Code Challenge progress at solution lecture time.

Author: bitcointroy

Troy_Bradley_High_Dimensional_Vector_Distance_CC.ipynb

@@ -0,0 +1,328 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "name": "Troy Bradley High Dimensional Vector Distance CC - Master.ipynb",
+      "version": "0.3.2",
+      "provenance": [],
+      "collapsed_sections": []
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "view-in-github",
+        "colab_type": "text"
+      },
+      "source": [
+        "[View in Colaboratory](https://colab.research.google.com/github/bitcointroy/MLcodechallenges/blob/master/Troy_Bradley_High_Dimensional_Vector_Distance_CC.ipynb)"
+      ]
+    },
+    {
+      "metadata": {
+        "id": "luCg81YEjaP1",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "cell_type": "code",
+      "source": [
+        "import numpy as np\n",
+        "import matplotlib.pyplot as plt"
+      ],
+      "execution_count": 0,
+      "outputs": []
+    },
+    {
+      "metadata": {
+        "id": "k3P7Si8cj37a",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "First, define a function that takes two inputs (a mean and a standard deviation) and spits out a random number.\n",
+        "The number should be generated randomly from a normal distribution with that mean and that standard deviation. See [numpy.random.normal](https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.normal.html), though, implementing the PDF for a normal distribution is a good exercise if you finish early."
+      ]
+    },
+    {
+      "metadata": {
+        "id": "wMkZOsQ2kUpX",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "e1aa1926-4eed-4e95-d8fa-134b4cb18abd"
+      },
+      "cell_type": "code",
+      "source": [
+        "def rand_val(mean, stdev):\n",
+        "  return np.random.normal(mean, stdev)\n",
+        "  \n",
+        "rand_val(10, 2)\n",
+        "    "
+      ],
+      "execution_count": 63,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "11.051335018124922"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          },
+          "execution_count": 63
+        }
+      ]
+    },
+    {
+      "metadata": {
+        "id": "nayMEH_3nRZC",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "Now define a function that takes in a mean, a standard deviation, and a number n, and returns a numpy vector with n components.\n",
+        "The components should be randomly generated from a normal distribution with that mean and standard deviation"
+      ]
+    },
+    {
+      "metadata": {
+        "id": "ExAJD2CxngF1",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 136
+        },
+        "outputId": "0ece737d-f53a-4517-ee01-dc489afee13f"
+      },
+      "cell_type": "code",
+      "source": [
+        "new_vec = []\n",
+        "def rand_vec(mean, stdev, n):\n",
+        "  new_vec = np.random.normal(mean, stdev, size=n)\n",
+        "  return new_vec\n",
+        "\n",
+        "print('random: \\n', rand_vec(10,2,(5,2)))\n",
+        "print('new: ', new_vec)"
+      ],
+      "execution_count": 73,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "random: \n",
+            "\r [[ 9.2406166   7.39290715]\n",
+            " [ 9.32357534 10.89028469]\n",
+            " [11.63520949 11.31414626]\n",
+            " [11.11438854 12.81961532]\n",
+            " [12.29890036  8.6219731 ]]\n",
+            "new:  []\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "metadata": {
+        "id": "FdU1-hoOsyXz",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "Recall that there are many ways to compute the distance between two vectors. However you wish to do so, write a function that takes in\n",
+        "two vectors and returns the distance between them. Since this function only makes sense if the two vectors have the same number of\n",
+        "components, this function should return -1 if the two vectors live in different numbers of dimensions"
+      ]
+    },
+    {
+      "metadata": {
+        "id": "F6OKPxP8nvFn",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "cell_type": "code",
+      "source": [
+        "def vec_dist(vecA, vecB):\n",
+        "  if vecA.shape !== vecB.shape\n",
+        "  "
+      ],
+      "execution_count": 0,
+      "outputs": []
+    },
+    {
+      "metadata": {
+        "id": "tEPgA2qHuaFT",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "From here on out, every component you randomly generate should come from a normal distribution centered at 0 with standard\n",
+        "deviation 1. With that in mind, write a function that takes in a number n (the number of dimensions), creates two random\n",
+        "vectors in n-dimensional space, calculates the distance between them, and returns that distance."
+      ]
+    },
+    {
+      "metadata": {
+        "id": "8dAXAmjyuZGm",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "cell_type": "code",
+      "source": [
+        "def rand_vec_dist(n):\n",
+        "    return None\n",
+        "    ##################\n",
+        "    # Your Code Here #\n",
+        "    ##################"
+      ],
+      "execution_count": 0,
+      "outputs": []
+    },
+    {
+      "metadata": {
+        "id": "MuRwge4GvZrS",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "Using what you've made so far, what is the average distance between two points in 1-dimensional space? In other words, between\n",
+        "two regular old floating point numbers with mean 0 and standard deviation 1. After you calculate this, store it as the first\n",
+        "component in a Pythin list named average_dist_list."
+      ]
+    },
+    {
+      "metadata": {
+        "id": "-xBiAWMHvw3h",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "ccdcd419-85cf-47ca-9c3d-5fe6bf147f9e"
+      },
+      "cell_type": "code",
+      "source": [
+        "def average_dist_calculator(n, trials):\n",
+        "    return None\n",
+        "    ##################\n",
+        "    # Your Code Here #\n",
+        "    ##################\n",
+        "average_dist_list = []\n",
+        "print(average_dist_list)"
+      ],
+      "execution_count": 0,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "[]\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "metadata": {
+        "id": "8mPH39jfzLM4",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "What's the average distance between two points in 2-dimensional space? What about 3? Keep calculating these average distances and\n",
+        "appending them to average_dist_list up through 200-dimensional space."
+      ]
+    },
+    {
+      "metadata": {
+        "id": "dxHLm6J1wMwP",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 34
+        },
+        "outputId": "3d843ecd-308b-473c-f682-a97ba2358fbe"
+      },
+      "cell_type": "code",
+      "source": [
+        "##################\n",
+        "# Your Code Here #\n",
+        "##################\n",
+        "print(average_dist_list)"
+      ],
+      "execution_count": 0,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "[]\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "metadata": {
+        "id": "t_DED4x70zMV",
+        "colab_type": "code",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 347
+        },
+        "outputId": "82f21134-4fe5-4051-900f-19787f0f22c6"
+      },
+      "cell_type": "code",
+      "source": [
+        "plt.plot(np.arange(0,0),average_dist_list);"
+      ],
+      "execution_count": 0,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "image/png": 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+            "text/plain": [
+              "<matplotlib.figure.Figure at 0x7f6e708e2b38>"
+            ]
+          },
+          "metadata": {
+            "tags": []
+          }
+        }
+      ]
+    },
+    {
+      "metadata": {
+        "id": "urd9Ficj4axm",
+        "colab_type": "text"
+      },
+      "cell_type": "markdown",
+      "source": [
+        "As the number of dimensions n grows larger and larger, approximately how does the average distance grow?\n",
+        "\n",
+        "It should be well-approximated by the function f(n) = c*n^p for some numbers c and p. However you choose to do so, find the values of c and p."
+      ]
+    },
+    {
+      "metadata": {
+        "id": "YBVLh9gM16kI",
+        "colab_type": "code",
+        "colab": {}
+      },
+      "cell_type": "code",
+      "source": [
+        ""
+      ],
+      "execution_count": 0,
+      "outputs": []
+    }
+  ]
+}