ML_Lab01.ipynb

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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPT4VYkSAiH3JfuTBBIyRpt",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/PubudU99/ML-google-crash-course/blob/main/ML_Lab01.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Import Important Modules for the plotting the graphs"
      ],
      "metadata": {
        "id": "koeQF6NtNtvd"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "FaoHTaSwNhSp"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Example Code"
      ],
      "metadata": {
        "id": "3BXszaLhNsen"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Hello World!\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gP1qOJCVN_MY",
        "outputId": "a1f4714c-b769-4fc3-c9a8-86339ed07056"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Hello World!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Example codes for implementing relevent theory materials for the Probability**"
      ],
      "metadata": {
        "id": "GEqU1-S_ONb1"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "1. For getting dot product of two matrices\n",
        "\n"
      ],
      "metadata": {
        "id": "SE-YM6SoOreQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.array([1, 2])\n",
        "y = np.array([2, 1])\n",
        "a = np.dot(x, y)\n",
        "print(a)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BXq9o9oPOZQ-",
        "outputId": "9e67be0c-4da3-43c0-f3d5-bd0555a51d2a"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "4\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "        2.For getting Linear Norm"
      ],
      "metadata": {
        "id": "BDE_Hbq2O-6F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b = np.linalg.norm(x)\n",
        "c = np.sqrt(x[0]**2 + x[1]**2)\n",
        "print(b, c)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "eyW5-9_6Pr_a",
        "outputId": "6ab330f2-d4cf-427f-e45f-aec200359cf6"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.23606797749979 2.23606797749979\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "3. Angle between two vectors"
      ],
      "metadata": {
        "id": "4aSgkgvJQDc0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "theta = np.arccos(np.dot(x,y) / (np.linalg.norm(x) * np.linalg.norm(y)))\n",
        "print(theta)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zet9NEGEQH5K",
        "outputId": "5a4b49cc-5632-4c74-8a1f-28f7d6bf5a8c"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.6435011087932847\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "4. Symmetric matrix"
      ],
      "metadata": {
        "id": "jzkBP_dcRJyp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "B = np.array([[3,2,1], [2,6,5], [1,5,9]], dtype=float)\n",
        "print(B)\n",
        "print(B - B.T) # Thois represents the Transpose of the B Matrice\n",
        "#By seen the results we can see that (B - B.T) GiVES 0."
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rUSwgZ2iRPy4",
        "outputId": "8285ae3d-334b-44af-97d1-08a61a106b78"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[3. 2. 1.]\n",
            " [2. 6. 5.]\n",
            " [1. 5. 9.]]\n",
            "[[0. 0. 0.]\n",
            " [0. 0. 0.]\n",
            " [0. 0. 0.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "5.  Rank of a matrix as the number of linearly independent rows/columns"
      ],
      "metadata": {
        "id": "mLpd49xwSyZ8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "z = np.random.rand(3)\n",
        "print(z)\n",
        "v = B @ z\n",
        "print(v.shape)\n",
        "# rank = np.linalg.matrix_rank(v.shape)\n",
        "# print(rank)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WP0iV5VyS21C",
        "outputId": "6e18e78d-9b72-4bdd-ab80-f284dfe80fef"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.35159347 0.29573039 0.78998417]\n",
            "1\n",
            "(3,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "gjMpjxHuSyWm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(z.T @ B @ z)"
      ],
      "metadata": {
        "id": "VXQB0gk4WY4W"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "dd"
      ],
      "metadata": {
        "id": "fhwSz4v2WciP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(np.trace(B))\n",
        "print(np.linalg.det(B))\n"
      ],
      "metadata": {
        "id": "aw6jamebWeOZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "1e2aV52UWfL9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "D, U = np.linalg.eig(B)\n",
        "print(D)\n",
        "print(U)"
      ],
      "metadata": {
        "id": "Q-Gqj-YvWgDv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "Nycr9ngdWkNm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print(np.dot(U[:,0], U[:,1]))\n",
        "print(U @ U.T)"
      ],
      "metadata": {
        "id": "VAgq0mOQWkpe"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Plotting random Graphs for the 1000 data"
      ],
      "metadata": {
        "id": "pNjNAO6HaO4p"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "x = np.random.rand(10000, 1)\n",
        "# print(x)\n",
        "\n",
        "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))\n",
        "n1bins, n2bins = 4, 100\n",
        "\n",
        "# Histogram with borders\n",
        "ax[0].hist(x, bins=n1bins, edgecolor='black')\n",
        "ax[0].set_ylim(0, 10000)\n",
        "ax[0].set_xlabel(\"Bins\", fontsize=16)\n",
        "ax[0].set_ylabel(\"Count\", fontsize=16)\n",
        "ax[0].tick_params(axis='both', which='major', labelsize=14)\n",
        "ax[0].set_title(\"Histogram: bins=%4d\" % (n1bins), fontsize=16)\n",
        "\n",
        "# Histogram with borders\n",
        "ax[1].hist(x, bins=n2bins, edgecolor='black')\n",
        "ax[1].set_ylim(0, 250)\n",
        "ax[1].set_xlabel(\"Bins\", fontsize=16)\n",
        "ax[1].set_ylabel(\"Count\", fontsize=16)\n",
        "ax[1].tick_params(axis='both', which='major', labelsize=14)\n",
        "ax[1].set_title(\"Histogram: bins=%4d\" % (n2bins), fontsize=16)\n",
        "\n",
        "plt.savefig(\"histograms_uniform.png\")\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 407
        },
        "id": "Dt_s03mVaXdx",
        "outputId": "e1052d28-ba9c-4255-990d-bfe144f0e9cc"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x400 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "Q1. The histograms do not appear flat even though the data is from a uniform distribution because the number of bins used in each histogram is different.\n",
        "\n",
        "Q2. Because the data is different each time, the histogram that is generated from that data will also be different. This is expected behavior when working with random data and is one of the reasons why it's important to set a random seed if you want reproducible results.\n",
        "\n",
        "Q3. Working with more data points can lead to more stable and reliable results, providing a better understanding of the underlying distribution and reducing the impact of random fluctuations."
      ],
      "metadata": {
        "id": "Yc_1LhoE1jpd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "N = 10000\n",
        "x1 = np.zeros(N)\n",
        "for n in range(N):\n",
        "\n",
        "  x1[n] = np.sum(np.random.rand(12,1)) - np.sum(np.random.rand(12,1))\n",
        "# print(x1)\n",
        "fig, ax = plt.subplots(figsize=(5,5))\n",
        "ax.hist(x1, 20)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 637
        },
        "id": "fe90uORbvFGW",
        "outputId": "9e493cc9-ce9e-4cb3-994c-7bb87ac0242a"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([1.000e+00, 2.000e+00, 6.000e+00, 2.300e+01, 6.100e+01, 1.580e+02,\n",
              "        3.210e+02, 6.130e+02, 9.630e+02, 1.297e+03, 1.540e+03, 1.543e+03,\n",
              "        1.278e+03, 9.910e+02, 6.150e+02, 3.330e+02, 1.410e+02, 8.800e+01,\n",
              "        2.000e+01, 6.000e+00]),\n",
              " array([-6.06068684e+00, -5.50996462e+00, -4.95924241e+00, -4.40852019e+00,\n",
              "        -3.85779797e+00, -3.30707575e+00, -2.75635353e+00, -2.20563131e+00,\n",
              "        -1.65490910e+00, -1.10418688e+00, -5.53464659e-01, -2.74244016e-03,\n",
              "         5.47979778e-01,  1.09870200e+00,  1.64942422e+00,  2.20014643e+00,\n",
              "         2.75086865e+00,  3.30159087e+00,  3.85231309e+00,  4.40303531e+00,\n",
              "         4.95375753e+00]),\n",
              " <BarContainer object of 20 artists>)"
            ]
          },
          "metadata": {},
          "execution_count": 33
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Questions**\n",
        "\n",
        "\n",
        "*   The Central Limit Theorem (CLT) explains this observation. The CLT states that the distribution of the sum (or difference) of a large number of independent, identically distributed random variables approaches a normal distribution, regardless of the shape of the original distribution. As you increase the number of random numbers involved in the sums and subtractions, you are effectively summing (or differencing) more independent, identically distributed random variables, leading to a distribution that more closely approximates a normal distribution.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "McjOLzSk2Riw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 2. Uncertainty in Estimation"
      ],
      "metadata": {
        "id": "WU1Cf_3R2900"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "MaxTrial = 2000\n",
        "sampleSizeRange = np.linspace(100, 200, 40)\n",
        "plotVar = np.zeros(len(sampleSizeRange))\n",
        "for sSize in range(len(sampleSizeRange)):\n",
        "  numSamples = int(sampleSizeRange[sSize])\n",
        "  vStrial = np.zeros(MaxTrial)\n",
        "  for trial in range(MaxTrial):\n",
        "    xx = np.random.randn(numSamples,1)\n",
        "    vStrial[trial] = np.var(xx)\n",
        "  plotVar[sSize] = np.var(vStrial)\n",
        "fig, ax = plt.subplots(figsize=(4,4))\n",
        "ax.plot((plotVar))"
      ],
      "metadata": {
        "id": "dQX66Pvo2cfh",
        "outputId": "ba081f32-973b-4f37-a87b-a8be75903639",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 389
        }
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x788ccba962c0>]"
            ]
          },
          "metadata": {},
          "execution_count": 34
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 400x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}