Playing with PyTorch Gradients.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H25XmZfr9lGW"
      },
      "source": [
        "# Playing with PyTorch Gradients\n",
        "\n",
        "**GPU**\n",
        "- N = 1,000 & p = 1,000,000 || Runtime = 15s\n",
        "\n",
        "**CPU**\n",
        "- N = 1,000 & p = 1,000,000 || Runtime = 5m29"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GNHav_Qk6EaS",
        "outputId": "0a19916e-d3da-40dd-98c6-4d367c78be48"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Device is cpu\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "from sklearn.model_selection import train_test_split\n",
        "from tqdm.auto import trange\n",
        "\n",
        "import matplotlib.pyplot as graph\n",
        "graph.style.use('fivethirtyeight')\n",
        "torch.manual_seed(42)\n",
        "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
        "# device = \"cpu\"\n",
        "if device == \"cuda\":\n",
        "    torch.set_default_dtype(torch.float16)  # halfs our memory usage\n",
        "print(f'Device is {device}')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UeHujTjG6dOH",
        "outputId": "ae7e3103-9519-4d60-e210-6e29779cd9a6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "tensor([ 2., -2.,  2.,  ...,  0.,  0.,  0.])\n",
            "torch.Size([1000, 1000000]) torch.Size([1000])\n",
            "torch.Size([900, 1000000]) torch.Size([900])\n",
            "torch.Size([100, 1000000]) torch.Size([100])\n"
          ]
        }
      ],
      "source": [
        "# Toy data\n",
        "n, p = int(1e3), int(1e6)\n",
        "\n",
        "true_beta = torch.zeros(p)\n",
        "true_beta[:4] = torch.tensor([2.0, -2.0, 2.0, 3.0])\n",
        "print(true_beta)\n",
        "\n",
        "x = torch.randn(n, p)\n",
        "y = x @ true_beta + 2.5 * torch.randn(n)\n",
        "\n",
        "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.1, random_state=42)\n",
        "\n",
        "print(x.shape, y.shape)\n",
        "print(x_train.shape, y_train.shape)\n",
        "print(x_test.shape, y_test.shape)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 562,
          "referenced_widgets": [
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        "outputId": "85b8d0f7-912d-4bb2-81b7-a37f54a4eebb"
      },
      "outputs": [
        {
          "data": {
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              "model_id": "b5ad4d32225a4ba4ae76b9f9e85846e1",
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            "text/plain": [
              "  0%|          | 0/1000 [00:00<?, ?it/s]"
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          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Parameter containing:\n",
            "tensor([ 1.6620, -1.7095,  1.7882,  ...,  0.0000,  0.0000,  0.0000],\n",
            "       requires_grad=True)\n"
          ]
        },
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "class Lasso(nn.Module):\n",
        "    def __init__(self, p, lam=0.1, eps=1e-3):\n",
        "        super().__init__()\n",
        "        self.m = nn.Parameter(torch.zeros(p))\n",
        "        self.b = nn.Parameter(torch.zeros(1))\n",
        "        self.lam = lam\n",
        "        self.eps = eps\n",
        "\n",
        "        self.hist = []\n",
        "\n",
        "    def forward(self, x):\n",
        "        return x @ self.m + self.b\n",
        "\n",
        "    def calc_loss(self, y_pred, y_true):\n",
        "        # MSE + lam*||m||_1\n",
        "        return torch.mean((y_pred - y_true) ** 2) + self.lam * torch.sum(torch.abs(self.m))\n",
        "\n",
        "    def fit(self, x, y, epochs=1000, lr=0.1):\n",
        "        self.hist = []\n",
        "        self.b = nn.Parameter(torch.mean(y))\n",
        "\n",
        "        iterator = trange(epochs)\n",
        "        for _ in iterator:\n",
        "            # Zero gradients\n",
        "            self.zero_grad()\n",
        "\n",
        "            # Forward pass\n",
        "            y_hat = self.forward(x)\n",
        "\n",
        "            # Backward pass\n",
        "            loss = self.calc_loss(y_hat, y)\n",
        "            iterator.set_description(f\"Loss: {loss.item():.4f}\")\n",
        "\n",
        "            if len(self.hist) > 0 and abs(self.hist[-1] - loss.item()) < self.eps:\n",
        "                break\n",
        "\n",
        "            loss.backward()\n",
        "            with torch.no_grad():\n",
        "                m_grad_argmax = torch.argmax(torch.abs(self.m.grad))\n",
        "                m_max_grad = self.m.grad[m_grad_argmax]\n",
        "                m_new = torch.zeros_like(self.m.grad)\n",
        "                m_new[m_grad_argmax] = m_max_grad\n",
        "                m_new *= -lr\n",
        "\n",
        "                # Update parameters\n",
        "                self.m += m_new\n",
        "                self.hist.append(loss.item())\n",
        "\n",
        "        # Polishing step\n",
        "        with torch.no_grad():\n",
        "            self.m[torch.abs(self.m) < self.lam] = 0.0\n",
        "\n",
        "model = Lasso(p).to(device)\n",
        "model.fit(x_train.to(device), y_train.to(device))\n",
        "print(model.m)\n",
        "\n",
        "graph.plot(model.hist)\n",
        "graph.xlabel(\"Epochs\")\n",
        "graph.ylabel(\"Loss\")\n",
        "graph.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 478
        },
        "id": "2GT-xahL6uH4",
        "outputId": "d92e3700-ea94-4f84-d377-abe892ab918d"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "graph.plot(true_beta[:10], '*', linewidth=2, label='True Coef')\n",
        "graph.plot(model.m[:10].detach().cpu(), 'x', linewidth=2, label='Estimated Coef')\n",
        "graph.ylabel('Coef')\n",
        "graph.xlabel('j')\n",
        "graph.legend()\n",
        "graph.xlim([-1, 10])\n",
        "graph.show()"
      ]
    }
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