seminars/seminar1/1D_histogram.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "1D_histogram.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "## Training model on discrete 1D data"
      ],
      "metadata": {
        "id": "ct1AnX1crxBK"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "Zm-8xIQzqUcI"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 1. Generating of 1D Data "
      ],
      "metadata": {
        "id": "N_BJc8tkrjBs"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Вопрос 1\n",
        "\n",
        "Как зная математическое ожидание $\\mu$ и стандартное отклонение $\\sigma$ распределения , получать семплы из него $\\mathcal{N}(\\mu,\\sigma^{2})$?"
      ],
      "metadata": {
        "id": "gX_rvC0zckxw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mu = 0.1*torch.ones(1)\n",
        "std = 2*torch.ones(1)\n",
        "x = mu + std*torch.randn(100)"
      ],
      "metadata": {
        "id": "WptYDOtbQHc0"
      },
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "X9j-4BENQt6s",
        "outputId": "6597afdb-286a-4dc0-deb2-f141595816e1"
      },
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 1.5487, -2.1133,  1.6143,  0.4453,  0.1344,  2.3123,  2.7664, -0.4326,\n",
              "        -1.8682, -0.9319, -1.4333,  0.7801,  1.6060,  4.5341, -1.5975, -0.0430,\n",
              "        -2.3000,  0.6921,  3.1050, -2.2594, -1.6563, -0.6555,  3.9745, -5.2941,\n",
              "        -0.6380,  1.5823, -1.8207,  1.5011,  1.4499, -3.2087,  2.0418, -1.5248,\n",
              "        -1.6138, -4.3225,  0.5161,  3.6834,  1.3778, -2.2198,  1.8132, -2.1061,\n",
              "         2.1571, -1.2595, -3.0131,  1.1720, -0.0144,  1.9751,  3.7404,  2.1737,\n",
              "        -0.9230, -2.5240,  3.1794,  1.2982, -1.3567,  2.3212,  3.0335,  0.6802,\n",
              "        -0.2462,  3.3293,  2.3303, -3.0991,  1.7637,  0.3436, -1.1426,  1.1958,\n",
              "        -2.7983, -1.3413,  0.9054, -1.1921, -2.3196, -0.6170, -1.0994, -4.5979,\n",
              "        -3.0311, -0.8888,  0.1292, -0.7151,  1.8252, -1.7209, -0.1593,  2.2709,\n",
              "        -0.5903, -2.9041, -0.8307,  1.6341, -4.7289,  1.9450, -1.9765, -2.1813,\n",
              "        -0.1856,  4.9264, -0.4215,  0.8921, -1.9401,  0.5773, -2.5428,  1.0039,\n",
              "        -1.2352, -3.9116, -2.0758,  0.5590])"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def generate_1d_data(count, bins):\n",
        "    np.random.seed(42)\n",
        "\n",
        "    a = 0.2 + 0.05 * np.random.randn(count)\n",
        "    b = 0.6 + 0.15 * np.random.randn(count)\n",
        "\n",
        "    mask = np.random.rand(count) < 0.5\n",
        "\n",
        "    samples = (a * mask + b * (1 - mask)) * (bins - 1)\n",
        "    \n",
        "    data = np.clip(samples.astype('int'), 0.0, (bins - 1))\n",
        "    \n",
        "    split = int(0.8 * count)\n",
        "    train_data, test_data = data[:split], data[split:]\n",
        "    return train_data, test_data"
      ],
      "metadata": {
        "id": "JxuiijNxr5Eu"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_1d_data(train_data, test_data):\n",
        "    bins = int(max(test_data.max(), train_data.max()) - min(test_data.min(), train_data.min())) + 1\n",
        "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5))\n",
        "    ax1.set_title('train')\n",
        "    ax1.hist(train_data, bins=bins, density=True)\n",
        "    ax1.set_xlabel('x')\n",
        "    ax2.set_title('test')\n",
        "    ax2.hist(test_data, bins=np.arange(bins), density=True)\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "v_hAxdWqrvse"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "BINS = 100\n",
        "COUNT = 5000\n",
        "\n",
        "train_data, test_data = generate_1d_data(COUNT, BINS)\n",
        "plot_1d_data(train_data, test_data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "id": "cmlRB2zFsCub",
        "outputId": "1bcf21a6-ff10-4208-d071-c9de5d3779ec"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 720x360 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 2. Model for training"
      ],
      "metadata": {
        "id": "tpUtkHiXsuYd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Вопрос 2 \n",
        "\n",
        "- Запрашивает ли градиент переменная проиницилизированная как torch.nn.Parameter(data) ?\n",
        "\n",
        "- Что такое torch.unsqueeze? Отличается ли это от torch.view и если да то чем?\n",
        "\n",
        "- Значения функции Softmax лежат между какими значениями?"
      ],
      "metadata": {
        "id": "1Ra65HK9ughQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "class SoftmaxModel(torch.nn.Module):\n",
        "\n",
        "    def __init__(self, bins):\n",
        "        \"\"\"\n",
        "        logits - torch.tensor of shape [bins]\n",
        "\n",
        "        \"\"\"\n",
        "        super().__init__()\n",
        "\n",
        "        self.bins = bins\n",
        "        self.logits = torch.nn.Parameter(torch.zeros(bins)) # torch.Size([bins])\n",
        "\n",
        "    def forward(self, x):\n",
        "        \n",
        "        \"\"\"\n",
        "        x -  torch.tensor of shape [B,1]\n",
        "\n",
        "        \"\"\"\n",
        "        \n",
        "        logits = self.logits.unsqueeze(0).repeat(x.shape[0], 1) # torch.tensor [1,bins] -> [B,bins]\n",
        "     \n",
        "        return logits"
      ],
      "metadata": {
        "id": "fI8P7JhDsdEl"
      },
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def get_distribution(model):\n",
        "    distribution = torch.nn.functional.softmax(model.logits, dim=0)\n",
        "    return distribution.detach().cpu().numpy()"
      ],
      "metadata": {
        "id": "H-i9D8PquboS"
      },
      "execution_count": 29,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# check that your model outputs right shape\n",
        "model = SoftmaxModel(BINS)\n",
        "assert [10, BINS] == list(model(torch.rand((10,))).size())"
      ],
      "metadata": {
        "id": "aUWuQbiEuu53"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let $\\theta = \\{\\theta_{0},...,\\theta_{d}\\}$ : Your model is softmax $ p(k|\\theta) = \\frac{e^{\\theta_{k}}}{\\sum_{l=1}^{d} e^{\\theta_{l}}} $"
      ],
      "metadata": {
        "id": "1295DDyQL7FO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3. Training of model"
      ],
      "metadata": {
        "id": "0VgntR6Wu5x5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Вопрос 3\n",
        "\n",
        "- Как будет устроен лосс данной задачи ?\n",
        "- В чем разница между model.train(False) и model.eval()?\n",
        "- Что произойдет если на валидации не написать model.eval()?"
      ],
      "metadata": {
        "id": "jkS3pTq0rCa6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "[B] - [B/4] [B/4] [B/4] [B/4]\n",
        "model.backward(retain_graph = False)\n",
        "\n",
        "# cuda out of memory"
      ],
      "metadata": {
        "id": "AWd0K38cVZo3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def get_cross_entropy_loss(model, x):\n",
        "    # we advice you firstly understand the 1st task\n",
        "    # and then return to this code\n",
        "    # your code\n",
        "    return torch.nn.functional.cross_entropy(model(x), x.long())"
      ],
      "metadata": {
        "id": "gGCqOkFTvBgu"
      },
      "execution_count": 56,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def train_epoch(model, train_loader, optimizer, use_cuda):\n",
        "    model.train()\n",
        "  \n",
        "    train_losses = []\n",
        "    for x in train_loader:\n",
        "        if use_cuda:\n",
        "            x = x.cuda()\n",
        "        loss = get_cross_entropy_loss(model, x)\n",
        "        optimizer.zero_grad()\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "        train_losses.append(loss.item())\n",
        "    return train_losses"
      ],
      "metadata": {
        "id": "7RENGqJZvBjc"
      },
      "execution_count": 57,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def eval_model(model, data_loader, use_cuda):\n",
        "    model.eval()\n",
        "    total_loss = 0\n",
        "    with torch.no_grad():\n",
        "        for x in data_loader:\n",
        "            if use_cuda:\n",
        "                x = x.cuda()\n",
        "            loss = get_cross_entropy_loss(model, x)\n",
        "            total_loss += loss * x.shape[0]\n",
        "        avg_loss = total_loss / len(data_loader.dataset)\n",
        "    return avg_loss.item()\n",
        "\n",
        "\n",
        "def train_model(model, train_loader, test_loader, epochs, lr, use_cuda=False):\n",
        "    if use_cuda:\n",
        "        model = model.cuda()\n",
        "    optimizer = torch.optim.Adam(model.parameters(), lr=lr)\n",
        "\n",
        "    train_losses = []\n",
        "    test_losses = [eval_model(model, test_loader, use_cuda)]\n",
        "    for epoch in range(epochs):\n",
        "        model.train()\n",
        "        train_losses.extend(train_epoch(model, train_loader, optimizer, use_cuda))\n",
        "        test_loss = eval_model(model, test_loader, use_cuda)\n",
        "        test_losses.append(test_loss)\n",
        "\n",
        "    return train_losses, test_losses"
      ],
      "metadata": {
        "id": "CI9F5Crsu7qz"
      },
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "BATCH_SIZE = 128\n",
        "EPOCHS = 100\n",
        "LR = 0.01\n",
        "USE_CUDA = False\n",
        "\n",
        "train_loader = torch.utils.data.DataLoader(train_data, batch_size=BATCH_SIZE, shuffle=True)\n",
        "test_loader = torch.utils.data.DataLoader(test_data, batch_size=BATCH_SIZE)\n",
        "train_losses, test_losses = train_model(model, train_loader, test_loader, epochs=EPOCHS, lr=LR, use_cuda=USE_CUDA)\n",
        "\n",
        "# check that your loss is not too large\n",
        "assert test_losses[-1] < 4.25"
      ],
      "metadata": {
        "id": "O3Jt14RKvJZu"
      },
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_training_curves(train_losses, test_losses):\n",
        "    plt.figure(figsize=(8, 6))\n",
        "    n_epochs = len(test_losses) - 1\n",
        "    x_train = np.linspace(0, n_epochs, len(train_losses))\n",
        "    x_test = np.arange(n_epochs + 1)\n",
        "\n",
        "    plt.plot(x_train, train_losses, label='train loss')\n",
        "    plt.plot(x_test, test_losses, label='test loss')\n",
        "    plt.legend()\n",
        "    plt.title('training curves')\n",
        "    plt.xlabel('Epoch')\n",
        "    plt.ylabel('NLL')\n",
        "    \n",
        "    \n",
        "def plot_1d_distribution(data, distribution):\n",
        "    size = len(distribution)\n",
        "\n",
        "    plt.figure(figsize=(8, 6))\n",
        "    plt.hist(data, bins=np.arange(size) - 0.5, label='train data', density=True)\n",
        "\n",
        "    x = np.linspace(-0.5, size - 0.5, 1000)\n",
        "    y = distribution.repeat(1000 // size)\n",
        "    plt.plot(x, y, label='learned distribution')\n",
        "\n",
        "    plt.title('learned distribution')\n",
        "    plt.xlabel('x')\n",
        "    plt.ylabel('Probability')\n",
        "    plt.legend()"
      ],
      "metadata": {
        "id": "zE0u3Mo1sdpf"
      },
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "distribution = get_distribution(model)\n",
        "\n",
        "assert isinstance(distribution, np.ndarray)\n",
        "assert distribution.shape == (BINS,)\n",
        "\n",
        "plot_training_curves(train_losses, test_losses)\n",
        "plot_1d_distribution(train_data, distribution)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 791
        },
        "id": "agAlPzy9vRn7",
        "outputId": "73df5e77-be85-4b73-9eba-90e87a76d3be"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "0U7D5YVCvTgR"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}