1.线性回归.ipynb

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    "## 1.线性回归（1855年）\n",
    "\n",
    "**学习目标**\n",
    "\n",
    "1. 熟练使用Pandas处理CSV格式的数据\n",
    "   \n",
    "2. 熟练使用matplotlib绘制散点图\n",
    "   \n",
    "3. 熟练使用均方误差（MSE）损失函数\n",
    "\n",
    "4. 会使用最小二乘法优化MSE损失函数\n",
    "   \n",
    "5. 能够使用PyTorch构建和训练线性回归模型\n",
    "\n",
    "****"
   ]
  },
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   "cell_type": "markdown",
   "id": "892164e2",
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   "source": [
    "线性回归最早是由英国发明家、人类学家、探险家、地理学家、气象学家、心理学家、遗传学家和统计学家弗朗西斯·高尔顿（Francis Galton）爵士提出的。\n",
    "\n",
    "### 1.1  弗朗西斯·高尔顿\n",
    "\n",
    "高尔顿于1822年2月16日出生于英国伯明翰一个富有的银行家家庭，他是著名博物学家查尔斯·达尔文（Charles Darwin）的表弟。高尔顿和达尔文的祖父伊拉斯谟·达尔文也是一位著名的博物学家和哲学家。1840年高尔顿进入剑桥大学学习，但从未获得过学位。高尔顿在他富有的父亲去世后继承了一笔丰厚的遗产，因此可以自由的过着想要的生活，包括冒险。1850年，他先后远赴马耳他、埃及尼罗河流域和南非，还曾只身进入巴勒斯坦腹地，这使他成为一位大无畏的知名探险家，他在非洲未开发地区的探险为他赢得了法国地理学会的银质奖章。1853年被选为皇家地理学会会员，1856年又被选为皇家学会会员，时年34岁。1857年，他从非洲回来后与妻子定居在伦敦的庄园，正式开始了他的书斋式的科研生活。高尔顿痴迷于测量，他对测量方法的大量使用使他发现并确立了指纹识别可以作为一种可靠的身份识别方法。在收集了数百个指纹样本后，高尔顿创建了一个分类系统，该系统至今仍被21世纪的法医和科学家广泛使用。\n",
    "\n",
    "高尔顿平生著作，据皮尔逊不完全统计，著书15种，撰写各种学术论文220篇，涉猎范围包括地理、天文、气象、物理、机械、人类学、民族学、社会学、统计学、教育学、医学、生理学、心理学、遗传学、优生学、指纹学、照像术、登山术、音乐、美术、宗教等，是一位百科全书式的学者。\n",
    "\n",
    "1909年，高尔顿被封为爵士，1911年1月17日，高尔顿病逝于英格兰南部哈斯里梅尔，享年89岁。在人类历史上，很少有像高尔顿那样特立独行、知识渊博而又毁誉参半的科学家。高尔顿被同时代的人赋予了很多称号：“维多利亚时代最博学之人”、“人类追求自身完美这一崇高目标的化身”以及“种族主义者和法西斯精神领袖”。\n",
    "\n",
    "<img src=\"./images/Sir Galton.png\" style=\"zoom:60%;\" />\n",
    "\n",
    "#### 1.高尔顿的遗传学研究\n",
    "\n",
    "​1859年，达尔文的《物种起源》问世，高尔顿怀着极大的兴趣和热情阅读了这本书。这本书激发了他内心深处的复杂情感，既有对表哥成就的钦佩，也有对自己学术追求的自豪，或许还夹杂着一丝嫉妒。在一封充满热情的信件中，高尔顿向达尔文表达了自己的感受，称这本书为他打开了\"一个全新知识领域的大门\"。受到达尔文《物种起源》的深刻影响，高尔顿在19世纪60年代中期开始了他对遗传学的研究。他的研究重点由之前的数据测量转向探索遗传的内在机制。\n",
    "\n",
    "​为了充实他的研究，高尔顿着手对历史上的名人家谱进行了深入的整理和分析。在对1453年至1853年间的605位杰出人物进行研究时，他发现其中有102位存在血缘关系，这表明在这些成功人士中，大约每六人中就有一人与其他成功人士有亲属关系。基于这一发现，高尔顿推测，如果一个杰出人物有了孩子，那么这个孩子成为杰出人物的概率大约是1/12，而这一概率在普通人群中则降至1/3000。高尔顿坚信遗传在决定个人成就中作用。他认为，贵族之所以能够世代传承，其根本原因在于智力而非社会地位。他认为个人的天赋和成功的潜力是由遗传因素决定的，并且这些天赋应当是遗传的一部分。\n",
    "\n",
    "#### 2.优生学\n",
    "\n",
    "​1883年，高尔顿出版了一本著作叫《人类才能及其发展的研究》。在这部颇有争议的书中，他为优化人种制订了一个战略计划。高尔顿的想法非常简单：他打算模仿自然选择的机制。既然自然界可以通过生存和选择来对动物种群产生显著影响，那么高尔顿设想通过人工干预也可以加速人类进步的过程。他将自己宏大的战略构想起了个名字——“优生学”，即优化种族的科学。\n",
    "\n",
    "​高尔顿的优生学理论后来得到了继承和发展。其中，卡尔·皮尔逊（Karl Pearson）和罗纳德·费希尔（Ronald Fisher）是这一领域的代表人物。他们不仅继承了高尔顿的思想，还在统计学和遗传学领域做出了重要贡献，为优生学理论提供了更为坚实的基础。\n",
    "\n",
    "然而，高尔顿及其追随者的优生学理论也包含了一些种族主义的言论：\n",
    "\n",
    "- 高尔顿：“黑人种族的平均智力标准比我们低两个等级。”\n",
    "\n",
    "- 皮尔逊：“历史向我展现了一种方式，也只有这种方式，能够造就高级文明，就是种族之间的斗争，生理和心理都更优越的种族才会生存下来。”\n",
    "\n",
    "- 费希尔：“社会更低阶层的过高生育率会拖垮任何文明。”\n",
    "\n",
    "这些言论在当时的社会背景下可能被视为科学的观点，但今天看来，它们显然带有明显的种族歧视色彩。\n",
    "\n",
    "#### 3. 罪恶之花\n",
    "\n",
    "​优生学的目标是让优质的种族或血统得以延续，并且以较大的优势快速压制劣质的种族或血统。为了实现这个理想，高尔顿建议要选择性繁育身强体壮的后代。1904年春天，高尔顿在伦敦经济学院的一场公开演讲中向世人传播了他的优生学。在这之后，优生学成为人人追捧的新兴学科。\n",
    "\n",
    "​1912年，第一届国际优生学大会在伦敦塞西尔酒店开幕。在大会发言中，德国学者阿尔弗雷德·普洛兹用狂热且精准的语言展示了“种族优生”理论，并充满激情地宣布，德国正在启动种族清洗计划，这对于即将到来的黑暗年代是个不祥的预兆。在另一个报告中，美国优生运动之父达文波特的门生在会议上踌躇满志地讲述着美国国内为清除“缺陷品种”而展开的努力工作。例如，为不适合繁育后代的人群设立隔离中心的工作已经在计划实施。\n",
    "​\n",
    "从此，人类历史上开始了一段血雨腥风的优生运动。20世纪40年代，纳粹德国为了实现上述目标已经达到疯狂的极限，他们利用某些残忍的人体实验来验证优生学理论，其中包括绝育和灭绝人性的屠杀。高尔顿创造的优生学成为了纳粹手中的杀人工具，吞噬了数百万人的性命。\n",
    "\n",
    "​虽然高尔顿的初衷可能是希望创造一个更加优秀的社会，但他的理论被极端化并用于不人道的目的。这段历史提醒我们，科学理念必须谨慎对待，避免被滥用以造成灾难性的后果。现代社会强调人权、平等和尊重生命，反对任何形式的种族歧视和优生学实践。我们必须从历史中吸取教训，确保科学发展服务于人类的福祉，而不是成为伤害人类的工具。"
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   "source": [
    "### 1.2 线性回归"
   ]
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    "#### 1. 什么是线性回归？\n",
    "\n",
    "​\t1855年， 高尔顿发表《遗传的身高向平均数方向的回归》一文，高尔顿和他的学生卡尔·皮尔逊（Karl Pearson）收集了1078对夫妇及其子女的身高数据。\n",
    "\n",
    "<img src=\"./images/galton1.png\" style=\"zoom:60%;\" />\n",
    "\n",
    "通过分析这些数据，他们发现父母身高和子女身高之间存在线性关系。如果用x表示父母的平均身高，用y表示子女的平均身高，它们的关系可以用一条直线表示：\n",
    "\n",
    "y = 0.516*x + 0.8567 (单位：米)\n",
    "\n",
    "那么，什么时候父母的平均身高和子女是相同的呢？\n",
    "\n",
    "答案是 x = 0.516*x + 0.8567，计算得 x = 1.77。\n",
    "\n",
    "现在我们可以根据公式计算得到 x = 1.80, y = 1.786；x = 1.70, y = 1.73.\n",
    "\n",
    "这就是高尔顿发现的有趣现象：如果父母的身高偏离平均身高，那么他们的子女的身高往往会向平均身高“回归”。换句话说，当父母身高走向极端，子女的身高不会象父母身高那样极端化，其身高要比父母们的身高更接近平均身高，即有“回归”到平均数去的趋势，这就是“回归”最初的统计学涵义，高尔顿把这一现象叫做“向平均数方向的回归”（regression toward mediocrity），这是首次使用“回归”一词来描述这种趋势。\n",
    "\n",
    "​\t线性回归是一种基础的统计学工具，它用于预测和分析数据之间的关系。线性回归的目标是探索一个或多个自变量与一个因变量之间的线性关系。这种关系通常是一条直线，可以用公式 y = w*x + b 来表示，其斜率w和截距b是模型参数。\n",
    "\n",
    "对于上面例子中父母和子女身高的线性关系，我们可以绘制出图像：\n",
    "\n",
    "<img src=\"./images/linear1.jpg\" style=\"zoom:80%;\" />\n",
    "\n",
    "现在我们有个疑问，参数w = 0.516, b = 0.8567，是如何确定出来的？答案是最小二乘法。\n",
    "\n",
    "#### 2. 线性回归的优化方法——最小二乘法\n",
    "\n",
    "​\t衡量模型预测值与实际观测值之间差异的指标在机器学习中被称为**损失函数**，线性回归模型的损失函数可以通过计算所有观测值误差的平方和来实现，这就是均方误差（Mean Squared Error，MSE）损失函数。MSE损失函数的公式可以表示为：\n",
    "\n",
    "$$\n",
    "\\text{MSE} = \\frac{1}{n} \\sum_{i=1}^{n} (y_i - \\hat{y}_i)^2\n",
    "$$\n",
    "\n",
    "所谓的优化，就是最小化损失函数来确定模型参数。最小二乘法是一种数值优化算法，它通过最小化MSE损失函数来找到最佳拟合线。这种方法的优势在于它提供了一个明确且易于计算的最优解。\n",
    "\n",
    "​\t最小二乘法的公式为：\n",
    "\n",
    "$$\n",
    "w = \\frac{n \\sum(xy) - \\sum(x) \\sum(y)}{n \\sum(x^2) - (\\sum(x))^2}\n",
    "$$\n",
    "\n",
    "$$\n",
    "b = \\frac{\\sum(y) - w \\sum(x)}{n}\n",
    "$$\n",
    "\n",
    "假设有5个观测值(x,y)，如下表所示：\n",
    "\n",
    "| x   |   y   |\n",
    "| --- | ----- |\n",
    "| 1   | 2.2   |\n",
    "| 2   | 3.8   |\n",
    "| 3   | 4.5   |\n",
    "| 4   | 5.9   |\n",
    "| 5   | 6.7   |\n",
    "\n",
    "我们可以编程实现最小二乘法，求解出参数w和b。"
   ]
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   "execution_count": 9,
   "id": "f0bee103",
   "metadata": {},
   "outputs": [
    {
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     "text": [
      " w = 1.11000\n",
      " b = 1.29000\n"
     ]
    }
   ],
   "source": [
    "# 最小二乘法求线性回归系数\n",
    "import numpy as np\n",
    "\n",
    "# 样本数据\n",
    "x = np.array([1, 2, 3, 4, 5])\n",
    "y = np.array([2.2, 3.8, 4.5, 5.9, 6.7])\n",
    "\n",
    "# 计算参数w和b\n",
    "n = len(x)\n",
    "w = (n * np.sum(x * y) - np.sum(x) * np.sum(y)) / (n * np.sum(x**2) - np.sum(x)**2)\n",
    "b = (np.sum(y) - w * np.sum(x)) / n\n",
    "\n",
    "print(f\" w = {w:.5f}\")\n",
    "print(f\" b = {b:.5f}\")"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "#### 3. 使用Adam优化器训练模型\n",
    "\n",
    "最小二乘法虽然能够得到最优解，但是缺陷也比较明显：\n",
    "\n",
    "一是最小二乘法对异常点高度敏感，由于求解的误差是平方的，异常点（即远离大多数数据点的点）会对拟合结果产生较大的影响。这些异常点的误差平方会非常大，从而导致模型过度拟合这些异常点，使得模型的预测能力下降。\n",
    "\n",
    "二是最小二乘法处理大规模数据集效率低下。它的计算复杂度主要来自于求解正规方程（normal equation），即求解矩阵的逆。对于大规模数据集，矩阵的维度会变得非常大，导致计算量急剧增加，尤其是在内存有限的情况下，计算速度会变得非常缓慢。\n",
    "\n",
    "在AI领域，尤其是在处理大规模数据集时，随机梯度下降（SGD）因其在收敛速度上的优势而被广泛采用。SGD通过迭代地调整模型参数来最小化损失函数，这里的损失函数是均方误差（MSE）。\n",
    "\n",
    "本节内容不过多的纠结SGD的原理，而是直接使用SGD的改进算法——Adam优化器来训练模型。下面我们就来看一个用Adam优化器训练线性回归模型的例子。"
   ]
  },
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   "metadata": {},
   "source": [
    "### 1.3 线性回归的应用——草莓含糖量无损检测"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92ffa8fb",
   "metadata": {},
   "source": [
    "草莓果肉多汁，营养价值高，生长周期短，见效快，经济效益高，正成为我国果树业和设施农业中发展最快的新兴产业，种植面积逐年增加。目前，我国已拥有草莓播种面积126.13千公顷，产量322.19万吨，是全球最大的草莓生产与消费国。\n",
    "\n",
    "<img src=\"./images/strawberry.jpg\" style=\"zoom:80%;\" />\n",
    "\n",
    "草莓是重要的经济作物，它的售价和草莓的品质密切相关，含糖量是判断草莓质量的一个重要指标。想要知道一颗草莓的含糖量，可以使用水果糖度仪来测量草莓含糖量。但是，水果糖度仪在测量草莓含糖量时会对草莓造成损坏。对于售卖的草莓来说，将其全部破坏来测量含糖量是不切实际的。\n",
    "\n",
    "科学研究表明，草莓的含糖量将会影响到其对红外线的吸收量，可以通过测量草莓对红外光谱吸收值来估算它的含糖量，做到对草莓含糖量的无损检测。\n",
    "\n",
    "下面我们来学习如何使用线性回归实现草莓含糖量的无损检测。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27ac2469",
   "metadata": {},
   "source": [
    "1.相关依赖包或模块"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "8c67d691",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "from torch import nn\n",
    "from torch import optim"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fd743ee",
   "metadata": {},
   "source": [
    "2.加载数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "3a856cf6",
   "metadata": {},
   "outputs": [
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       "      <th>0</th>\n",
       "      <td>7.0</td>\n",
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       "      <th>1</th>\n",
       "      <td>6.8</td>\n",
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       "      <th>4</th>\n",
       "      <td>5.5</td>\n",
       "      <td>0.653701</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SSC         R\n",
       "0  7.0  0.807545\n",
       "1  6.8  0.774170\n",
       "2  6.3  0.751000\n",
       "3  6.2  0.796043\n",
       "4  5.5  0.653701"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"./datasets/strawberry/strawberry_reg.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "79ed3271",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0      0.807545\n",
      "1      0.774170\n",
      "2      0.751000\n",
      "3      0.796043\n",
      "4      0.653701\n",
      "         ...   \n",
      "175    0.768821\n",
      "176    0.824843\n",
      "177    0.734260\n",
      "178    0.727337\n",
      "179    0.873563\n",
      "Name: R, Length: 180, dtype: float64 \n",
      " 0      7.0\n",
      "1      6.8\n",
      "2      6.3\n",
      "3      6.2\n",
      "4      5.5\n",
      "      ... \n",
      "175    6.6\n",
      "176    7.5\n",
      "177    6.7\n",
      "178    6.5\n",
      "179    7.2\n",
      "Name: SSC, Length: 180, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "x_data, y_data =  df.R, df.SSC\n",
    "print(x_data,'\\n', y_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d761d8c",
   "metadata": {},
   "source": [
    "3.数据可视化"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0538bf2c",
   "metadata": {},
   "source": [
    "本次任务是找到草莓含糖量SSC和红外光谱吸收值R之间的关系。我们可以首先将其可视化出来:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "97bfa64f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['font.sans-serif'] = 'SimHei'\n",
    "\n",
    "plt.figure(figsize=(6, 4))\n",
    "plt.scatter(x_data, y_data,  color='pink', marker='*', label='草莓')\n",
    "plt.xlabel('红外光谱吸收值（R)')\n",
    "plt.ylabel('含糖量(SSC)')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b7a779a",
   "metadata": {},
   "source": [
    "4.数据预处理\n",
    "\n",
    ".values 通常用于 pandas DataFrame 或 Series 对象，以获取其数据的原始值。当你对一个 pandas DataFrame 或 Series 使用 .values 属性时，它会返回一个 NumPy 数组，包含该 DataFrame 或 Series 的数据。这个数组的形状取决于 DataFrame 或 Series 的维度。\n",
    "\n",
    ".view(-1, 1) 用于改变张量的形状，将张量重塑为一个二维张量，其中每行只有一个元素。。-1 是一个特殊的参数，它告诉 PyTorch 自动计算这个维度的大小，以确保张量的总元素数量保持不变。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "0b47d8eb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([180, 1])\n",
      "torch.Size([180, 1])\n"
     ]
    }
   ],
   "source": [
    "# 数据转换 -> [样本，特征]\n",
    "X = torch.tensor(x_data.values, dtype=torch.float32).view(-1, 1)\n",
    "y = torch.tensor(y_data.values, dtype=torch.float32).view(-1, 1)\n",
    "\n",
    "print(X.shape)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0918b57",
   "metadata": {},
   "source": [
    "5.模型构建"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53666c75",
   "metadata": {},
   "source": [
    "(1) 参数设置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "8f602892",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_epochs = 6000"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7af6821",
   "metadata": {},
   "source": [
    "线性回归和神经元之间存在直接的联系，特别是在神经网络的上下文中。实际上，一个简单的线性回归模型可以被视为一个单层神经网络，其中只有一个神经元。（线性回归模型 + 阶跃函数 = 感知器（单个神经元））\n",
    "\n",
    "（2）构建线性回归模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "c9e4d01a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sequential(\n",
      "  (0): Linear(in_features=1, out_features=1, bias=True)\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "model = nn.Sequential(nn.Linear(1, 1))\n",
    "\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed1b155e",
   "metadata": {},
   "source": [
    "（3）设置损失函数和优化器"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "f1c3b213",
   "metadata": {},
   "outputs": [],
   "source": [
    "criterion = nn.MSELoss()\n",
    "optimizer = optim.Adam(model.parameters(), lr=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "615fb55e",
   "metadata": {},
   "source": [
    "nn.MSELoss() 是 PyTorch 框架中的一种损失函数，用于衡量模型预测值与真实值之间的平均平方误差。MSE 代表均方误差（Mean Squared Error），是回归问题中常用的损失函数之一。\n",
    "\n",
    "使用场景:\n",
    "\n",
    "nn.MSELoss() 通常用于回归问题，例如房价预测、股票价格预测等。\n",
    "\n",
    "特点:\n",
    "\n",
    "敏感性：MSE 对预测误差的平方非常敏感，这意味着较大的误差会对损失函数产生更大的影响。\n",
    "\n",
    "非负性：MSE 总是非负的，这使得它在优化问题中易于处理。\n",
    "\n",
    "可导性：MSE 是可导的，这使得它适用于基于梯度的优化算法。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09b9ad36",
   "metadata": {},
   "source": [
    "6.模型训练"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "8542bc13",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch [1000/6000], Loss: 0.23412\n",
      "Epoch [2000/6000], Loss: 0.16315\n",
      "Epoch [3000/6000], Loss: 0.14836\n",
      "Epoch [4000/6000], Loss: 0.14767\n",
      "Epoch [5000/6000], Loss: 0.14767\n",
      "Epoch [6000/6000], Loss: 0.14767\n"
     ]
    }
   ],
   "source": [
    "for epoch in range(num_epochs):\n",
    "    model.train()\n",
    "    \n",
    "    outputs = model(X)\n",
    "    loss = criterion(outputs, y)\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "\n",
    "    if (epoch+1) % 1000 == 0 or epoch == num_epochs - 1:\n",
    "        print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.5f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52951edf",
   "metadata": {},
   "source": [
    "7.模型测试"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a022d8ee",
   "metadata": {},
   "source": [
    "model[0].weight.data 返回权重参数的值。\n",
    "\n",
    "model[0].bias.data 返回偏置参数的值。\n",
    "\n",
    ".data属性用于访问参数的值。\n",
    "\n",
    "在PyTorch中，参数是一个特殊的对象，具有 .data、.grad 等属性。.data 包含了参数的当前值，而 .grad 包含了梯度（在反向传播后）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "cae49e3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test_loss: 0.1477\n",
      "Sequential(\n",
      "  (0): Linear(in_features=1, out_features=1, bias=True)\n",
      ")\n",
      "weights: tensor([[7.9159]])\n",
      "bias: tensor([0.5546])\n"
     ]
    }
   ],
   "source": [
    "model.eval()\n",
    "\n",
    "with torch.no_grad():\n",
    "    y_pred = model(X)\n",
    "    test_loss = criterion(y_pred, y)\n",
    "    print(f'test_loss: {test_loss.item():.4f}')\n",
    "\n",
    "# 打印模型参数\n",
    "print(model)\n",
    "print(f'weights: {model[0].weight.data}')  # 返回权重参数的值\n",
    "print(f'bias: {model[0].bias.data}')  # 返回偏置参数的值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b934a1a5",
   "metadata": {},
   "source": [
    "8.结果可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "96bbfaf4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, y,  color='pink', marker='*', label='草莓')\n",
    "plt.plot(X, y_pred)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f731172",
   "metadata": {},
   "source": [
    "9.模型推理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "0552f8c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test = torch.arange(0.5, 1.1, 0.05).view(-1, 1)\n",
    "\n",
    "model.eval()\n",
    "with torch.no_grad():\n",
    "    y_hat = model(x_test)\n",
    "    # print(f'y_pred: {y_hat}')\n",
    "\n",
    "plt.scatter(X, y,  color='r', marker='*', label='草莓')\n",
    "plt.plot(x_test, y_hat)  # x_test, y_hat都为张量\n",
    "plt.xlim(0.5, 1.1)\n",
    "plt.ylim(0, 10)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60fbe424",
   "metadata": {},
   "source": [
    "​\t线性回归是回归分析中最早经过严格研究并在实际应用中广泛使用的类型。它因其模型相对容易拟合，且估计的统计特性容易确定，而被广泛应用于经济学、心理学、医学、工程和物理学等领域。随着时间的发展，线性回归的概念和应用不断扩展，包括对非线性模型的最小二乘拟合，以及在商业和工业中的业务决策和流程优化。\n",
    "\n",
    "​\t线性回归作为一种基础的统计方法，在数据科学和机器学习领域扮演着重要角色。通过理解其原理、优化方法以及局限性，我们可以更有效地应用线性回归来解决实际问题，并根据需要选择合适的模型和算法进行数据分析。\n",
    "\n",
    "​\t尽管线性回归是一个强大的工具，但它也有其局限性：\n",
    "\n",
    "- 线性回归假设自变量和因变量之间存在线性关系，这在现实世界中并不总是成立。\n",
    "- 在多元线性回归中，自变量之间可能存在高度相关性，这会导致模型参数估计的不稳定性。\n",
    "\n",
    "​\t为了克服这些局限性，研究者们开发了多种改进方法，如岭回归（Ridge Regression）和套索回归（Lasso Regression），它们通过引入惩罚项来减少模型复杂度，防止过拟合。\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b045579",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69bbd4b0",
   "metadata": {},
   "source": [
    "### 扩展阅读\n",
    "\n",
    "#### 卡尔·皮尔逊\n",
    "\n",
    "​\t英国数学家，生物统计学家，数理统计学的创立者，现代统计学先驱。他对生物统计学、气象学、社会达尔文主义理论和优生学做出了重大贡献。\n",
    "\n",
    "​\t1889年，高尔顿出版了著作《自然遗传》。书中概括了作者关于遗传的相关和回归概念以及技巧方面的工作，明确思考了它们在研究生命形式中的可用性和价值。皮尔逊对高尔顿的“相关”这概念十分着迷，认为这是一个比因果性更为广泛的范畴。皮尔逊立即决定全力为统计学这一新学科奠定基础，他在接着的15年内几乎是单枪匹马地奋战在这一前沿领域。\n",
    "\n",
    "​\t他讨论了概率理论和相关概念，并用掷硬币、抽纸牌和观察自然现象来证明它们。皮尔逊在高尔顿等人关于相关和回归统计概念和技巧的基础上，建立了后来所称的极大似然法。\n",
    "\n",
    "卡尔·皮尔逊的统计学贡献：\n",
    "\n",
    "（1）概率论与统计学的融合\n",
    "\n",
    "​\t皮尔逊在高尔顿的影响下，从十九世纪九十年代初开始进军生物统计学。他在先辈们通过赌博进行概率论研究的基础上，导入了许多新的概念，把生物统计方法提炼成为一般处理统计资料的通用方法，发展了统计方法论，把概率论与统计学两者熔为一炉。\n",
    "\n",
    "（2）分布曲线理论\n",
    "\n",
    "​\t在皮尔逊之前，人们普遍认为，几乎所有社会现象都是接近于正态分布的。如果所得到的统计资料呈非正态分布则往往怀疑统计资料不够或有偏差，而不重视非正态分布的研究，甚至对个别提出非正态分布理论的人加以压制。皮尔逊认为，正态分布只是一种分布形态，他在高尔登优生学统计方法的启示下，1894年发表了《关于不对称曲线的剖析》，在这篇论文中，提出了**标准差**及其符号**σ**。1895年发表了《同类资料的偏斜变异》等论文。在这些论文中，得到包括正态分布、矩形分布、J型分布、U型分布等13种曲线及其方程式。他的这一成果，打破了以往“唯正态”观念，推进了次数分布曲线理论的发展和应用，为大样本理论奠定了基础。\n",
    "\n",
    "（3）卡方（χ2）检验\n",
    "\n",
    "​\t皮尔逊认为，不管理论分布造得如何好，它与实际分布之间总存在着或多或少的差异。这些差异到底是由于观察次数不充分、随机误差太大引入的，还是由于所选的理论分布本身就与实际分布有实质性差异，还需要用一种方法来检验。\n",
    "\n",
    "​\t1900年，皮尔逊发表了一个著名的统计量，称之为卡方（χ2），用来检验实际值的分布数列与理论数列是否在合理范围内相符合，即用以测定观察值与期望值之间的差异显著性。卡方检验提出后得到了广泛的应用，在现代统计理论中占有重要地位。\n",
    "\n",
    "（4）发展了相关和回归理论\n",
    "\n",
    "​\t皮尔逊推广了高尔顿的相关结论和方法，推导出人们称之为 “皮尔逊积动差”的公式。他提出了净相关、复相关、总相关、相关比等概念，发明了计算复相关和净相关的方法及相关系数的公式。"
   ]
  }
 ],
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