, "id2"], [37, "id3"], [37, "id4"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of deep learning": [[38, "mathematics-of-deep-learning"], [39, "mathematics-of-deep-learning"]], "Mathematics of deep learning and neural networks": [[38, "mathematics-of-deep-learning-and-neural-networks"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [32, "mathematics-of-the-svd-and-implications"], [33, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[31, "matrices-in-python"]], "Matrix multiplication": [[1, "matrix-multiplication"], [39, "matrix-multiplication"]], "Matrix multiplications": [[39, "matrix-multiplications"]], "Matrix-vector notation": [[37, "matrix-vector-notation"]], "Matrix-vector notation and activation": [[12, "matrix-vector-notation-and-activation"], [37, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[35, "maximum-likelihood-estimation-mle"]], "Maximum likelihood": [[36, "maximum-likelihood"], [37, "maximum-likelihood"]], "Meet the covariance!": [[28, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [32, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[32, "meet-the-hessian-matrix"]], "Meet the Pandas": [[31, "meet-the-pandas"]], "Memory Usage and Scalability": [[34, "memory-usage-and-scalability"]], "Memory constraints": [[34, "memory-constraints"]], "Min-Max Scaling": [[32, "min-max-scaling"]], "Minimizing the cross entropy": [[36, "minimizing-the-cross-entropy"], [37, "minimizing-the-cross-entropy"]], "Momentum based GD": [[13, "momentum-based-gd"], [34, "momentum-based-gd"]], "More classes": [[36, "more-classes"], [37, "more-classes"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More complicated function": [[38, "more-complicated-function"]], "More considerations": [[38, "more-considerations"], [39, "more-considerations"]], "More examples on bootstrap and cross-validation and errors": [[35, "more-examples-on-bootstrap-and-cross-validation-and-errors"], [36, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[32, "more-interpretations"], [33, "more-interpretations"], [33, "id5"]], "More limitations": [[39, "more-limitations"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[33, "more-on-steepest-descent"]], "More on activation functions, output layers": [[39, "more-on-activation-functions-output-layers"]], "More on convex functions": [[33, "more-on-convex-functions"]], "More on the general approximation theorem": [[38, "more-on-the-general-approximation-theorem"]], "More preprocessing": [[32, "more-preprocessing"], [34, "more-preprocessing"]], "More top-down perspectives": [[39, "more-top-down-perspectives"]], "Motivation for Adaptive Step Sizes": [[34, "motivation-for-adaptive-step-sizes"]], "Multiclass classification": [[39, "multiclass-classification"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"], [37, "multilayer-perceptrons"], [38, "multilayer-perceptrons"]], "Multivariable functions": [[38, "multivariable-functions"]], "Network requirements": [[2, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural network types": [[37, "neural-network-types"], [38, "neural-network-types"]], "Neural networks": [[12, null]], "New expression for the derivative": [[38, "new-expression-for-the-derivative"]], "Non-Convex Problems": [[34, "non-convex-problems"]], "Note about SVD Calculations": [[32, "note-about-svd-calculations"], [33, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[33, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[28, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[24, "numpy-and-arrays"], [31, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[31, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and Deep learning": [[36, "optimization-and-deep-learning"], [37, "optimization-and-deep-learning"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[33, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null], [36, "optimization-the-central-part-of-any-machine-learning-algortithm"], [37, "optimization-the-central-part-of-any-machine-learning-algortithm"]], "Optimizing our parameters": [[31, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[31, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"], [39, "optimizing-the-cost-function"]], "Optimizing the parameters": [[38, "optimizing-the-parameters"], [39, "optimizing-the-parameters"]], "Optional (Note that you should include at least two of these in the report):": [[26, "optional-note-that-you-should-include-at-least-two-of-these-in-the-report"]], "Organizing our data": [[0, "organizing-our-data"], [31, "organizing-our-data"]], "Other Matrix and Vector Operations": [[24, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning at UiO": [[31, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning at UiO, contn": [[31, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other ingredients of a neural network": [[38, "other-ingredients-of-a-neural-network"]], "Other measures in classification studies": [[37, "other-measures-in-classification-studies"]], "Other parameters": [[38, "other-parameters"]], "Other popular texts": [[31, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"], [37, "other-types-of-networks"], [38, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[31, "our-model-for-the-nuclear-binding-energies"]], "Output layer": [[38, "output-layer"], [39, "output-layer"]], "Overarching aims of the exercises this week": [[21, "overarching-aims-of-the-exercises-this-week"], [22, "overarching-aims-of-the-exercises-this-week"]], "Overarching view of a neural network": [[38, "overarching-view-of-a-neural-network"]], "Overview of first week": [[31, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[34, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[31, "own-code-for-ordinary-least-squares"], [32, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[31, "pandas-ai"]], "Parameters of neural networks": [[38, "parameters-of-neural-networks"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[25, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part a): Analytical warm-up": [[26, "part-a-analytical-warm-up"]], "Part b): Writing your own Neural Network code": [[26, "part-b-writing-your-own-neural-network-code"]], "Part b: Adding Ridge regression for the Runge function": [[25, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c): Testing against other software libraries": [[26, "part-c-testing-against-other-software-libraries"]], "Part c: Writing your own gradient descent code": [[25, "part-c-writing-your-own-gradient-descent-code"]], "Part d): Testing different activation functions and depths of the neural network": [[26, "part-d-testing-different-activation-functions-and-depths-of-the-neural-network"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[25, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e): Testing different norms": [[26, "part-e-testing-different-norms"]], "Part e: Writing our own code for Lasso regression": [[25, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f): Classification analysis using neural networks": [[26, "part-f-classification-analysis-using-neural-networks"]], "Part f: Stochastic gradient descent": [[25, "part-f-stochastic-gradient-descent"]], "Part g) Critical evaluation of the various algorithms": [[26, "part-g-critical-evaluation-of-the-various-algorithms"]], "Part g: Bias-variance trade-off and resampling techniques": [[25, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[25, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"]], "Plan for week 39, September 22-26, 2025": [[36, "plan-for-week-39-september-22-26-2025"]], "Plan for week 41, October 6-10": [[38, "plan-for-week-41-october-6-10"]], "Plans for week 35": [[32, "plans-for-week-35"]], "Plans for week 36": [[33, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[34, "plans-for-week-37-lecture-monday"]], "Plans for week 38, lecture Monday September 15": [[35, "plans-for-week-38-lecture-monday-september-15"]], "Plotting the Histogram": [[35, "plotting-the-histogram"]], "Plotting the mean value for each group": [[36, "plotting-the-mean-value-for-each-group"]], "Practical tips": [[13, "practical-tips"], [34, "practical-tips"]], "Practicalities": [[29, "practicalities"], [29, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[25, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"], [26, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[32, "preprocessing-our-data"]], "Prerequisites": [[31, "prerequisites"]], "Prerequisites and background": [[23, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[28, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[33, "program-example-for-gradient-descent-with-ridge-regression"], [34, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[25, null]], "Project 2 on Machine Learning, deadline November 10 (Midnight)": [[26, null]], "Properties of PDFs": [[28, "properties-of-pdfs"]], "Pros and cons": [[34, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[23, "python-installers"], [31, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[34, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[34, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[34, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "Random Numbers": [[28, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[31, "reading-material"]], "Reading recommendations": [[39, "reading-recommendations"]], "Reading recommendations:": [[32, "reading-recommendations"]], "Reading suggestions week 34": [[31, "reading-suggestions-week-34"]], "Readings and Videos": [[35, "readings-and-videos"]], "Readings and Videos, logistic regression": [[36, "readings-and-videos-logistic-regression"]], "Readings and Videos, resampling methods": [[36, "readings-and-videos-resampling-methods"]], "Readings and Videos:": [[34, "readings-and-videos"], [38, "readings-and-videos"]], "Readings and videos": [[39, "readings-and-videos"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"], [37, "recurrent-neural-networks"], [38, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [32, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reducing the number of operations": [[38, "reducing-the-number-of-operations"]], "Reformulating the problem": [[2, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis and resampling methods": [[25, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[31, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[31, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"], [39, "regularization"]], "Relevance": [[37, "relevance"], [39, "relevance"]], "Reminder about the gradient machinery from project 1": [[26, "reminder-about-the-gradient-machinery-from-project-1"]], "Reminder from last week": [[32, "reminder-from-last-week"]], "Reminder from last week: First network example, simple percepetron with one input": [[39, "reminder-from-last-week-first-network-example-simple-percepetron-with-one-input"]], "Reminder on Newton-Raphson\u2019s method": [[33, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on books with hands-on material and codes": [[38, "reminder-on-books-with-hands-on-material-and-codes"], [39, "reminder-on-books-with-hands-on-material-and-codes"]], "Reminder on different scaling methods": [[34, "reminder-on-different-scaling-methods"]], "Reminder on the chain rule and gradients": [[38, "reminder-on-the-chain-rule-and-gradients"]], "Replace or not": [[13, "replace-or-not"], [34, "replace-or-not"]], "Required Analysis:": [[26, "required-analysis"]], "Required Technologies": [[23, "required-technologies"]], "Resampling Methods": [[6, null]], "Resampling and the Bias-Variance Trade-off": [[19, "resampling-and-the-bias-variance-trade-off"]], "Resampling approaches can be computationally expensive": [[35, "resampling-approaches-can-be-computationally-expensive"], [36, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[6, "id1"], [35, "resampling-methods"], [35, "id2"], [36, "resampling-methods"], [36, "id1"]], "Resampling methods: Bootstrap": [[35, "resampling-methods-bootstrap"], [36, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[35, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[35, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[35, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[35, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[32, "residual-error"], [33, "residual-error"]], "Resources on differential equations and deep learning": [[2, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[33, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[13, "revisiting-our-linear-regression-solvers"]], "Revisiting our Logistic Regression case": [[36, "revisiting-our-logistic-regression-case"], [37, "revisiting-our-logistic-regression-case"]], "Rewriting the Covariance and/or Correlation Matrix": [[32, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the \\delta-function": [[35, "rewriting-the-delta-function"]], "Rewriting the fitting procedure as a linear algebra problem": [[31, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[31, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[33, "ridge-regression"]], "Ridge and LASSO Regression": [[32, "ridge-and-lasso-regression"], [33, "ridge-and-lasso-regression"], [33, "id2"]], "Ridge and Lasso Regression": [[5, null], [5, "id1"]], "SGD example": [[34, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[34, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[33, "svd-analysis"]], "Same code but now with momentum gradient descent": [[13, "same-code-but-now-with-momentum-gradient-descent"], [34, "same-code-but-now-with-momentum-gradient-descent"], [34, "id3"], [34, "id4"]], "Schedule first week": [[31, "schedule-first-week"]], "Schematic Regression Procedure": [[9, "schematic-regression-procedure"]], "Second moment of the gradient": [[34, "second-moment-of-the-gradient"]], "September 15-19": [[19, "september-15-19"]], "Setting up a Multi-layer perceptron model for classification": [[39, "setting-up-a-multi-layer-perceptron-model-for-classification"]], "Setting up the Back propagation algorithm": [[12, "setting-up-the-back-propagation-algorithm"]], "Setting up the Back propagation algorithm, part 3": [[38, "setting-up-the-back-propagation-algorithm-part-3"], [39, "setting-up-the-back-propagation-algorithm-part-3"]], "Setting up the Matrix to be inverted": [[32, "setting-up-the-matrix-to-be-inverted"], [33, "setting-up-the-matrix-to-be-inverted"]], "Setting up the back propagation algorithm": [[38, "setting-up-the-back-propagation-algorithm"]], "Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations": [[39, "setting-up-the-back-propagation-algorithm-and-algorithm-for-a-feed-forward-nn-initalizations"]], "Setting up the back propagation algorithm, part 1": [[39, "setting-up-the-back-propagation-algorithm-part-1"]], "Setting up the back propagation algorithm, part 2": [[38, "setting-up-the-back-propagation-algorithm-part-2"], [39, "setting-up-the-back-propagation-algorithm-part-2"]], "Setting up the equations for a neural network": [[38, "setting-up-the-equations-for-a-neural-network"], [39, "setting-up-the-equations-for-a-neural-network"]], "Setting up the network using Autograd; The full program": [[2, "setting-up-the-network-using-autograd-the-full-program"]], "Similar (second order function now) problem but now with AdaGrad": [[13, "similar-second-order-function-now-problem-but-now-with-adagrad"], [34, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[9, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple case": [[32, "simple-case"], [33, "simple-case"]], "Simple code for solving the above problem": [[33, "simple-code-for-solving-the-above-problem"]], "Simple example": [[36, "simple-example"], [38, "simple-example"]], "Simple example code": [[34, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[33, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[33, "simple-geometric-interpretation"]], "Simple linear regression model using scikit-learn": [[0, "simple-linear-regression-model-using-scikit-learn"], [31, "simple-linear-regression-model-using-scikit-learn"]], "Simple neural 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No newline at end of file diff --git a/doc/LectureNotes/_build/html/week42.html b/doc/LectureNotes/_build/html/week42.html index bc75152dc..d271a302e 100644 --- a/doc/LectureNotes/_build/html/week42.html +++ b/doc/LectureNotes/_build/html/week42.html @@ -547,10 +547,8 @@ doconce format html week42.do.txt --no_mako -->

    Readings and videos#

    1. These lecture notes

      2. -
    - - -
      +

    1. Video of lecture at https://youtu.be/eqyNrEYRXnY

      2. +

    2. Whiteboard notes at CompPhysics/MachineLearning

    3. For a more in depth discussion on neural networks we recommend Goodfellow et al chapters 6 and 7. For the optimization part, see chapter 8.

    4. Neural Networks demystified at https://www.youtube.com/watch?v=bxe2T-V8XRs&list=PLiaHhY2iBX9hdHaRr6b7XevZtgZRa1PoU&ab_channel=WelchLabs

    5. Building Neural Networks from scratch at https://www.youtube.com/watch?v=Wo5dMEP_BbI&list=PLQVvvaa0QuDcjD5BAw2DxE6OF2tius3V3&ab_channel=sentdex

      6. diff --git a/doc/LectureNotes/_build/jupyter_execute/project2.ipynb b/doc/LectureNotes/_build/jupyter_execute/project2.ipynb index 50c44b123..f2130ba5a 100644 --- a/doc/LectureNotes/_build/jupyter_execute/project2.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/project2.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "061af572", + "id": "96e577ca", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "22578683", + "id": "067c02b9", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "61fb162f", + "id": "01f9fedd", "metadata": { "editable": true }, @@ -58,7 +58,7 @@ }, { "cell_type": "markdown", - "id": "104c69e1", + "id": "9f8e4871", "metadata": { "editable": true }, @@ -104,7 +104,7 @@ }, { "cell_type": "markdown", - "id": "0d2c42e3", + "id": "460cc6ea", "metadata": { "editable": true }, @@ -121,7 +121,7 @@ "\n", "* Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be\n", "\n", - " * The simple one-dimensional function Runge function from project 1, that is $f(x) = \\frac{1}{1+25x^2}$. We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", + " * The simple one-dimensional function Runge function from project 1, that is $f(x) = \\frac{1}{1+25x^2}$. We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", "\n", "* Classification.\n", "\n", @@ -132,7 +132,7 @@ }, { "cell_type": "markdown", - "id": "d8baab67", + "id": "d62a07ef", "metadata": { "editable": true }, @@ -162,7 +162,7 @@ }, { "cell_type": "markdown", - "id": "87e7ed71", + "id": "9cd8b8ac", "metadata": { "editable": true }, @@ -189,7 +189,7 @@ }, { "cell_type": "markdown", - "id": "5a26b6ad", + "id": "5931b155", "metadata": { "editable": true }, @@ -205,7 +205,7 @@ }, { "cell_type": "markdown", - "id": "096fe6c4", + "id": "b273fc8a", "metadata": { "editable": true }, @@ -217,7 +217,7 @@ }, { "cell_type": "markdown", - "id": "fd986596", + "id": "e13db1ec", "metadata": { "editable": true }, @@ -252,7 +252,7 @@ }, { "cell_type": "markdown", - "id": "e853d4b6", + "id": "4f864e31", "metadata": { "editable": true }, @@ -270,7 +270,7 @@ }, { "cell_type": "markdown", - "id": "fc2d413b", + "id": "c9faeafd", "metadata": { "editable": true }, @@ -285,7 +285,7 @@ }, { "cell_type": "markdown", - "id": "e6821051", + "id": "d865c22b", "metadata": { "editable": true }, @@ -302,7 +302,7 @@ }, { "cell_type": "markdown", - "id": "cba72d68", + "id": "5270af8f", "metadata": { "editable": true }, @@ -328,7 +328,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "e16fb528", + "id": "4e0e1fea", "metadata": { "collapsed": false, "editable": true @@ -347,7 +347,7 @@ }, { "cell_type": "markdown", - "id": "73599f42", + "id": "8fe85677", "metadata": { "editable": true }, @@ -358,7 +358,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "f1a639ef", + "id": "b28318b2", "metadata": { "collapsed": false, "editable": true @@ -370,7 +370,7 @@ }, { "cell_type": "markdown", - "id": "90fb7b41", + "id": "97e02c71", "metadata": { "editable": true }, @@ -381,7 +381,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "424af629", + "id": "88af355c", "metadata": { "collapsed": false, "editable": true @@ -394,7 +394,7 @@ }, { "cell_type": "markdown", - "id": "3c006080", + "id": "d1f8f0ed", "metadata": { "editable": true }, @@ -407,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "a18ddd54", + "id": "554b3a48", "metadata": { "editable": true }, @@ -419,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "1a1afaf9", + "id": "77bfdd5c", "metadata": { "editable": true }, @@ -434,7 +434,7 @@ "code for classification and pertinent results against a similar code using **Scikit-Learn** or **tensorflow/keras** or **pytorch**.\n", "\n", "If you have time, you can use the functionality of **scikit-learn** and compare your neural network results with those from Logistic regression. This is optional.\n", - "The weblink here compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article. Your neural network code can implement the equivalent of logistic regression by simply setting the number of hidden layers to zero. \n", + "The weblink here compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article. Your neural network code can implement the equivalent of logistic regression by simply setting the number of hidden layers to zero and keeping just the input and the output layers. \n", "\n", "If you wish to compare with say Logisti Regression from **scikit-learn**, the following code uses the above data set" ] @@ -442,7 +442,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "3c37cbaf", + "id": "eaa9e72e", "metadata": { "collapsed": false, "editable": true @@ -464,7 +464,7 @@ }, { "cell_type": "markdown", - "id": "106b9303", + "id": "c7ba883e", "metadata": { "editable": true }, @@ -480,7 +480,88 @@ }, { "cell_type": "markdown", - "id": "55da0d7f", + "id": "595be693", + "metadata": { + "editable": true + }, + "source": [ + "## Summary of methods to implement and analyze\n", + "\n", + "**Required Implementation:**\n", + "1. Reuse the regression code and results from project 1, these will act as a benchmark for seeing how suited a neural network is for this regression task.\n", + "\n", + "2. Implement a neural network with\n", + "\n", + " * A flexible number of layers\n", + "\n", + " * A flexible number of nodes in each layer\n", + "\n", + " * A changeable activation function in each layer (Sigmoid, ReLU, LeakyReLU, as well as Linear and Softmax)\n", + "\n", + " * A changeable cost function, which will be set to MSE for regression and cross-entropy for multiple-classification\n", + "\n", + " * An optional L1 or L2 norm of the weights and biases in the cost function (only used for computing gradients, not interpretable metrics)\n", + "\n", + "3. Implement the back-propagation algorithm to compute the gradient of your neural network\n", + "\n", + "4. Reuse the implementation of Plain and Stochastic Gradient Descent from Project 1 (and adapt the code to work with the your neural network)\n", + "\n", + " * With no optimization algorithm\n", + "\n", + " * With RMS Prop\n", + "\n", + " * With ADAM\n", + "\n", + "5. Implement scaling and train-test splitting of your data, preferably using sklearn\n", + "\n", + "6. Implement and compute metrics like the MSE and Accuracy" + ] + }, + { + "cell_type": "markdown", + "id": "35138b41", + "metadata": { + "editable": true + }, + "source": [ + "### Required Analysis:\n", + "\n", + "1. Briefly show and argue for the advantages and disadvantages of the methods from Project 1.\n", + "\n", + "2. Explore and show the impact of changing the number of layers, nodes per layer, choice of activation function, and inclusion of L1 and L2 norms. Present only the most interesting results from this exploration. 2D Heatmaps will be good for this: Start with finding a well performing set of hyper-parameters, then change two at a time in a range that shows good and bad performance.\n", + "\n", + "3. Show and argue for the advantages and disadvantages of using a neural network for regression on your data\n", + "\n", + "4. Show and argue for the advantages and disadvantages of using a neural network for classification on your data\n", + "\n", + "5. Show and argue for the advantages and disadvantages of the different gradient methods and learning rates when training the neural network" + ] + }, + { + "cell_type": "markdown", + "id": "b18bea03", + "metadata": { + "editable": true + }, + "source": [ + "### Optional (Note that you should include at least two of these in the report):\n", + "\n", + "1. Implement Logistic Regression as simple classification model case (equivalent to a Neural Network with just the output layer)\n", + "\n", + "2. Compute the gradient of the neural network with autograd, to show that it gives the same result as your hand-written backpropagation.\n", + "\n", + "3. Compare your results with results from using a machine-learning library like pytorch (https://docs.pytorch.org/tutorials/beginner/basics/buildmodel_tutorial.html)\n", + "\n", + "4. Use a more complex classification dataset instead, like the fashion MNIST (see )\n", + "\n", + "5. Use a more complex regression dataset instead, like the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", + "\n", + "6. Compute and interpret a confusion matrix of your best classification model (see )" + ] + }, + { + "cell_type": "markdown", + "id": "580d8424", "metadata": { "editable": true }, @@ -496,7 +577,7 @@ }, { "cell_type": "markdown", - "id": "d3731e2c", + "id": "96f5c67e", "metadata": { "editable": true }, @@ -527,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "6c7c5340", + "id": "d1bc28ba", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/_build/jupyter_execute/week42.ipynb b/doc/LectureNotes/_build/jupyter_execute/week42.ipynb index 50274c3c7..c3af30dea 100644 --- a/doc/LectureNotes/_build/jupyter_execute/week42.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/week42.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7dcf8613", + "id": "d231eeee", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "98019924", + "id": "5e782cb1", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "ab0e660a", + "id": "53309290", "metadata": { "editable": true }, @@ -40,32 +40,34 @@ }, { "cell_type": "markdown", - "id": "bcea021f", + "id": "71367514", "metadata": { "editable": true }, "source": [ "## Readings and videos\n", "1. These lecture notes\n", - "\n", - "\n", "\n", - "2. For a more in depth discussion on neural networks we recommend Goodfellow et al chapters 6 and 7. For the optimization part, see chapter 8. \n", + "2. Video of lecture at \n", "\n", - "3. Neural Networks demystified at \n", + "3. Whiteboard notes at \n", "\n", - "4. Building Neural Networks from scratch at \n", + "4. For a more in depth discussion on neural networks we recommend Goodfellow et al chapters 6 and 7. For the optimization part, see chapter 8. \n", "\n", - "5. Video on Neural Networks at \n", + "5. Neural Networks demystified at \n", "\n", - "6. Video on the back propagation algorithm at \n", + "6. Building Neural Networks from scratch at \n", + "\n", + "7. Video on Neural Networks at \n", + "\n", + "8. Video on the back propagation algorithm at \n", "\n", "I also recommend Michael Nielsen's intuitive approach to the neural networks and the universal approximation theorem, see the slides at ." ] }, { "cell_type": "markdown", - "id": "fd77cd6b", + "id": "c7be87be", "metadata": { "editable": true }, @@ -78,7 +80,7 @@ }, { "cell_type": "markdown", - "id": "7d93059a", + "id": "8e0567a2", "metadata": { "editable": true }, @@ -97,7 +99,7 @@ }, { "cell_type": "markdown", - "id": "5156bf60", + "id": "549dcc05", "metadata": { "editable": true }, @@ -113,7 +115,7 @@ }, { "cell_type": "markdown", - "id": "4f5d5b27", + "id": "21203bae", "metadata": { "editable": true }, @@ -124,7 +126,7 @@ }, { "cell_type": "markdown", - "id": "0a490014", + "id": "1c102a30", "metadata": { "editable": true }, @@ -138,7 +140,7 @@ }, { "cell_type": "markdown", - "id": "9fa74383", + "id": "53f11afe", "metadata": { "editable": true }, @@ -153,7 +155,7 @@ }, { "cell_type": "markdown", - "id": "417ce076", + "id": "afa8c42a", "metadata": { "editable": true }, @@ -165,7 +167,7 @@ }, { "cell_type": "markdown", - "id": "07ed6afb", + "id": "cb5c959f", "metadata": { "editable": true }, @@ -179,7 +181,7 @@ }, { "cell_type": "markdown", - "id": "3b926536", + "id": "0083ae15", "metadata": { "editable": true }, @@ -191,7 +193,7 @@ }, { "cell_type": "markdown", - "id": "0e1bd556", + "id": "f4931203", "metadata": { "editable": true }, @@ -207,7 +209,7 @@ }, { "cell_type": "markdown", - "id": "edebc935", + "id": "d3a3754d", "metadata": { "editable": true }, @@ -223,7 +225,7 @@ }, { "cell_type": "markdown", - "id": "3e2794ac", + "id": "bcd5dbab", "metadata": { "editable": true }, @@ -235,7 +237,7 @@ }, { "cell_type": "markdown", - "id": "54f91430", + "id": "2cbc30f1", "metadata": { "editable": true }, @@ -245,7 +247,7 @@ }, { "cell_type": "markdown", - "id": "f1e0a166", + "id": "1a1d803d", "metadata": { "editable": true }, @@ -257,7 +259,7 @@ }, { "cell_type": "markdown", - "id": "ad62ed90", + "id": "776735c7", "metadata": { "editable": true }, @@ -267,7 +269,7 @@ }, { "cell_type": "markdown", - "id": "57dac362", + "id": "c1a2e5af", "metadata": { "editable": true }, @@ -279,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "a4dc4050", + "id": "9e603df9", "metadata": { "editable": true }, @@ -289,7 +291,7 @@ }, { "cell_type": "markdown", - "id": "b223c83d", + "id": "533212cd", "metadata": { "editable": true }, @@ -301,7 +303,7 @@ }, { "cell_type": "markdown", - "id": "a1c9b5e7", + "id": "09d91067", "metadata": { "editable": true }, @@ -317,7 +319,7 @@ }, { "cell_type": "markdown", - "id": "9c3b03c0", + "id": "f767afe7", "metadata": { "editable": true }, @@ -329,7 +331,7 @@ }, { "cell_type": "markdown", - "id": "186485f2", + "id": "f38ded54", "metadata": { "editable": true }, @@ -341,7 +343,7 @@ }, { "cell_type": "markdown", - "id": "c2f1b30b", + "id": "f3f03bc3", "metadata": { "editable": true }, @@ -351,7 +353,7 @@ }, { "cell_type": "markdown", - "id": "13142fad", + "id": "9062730e", "metadata": { "editable": true }, @@ -363,7 +365,7 @@ }, { "cell_type": "markdown", - "id": "b441f95a", + "id": "75bbc32c", "metadata": { "editable": true }, @@ -373,7 +375,7 @@ }, { "cell_type": "markdown", - "id": "46e57fd2", + "id": "fcf02dbf", "metadata": { "editable": true }, @@ -389,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "50158555", + "id": "aa97678f", "metadata": { "editable": true }, @@ -401,7 +403,7 @@ }, { "cell_type": "markdown", - "id": "4174ea9e", + "id": "98f68e27", "metadata": { "editable": true }, @@ -413,7 +415,7 @@ }, { "cell_type": "markdown", - "id": "f7a29d74", + "id": "c4528178", "metadata": { "editable": true }, @@ -425,7 +427,7 @@ }, { "cell_type": "markdown", - "id": "cb1a387b", + "id": "d6304298", "metadata": { "editable": true }, @@ -437,7 +439,7 @@ }, { "cell_type": "markdown", - "id": "125bcb29", + "id": "dfc47ba6", "metadata": { "editable": true }, @@ -449,7 +451,7 @@ }, { "cell_type": "markdown", - "id": "76272ae9", + "id": "8834c3dc", "metadata": { "editable": true }, @@ -459,7 +461,7 @@ }, { "cell_type": "markdown", - "id": "7e0d1157", + "id": "40956770", "metadata": { "editable": true }, @@ -475,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "53dfc3bd", + "id": "69e7fdcf", "metadata": { "editable": true }, @@ -487,7 +489,7 @@ }, { "cell_type": "markdown", - "id": "126420bb", + "id": "726d4c90", "metadata": { "editable": true }, @@ -499,7 +501,7 @@ }, { "cell_type": "markdown", - "id": "2114b4ba", + "id": "0ee83d1c", "metadata": { "editable": true }, @@ -509,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "7d3549bb", + "id": "f5b3b5a5", "metadata": { "editable": true }, @@ -521,7 +523,7 @@ }, { "cell_type": "markdown", - "id": "80265b39", + "id": "b2746792", "metadata": { "editable": true }, @@ -535,7 +537,7 @@ }, { "cell_type": "markdown", - "id": "df2f78ac", + "id": "76e2e41a", "metadata": { "editable": true }, @@ -553,7 +555,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "0ec652bf", + "id": "1c4719c1", "metadata": { "collapsed": false, "editable": true @@ -626,7 +628,7 @@ }, { "cell_type": "markdown", - "id": "c382e2f2", + "id": "debaaadc", "metadata": { "editable": true }, @@ -636,7 +638,7 @@ }, { "cell_type": "markdown", - "id": "1bec2330", + "id": "7d576f19", "metadata": { "editable": true }, @@ -653,7 +655,7 @@ }, { "cell_type": "markdown", - "id": "165fb3f3", + "id": "582b3b43", "metadata": { "editable": true }, @@ -665,7 +667,7 @@ }, { "cell_type": "markdown", - "id": "7ae8de36", + "id": "c8eace47", "metadata": { "editable": true }, @@ -675,7 +677,7 @@ }, { "cell_type": "markdown", - "id": "9a2729ab", + "id": "81ec9945", "metadata": { "editable": true }, @@ -687,7 +689,7 @@ }, { "cell_type": "markdown", - "id": "372f0fac", + "id": "c35e1f69", "metadata": { "editable": true }, @@ -703,7 +705,7 @@ }, { "cell_type": "markdown", - "id": "d4f432cc", + "id": "05b8eea9", "metadata": { "editable": true }, @@ -715,7 +717,7 @@ }, { "cell_type": "markdown", - "id": "064af49b", + "id": "7ef9cb55", "metadata": { "editable": true }, @@ -727,7 +729,7 @@ }, { "cell_type": "markdown", - "id": "91115cc6", + "id": "1eb5c5ac", "metadata": { "editable": true }, @@ -738,7 +740,7 @@ }, { "cell_type": "markdown", - "id": "c38d1990", + "id": "00492358", "metadata": { "editable": true }, @@ -750,7 +752,7 @@ }, { "cell_type": "markdown", - "id": "43de152e", + "id": "45cca5aa", "metadata": { "editable": true }, @@ -763,7 +765,7 @@ }, { "cell_type": "markdown", - "id": "f935912b", + "id": "22cfb40b", "metadata": { "editable": true }, @@ -775,7 +777,7 @@ }, { "cell_type": "markdown", - "id": "15b380de", + "id": "45b30d06", "metadata": { "editable": true }, @@ -785,7 +787,7 @@ }, { "cell_type": "markdown", - "id": "302da250", + "id": "ebd6a7a5", "metadata": { "editable": true }, @@ -797,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "3faf23cf", + "id": "659dd686", "metadata": { "editable": true }, @@ -809,7 +811,7 @@ }, { "cell_type": "markdown", - "id": "4fe83376", + "id": "34a1d4ca", "metadata": { "editable": true }, @@ -821,7 +823,7 @@ }, { "cell_type": "markdown", - "id": "9bee26b1", + "id": "34471712", "metadata": { "editable": true }, @@ -831,7 +833,7 @@ }, { "cell_type": "markdown", - "id": "9affa08f", + "id": "0b3a74fd", "metadata": { "editable": true }, @@ -843,7 +845,7 @@ }, { "cell_type": "markdown", - "id": "1866378d", + "id": "1a5bdab3", "metadata": { "editable": true }, @@ -859,7 +861,7 @@ }, { "cell_type": "markdown", - "id": "e6d27f9d", + "id": "37f19e78", "metadata": { "editable": true }, @@ -871,7 +873,7 @@ }, { "cell_type": "markdown", - "id": "b33dac74", + "id": "5505aab8", "metadata": { "editable": true }, @@ -881,7 +883,7 @@ }, { "cell_type": "markdown", - "id": "27c367b4", + "id": "d55d045c", "metadata": { "editable": true }, @@ -893,7 +895,7 @@ }, { "cell_type": "markdown", - "id": "18898e14", + "id": "04f101e7", "metadata": { "editable": true }, @@ -903,7 +905,7 @@ }, { "cell_type": "markdown", - "id": "31fcc7f9", + "id": "bfab2e91", "metadata": { "editable": true }, @@ -915,7 +917,7 @@ }, { "cell_type": "markdown", - "id": "76219fdd", + "id": "77f35b7e", "metadata": { "editable": true }, @@ -927,7 +929,7 @@ }, { "cell_type": "markdown", - "id": "2cbccf94", + "id": "8cf4a606", "metadata": { "editable": true }, @@ -940,7 +942,7 @@ }, { "cell_type": "markdown", - "id": "ccdb071b", + "id": "86951351", "metadata": { "editable": true }, @@ -950,7 +952,7 @@ }, { "cell_type": "markdown", - "id": "55e4bed1", + "id": "73414e65", "metadata": { "editable": true }, @@ -962,7 +964,7 @@ }, { "cell_type": "markdown", - "id": "c00fd151", + "id": "8f0aaa15", "metadata": { "editable": true }, @@ -972,7 +974,7 @@ }, { "cell_type": "markdown", - "id": "d49ae60d", + "id": "730c5415", "metadata": { "editable": true }, @@ -984,7 +986,7 @@ }, { "cell_type": "markdown", - "id": "920db2dd", + "id": "1afcb5a1", "metadata": { "editable": true }, @@ -995,7 +997,7 @@ }, { "cell_type": "markdown", - "id": "62806f12", + "id": "7f30cb44", "metadata": { "editable": true }, @@ -1007,7 +1009,7 @@ }, { "cell_type": "markdown", - "id": "f1d3e7b6", + "id": "14c045ce", "metadata": { "editable": true }, @@ -1017,7 +1019,7 @@ }, { "cell_type": "markdown", - "id": "51fd0b81", + "id": "0c1a2c68", "metadata": { "editable": true }, @@ -1029,7 +1031,7 @@ }, { "cell_type": "markdown", - "id": "ba9dd4ad", + "id": "a3385222", "metadata": { "editable": true }, @@ -1039,7 +1041,7 @@ }, { "cell_type": "markdown", - "id": "91137440", + "id": "18ee3804", "metadata": { "editable": true }, @@ -1051,7 +1053,7 @@ }, { "cell_type": "markdown", - "id": "8e2ecb8c", + "id": "ad741d56", "metadata": { "editable": true }, @@ -1063,7 +1065,7 @@ }, { "cell_type": "markdown", - "id": "8d91daf9", + "id": "65870a70", "metadata": { "editable": true }, @@ -1075,7 +1077,7 @@ }, { "cell_type": "markdown", - "id": "8450f964", + "id": "f7807fdc", "metadata": { "editable": true }, @@ -1085,7 +1087,7 @@ }, { "cell_type": "markdown", - "id": "1e662a52", + "id": "9af4a759", "metadata": { "editable": true }, @@ -1097,7 +1099,7 @@ }, { "cell_type": "markdown", - "id": "e90d34b5", + "id": "dc548cb7", "metadata": { "editable": true }, @@ -1107,7 +1109,7 @@ }, { "cell_type": "markdown", - "id": "2d4b194d", + "id": "83b75e94", "metadata": { "editable": true }, @@ -1119,7 +1121,7 @@ }, { "cell_type": "markdown", - "id": "8990fe0b", + "id": "1c2be559", "metadata": { "editable": true }, @@ -1131,7 +1133,7 @@ }, { "cell_type": "markdown", - "id": "37e9e142", + "id": "18b85f86", "metadata": { "editable": true }, @@ -1143,7 +1145,7 @@ }, { "cell_type": "markdown", - "id": "5f66c64a", + "id": "63e39eb4", "metadata": { "editable": true }, @@ -1153,7 +1155,7 @@ }, { "cell_type": "markdown", - "id": "03e836ad", + "id": "a55371c1", "metadata": { "editable": true }, @@ -1165,7 +1167,7 @@ }, { "cell_type": "markdown", - "id": "1ea8a6ff", + "id": "fa31a9b3", "metadata": { "editable": true }, @@ -1175,7 +1177,7 @@ }, { "cell_type": "markdown", - "id": "84537cc9", + "id": "580df891", "metadata": { "editable": true }, @@ -1188,7 +1190,7 @@ }, { "cell_type": "markdown", - "id": "2bad6141", + "id": "c10bf2ce", "metadata": { "editable": true }, @@ -1200,7 +1202,7 @@ }, { "cell_type": "markdown", - "id": "5150b413", + "id": "0bae11f8", "metadata": { "editable": true }, @@ -1210,7 +1212,7 @@ }, { "cell_type": "markdown", - "id": "4166af55", + "id": "ed4a8b93", "metadata": { "editable": true }, @@ -1222,7 +1224,7 @@ }, { "cell_type": "markdown", - "id": "e5101f70", + "id": "2d582987", "metadata": { "editable": true }, @@ -1232,7 +1234,7 @@ }, { "cell_type": "markdown", - "id": "0c662571", + "id": "5fa760a1", "metadata": { "editable": true }, @@ -1244,7 +1246,7 @@ }, { "cell_type": "markdown", - "id": "a7e1af99", + "id": "bc9de8bf", "metadata": { "editable": true }, @@ -1254,7 +1256,7 @@ }, { "cell_type": "markdown", - "id": "5a73623e", + "id": "f00e3ace", "metadata": { "editable": true }, @@ -1266,7 +1268,7 @@ }, { "cell_type": "markdown", - "id": "b1d5327b", + "id": "7ac96362", "metadata": { "editable": true }, @@ -1276,7 +1278,7 @@ }, { "cell_type": "markdown", - "id": "5cc5921c", + "id": "9c46f966", "metadata": { "editable": true }, @@ -1293,7 +1295,7 @@ }, { "cell_type": "markdown", - "id": "21633b14", + "id": "ea509b11", "metadata": { "editable": true }, @@ -1305,7 +1307,7 @@ }, { "cell_type": "markdown", - "id": "171782c4", + "id": "e08ff771", "metadata": { "editable": true }, @@ -1317,7 +1319,7 @@ }, { "cell_type": "markdown", - "id": "830e0cc3", + "id": "6f476983", "metadata": { "editable": true }, @@ -1333,7 +1335,7 @@ }, { "cell_type": "markdown", - "id": "3de97402", + "id": "0535d087", "metadata": { "editable": true }, @@ -1350,7 +1352,7 @@ }, { "cell_type": "markdown", - "id": "f4a20e55", + "id": "5e024ec1", "metadata": { "editable": true }, @@ -1362,7 +1364,7 @@ }, { "cell_type": "markdown", - "id": "e373e6cc", + "id": "239fb4c6", "metadata": { "editable": true }, @@ -1375,7 +1377,7 @@ }, { "cell_type": "markdown", - "id": "a9fa6a69", + "id": "7e4fa6c5", "metadata": { "editable": true }, @@ -1387,7 +1389,7 @@ }, { "cell_type": "markdown", - "id": "f1730e5a", + "id": "c47cc3c6", "metadata": { "editable": true }, @@ -1403,7 +1405,7 @@ }, { "cell_type": "markdown", - "id": "59d7d98a", + "id": "4eb89f11", "metadata": { "editable": true }, @@ -1415,7 +1417,7 @@ }, { "cell_type": "markdown", - "id": "5a3d0931", + "id": "92744a90", "metadata": { "editable": true }, @@ -1431,7 +1433,7 @@ }, { "cell_type": "markdown", - "id": "c56d749e", + "id": "35424d45", "metadata": { "editable": true }, @@ -1443,7 +1445,7 @@ }, { "cell_type": "markdown", - "id": "f3dd37e7", + "id": "b8502930", "metadata": { "editable": true }, @@ -1455,7 +1457,7 @@ }, { "cell_type": "markdown", - "id": "7654c47c", + "id": "81ad45a5", "metadata": { "editable": true }, @@ -1465,7 +1467,7 @@ }, { "cell_type": "markdown", - "id": "cb1aa2a9", + "id": "11bb8afb", "metadata": { "editable": true }, @@ -1477,7 +1479,7 @@ }, { "cell_type": "markdown", - "id": "11607454", + "id": "b53ec752", "metadata": { "editable": true }, @@ -1487,7 +1489,7 @@ }, { "cell_type": "markdown", - "id": "29a881cd", + "id": "b7519a84", "metadata": { "editable": true }, @@ -1499,7 +1501,7 @@ }, { "cell_type": "markdown", - "id": "1244c442", + "id": "c57689db", "metadata": { "editable": true }, @@ -1513,7 +1515,7 @@ }, { "cell_type": "markdown", - "id": "7d43f636", + "id": "a9f83b15", "metadata": { "editable": true }, @@ -1525,7 +1527,7 @@ }, { "cell_type": "markdown", - "id": "c23708ab", + "id": "067c2583", "metadata": { "editable": true }, @@ -1535,7 +1537,7 @@ }, { "cell_type": "markdown", - "id": "3a3d49b9", + "id": "43545710", "metadata": { "editable": true }, @@ -1547,7 +1549,7 @@ }, { "cell_type": "markdown", - "id": "31b8b489", + "id": "1eb33717", "metadata": { "editable": true }, @@ -1557,7 +1559,7 @@ }, { "cell_type": "markdown", - "id": "2cb11e87", + "id": "e09a8734", "metadata": { "editable": true }, @@ -1569,7 +1571,7 @@ }, { "cell_type": "markdown", - "id": "85b6783b", + "id": "3dc0f5a3", "metadata": { "editable": true }, @@ -1581,7 +1583,7 @@ }, { "cell_type": "markdown", - "id": "1d9102e8", + "id": "bb58784b", "metadata": { "editable": true }, @@ -1593,7 +1595,7 @@ }, { "cell_type": "markdown", - "id": "92547c80", + "id": "10aea094", "metadata": { "editable": true }, @@ -1603,7 +1605,7 @@ }, { "cell_type": "markdown", - "id": "e06d7f47", + "id": "b7cc2db8", "metadata": { "editable": true }, @@ -1615,7 +1617,7 @@ }, { "cell_type": "markdown", - "id": "a15b2c15", + "id": "6cce9a62", "metadata": { "editable": true }, @@ -1625,7 +1627,7 @@ }, { "cell_type": "markdown", - "id": "69a96bb6", + "id": "43e5a84b", "metadata": { "editable": true }, @@ -1637,7 +1639,7 @@ }, { "cell_type": "markdown", - "id": "6954d50b", + "id": "d5c607a7", "metadata": { "editable": true }, @@ -1655,7 +1657,7 @@ }, { "cell_type": "markdown", - "id": "a8d2b720", + "id": "a51b3b58", "metadata": { "editable": true }, @@ -1673,7 +1675,7 @@ }, { "cell_type": "markdown", - "id": "b40feaea", + "id": "4cd9d058", "metadata": { "editable": true }, @@ -1685,7 +1687,7 @@ }, { "cell_type": "markdown", - "id": "04d0916c", + "id": "c80b630d", "metadata": { "editable": true }, @@ -1695,7 +1697,7 @@ }, { "cell_type": "markdown", - "id": "4067515f", + "id": "dc0c1a06", "metadata": { "editable": true }, @@ -1707,7 +1709,7 @@ }, { "cell_type": "markdown", - "id": "572f5043", + "id": "8f2065b7", "metadata": { "editable": true }, @@ -1719,7 +1721,7 @@ }, { "cell_type": "markdown", - "id": "4272e56c", + "id": "7f89b9d8", "metadata": { "editable": true }, @@ -1731,7 +1733,7 @@ }, { "cell_type": "markdown", - "id": "3ffcc3a4", + "id": "49c2cd3f", "metadata": { "editable": true }, @@ -1741,7 +1743,7 @@ }, { "cell_type": "markdown", - "id": "87dc5557", + "id": "517b1a37", "metadata": { "editable": true }, @@ -1753,7 +1755,7 @@ }, { "cell_type": "markdown", - "id": "36f9508b", + "id": "65c8107f", "metadata": { "editable": true }, @@ -1763,7 +1765,7 @@ }, { "cell_type": "markdown", - "id": "5e7f7ab6", + "id": "2a10f902", "metadata": { "editable": true }, @@ -1775,7 +1777,7 @@ }, { "cell_type": "markdown", - "id": "b5caac62", + "id": "b2ebf9c2", "metadata": { "editable": true }, @@ -1793,7 +1795,7 @@ }, { "cell_type": "markdown", - "id": "beffe853", + "id": "90336322", "metadata": { "editable": true }, @@ -1803,7 +1805,7 @@ }, { "cell_type": "markdown", - "id": "9ff991bb", + "id": "f25ff166", "metadata": { "editable": true }, @@ -1821,7 +1823,7 @@ }, { "cell_type": "markdown", - "id": "5c75d805", + "id": "4cf11d5e", "metadata": { "editable": true }, @@ -1831,7 +1833,7 @@ }, { "cell_type": "markdown", - "id": "df242f2d", + "id": "2670748d", "metadata": { "editable": true }, @@ -1849,7 +1851,7 @@ }, { "cell_type": "markdown", - "id": "18a65420", + "id": "18c29f71", "metadata": { "editable": true }, @@ -1861,7 +1863,7 @@ }, { "cell_type": "markdown", - "id": "04cb64d1", + "id": "c593470c", "metadata": { "editable": true }, @@ -1873,7 +1875,7 @@ }, { "cell_type": "markdown", - "id": "c5320606", + "id": "28e8caef", "metadata": { "editable": true }, @@ -1883,7 +1885,7 @@ }, { "cell_type": "markdown", - "id": "58b67295", + "id": "516de9d7", "metadata": { "editable": true }, @@ -1895,7 +1897,7 @@ }, { "cell_type": "markdown", - "id": "3b7c74a4", + "id": "004c0bf4", "metadata": { "editable": true }, @@ -1907,7 +1909,7 @@ }, { "cell_type": "markdown", - "id": "76ff59e0", + "id": "d62a3b1f", "metadata": { "editable": true }, @@ -1917,7 +1919,7 @@ }, { "cell_type": "markdown", - "id": "60a7be03", + "id": "e9af770e", "metadata": { "editable": true }, @@ -1929,7 +1931,7 @@ }, { "cell_type": "markdown", - "id": "27739d6d", + "id": "eca56f17", "metadata": { "editable": true }, @@ -1939,7 +1941,7 @@ }, { "cell_type": "markdown", - "id": "1efdb6f5", + "id": "bb0e4414", "metadata": { "editable": true }, @@ -1951,7 +1953,7 @@ }, { "cell_type": "markdown", - "id": "b0b04f61", + "id": "a4b190fc", "metadata": { "editable": true }, @@ -1963,7 +1965,7 @@ }, { "cell_type": "markdown", - "id": "e6c4318c", + "id": "ec0f87c0", "metadata": { "editable": true }, @@ -1989,7 +1991,7 @@ }, { "cell_type": "markdown", - "id": "4e58634a", + "id": "2fb45155", "metadata": { "editable": true }, @@ -2012,7 +2014,7 @@ }, { "cell_type": "markdown", - "id": "690eb424", + "id": "3d5c2a0e", "metadata": { "editable": true }, @@ -2024,7 +2026,7 @@ }, { "cell_type": "markdown", - "id": "5f475d02", + "id": "9183bbd0", "metadata": { "editable": true }, @@ -2036,7 +2038,7 @@ }, { "cell_type": "markdown", - "id": "016ce549", + "id": "32ece956", "metadata": { "editable": true }, @@ -2046,7 +2048,7 @@ }, { "cell_type": "markdown", - "id": "51f9ed82", + "id": "466d6bda", "metadata": { "editable": true }, @@ -2058,7 +2060,7 @@ }, { "cell_type": "markdown", - "id": "a8996176", + "id": "9f31b228", "metadata": { "editable": true }, @@ -2072,7 +2074,7 @@ }, { "cell_type": "markdown", - "id": "aaf186a8", + "id": "fbeac005", "metadata": { "editable": true }, @@ -2084,7 +2086,7 @@ }, { "cell_type": "markdown", - "id": "3b8a0a79", + "id": "bc6ae984", "metadata": { "editable": true }, @@ -2096,7 +2098,7 @@ }, { "cell_type": "markdown", - "id": "299cc7bb", + "id": "65f3133d", "metadata": { "editable": true }, @@ -2106,7 +2108,7 @@ }, { "cell_type": "markdown", - "id": "3b10a1a0", + "id": "5d27bbe1", "metadata": { "editable": true }, @@ -2118,7 +2120,7 @@ }, { "cell_type": "markdown", - "id": "0f8769f8", + "id": "5e5d0aa0", "metadata": { "editable": true }, @@ -2130,7 +2132,7 @@ }, { "cell_type": "markdown", - "id": "03860e2f", + "id": "ea32e5bb", "metadata": { "editable": true }, @@ -2140,7 +2142,7 @@ }, { "cell_type": "markdown", - "id": "00cea1da", + "id": "3a9bb5a6", "metadata": { "editable": true }, @@ -2152,7 +2154,7 @@ }, { "cell_type": "markdown", - "id": "fe5bbd2a", + "id": "9008dcf8", "metadata": { "editable": true }, @@ -2164,7 +2166,7 @@ }, { "cell_type": "markdown", - "id": "e791fb56", + "id": "89aba7d6", "metadata": { "editable": true }, @@ -2187,7 +2189,7 @@ }, { "cell_type": "markdown", - "id": "14ed4124", + "id": "ea0cdce2", "metadata": { "editable": true }, @@ -2206,7 +2208,7 @@ }, { "cell_type": "markdown", - "id": "d6b31eb8", + "id": "91342c80", "metadata": { "editable": true }, @@ -2218,7 +2220,7 @@ }, { "cell_type": "markdown", - "id": "2be10af5", + "id": "bd6eb22a", "metadata": { "editable": true }, @@ -2228,7 +2230,7 @@ }, { "cell_type": "markdown", - "id": "f45b9a99", + "id": "4e75b2ab", "metadata": { "editable": true }, @@ -2240,7 +2242,7 @@ }, { "cell_type": "markdown", - "id": "865d802b", + "id": "1626d9b7", "metadata": { "editable": true }, @@ -2257,7 +2259,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "37773874", + "id": "4ac7c23c", "metadata": { "collapsed": false, "editable": true @@ -2341,7 +2343,7 @@ }, { "cell_type": "markdown", - "id": "9cccb9ca", + "id": "6aeb0ee4", "metadata": { "editable": true }, @@ -2363,7 +2365,7 @@ }, { "cell_type": "markdown", - "id": "a42f7226", + "id": "ea47d1d6", "metadata": { "editable": true }, @@ -2381,7 +2383,7 @@ }, { "cell_type": "markdown", - "id": "0f57d23f", + "id": "1947aa95", "metadata": { "editable": true }, @@ -2404,7 +2406,7 @@ }, { "cell_type": "markdown", - "id": "ad459faf", + "id": "d024119f", "metadata": { "editable": true }, @@ -2423,7 +2425,7 @@ }, { "cell_type": "markdown", - "id": "1e307870", + "id": "c9178132", "metadata": { "editable": true }, @@ -2451,7 +2453,7 @@ }, { "cell_type": "markdown", - "id": "06fe5be6", + "id": "756185f5", "metadata": { "editable": true }, @@ -2471,7 +2473,7 @@ }, { "cell_type": "markdown", - "id": "736441f3", + "id": "3d92cad4", "metadata": { "editable": true }, @@ -2492,7 +2494,7 @@ }, { "cell_type": "markdown", - "id": "9ac6f21d", + "id": "cbc6f721", "metadata": { "editable": true }, @@ -2506,7 +2508,7 @@ }, { "cell_type": "markdown", - "id": "80ebd77c", + "id": "9249dc7b", "metadata": { "editable": true }, @@ -2518,7 +2520,7 @@ }, { "cell_type": "markdown", - "id": "2566a903", + "id": "e59de3af", "metadata": { "editable": true }, @@ -2540,7 +2542,7 @@ }, { "cell_type": "markdown", - "id": "382f5fe1", + "id": "e2da998c", "metadata": { "editable": true }, @@ -2562,7 +2564,7 @@ }, { "cell_type": "markdown", - "id": "fed07226", + "id": "e1abf01e", "metadata": { "editable": true }, @@ -2591,7 +2593,7 @@ }, { "cell_type": "markdown", - "id": "9ddc2586", + "id": "a8ded7cd", "metadata": { "editable": true }, @@ -2617,7 +2619,7 @@ }, { "cell_type": "markdown", - "id": "d327b303", + "id": "96da4f48", "metadata": { "editable": true }, @@ -2643,7 +2645,7 @@ }, { "cell_type": "markdown", - "id": "a3f4a57d", + "id": "395346a7", "metadata": { "editable": true }, @@ -2663,7 +2665,7 @@ }, { "cell_type": "markdown", - "id": "da0c8dbe", + "id": "9c712bbb", "metadata": { "editable": true }, @@ -2683,7 +2685,7 @@ }, { "cell_type": "markdown", - "id": "60e3da23", + "id": "2b66ea72", "metadata": { "editable": true }, @@ -2709,7 +2711,7 @@ }, { "cell_type": "markdown", - "id": "17f8f5ed", + "id": "5acbc082", "metadata": { "editable": true }, @@ -2738,7 +2740,7 @@ }, { "cell_type": "markdown", - "id": "06ba3896", + "id": "31825b65", "metadata": { "editable": true }, @@ -2756,7 +2758,7 @@ }, { "cell_type": "markdown", - "id": "72bc99e6", + "id": "c76d9af9", "metadata": { "editable": true }, @@ -2772,7 +2774,7 @@ }, { "cell_type": "markdown", - "id": "d5f452a2", + "id": "bdc93363", "metadata": { "editable": true }, @@ -2784,7 +2786,7 @@ }, { "cell_type": "markdown", - "id": "63889ee1", + "id": "a1d6ff64", "metadata": { "editable": true }, @@ -2798,7 +2800,7 @@ }, { "cell_type": "markdown", - "id": "5f47ef0f", + "id": "0c2e5742", "metadata": { "editable": true }, @@ -2826,7 +2828,7 @@ }, { "cell_type": "markdown", - "id": "b08a7b7e", + "id": "d4da3f02", "metadata": { "editable": true }, @@ -2838,7 +2840,7 @@ }, { "cell_type": "markdown", - "id": "10220190", + "id": "01ea2e0b", "metadata": { "editable": true }, @@ -2848,7 +2850,7 @@ }, { "cell_type": "markdown", - "id": "0fb4d5ad", + "id": "9c1c7bec", "metadata": { "editable": true }, @@ -2860,7 +2862,7 @@ }, { "cell_type": "markdown", - "id": "f8aa1bae", + "id": "9238ff2d", "metadata": { "editable": true }, @@ -2871,7 +2873,7 @@ }, { "cell_type": "markdown", - "id": "17de8e22", + "id": "3be74bd1", "metadata": { "editable": true }, @@ -2883,7 +2885,7 @@ }, { "cell_type": "markdown", - "id": "ca8f4f94", + "id": "2e2fd39c", "metadata": { "editable": true }, @@ -2896,7 +2898,7 @@ }, { "cell_type": "markdown", - "id": "ca998f7f", + "id": "42b1d26b", "metadata": { "editable": true }, @@ -2921,7 +2923,7 @@ }, { "cell_type": "markdown", - "id": "525b0573", + "id": "f740a484", "metadata": { "editable": true }, @@ -2934,7 +2936,7 @@ }, { "cell_type": "markdown", - "id": "a9279995", + "id": "19189bfc", "metadata": { "editable": true }, @@ -2946,7 +2948,7 @@ }, { "cell_type": "markdown", - "id": "e6cef751", + "id": "aeb3ef60", "metadata": { "editable": true }, @@ -2958,7 +2960,7 @@ }, { "cell_type": "markdown", - "id": "0ec11e1d", + "id": "dbf419a1", "metadata": { "editable": true }, @@ -2968,7 +2970,7 @@ }, { "cell_type": "markdown", - "id": "e5d6a067", + "id": "9e345753", "metadata": { "editable": true }, @@ -2980,7 +2982,7 @@ }, { "cell_type": "markdown", - "id": "add6e597", + "id": "3b13095e", "metadata": { "editable": true }, @@ -2992,7 +2994,7 @@ }, { "cell_type": "markdown", - "id": "dc7ca42d", + "id": "96501a91", "metadata": { "editable": true }, @@ -3004,7 +3006,7 @@ }, { "cell_type": "markdown", - "id": "80b56aa5", + "id": "48cf79fe", "metadata": { "editable": true }, @@ -3016,7 +3018,7 @@ }, { "cell_type": "markdown", - "id": "72a87573", + "id": "3243c0b1", "metadata": { "editable": true }, @@ -3026,7 +3028,7 @@ }, { "cell_type": "markdown", - "id": "ff8418ea", + "id": "bb312a09", "metadata": { "editable": true }, @@ -3038,7 +3040,7 @@ }, { "cell_type": "markdown", - "id": "dd978909", + "id": "484cf2b4", "metadata": { "editable": true }, @@ -3048,7 +3050,7 @@ }, { "cell_type": "markdown", - "id": "ce5a0650", + "id": "2b9c5483", "metadata": { "editable": true }, @@ -3060,7 +3062,7 @@ }, { "cell_type": "markdown", - "id": "dce8478b", + "id": "5ca21f09", "metadata": { "editable": true }, @@ -3073,7 +3075,7 @@ }, { "cell_type": "markdown", - "id": "92f7282e", + "id": "4852e4d2", "metadata": { "editable": true }, @@ -3085,7 +3087,7 @@ }, { "cell_type": "markdown", - "id": "e83bc7a2", + "id": "e3b7cbef", "metadata": { "editable": true }, @@ -3095,7 +3097,7 @@ }, { "cell_type": "markdown", - "id": "04f9d7f2", + "id": "0c1e69a1", "metadata": { "editable": true }, @@ -3107,7 +3109,7 @@ }, { "cell_type": "markdown", - "id": "c70ab677", + "id": "e71df7f4", "metadata": { "editable": true }, @@ -3118,7 +3120,7 @@ }, { "cell_type": "markdown", - "id": "801a6bd2", + "id": "50d6fecc", "metadata": { "editable": true }, @@ -3130,7 +3132,7 @@ }, { "cell_type": "markdown", - "id": "38eeee4b", + "id": "e145e461", "metadata": { "editable": true }, @@ -3140,7 +3142,7 @@ }, { "cell_type": "markdown", - "id": "d70ddf11", + "id": "97f13260", "metadata": { "editable": true }, @@ -3152,7 +3154,7 @@ }, { "cell_type": "markdown", - "id": "324ee5e0", + "id": "4361ce3b", "metadata": { "editable": true }, @@ -3162,7 +3164,7 @@ }, { "cell_type": "markdown", - "id": "3366df27", + "id": "52a16654", "metadata": { "editable": true }, @@ -3173,7 +3175,7 @@ }, { "cell_type": "markdown", - "id": "c9a2bd62", + "id": "3bfb321e", "metadata": { "editable": true }, @@ -3186,7 +3188,7 @@ }, { "cell_type": "markdown", - "id": "401183f6", + "id": "eccac6c9", "metadata": { "editable": true }, @@ -3196,7 +3198,7 @@ }, { "cell_type": "markdown", - "id": "d4e6a79e", + "id": "23634198", "metadata": { "editable": true }, @@ -3208,7 +3210,7 @@ }, { "cell_type": "markdown", - "id": "61cfab52", + "id": "7a2e75ba", "metadata": { "editable": true }, @@ -3218,7 +3220,7 @@ }, { "cell_type": "markdown", - "id": "fc5cf891", + "id": "2dad2d14", "metadata": { "editable": true }, @@ -3230,7 +3232,7 @@ }, { "cell_type": "markdown", - "id": "2e7f3950", + "id": "46415917", "metadata": { "editable": true }, @@ -3240,7 +3242,7 @@ }, { "cell_type": "markdown", - "id": "144969f6", + "id": "6adc7c1e", "metadata": { "editable": true }, @@ -3264,7 +3266,7 @@ }, { "cell_type": "markdown", - "id": "b6e503bd", + "id": "4110d83e", "metadata": { "editable": true }, @@ -3314,7 +3316,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "54230ef9", + "id": "070c610d", "metadata": { "collapsed": false, "editable": true @@ -3367,7 +3369,7 @@ }, { "cell_type": "markdown", - "id": "6738e7b4", + "id": "28bb6085", "metadata": { "editable": true }, @@ -3388,7 +3390,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "f369aa9d", + "id": "5a6ae0b0", "metadata": { "collapsed": false, "editable": true @@ -3426,7 +3428,7 @@ }, { "cell_type": "markdown", - "id": "f8bf8d16", + "id": "c26d604d", "metadata": { "editable": true }, @@ -3470,7 +3472,7 @@ }, { "cell_type": "markdown", - "id": "112b8cc3", + "id": "2775283b", "metadata": { "editable": true }, @@ -3510,7 +3512,7 @@ }, { "cell_type": "markdown", - "id": "e4166103", + "id": "f7455c00", "metadata": { "editable": true }, @@ -3531,7 +3533,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "36399cb5", + "id": "20b3c8c0", "metadata": { "collapsed": false, "editable": true @@ -3557,7 +3559,7 @@ }, { "cell_type": "markdown", - "id": "5eaf095b", + "id": "a41d9acd", "metadata": { "editable": true }, @@ -3585,7 +3587,7 @@ }, { "cell_type": "markdown", - "id": "91eec6b8", + "id": "b2f64238", "metadata": { "editable": true }, @@ -3622,7 +3624,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "ef497434", + "id": "1f5589af", "metadata": { "collapsed": false, "editable": true @@ -3668,7 +3670,7 @@ }, { "cell_type": "markdown", - "id": "ab88238a", + "id": "4518e911", "metadata": { "editable": true }, @@ -3699,7 +3701,7 @@ }, { "cell_type": "markdown", - "id": "506145ff", + "id": "d519516b", "metadata": { "editable": true }, @@ -3737,7 +3739,7 @@ }, { "cell_type": "markdown", - "id": "e8138025", + "id": "46b71202", "metadata": { "editable": true }, @@ -3771,7 +3773,7 @@ }, { "cell_type": "markdown", - "id": "25becf76", + "id": "129c39d3", "metadata": { "editable": true }, @@ -3812,7 +3814,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "657c604c", + "id": "8abafb44", "metadata": { "collapsed": false, "editable": true @@ -3891,7 +3893,7 @@ }, { "cell_type": "markdown", - "id": "3c595805", + "id": "e95c7166", "metadata": { "editable": true }, @@ -3912,7 +3914,7 @@ }, { "cell_type": "markdown", - "id": "17d5f534", + "id": "b4365471", "metadata": { "editable": true }, @@ -3926,7 +3928,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "5aeaa0cd", + "id": "5a0357b2", "metadata": { "collapsed": false, "editable": true @@ -4036,7 +4038,7 @@ }, { "cell_type": "markdown", - "id": "77f30e1e", + "id": "a417307d", "metadata": { "editable": true }, @@ -4055,7 +4057,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "c1ab41e1", + "id": "8ee4b306", "metadata": { "collapsed": false, "editable": true @@ -4082,7 +4084,7 @@ }, { "cell_type": "markdown", - "id": "1b2b35c3", + "id": "efcbd954", "metadata": { "editable": true }, @@ -4096,7 +4098,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "ac2ab4a6", + "id": "bb527e6e", "metadata": { "collapsed": false, "editable": true @@ -4127,7 +4129,7 @@ }, { "cell_type": "markdown", - "id": "f3e5dfec", + "id": "d282951d", "metadata": { "editable": true }, @@ -4138,7 +4140,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "6d875555", + "id": "69d3d9c8", "metadata": { "collapsed": false, "editable": true @@ -4182,7 +4184,7 @@ }, { "cell_type": "markdown", - "id": "81c742e3", + "id": "99f5058c", "metadata": { "editable": true }, @@ -4205,7 +4207,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "d21828bb", + "id": "7898d99f", "metadata": { "collapsed": false, "editable": true @@ -4232,7 +4234,7 @@ }, { "cell_type": "markdown", - "id": "4b40579d", + "id": "7ceec918", "metadata": { "editable": true }, @@ -4243,7 +4245,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "bfc97198", + "id": "98abf229", "metadata": { "collapsed": false, "editable": true @@ -4288,7 +4290,7 @@ }, { "cell_type": "markdown", - "id": "550680d5", + "id": "ba07c374", "metadata": { "editable": true }, @@ -4306,7 +4308,7 @@ }, { "cell_type": "markdown", - "id": "bbade60e", + "id": "1cf09819", "metadata": { "editable": true }, @@ -4341,7 +4343,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "e5505ed3", + "id": "2c2c3ec5", "metadata": { "collapsed": false, "editable": true @@ -4353,7 +4355,7 @@ }, { "cell_type": "markdown", - "id": "98d4797a", + "id": "39d013b1", "metadata": { "editable": true }, @@ -4365,7 +4367,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "95b05730", + "id": "fbf36c26", "metadata": { "collapsed": false, "editable": true @@ -4378,7 +4380,7 @@ }, { "cell_type": "markdown", - "id": "94170f18", + "id": "94e66380", "metadata": { "editable": true }, @@ -4389,7 +4391,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "65ae6e69", + "id": "5e72b1d2", "metadata": { "collapsed": false, "editable": true @@ -4402,7 +4404,7 @@ }, { "cell_type": "markdown", - "id": "df39c5c6", + "id": "40470dbd", "metadata": { "editable": true }, @@ -4417,7 +4419,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "d0d627f6", + "id": "f2cd4f41", "metadata": { "collapsed": false, "editable": true @@ -4429,7 +4431,7 @@ }, { "cell_type": "markdown", - "id": "4124b5af", + "id": "636940c6", "metadata": { "editable": true }, @@ -4441,7 +4443,7 @@ }, { "cell_type": "markdown", - "id": "22dc977c", + "id": "d9f47b57", "metadata": { "editable": true }, @@ -4454,7 +4456,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "7df2e4d4", + "id": "1489b5d5", "metadata": { "collapsed": false, "editable": true @@ -4509,7 +4511,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "4f5bff6f", + "id": "672dc5a2", "metadata": { "collapsed": false, "editable": true @@ -4538,7 +4540,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "3ae517ea", + "id": "0513084f", "metadata": { "collapsed": false, "editable": true @@ -4568,7 +4570,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "c880b209", + "id": "02a34777", "metadata": { "collapsed": false, "editable": true @@ -4595,7 +4597,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "cf8cea73", + "id": "52c1d6e2", "metadata": { "collapsed": false, "editable": true @@ -4637,7 +4639,7 @@ }, { "cell_type": "markdown", - "id": "3024761c", + "id": "53f9be79", "metadata": { "editable": true }, @@ -4656,7 +4658,7 @@ }, { "cell_type": "markdown", - "id": "53987675", + "id": "39bd1718", "metadata": { "editable": true }, @@ -4678,7 +4680,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "5ed03631", + "id": "4c1f42f1", "metadata": { "collapsed": false, "editable": true @@ -4819,7 +4821,7 @@ }, { "cell_type": "markdown", - "id": "8b98c385", + "id": "532aecc2", "metadata": { "editable": true }, @@ -4835,7 +4837,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "54298abd", + "id": "b24b4414", "metadata": { "collapsed": false, "editable": true @@ -4848,7 +4850,7 @@ }, { "cell_type": "markdown", - "id": "c03dc1b1", + "id": "32a25c0b", "metadata": { "editable": true }, @@ -4860,7 +4862,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "5a2f7871", + "id": "7a7d273f", "metadata": { "collapsed": false, "editable": true @@ -4882,7 +4884,7 @@ }, { "cell_type": "markdown", - "id": "07fa559a", + "id": "d34cd45c", "metadata": { "editable": true }, @@ -4898,7 +4900,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "718450a2", + "id": "9ad6425d", "metadata": { "collapsed": false, "editable": true @@ -4936,7 +4938,7 @@ }, { "cell_type": "markdown", - "id": "0db28b52", + "id": "baaaff79", "metadata": { "editable": true }, @@ -4949,7 +4951,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "1479de5a", + "id": "78f11b83", "metadata": { "collapsed": false, "editable": true @@ -4970,7 +4972,7 @@ }, { "cell_type": "markdown", - "id": "d42e1ccf", + "id": "05285af5", "metadata": { "editable": true }, @@ -4986,7 +4988,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "2c2a8d32", + "id": "7ac52c84", "metadata": { "collapsed": false, "editable": true @@ -5044,7 +5046,7 @@ }, { "cell_type": "markdown", - "id": "65e7caab", + "id": "873e7caa", "metadata": { "editable": true }, @@ -5059,7 +5061,7 @@ { "cell_type": "code", "execution_count": 29, - "id": "75e9399d", + "id": "bd43ac18", "metadata": { "collapsed": false, "editable": true @@ -5080,7 +5082,7 @@ }, { "cell_type": "markdown", - "id": "0b0b82e8", + "id": "3dc2175e", "metadata": { "editable": true }, @@ -5104,7 +5106,7 @@ { "cell_type": "code", "execution_count": 30, - "id": "5351bfd6", + "id": "5b4b161c", "metadata": { "collapsed": false, "editable": true @@ -5576,7 +5578,7 @@ }, { "cell_type": "markdown", - "id": "2d63ec5b", + "id": "9596ae53", "metadata": { "editable": true }, @@ -5588,7 +5590,7 @@ { "cell_type": "code", "execution_count": 31, - "id": "85a6b185", + "id": "a11f680f", "metadata": { "collapsed": false, "editable": true @@ -5632,7 +5634,7 @@ }, { "cell_type": "markdown", - "id": "f8842209", + "id": "0fc39e40", "metadata": { "editable": true }, @@ -5648,7 +5650,7 @@ { "cell_type": "code", "execution_count": 32, - "id": "b7b14d8f", + "id": "a67ab3a0", "metadata": { "collapsed": false, "editable": true @@ -5663,7 +5665,7 @@ }, { "cell_type": "markdown", - "id": "3e35cc67", + "id": "3add8665", "metadata": { "editable": true }, @@ -5674,7 +5676,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "c2b3e7a3", + "id": "4a4fbc7a", "metadata": { "collapsed": false, "editable": true @@ -5689,7 +5691,7 @@ }, { "cell_type": "markdown", - "id": "9d0eb8b2", + "id": "4dff1871", "metadata": { "editable": true }, @@ -5705,7 +5707,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "19fd68fe", + "id": "ad40e38c", "metadata": { "collapsed": false, "editable": true @@ -5719,7 +5721,7 @@ }, { "cell_type": "markdown", - "id": "ecbc4c88", + "id": "43cd1e22", "metadata": { "editable": true }, @@ -5734,7 +5736,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "c62f0877", + "id": "cde36b38", "metadata": { "collapsed": false, "editable": true @@ -5760,7 +5762,7 @@ { "cell_type": "code", "execution_count": 36, - "id": "5b955b7a", + "id": "2bc572a4", "metadata": { "collapsed": false, "editable": true @@ -5775,7 +5777,7 @@ }, { "cell_type": "markdown", - "id": "e4c3e9cc", + "id": "e3e6fa31", "metadata": { "editable": true }, @@ -5786,7 +5788,7 @@ { "cell_type": "code", "execution_count": 37, - "id": "4e994594", + "id": "575ceb29", "metadata": { "collapsed": false, "editable": true @@ -5801,7 +5803,7 @@ }, { "cell_type": "markdown", - "id": "690debd0", + "id": "622015f0", "metadata": { "editable": true }, @@ -5812,7 +5814,7 @@ { "cell_type": "code", "execution_count": 38, - "id": "ea04ae66", + "id": "9c075b36", "metadata": { "collapsed": false, "editable": true @@ -5832,7 +5834,7 @@ { "cell_type": "code", "execution_count": 39, - "id": "cd892db0", + "id": "44ded771", "metadata": { "collapsed": false, "editable": true @@ -5847,7 +5849,7 @@ }, { "cell_type": "markdown", - "id": "c85e6aa4", + "id": "317e6e5c", "metadata": { "editable": true }, @@ -5862,7 +5864,7 @@ { "cell_type": "code", "execution_count": 40, - "id": "1dc44b4d", + "id": "8911de9d", "metadata": { "collapsed": false, "editable": true @@ -5899,7 +5901,7 @@ }, { "cell_type": "markdown", - "id": "785a6539", + "id": "82d61377", "metadata": { "editable": true }, @@ -5912,7 +5914,7 @@ { "cell_type": "code", "execution_count": 41, - "id": "f2137088", + "id": "2a72a374", "metadata": { "collapsed": false, "editable": true @@ -5935,7 +5937,7 @@ }, { "cell_type": "markdown", - "id": "6caa78c7", + "id": "2d892009", "metadata": { "editable": true }, diff --git a/doc/LectureNotes/project2.ipynb b/doc/LectureNotes/project2.ipynb index b22fbdd58..faf4aee16 100644 --- a/doc/LectureNotes/project2.ipynb +++ b/doc/LectureNotes/project2.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "061af572", + "id": "96e577ca", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "22578683", + "id": "067c02b9", "metadata": { "editable": true }, @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "61fb162f", + "id": "01f9fedd", "metadata": { "editable": true }, @@ -58,7 +58,7 @@ }, { "cell_type": "markdown", - "id": "104c69e1", + "id": "9f8e4871", "metadata": { "editable": true }, @@ -104,7 +104,7 @@ }, { "cell_type": "markdown", - "id": "0d2c42e3", + "id": "460cc6ea", "metadata": { "editable": true }, @@ -121,7 +121,7 @@ "\n", "* Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be\n", "\n", - " * The simple one-dimensional function Runge function from project 1, that is $f(x) = \\frac{1}{1+25x^2}$. We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", + " * The simple one-dimensional function Runge function from project 1, that is $f(x) = \\frac{1}{1+25x^2}$. We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", "\n", "* Classification.\n", "\n", @@ -132,7 +132,7 @@ }, { "cell_type": "markdown", - "id": "d8baab67", + "id": "d62a07ef", "metadata": { "editable": true }, @@ -162,7 +162,7 @@ }, { "cell_type": "markdown", - "id": "87e7ed71", + "id": "9cd8b8ac", "metadata": { "editable": true }, @@ -189,7 +189,7 @@ }, { "cell_type": "markdown", - "id": "5a26b6ad", + "id": "5931b155", "metadata": { "editable": true }, @@ -205,7 +205,7 @@ }, { "cell_type": "markdown", - "id": "096fe6c4", + "id": "b273fc8a", "metadata": { "editable": true }, @@ -217,7 +217,7 @@ }, { "cell_type": "markdown", - "id": "fd986596", + "id": "e13db1ec", "metadata": { "editable": true }, @@ -252,7 +252,7 @@ }, { "cell_type": "markdown", - "id": "e853d4b6", + "id": "4f864e31", "metadata": { "editable": true }, @@ -270,7 +270,7 @@ }, { "cell_type": "markdown", - "id": "fc2d413b", + "id": "c9faeafd", "metadata": { "editable": true }, @@ -285,7 +285,7 @@ }, { "cell_type": "markdown", - "id": "e6821051", + "id": "d865c22b", "metadata": { "editable": true }, @@ -302,7 +302,7 @@ }, { "cell_type": "markdown", - "id": "cba72d68", + "id": "5270af8f", "metadata": { "editable": true }, @@ -328,7 +328,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "e16fb528", + "id": "4e0e1fea", "metadata": { "collapsed": false, "editable": true @@ -347,7 +347,7 @@ }, { "cell_type": "markdown", - "id": "73599f42", + "id": "8fe85677", "metadata": { "editable": true }, @@ -358,7 +358,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "f1a639ef", + "id": "b28318b2", "metadata": { "collapsed": false, "editable": true @@ -370,7 +370,7 @@ }, { "cell_type": "markdown", - "id": "90fb7b41", + "id": "97e02c71", "metadata": { "editable": true }, @@ -381,7 +381,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "424af629", + "id": "88af355c", "metadata": { "collapsed": false, "editable": true @@ -394,7 +394,7 @@ }, { "cell_type": "markdown", - "id": "3c006080", + "id": "d1f8f0ed", "metadata": { "editable": true }, @@ -407,7 +407,7 @@ }, { "cell_type": "markdown", - "id": "a18ddd54", + "id": "554b3a48", "metadata": { "editable": true }, @@ -419,7 +419,7 @@ }, { "cell_type": "markdown", - "id": "1a1afaf9", + "id": "77bfdd5c", "metadata": { "editable": true }, @@ -434,7 +434,7 @@ "code for classification and pertinent results against a similar code using **Scikit-Learn** or **tensorflow/keras** or **pytorch**.\n", "\n", "If you have time, you can use the functionality of **scikit-learn** and compare your neural network results with those from Logistic regression. This is optional.\n", - "The weblink here compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article. Your neural network code can implement the equivalent of logistic regression by simply setting the number of hidden layers to zero. \n", + "The weblink here compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article. Your neural network code can implement the equivalent of logistic regression by simply setting the number of hidden layers to zero and keeping just the input and the output layers. \n", "\n", "If you wish to compare with say Logisti Regression from **scikit-learn**, the following code uses the above data set" ] @@ -442,7 +442,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "3c37cbaf", + "id": "eaa9e72e", "metadata": { "collapsed": false, "editable": true @@ -464,7 +464,7 @@ }, { "cell_type": "markdown", - "id": "106b9303", + "id": "c7ba883e", "metadata": { "editable": true }, @@ -480,7 +480,88 @@ }, { "cell_type": "markdown", - "id": "55da0d7f", + "id": "595be693", + "metadata": { + "editable": true + }, + "source": [ + "## Summary of methods to implement and analyze\n", + "\n", + "**Required Implementation:**\n", + "1. Reuse the regression code and results from project 1, these will act as a benchmark for seeing how suited a neural network is for this regression task.\n", + "\n", + "2. Implement a neural network with\n", + "\n", + " * A flexible number of layers\n", + "\n", + " * A flexible number of nodes in each layer\n", + "\n", + " * A changeable activation function in each layer (Sigmoid, ReLU, LeakyReLU, as well as Linear and Softmax)\n", + "\n", + " * A changeable cost function, which will be set to MSE for regression and cross-entropy for multiple-classification\n", + "\n", + " * An optional L1 or L2 norm of the weights and biases in the cost function (only used for computing gradients, not interpretable metrics)\n", + "\n", + "3. Implement the back-propagation algorithm to compute the gradient of your neural network\n", + "\n", + "4. Reuse the implementation of Plain and Stochastic Gradient Descent from Project 1 (and adapt the code to work with the your neural network)\n", + "\n", + " * With no optimization algorithm\n", + "\n", + " * With RMS Prop\n", + "\n", + " * With ADAM\n", + "\n", + "5. Implement scaling and train-test splitting of your data, preferably using sklearn\n", + "\n", + "6. Implement and compute metrics like the MSE and Accuracy" + ] + }, + { + "cell_type": "markdown", + "id": "35138b41", + "metadata": { + "editable": true + }, + "source": [ + "### Required Analysis:\n", + "\n", + "1. Briefly show and argue for the advantages and disadvantages of the methods from Project 1.\n", + "\n", + "2. Explore and show the impact of changing the number of layers, nodes per layer, choice of activation function, and inclusion of L1 and L2 norms. Present only the most interesting results from this exploration. 2D Heatmaps will be good for this: Start with finding a well performing set of hyper-parameters, then change two at a time in a range that shows good and bad performance.\n", + "\n", + "3. Show and argue for the advantages and disadvantages of using a neural network for regression on your data\n", + "\n", + "4. Show and argue for the advantages and disadvantages of using a neural network for classification on your data\n", + "\n", + "5. Show and argue for the advantages and disadvantages of the different gradient methods and learning rates when training the neural network" + ] + }, + { + "cell_type": "markdown", + "id": "b18bea03", + "metadata": { + "editable": true + }, + "source": [ + "### Optional (Note that you should include at least two of these in the report):\n", + "\n", + "1. Implement Logistic Regression as simple classification model case (equivalent to a Neural Network with just the output layer)\n", + "\n", + "2. Compute the gradient of the neural network with autograd, to show that it gives the same result as your hand-written backpropagation.\n", + "\n", + "3. Compare your results with results from using a machine-learning library like pytorch (https://docs.pytorch.org/tutorials/beginner/basics/buildmodel_tutorial.html)\n", + "\n", + "4. Use a more complex classification dataset instead, like the fashion MNIST (see )\n", + "\n", + "5. Use a more complex regression dataset instead, like the two-dimensional Runge function $f(x,y)=\\left[(10x - 5)^2 + (10y - 5)^2 + 1 \\right]^{-1}$, or even more complicated two-dimensional functions (see the supplementary material of for an extensive list of two-dimensional functions). \n", + "\n", + "6. Compute and interpret a confusion matrix of your best classification model (see )" + ] + }, + { + "cell_type": "markdown", + "id": "580d8424", "metadata": { "editable": true }, @@ -496,7 +577,7 @@ }, { "cell_type": "markdown", - "id": "d3731e2c", + "id": "96f5c67e", "metadata": { "editable": true }, @@ -527,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "6c7c5340", + "id": "d1bc28ba", "metadata": { "editable": true },