Linear Regression from Scratch Using MXNet

linearregression.ipynb

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    "colab": {
      "name": "LinearRegression.ipynb",
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    {
      "cell_type": "markdown",
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        "id": "view-in-github",
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      "source": [
        "<a href=\"https://colab.research.google.com/gist/devil-cyber/f1dd3c440c01824f38fd959f28ba541d/linearregression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "**To keep things simple, we will construct an artificial dataset according to a linear model with additive noise. Our task will be to recover this modelʼs parameters using the finite set of examples contained in our dataset. We will keep the data low-dimensional so we can visualize it easily. Inthe following code snippet, we generate a dataset containing 1000 examples, each consisting of 2 features sampled from a standard normal distribution. Thus our synthetic dataset will be a matrix of (1000,2)**"
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    {
      "cell_type": "code",
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      "source": [
        "# First install the required library"
      ],
      "id": "cac5b33e",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "44908e75"
      },
      "source": [
        "!pip intsall mxnet\n",
        "!pip install d2l"
      ],
      "id": "44908e75",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "12518da6"
      },
      "source": [
        "import random\n",
        "from mxnet import autograd,np,npx\n",
        "from d2l import mxnet as d2l"
      ],
      "id": "12518da6",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bfc4ed89"
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      "source": [
        "npx.set_np()"
      ],
      "id": "bfc4ed89",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
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      "source": [
        "def synthatic_data(w,b,number_example):\n",
        "    X=np.random.normal(0,1,(number_example,len(w)))\n",
        "    y=np.dot(X,w)+b\n",
        "    y+=np.random.normal(0,0.01,number_example)\n",
        "    return X,y.reshape(-1,1)"
      ],
      "id": "582d9ab7",
      "execution_count": null,
      "outputs": []
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      "source": [
        "true_w=np.array([2,-3.4])\n",
        "true_b=4.2\n",
        "features,labels=synthatic_data(true_w,true_b,1000)"
      ],
      "id": "631bee0c",
      "execution_count": null,
      "outputs": []
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    {
      "cell_type": "code",
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        "id": "4d8c29f3",
        "outputId": "f2a5c70b-3449-43b8-f6fa-a909d4b8fc13"
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      "source": [
        "print('features:',features[0],'\\nlabel:',labels[0])"
      ],
      "id": "4d8c29f3",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "features: [-0.07779644 -0.29604757] \n",
            "label: [5.038374]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "73bb8c08",
        "outputId": "d8f59429-ac86-4f94-b444-a31e17893f7e"
      },
      "source": [
        "d2l.set_figsize(figsize=(5,5))\n",
        "d2l.plt.scatter(features[:,(1)].asnumpy(),labels.asnumpy())\n",
        "d2l.plt.xlabel('features')\n",
        "d2l.plt.ylabel('label')\n",
        "d2l.plt.show()"
      ],
      "id": "73bb8c08",
      "execution_count": null,
      "outputs": [
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            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a2aa2aea"
      },
      "source": [
        "**Training models consists of making multiple passes over the\n",
        "datasets, grabbing one mini batch of examples at a time, \n",
        "and using them to update our model. Since this process is \n",
        "so fundamental to training machine learning algorithms, \n",
        "it is worth defining a utility function to shuffle \n",
        "the datasets and access it in mini batches.**\n"
      ],
      "id": "a2aa2aea"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "58ca50e4"
      },
      "source": [
        "def data_iter(batch_size,features,labels):\n",
        "    num_example=len(features)\n",
        "    indices=list(range(num_example))\n",
        "    random.shuffle(indices)\n",
        "    for i in range(0,num_example,batch_size):\n",
        "        batch_indices=np.array(indices[i:min(i+batch_size,num_example)])\n",
        "        yield features[batch_indices],labels[batch_indices]"
      ],
      "id": "58ca50e4",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ff0bb69c",
        "outputId": "d95cb2bb-b69c-4161-fd4c-3d3bf38060d3"
      },
      "source": [
        "batch_size=10\n",
        "for x,y in data_iter(batch_size,features,labels):\n",
        "    print(x,'\\n',y)\n",
        "    break"
      ],
      "id": "ff0bb69c",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-0.962749   -0.55384135]\n",
            " [-0.0405596  -1.235375  ]\n",
            " [-1.5954542   0.4391431 ]\n",
            " [-1.6199528  -0.07730079]\n",
            " [-1.107901   -0.7959186 ]\n",
            " [-0.36899024 -0.7729436 ]\n",
            " [-0.28542033 -0.35447767]\n",
            " [ 1.2201017  -0.02195513]\n",
            " [-0.24894063 -0.5814291 ]\n",
            " [ 0.19986263 -1.1644106 ]] \n",
            " [[ 4.1553745 ]\n",
            " [ 8.3211155 ]\n",
            " [-0.47396895]\n",
            " [ 1.2183642 ]\n",
            " [ 4.700398  ]\n",
            " [ 6.1041307 ]\n",
            " [ 4.8193865 ]\n",
            " [ 6.7091627 ]\n",
            " [ 5.6857333 ]\n",
            " [ 8.565659  ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "87ea27c7"
      },
      "source": [
        "### Initializing Model Parameters & Defining the Model"
      ],
      "id": "87ea27c7"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3e8b52cf"
      },
      "source": [
        "w=np.random.normal(0,0.01,(2,1))\n",
        "b=np.zeros(1)\n",
        "w.attach_grad() #  to consider for gradient calculation graph\n",
        "b.attach_grad()\n",
        "\n",
        "def linreg(X,w,b):\n",
        "    return np.dot(X,w)+b"
      ],
      "id": "3e8b52cf",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c9a934d2"
      },
      "source": [
        "### Defining the Loss Function"
      ],
      "id": "c9a934d2"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "09058912"
      },
      "source": [
        "def squared_loss(y_hat,y):\n",
        "    return (y_hat-y.reshape(y_hat.shape))**2/2"
      ],
      "id": "09058912",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "56ed564b"
      },
      "source": [
        "### Defining the Optimization Algorithm"
      ],
      "id": "56ed564b"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b3f52807"
      },
      "source": [
        "def sgd(params,lr,batch_size):\n",
        "    for param in params:\n",
        "        param[:]=param-lr*param.grad/batch_size"
      ],
      "id": "b3f52807",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "71a2486f"
      },
      "source": [
        "lr=0.03 # learning rate\n",
        "num_epochs=5\n",
        "net = linreg\n",
        "loss = squared_loss"
      ],
      "id": "71a2486f",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cfcd0cde",
        "outputId": "f2a038ca-7203-45ef-dfe6-28a9c97b47b1"
      },
      "source": [
        "for epoch in range(num_epochs):\n",
        "    for X,y in data_iter(batch_size,features,labels):\n",
        "        with autograd.record():\n",
        "            l=loss(net(X,w,b),y)# Minibatch loss in `X` and `y`\n",
        "            # Because `l` has a shape (`batch_size`, 1) and is not a scalar\n",
        "            # variable, the elements in `l` are added together to obtain a new\n",
        "            # variable, on which gradients with respect to [`w`, `b`] are computed\n",
        "        l.backward()\n",
        "        sgd([w,b],lr,batch_size) # update parameter using their gradient\n",
        "    train_l = loss(net(features,w,b),labels)\n",
        "    print(f'epoch {epoch+1}, loss {float(train_l.mean()):f}')"
      ],
      "id": "cfcd0cde",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "epoch 1, loss 0.034540\n",
            "epoch 2, loss 0.000124\n",
            "epoch 3, loss 0.000049\n",
            "epoch 4, loss 0.000048\n",
            "epoch 5, loss 0.000048\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}