{
"cells": [
{
"cell_type": "markdown",
"id": "69865783",
"metadata": {},
"source": [
"# 第 05 章 簡單貝氏分類（Naive Bayesian Classification）\n",
"\n",
"本 notebook 搭配網站「醫學生的機器學習入門」第 05 章使用。可以直接在 Google Colab 執行（選單「執行階段 → 全部執行」），不需安裝額外套件。\n",
"\n",
"內容分三段：\n",
"\n",
"1. 用程式算一次貝氏定理：盛行率、敏感度、特異度 → 陽性預測值（PPV）\n",
"2. `GaussianNB` 分類乳癌細胞核特徵（WDBC，sklearn 內建）\n",
"3. `MultinomialNB` 把醫學論文摘要分成 5 個疾病大類（Medical Abstracts TC Corpus，需網路下載）\n",
"\n",
"> 圖上的文字一律用英文，因為 Colab 預設沒有中文字型。本例僅供學習，不構成臨床建議。"
]
},
{
"cell_type": "markdown",
"id": "297d03a3",
"metadata": {},
"source": [
"先印出套件版本。本教材以 Colab 的 scikit-learn 1.6 為相容底線，新版也能執行。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "cb614f00",
"metadata": {
"execution": {
"iopub.execute_input": "2026-09-29T20:02:48.099378Z",
"iopub.status.busy": "2026-09-29T20:02:48.099226Z",
"iopub.status.idle": "2026-09-29T20:02:48.775031Z",
"shell.execute_reply": "2026-09-29T20:02:48.774648Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"numpy 2.1.3 | pandas 2.2.3 | scikit-learn 1.6.1\n"
]
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import sklearn\n",
"\n",
"print(\"numpy\", np.__version__, \"| pandas\", pd.__version__, \"| scikit-learn\", sklearn.__version__)"
]
},
{
"cell_type": "markdown",
"id": "d206bfca",
"metadata": {},
"source": [
"## 1. 貝氏定理＝檢驗前後機率\n",
"\n",
"先寫一個小函式：給盛行率、敏感度、特異度，回傳 PPV 與 NPV。用「每 10,000 人」的自然頻率來算，和你在流病課畫 2×2 表完全一樣。"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "90243111",
"metadata": {
"execution": {
"iopub.execute_input": "2026-09-29T20:02:48.776312Z",
"iopub.status.busy": "2026-09-29T20:02:48.776212Z",
"iopub.status.idle": "2026-09-29T20:02:48.778596Z",
"shell.execute_reply": "2026-09-29T20:02:48.778161Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"prevalence 0.1% -> PPV 1.8% NPV 99.99%\n",
"prevalence 1.0% -> PPV 15.4% NPV 99.89%\n",
"prevalence 10.0% -> PPV 66.7% NPV 98.84%\n",
"prevalence 30.0% -> PPV 88.5% NPV 95.68%\n"
]
}
],
"source": [
"def ppv_npv(prevalence, sensitivity, specificity, n=10_000):\n",
" diseased = prevalence * n\n",
" healthy = n - diseased\n",
" tp = sensitivity * diseased # true positive\n",
" fn = diseased - tp # false negative\n",
" tn = specificity * healthy # true negative\n",
" fp = healthy - tn # false positive\n",
" return tp / (tp + fp), tn / (tn + fn)\n",
"\n",
"for prev in [0.001, 0.01, 0.1, 0.3]:\n",
" ppv, npv = ppv_npv(prev, sensitivity=0.90, specificity=0.95)\n",
" print(f\"prevalence {prev:>6.1%} -> PPV {ppv:6.1%} NPV {npv:7.2%}\")"
]
},
{
"cell_type": "markdown",
"id": "7e1f72a0",
"metadata": {},
"source": [
"同一支敏感度 90%、特異度 95% 的檢驗，盛行率 1% 時 PPV 只有約 15%，盛行率 30% 時卻接近 89%。檢驗本身沒變，變的是檢驗前機率。"
]
},
{
"cell_type": "markdown",
"id": "9e67a773",
"metadata": {},
"source": [
"換成勝算（odds）與概似比（likelihood ratio）的寫法：檢驗後勝算＝檢驗前勝算 × LR。連續做兩個檢驗時，**如果兩者在已知有無疾病下彼此獨立**，就可以一路乘下去——這正是 naive Bayes 的核心假設。"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6356db96",
"metadata": {
"execution": {
"iopub.execute_input": "2026-09-29T20:02:48.779653Z",
"iopub.status.busy": "2026-09-29T20:02:48.779599Z",
"iopub.status.idle": "2026-09-29T20:02:48.781565Z",
"shell.execute_reply": "2026-09-29T20:02:48.781293Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"LR+ = 18.0\n",
"after 1 positive test : 15.4%\n",
"after 2 positive tests: 76.6% (only valid if the tests are conditionally independent)\n"
]
}
],
"source": [
"def to_odds(p):\n",
" return p / (1 - p)\n",
"\n",
"def to_prob(odds):\n",
" return odds / (1 + odds)\n",
"\n",
"sens, spec = 0.90, 0.95\n",
"lr_pos = sens / (1 - spec) # LR+ = 18\n",
"pretest = 0.01\n",
"\n",
"post1 = to_prob(to_odds(pretest) * lr_pos)\n",
"post2 = to_prob(to_odds(pretest) * lr_pos * lr_pos) # a second, independent positive test\n",
"print(f\"LR+ = {lr_pos:.1f}\")\n",
"print(f\"after 1 positive test : {post1:.1%}\")\n",
"print(f\"after 2 positive tests: {post2:.1%} (only valid if the tests are conditionally independent)\")"
]
},
{
"cell_type": "markdown",
"id": "55880b4c",
"metadata": {},
"source": [
"第一次陽性之後機率從 1% 升到約 15.4%（和上面 PPV 相同），再一次獨立的陽性升到約 76.6%。若第二個檢驗其實和第一個高度相關（例如同一種原理的兩支試劑），這樣相乘就會高估。"
]
},
{
"cell_type": "markdown",
"id": "d4cc35c1",
"metadata": {},
"source": [
"## 2. GaussianNB：乳癌細胞核特徵\n",
"\n",
"WDBC 資料集的標籤 `0 = 惡性、1 = 良性`，和直覺相反。我們先把它翻成 `1 = 惡性`，再切出 25% 當測試集。"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "e2abc8a3",
"metadata": {
"execution": {
"iopub.execute_input": "2026-09-29T20:02:48.782625Z",
"iopub.status.busy": "2026-09-29T20:02:48.782557Z",
"iopub.status.idle": "2026-09-29T20:02:48.867611Z",
"shell.execute_reply": "2026-09-29T20:02:48.867205Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(426, 30) (143, 30) malignant rate: 0.373\n"
]
}
],
"source": [
"from sklearn.datasets import load_breast_cancer\n",
"from sklearn.model_selection import train_test_split\n",
"\n",
"X, y = load_breast_cancer(return_X_y=True, as_frame=True)\n",
"y = (y == 0).astype(int) # flip: 1 = malignant, 0 = benign\n",
"X_train, X_test, y_train, y_test = train_test_split(\n",
" X, y, test_size=0.25, stratify=y, random_state=42)\n",
"print(X_train.shape, X_test.shape, \"malignant rate:\", round(y.mean(), 3))"
]
},
{
"cell_type": "markdown",
"id": "57a78185",
"metadata": {},
"source": [
"訓練 `GaussianNB` 只要兩行，不需要標準化（每個特徵各自估平均與變異數，尺度不影響）。"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "30c77cfb",
"metadata": {
"execution": {
"iopub.execute_input": "2026-09-29T20:02:48.868904Z",
"iopub.status.busy": "2026-09-29T20:02:48.868818Z",
"iopub.status.idle": "2026-09-29T20:02:48.877267Z",
"shell.execute_reply": "2026-09-29T20:02:48.876809Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"accuracy: 0.944\n",
"[[90 0]\n",
" [ 8 45]]\n",
" precision recall f1-score support\n",
"\n",
" benign 0.918 1.000 0.957 90\n",
" malignant 1.000 0.849 0.918 53\n",
"\n",
" accuracy 0.944 143\n",
" macro avg 0.959 0.925 0.938 143\n",
"weighted avg 0.949 0.944 0.943 143\n",
"\n"
]
}
],
"source": [
"from sklearn.naive_bayes import GaussianNB\n",
"from sklearn.metrics import accuracy_score, confusion_matrix, classification_report\n",
"\n",
"nb = GaussianNB()\n",
"nb.fit(X_train, y_train)\n",
"y_pred = nb.predict(X_test)\n",
"\n",
"print(\"accuracy:\", round(accuracy_score(y_test, y_pred), 3))\n",
"print(confusion_matrix(y_test, y_pred)) # rows: true 0/1, cols: predicted 0/1\n",
"print(classification_report(y_test, y_pred, target_names=[\"benign\", \"malignant\"], digits=3))"
]
},
{
"cell_type": "markdown",
"id": "834704eb",
"metadata": {},
"source": [
"混淆矩陣的第二列是真正惡性的 53 例：抓到 45 例、漏掉 8 例（敏感度約 0.85），良性則全部判對。對醫學應用來說，偽陰性比偽陽性更值得注意。"
]
},
{
"cell_type": "markdown",
"id": "b3376db1",
"metadata": {},
"source": [
"模型「學到」的東西其實就是每個類別、每個特徵的平均與變異數，可以直接印出來看。"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "23c3e194",
"metadata": {
"execution": {
"iopub.execute_input": "2026-09-29T20:02:48.878326Z",
"iopub.status.busy": "2026-09-29T20:02:48.878260Z",
"iopub.status.idle": "2026-09-29T20:02:48.882525Z",
"shell.execute_reply": "2026-09-29T20:02:48.882131Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"class prior: [0.627 0.373]\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" benign_mean | \n",
" malignant_mean | \n",
"
\n",
" \n",
" \n",
" \n",
" | mean radius | \n",
" 12.166 | \n",
" 17.530 | \n",
"
\n",
" \n",
" | mean concave points | \n",
" 0.026 | \n",
" 0.088 | \n",
"
\n",
" \n",
" | worst area | \n",
" 563.221 | \n",
" 1446.654 | \n",
"
\n",
" \n",
"
\n",
"
"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"proba = nb.predict_proba(X_test)[:, 1] # predicted probability of malignant\n",
"print(\"corr(mean radius, mean perimeter) =\", round(X[\"mean radius\"].corr(X[\"mean perimeter\"]), 3))\n",
"print(\"share of predictions < 1% or > 99%:\", round(np.mean((proba < 0.01) | (proba > 0.99)), 3))\n",
"\n",
"wrong = y_pred != y_test.to_numpy()\n",
"print(\"misclassified cases:\", wrong.sum())\n",
"print(\"their predicted P(malignant):\", np.sort(proba[wrong]).round(4))\n",
"\n",
"fig, ax = plt.subplots(figsize=(6, 3.5))\n",
"ax.hist(proba, bins=20, range=(0, 1), color=\"#00897B\", edgecolor=\"white\")\n",
"ax.set_xlabel(\"predicted P(malignant)\")\n",
"ax.set_ylabel(\"number of test tumors\")\n",
"ax.set_title(\"GaussianNB probabilities pile up at 0 and 1\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "97e78742",
"metadata": {},
"source": [
"超過九成的預測落在 <1% 或 >99%；而被判錯的 8 例中，有 5 例模型給的惡性機率不到 1%。分類結果可以參考，但 `predict_proba` 的數字不能當成「這顆腫瘤的惡性風險」。"
]
},
{
"cell_type": "markdown",
"id": "5f61a1b7",
"metadata": {},
"source": [
"## 3. MultinomialNB：醫學摘要文字分類\n",
"\n",
"資料來自 Medical Abstracts TC Corpus（sebischair，GitHub），約 1.4 萬篇醫學摘要，標為 5 個疾病大類。需要網路下載（約 10 秒）。"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "be16effe",
"metadata": {
"execution": {
"iopub.execute_input": "2026-09-29T20:02:48.986566Z",
"iopub.status.busy": "2026-09-29T20:02:48.986500Z",
"iopub.status.idle": "2026-09-29T20:02:58.398943Z",
"shell.execute_reply": "2026-09-29T20:02:58.398313Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(11550, 2) (2888, 2)\n",
"condition_label\n",
"general 3844\n",
"neoplasms 2530\n",
"cardiovascular 2441\n",
"nervous 1540\n",
"digestive 1195\n",
"Name: count, dtype: int64\n",
"Tissue changes around loose prostheses. A canine model to investigate the effects of an antiinflammatory agent. The aseptically loosened prosthesis provided a means for investigating the in vivo and in vitro activity of the cells associated with the loosening process in seven dogs. The cells were is ...\n"
]
}
],
"source": [
"base = \"https://raw.githubusercontent.com/sebischair/Medical-Abstracts-TC-Corpus/main/\"\n",
"try:\n",
" train_df = pd.read_csv(base + \"medical_tc_train.csv\")\n",
" test_df = pd.read_csv(base + \"medical_tc_test.csv\")\n",
"except Exception as e:\n",
" raise RuntimeError(\n",
" \"下載 Medical Abstracts 失敗，請確認網路連線，或稍後再執行此格。原始錯誤：\" + str(e))\n",
"\n",
"label_names = {1: \"neoplasms\", 2: \"digestive\", 3: \"nervous\", 4: \"cardiovascular\", 5: \"general\"}\n",
"print(train_df.shape, test_df.shape)\n",
"print(train_df[\"condition_label\"].map(label_names).value_counts())\n",
"print(train_df[\"medical_abstract\"].iloc[0][:300], \"...\")"
]
},
{
"cell_type": "markdown",
"id": "84f7b826",
"metadata": {},
"source": [
"先用三句玩具句子看看詞袋模型（bag-of-words）在做什麼：每個字變成一欄，數它出現幾次，**字的順序被丟掉**。"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "dba22c38",
"metadata": {
"execution": {
"iopub.execute_input": "2026-09-29T20:02:58.400744Z",
"iopub.status.busy": "2026-09-29T20:02:58.400636Z",
"iopub.status.idle": "2026-09-29T20:02:58.406180Z",
"shell.execute_reply": "2026-09-29T20:02:58.405737Z"
}
},
"outputs": [
{
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