{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6ca179ca-ae81-4cf1-955a-9bf9ea033107",
   "metadata": {},
   "source": [
    "# 逻辑回归的数学模型"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acf7f852-d546-4eed-b00d-eaf0e42a98d5",
   "metadata": {},
   "source": [
    "- $y_{\\_} = sigmoid(xW + b)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42ae1498-cb86-4263-8dce-7cd40cb818c5",
   "metadata": {},
   "source": [
    "- $l = loss(y, y_{\\_})$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "022c8cd6-d615-40c2-948f-2eaf59d7493c",
   "metadata": {},
   "source": [
    "# 数据集（鸢尾花Iris）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f66c9221-f4e0-4ee7-8866-e1605d00dd13",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "import torch\n",
    "data, target = load_iris(return_X_y=True)\n",
    "# data, target\n",
    "x = data[50:150]\n",
    "y = target[:100]\n",
    "\n",
    "x = torch.Tensor(x)\n",
    "y = torch.Tensor(y).view(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3dc517ff-7cc5-470d-8009-62a894a006fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[6.4000, 3.2000, 4.5000, 1.5000],\n",
       "        [6.9000, 3.1000, 4.9000, 1.5000],\n",
       "        [5.5000, 2.3000, 4.0000, 1.3000],\n",
       "        [6.5000, 2.8000, 4.6000, 1.5000]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x [1:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "46231e73-6a41-411c-88dd-f86900642296",
   "metadata": {},
   "outputs": [],
   "source": [
    "# y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e559c14-4f07-45eb-81bd-dcceee254ea7",
   "metadata": {},
   "source": [
    "# 使用梯度下降思维进行机器学习（分类）"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d937048f-20c4-44d2-a166-9fa84a7147f6",
   "metadata": {},
   "source": [
    "- 随机一个w，b\n",
    "- 使用样本求预测值\n",
    "- 使用预测值与真实值求误差\n",
    "- 对误差函数求导\n",
    "- 使用导数 * 因子（学习率）更新w, b\n",
    "- 反复循环\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "eee5279b-6a81-4d85-96b7-98d888af5cb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "w1 = torch.randn(1, 4)\n",
    "b1 = torch.randn(1)\n",
    "\n",
    "w1.requires_grad = True\n",
    "b1.requires_grad = True\n",
    "\n",
    "# w1 = torch.randn(12, 4)\n",
    "# b1 = torch.randn(12)\n",
    "\n",
    "# w1.requires_grad = True\n",
    "# b1.requires_grad = True\n",
    "\n",
    "# w2 = torch.randn(9, 12)\n",
    "# b2 = torch.randn(9)\n",
    "\n",
    "# w2.requires_grad = True\n",
    "# b2.requires_grad = True\n",
    "\n",
    "# w3 = torch.randn(1, 9)\n",
    "# b3 = torch.randn(1)\n",
    "\n",
    "# w3.requires_grad = True\n",
    "# b3.requires_grad = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ec28048f-f04d-49a6-9ec7-3f3f2e1ea37b",
   "metadata": {},
   "outputs": [],
   "source": [
    "epoch = 100000\n",
    "lr = 0.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1d4525da-fe4a-4710-8d18-457df68f554f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "损失值：0.922623，\t准确率： 50.00%\n",
      "损失值：0.437713，\t准确率： 83.00%\n",
      "损失值：0.385350，\t准确率： 88.00%\n",
      "损失值：0.347146，\t准确率： 91.00%\n",
      "损失值：0.318071，\t准确率： 91.00%\n",
      "损失值：0.295188，\t准确率： 92.00%\n",
      "损失值：0.276688，\t准确率： 93.00%\n",
      "损失值：0.261402，\t准确率： 95.00%\n",
      "损失值：0.248542，\t准确率： 95.00%\n",
      "损失值：0.237560，\t准确率： 95.00%\n",
      "损失值：0.228061，\t准确率： 95.00%\n",
      "损失值：0.219754，\t准确率： 95.00%\n",
      "损失值：0.212422，\t准确率： 95.00%\n",
      "损失值：0.205897，\t准确率： 95.00%\n",
      "损失值：0.200048，\t准确率： 96.00%\n",
      "损失值：0.194771，\t准确率： 96.00%\n",
      "损失值：0.189983，\t准确率： 96.00%\n",
      "损失值：0.185618，\t准确率： 96.00%\n",
      "损失值：0.181617，\t准确率： 97.00%\n",
      "损失值：0.177934，\t准确率： 97.00%\n"
     ]
    }
   ],
   "source": [
    "for e in range(epoch):\n",
    "    # 预测\n",
    "    # y_ = w1 @ x.T + b1\n",
    "    y_ = torch.nn.functional.linear(input=x, weight=w1, bias=b1)\n",
    "    # y_ = torch.nn.functional.relu(y_)\n",
    "    # y_ = torch.nn.functional.linear(input=y_, weight=w2, bias=b2)\n",
    "    # y_ = torch.nn.functional.relu(y_)\n",
    "    # y_ = torch.nn.functional.linear(input=y_, weight=w3, bias=b3)\n",
    "    y_ = torch.sigmoid(y_)\n",
    "    # 求误差\n",
    "    loss = torch.nn.functional.binary_cross_entropy(y_, y)\n",
    "    # 自动求导\n",
    "    loss.backward()\n",
    "    with torch.no_grad():\n",
    "        # 使用梯度更新权重系数\n",
    "        w1 -= w1.grad * lr\n",
    "        b1 -= b1.grad * lr\n",
    "        # 梯度清零\n",
    "        w1.grad.zero_()\n",
    "        b1.grad.zero_()\n",
    "\n",
    "        # 统计下预测效果\n",
    "        y_ [y_ >=0.5] = 1\n",
    "        y_ [y_  <0.5] = 0\n",
    "\n",
    "        correct_rate = (y_ == y).float().mean()\n",
    "    if e % 5000 == 0:\n",
    "        print(F\"损失值：{loss:8.6f}，\\t准确率：{correct_rate*100: 5.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3a81e87-e742-49f3-9d0c-e5d046252c46",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6bdbf6e4-6397-46a7-bcc6-133e4ce91c2b",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "3bc7a505-0529-4d93-9551-5aee5efb553a",
   "metadata": {},
   "source": []
  }
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