blank_03_autograd_optim_nn_datasets.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/huakim/Create_Launcher/blob/master/blank_03_autograd_optim_nn_datasets.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6ktSXdQVb9Li"
      },
      "outputs": [],
      "source": [
        "from __future__ import annotations\n",
        "\n",
        "from pathlib import Path\n",
        "\n",
        "import torch\n",
        "import torch.nn as nn\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from matplotlib import pyplot as plt\n",
        "from sklearn.datasets import make_regression\n",
        "\n",
        "%config InlineBackend.figure_format='retina'\n",
        "\n",
        "%load_ext autoreload\n",
        "%autoreload 2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4L7Inb1JbiDy"
      },
      "source": [
        "## 3.1 Автоматическое дифференцирование в `torch`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6RDYqeQzd_mC",
        "outputId": "8f66328e-6219-4780-acb4-03c96987df93"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0., 0.])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "w = torch.tensor([1., 2.], requires_grad=True)\n",
        "x = torch.tensor([2., 3.])\n",
        "\n",
        "L = w @ x\n",
        "L.backward()\n",
        "\n",
        "with torch.no_grad():\n",
        "    w -= w.grad\n",
        "\n",
        "w.grad.zero_()\n",
        "w.grad"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HsZ69HZ0EsI7"
      },
      "source": [
        "3.1.1 Воспользовавшись классами `Neuron` и `SquaredLoss` из задачи 2.4.1 и автоматическим дифференцированием, которое предоставляет `torch`, решить задачу регрессии. Для оптимизации использовать стохастический градиетный спуск."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zynPAaOrRKTm"
      },
      "outputs": [],
      "source": [
        "X, y, coef = make_regression(n_features=4, n_informative=4, coef=True, bias=0.5)\n",
        "X = torch.from_numpy(X).to(dtype=torch.float32)\n",
        "y = torch.from_numpy(y).to(dtype=torch.float32)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wxWeyJw5lAqU"
      },
      "source": [
        "3.1.2 Воспользовавшись классами `Linear` и `MSELoss` из задачи 2.1.4 и 2.3.1, `ReLU` из 2.2.1 и автоматическим дифференцированием, которое предоставляет `torch`, решить задачу регрессии. Для оптимизации использовать пакетный градиентный спуск. Вывести график функции потерь в зависимости от номера эпохи. Вывести на одном графике исходные данные и предсказанные значения."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bnlAt1NEQoat"
      },
      "outputs": [],
      "source": [
        "X = torch.linspace(0, 1, 100).view(-1, 1)\n",
        "y = torch.sin(2 * np.pi * X) + 0.1 * torch.rand(X.size())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nifm0FVB2y5N"
      },
      "source": [
        "## 3.2 Алгоритмы оптимизации в `torch.optim`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "upUF6Lt8d_mN"
      },
      "outputs": [],
      "source": [
        "class MSELoss:\n",
        "    def forward(self, y_pred: torch.Tensor, y_true: torch.Tensor) -> torch.Tensor:\n",
        "        assert y_pred.ndim == y_true.ndim == 2, f'Ожидалось 2 измерений у y_pred, y_true, получил {y_pred.ndim}, {y_true.ndim}'\n",
        "        self.y_pred = y_pred\n",
        "        self.y_true = y_true\n",
        "        return ((y_pred - y_true) ** 2).mean()\n",
        "\n",
        "\n",
        "class Linear:\n",
        "    inputs: torch.Tensor | None = None\n",
        "    def __init__(self, n_features: int, n_outputs: int) -> None:\n",
        "        self.weights = torch.randn(n_features, n_outputs, requires_grad=True)\n",
        "        self.bias = torch.randn(1, n_outputs, requires_grad=True)\n",
        "\n",
        "    def forward(self, inputs: torch.Tensor) -> torch.Tensor:\n",
        "        self.inputs = inputs\n",
        "        return inputs @ self.weights + self.bias\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "zcLUs_JYd_mP",
        "outputId": "0f3ee90b-76d1-4bdb-fc15-8350a2c40fa8"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 547,
              "height": 413
            }
          }
        }
      ],
      "source": [
        "X = torch.linspace(0, 1, 100).view(-1, 1)\n",
        "y = torch.sin(2 * np.pi * X) + 0.1 * torch.rand(X.size())\n",
        "\n",
        "n_features = X.shape[1]\n",
        "n_outputs = y.shape[1]\n",
        "\n",
        "model = Linear(n_features=n_features, n_outputs=n_outputs)\n",
        "\n",
        "learning_rate = 1e-2\n",
        "optimizer = torch.optim.SGD([model.weights, model.bias], lr=learning_rate)\n",
        "\n",
        "loss = MSELoss()\n",
        "num_epochs = 1000\n",
        "\n",
        "loss_vals: list[float] = []\n",
        "\n",
        "for _ in range(num_epochs):\n",
        "    pred = model.forward(X)\n",
        "    loss_val = loss.forward(y_pred=pred, y_true=y)\n",
        "    loss_val.backward()\n",
        "    optimizer.step()\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    loss_vals.append(loss_val.item())\n",
        "\n",
        "plt.plot(loss_vals);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0oBFfJpmcwfn"
      },
      "source": [
        "3.2.1 Решить задачу 3.1.1, воспользовавшись оптимизатором `optim.SDG` для применения стохастического градиентого спуска"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X = torch.linspace(0, 1, 100).view(-1, 1)\n",
        "y = torch.sin(2 * np.pi * X) + 0.1 * torch.rand(X.size())\n",
        "\n",
        "n_features = X.shape[1]\n",
        "n_outputs = y.shape[1]\n",
        "\n",
        "model = Linear(n_features=n_features, n_outputs=n_outputs)\n",
        "\n",
        "learning_rate = 1e-2\n",
        "optimizer = torch.optim.SGD([model.weights, model.bias], lr=learning_rate)\n",
        "\n",
        "loss = MSELoss()\n",
        "num_epochs = 1000\n",
        "\n",
        "loss_vals: list[float] = []\n",
        "\n",
        "for _ in range(num_epochs):\n",
        "    pred = model.forward(X)\n",
        "    loss_val = loss.forward(y_pred=pred, y_true=y)\n",
        "    loss_val.backward()\n",
        "    optimizer.step()\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    loss_vals.append(loss_val.item())\n",
        "\n",
        "plt.plot(loss_vals);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "mq1ixqmievRe",
        "outputId": "4b3ab0e7-f36f-48e9-de35-530f5cc2aba8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 547,
              "height": 413
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1LFAacdy46bX"
      },
      "source": [
        "3.2.2 Решить задачу 3.1.2, воспользовавшись оптимизатором `optim.Adam` для применения пакетного градиентого спуска. Вывести график функции потерь в зависимости от номера эпохи. Вывести на одном графике исходные данные и предсказанные значения."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X = torch.linspace(0, 1, 100).view(-1, 1)\n",
        "y = torch.sin(2 * np.pi * X) + 0.1 * torch.rand(X.size())\n",
        "\n",
        "n_features = X.shape[1]\n",
        "n_outputs = y.shape[1]\n",
        "\n",
        "model = Linear(n_features=n_features, n_outputs=n_outputs)\n",
        "\n",
        "learning_rate = 1e-2\n",
        "optimizer = torch.optim.Adam([model.weights, model.bias], lr=learning_rate)\n",
        "\n",
        "loss = MSELoss()\n",
        "num_epochs = 1000\n",
        "\n",
        "loss_vals: list[float] = []\n",
        "\n",
        "for _ in range(num_epochs):\n",
        "    pred = model.forward(X)\n",
        "    loss_val = loss.forward(y_pred=pred, y_true=y)\n",
        "    loss_val.backward()\n",
        "    optimizer.step()\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    loss_vals.append(loss_val.item())\n",
        "\n",
        "plt.plot(loss_vals);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "xA_eQU0xe5P3",
        "outputId": "0328655a-0810-429d-ee45-cbb8d7c65f56"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 547,
              "height": 413
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n-qUqdALiN-G"
      },
      "source": [
        "## 3.3 Построение сетей при помощи `torch.nn`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Vxsck-1M6TAV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7c63a9ce-5cc7-4617-e79c-56d1bb7df08d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[Parameter containing:\n",
              " tensor([1.], requires_grad=True),\n",
              " Parameter containing:\n",
              " tensor([[-0.0855],\n",
              "         [ 0.9150],\n",
              "         [-0.4631]], requires_grad=True),\n",
              " Parameter containing:\n",
              " tensor([-0.1465,  0.2453,  0.1157], requires_grad=True),\n",
              " Parameter containing:\n",
              " tensor([[-0.0455,  0.3883, -0.4642]], requires_grad=True),\n",
              " Parameter containing:\n",
              " tensor([0.5587], requires_grad=True)]"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "class Model(nn.Module):\n",
        "    def __init__(self, n_features: int, n_outputs: int) -> None:\n",
        "        super().__init__()\n",
        "        self.layer1 = nn.Linear(n_features, 3)\n",
        "        self.layer2 = nn.ReLU()\n",
        "        self.layer3 = nn.Linear(3, n_outputs)\n",
        "\n",
        "        # Просто пример\n",
        "        self.custom_weight = nn.Parameter(torch.tensor([1.]))\n",
        "\n",
        "    def forward(self, x: torch.Tensor) -> torch.Tensor:\n",
        "        x = self.layer1(x)\n",
        "        x = self.layer2(x)\n",
        "        x = self.layer3(x)\n",
        "        return x\n",
        "\n",
        "\n",
        "model = Model(n_features=n_features, n_outputs=n_outputs)\n",
        "list(model.parameters())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9CCYO8DRd_mU"
      },
      "outputs": [],
      "source": [
        "model = nn.Sequential(\n",
        "    nn.Linear(n_features, 3),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(3, n_outputs),\n",
        ")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qKXmUkzsd_mU"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M0ICJtarif3_"
      },
      "source": [
        "3.3.1 Решить задачу регрессии, соблюдая следующие условия:\n",
        "\n",
        "1. Оформить нейронную сеть в виде класса - наследника `nn.Module`\n",
        "2. При создании сети использовать готовые блоки из `torch.nn`: слои, функции активации, функции потерь и т.д.\n",
        "3. Для оптимизации использовать любой алгоритм оптимизации из `torch.optim`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "L1bvXHhO7aWs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 843
        },
        "outputId": "71a2fb20-cf61-429e-dcf8-374873eabbb9"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 547,
              "height": 413
            }
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "image/png": {
              "width": 559,
              "height": 413
            }
          }
        }
      ],
      "source": [
        "class Model(nn.Module):\n",
        "    def __init__(self, n_features: int, n_outputs: int) -> None:\n",
        "        super().__init__()\n",
        "        self.body = nn.Sequential(\n",
        "            nn.Linear(n_features, 100),\n",
        "            nn.GELU(),\n",
        "            nn.Linear(100, 100),\n",
        "            nn.GELU(),\n",
        "            nn.Linear(100, 100),\n",
        "            nn.GELU(),\n",
        "            nn.Linear(100, 3),\n",
        "        )\n",
        "        self.last_layer = nn.Sequential(\n",
        "            nn.GELU(),\n",
        "            nn.Linear(3, n_outputs),\n",
        "        )\n",
        "\n",
        "    def forward(self, x: torch.Tensor) -> torch.Tensor:\n",
        "        x = self.body(x)\n",
        "        x = self.last_layer(x)\n",
        "\n",
        "        return x\n",
        "\n",
        "\n",
        "X = torch.linspace(0, 1, 100).view(-1, 1)\n",
        "y = torch.sin(2 * np.pi * X) + 0.1 * torch.rand(X.size())\n",
        "\n",
        "n_features = X.shape[1]\n",
        "n_outputs = y.shape[1]\n",
        "\n",
        "model = Model(n_features=n_features, n_outputs=n_outputs)\n",
        "\n",
        "learning_rate = 5e-3\n",
        "optimizer = torch.optim.Adam(model.parameters(), lr=learning_rate)\n",
        "\n",
        "loss = nn.MSELoss()\n",
        "num_epochs = 2000\n",
        "\n",
        "loss_vals: list[float] = []\n",
        "\n",
        "for epoch in range(num_epochs):\n",
        "    pred = model.forward(X)\n",
        "    loss_val = loss.forward(input=pred, target=y)\n",
        "    loss_val.backward()\n",
        "    optimizer.step()\n",
        "    optimizer.zero_grad()\n",
        "\n",
        "    loss_vals.append(loss_val.item())\n",
        "\n",
        "plt.plot(loss_vals)\n",
        "plt.show()\n",
        "plt.plot(pred.detach())\n",
        "plt.plot(y)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UPUW6fm5jbQd"
      },
      "source": [
        "3.3.2 Решить задачу регрессии, соблюдая следующие условия:\n",
        "\n",
        "1. Оформить нейронную сеть в виде объекта `nn.Sequential`\n",
        "2. При создании сети использовать готовые блоки из `torch.nn`: слои, функции активации, функции потерь и т.д.\n",
        "3. Для оптимизации использовать любой алгоритм оптимизации из `torch.optim`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BBwbAEd57a2r",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "12df49cf-ba06-4aa8-fc43-db7d6cfd8340"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch [100/1000], Loss: 0.2357\n",
            "Epoch [200/1000], Loss: 0.1647\n",
            "Epoch [300/1000], Loss: 0.1476\n",
            "Epoch [400/1000], Loss: 0.1315\n",
            "Epoch [500/1000], Loss: 0.1169\n",
            "Epoch [600/1000], Loss: 0.1019\n",
            "Epoch [700/1000], Loss: 0.0868\n",
            "Epoch [800/1000], Loss: 0.0719\n",
            "Epoch [900/1000], Loss: 0.0579\n",
            "Epoch [1000/1000], Loss: 0.0453\n"
          ]
        }
      ],
      "source": [
        "import torch\n",
        "import torch.nn as nn\n",
        "import torch.optim as optim\n",
        "\n",
        "# Входные данные и целевые значения\n",
        "X = torch.linspace(0, 1, 100).view(-1, 1)\n",
        "y = torch.sin(2 * np.pi * X) + 0.1 * torch.rand(X.size())\n",
        "\n",
        "# Определяем модель\n",
        "model = nn.Sequential(\n",
        "    nn.Linear(1, 64),\n",
        "    nn.ReLU(),\n",
        "    nn.Linear(64, 1)\n",
        ")\n",
        "\n",
        "# Определяем функцию потерь и оптимизатор\n",
        "criterion = nn.MSELoss()\n",
        "optimizer = optim.Adam(model.parameters(), lr=0.001)\n",
        "\n",
        "# Обучаем модель\n",
        "num_epochs = 1000\n",
        "for epoch in range(num_epochs):\n",
        "    outputs = model(X)\n",
        "    loss = criterion(outputs, y)\n",
        "\n",
        "    optimizer.zero_grad()\n",
        "    loss.backward()\n",
        "    optimizer.step()\n",
        "\n",
        "    if (epoch+1) % 100 == 0:\n",
        "        print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jQj0oVeLj2A1"
      },
      "source": [
        "## 3.4. Datasets and dataloaders"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "c82tAkXMjajm"
      },
      "outputs": [],
      "source": [
        "from torch.utils.data import Dataset, DataLoader"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hoFPckkp8yhz"
      },
      "source": [
        "3.4.1 Создать датасет, поставляющий данные из задачи 3.1.2.\n",
        "\n",
        "Создать `DataLoader` на основе этого датасета и проверить работоспособность.\n",
        "\n",
        "Воспользовавшись результатами 3.3.1 (или 3.3.2) обучите модель, пользуясь мини-пакетным градиентным спуском с размером пакета (`batch_size`) = 10"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tlcwQzCFRvFc"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "from torch.utils.data import Dataset\n",
        "import numpy as np\n",
        "\n",
        "class SinDataset(Dataset):\n",
        "    def __init__(self, num_samples=1000, amplitude=1.0, frequency=1.0, phase=0.0, noise_std=0.1):\n",
        "        self.num_samples = num_samples\n",
        "        self.amplitude = amplitude\n",
        "        self.frequency = frequency\n",
        "        self.phase = phase\n",
        "        self.noise_std = noise_std\n",
        "\n",
        "        self.x = torch.linspace(0, 2 * np.pi, num_samples)\n",
        "        self.y = self.amplitude * torch.sin(self.frequency * self.x + self.phase) + torch.randn(num_samples) * self.noise_std\n",
        "\n",
        "    def __len__(self):\n",
        "        return self.num_samples\n",
        "\n",
        "    def __getitem__(self, idx):\n",
        "        return self.x[idx], self.y[idx]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bxz02a3k_VQL"
      },
      "source": [
        "3.4.2 Предсказание цен алмазов\n",
        "\n",
        "3.4.2.1 Создайте датасет на основе файла diamonds.csv.\n",
        "\n",
        "1. Удалите все нечисловые столбцы\n",
        "2. Целевой столбец (`y`) - `price`\n",
        "3. Преобразуйте данные в тензоры корректных размеров\n",
        "\n",
        "3.4.2.2 Разбейте датасет на обучающий и тестовый датасет при помощи `torch.utils.data.random_split`.\n",
        "\n",
        "3.4.2.3 Обучите модель для предсказания цен при помощи мини-пакетного градиентного спуска (`batch_size = 256`).\n",
        "\n",
        "3.4.2.4 Выведите график функции потерь в зависимости от номера эпохи (значение потерь для эпохи рассчитывайте как среднее значение ошибок на каждом батче). Проверьте качество модели на тестовой выборке.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fEfTNJQI8emD"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import pandas as pd\n",
        "\n",
        "# Загрузка данных из файла\n",
        "df = pd.read_csv('diamonds.csv')\n",
        "\n",
        "# Удаление нечисловых столбцов\n",
        "df = df.select_dtypes(include=['float64', 'int64'])\n",
        "\n",
        "# Целевой столбец - price\n",
        "X = df.drop('price', axis=1)\n",
        "y = df['price']\n",
        "\n",
        "# Преобразование в тензоры\n",
        "X_tensor = torch.tensor(X.values, dtype=torch.float32)\n",
        "y_tensor = torch.tensor(y.values, dtype=torch.float32)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from torch.utils.data import random_split\n",
        "\n",
        "# Разбиение на обучающий и тестовый датасеты\n",
        "train_size = int(0.8 * len(X_tensor))\n",
        "test_size = len(X_tensor) - train_size\n",
        "\n",
        "train_X = X_tensor[:train_size]\n",
        "test_X = X_tensor[train_size:]\n",
        "train_y = y_tensor[:train_size]\n",
        "test_y = y_tensor[train_size:]"
      ],
      "metadata": {
        "id": "I0yn1MK5h9F9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Обучение модели\n",
        "model = nn.Linear(X_tensor.size(1), 1)\n",
        "criterion = nn.MSELoss()\n",
        "optimizer = optim.SGD(model.parameters(), lr=0.01)\n",
        "\n",
        "num_epochs = 100\n",
        "batch_size = 256\n",
        "\n",
        "train_losses = []\n",
        "for epoch in range(num_epochs):\n",
        "    # Итерация по батчам\n",
        "    for i in range(0, len(train_X), batch_size):\n",
        "        batch_X = train_X[i:i+batch_size]\n",
        "        batch_y = train_y[i:i+batch_size]\n",
        "\n",
        "        # Прямой проход\n",
        "        outputs = model(batch_X)\n",
        "        loss = criterion(outputs, batch_y.unsqueeze(1))\n",
        "\n",
        "        # Обратный проход и оптимизация\n",
        "        optimizer.zero_grad()\n",
        "        loss.backward()\n",
        "        optimizer.step()\n",
        "\n",
        "    # Расчет среднего значения ошибки на эпохе\n",
        "    train_loss = loss.item()\n",
        "    train_losses.append(train_loss)\n",
        "\n",
        "# Визуализация функции потерь\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(train_losses)\n",
        "plt.title('Функция потерь')\n",
        "plt.xlabel('Эпоха')\n",
        "plt.ylabel('Значение потерь')\n",
        "plt.show()\n",
        "\n",
        "# Оценка качества модели на тестовой выборке\n",
        "with torch.no_grad():\n",
        "    test_outputs = model(test_X)\n",
        "    test_loss = criterion(test_outputs, test_y.unsqueeze(1)).item()\n",
        "    print(f'Ошибка на тестовой выборке: {test_loss:.4f}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 582
        },
        "id": "0epBENfKiMLI",
        "outputId": "77c9ab28-e96c-44ab-e0b4-55d9b2bb56e3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "image/png": {
              "width": 866,
              "height": 546
            }
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ошибка на тестовой выборке: nan\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qE81cgQdGM7I"
      },
      "source": [
        "3.4.3 Модифицируйте метод `__init__` датасета из 3.4.2 таким образом, чтобы он мог принимать параметр `transform: callable`. Реализуйте класс `DropColsTransform` для удаления нечисловых данных из массива. Реализуйте класс `ToTensorTransorm` для трансформации массива в тензор."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "J02LNj_F8qxK"
      },
      "outputs": [],
      "source": [
        "class DiamondsDataset(Dataset):\n",
        "  def __init__(self, data, transform):\n",
        "    # ....\n",
        "    self.transform = transform\n",
        "    # ....\n",
        "\n",
        "  def __len__(self):\n",
        "    pass\n",
        "\n",
        "  def __getitem__(self, idx):\n",
        "    # ...\n",
        "    sample = self.X[idx], self.y[idx]\n",
        "    if self.transform:\n",
        "      sample = self.transform(sample)\n",
        "    # ...."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tJii-22pHIlU"
      },
      "outputs": [],
      "source": [
        "class DropColsTransform:\n",
        "  def __init__(self, drop):\n",
        "    pass\n",
        "\n",
        "  def __call__(self, sample):\n",
        "    X, y = sample\n",
        "    # <удаление из X столбцов self.drop>\n",
        "    return X, y"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dZZ-OKrVHnY5"
      },
      "outputs": [],
      "source": [
        "class ToTensorTransform:\n",
        "  def __call__(self, sample):\n",
        "    X, y = sample\n",
        "    # <преобразование X и y в тензоры>\n",
        "    return X, y"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GssBjT9JHt5g"
      },
      "outputs": [],
      "source": [
        "from torchvision import transforms\n",
        "\n",
        "drop = DropColsTransform(drop=[1, 2, 3])\n",
        "to_tensor = ToTensorTransform()\n",
        "dataset = DiamondsDataset(data, transforms.compose([drop, to_tensor]))\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
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      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.18"
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