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"slug": "box-cox-power-transform",
"title": "Box-Cox 幂变换偏态连续特征正态化",
"difficulty": "Easy",
"difficulty_breakdown": {
"concept": 2,
"implementation": 2,
"math_derivation": 2,
"boundary_complexity": 2
},
"category": "Math",
"tags": [
"Statistics",
"FeatureEngineering",
"BoxCox",
"TorchLeet"
],
"description_md": "### 题目描述\n实现统计学中的 Box-Cox 连续幂变换：给定严格为正的张量 `x`（$x_i > 0$）与参数 `lam` ($\\lambda$)：当 $|\\lambda| > 10^{-8}$ 时计算 $\\frac{x^\\lambda - 1}{\\lambda}$；当 $\\lambda = 0$ 时取连续极限 $\\ln(x)$。\n\n### 函数签名\n```python\ndef box_cox_transform(\n x: torch.Tensor,\n lam: float = 0.5,\n) -> torch.Tensor:\n```\n\n### 示例\n```python\n# 输入\nx = [1.0, 4.0, 9.0, 16.0]\nlam = 0.5\n\n# 输出 (Tensor, shape=[4], dtype=float32)\n[0.0, 2.0, 4.0, 6.0]\n```\n\n### 参数规格与约束\n- **`x`**：`torch.Tensor`，测试规格 `shape=[4], dtype=float32`\n- **`lam`**：`float`（默认 `0.5`）\n- **返回值**：`torch.Tensor`，输出规格 `shape=[4], dtype=float32`\n- **精度容差**：`atol=0.0001, rtol=0.0001`\n> 题目来源：改编自 [TorchLeet](https://github.com/Exorust/TorchLeet)（MIT License），已改写为函数式评测接口与中文题面。",
"entry_point": "box_cox_transform",
"starter_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import List, Tuple, Dict, Optional\n\ndef box_cox_transform(\n x: torch.Tensor,\n lam: float = 0.5,\n) -> torch.Tensor:\n # 请在此处编写你的实现代码\n pass\n",
"reference_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import List, Tuple, Dict, Optional\n\ndef box_cox_transform(x: torch.Tensor, lam: float = 0.5) -> torch.Tensor:\n if abs(lam) < 1e-8:\n return torch.log(x)\n return (torch.pow(x, lam) - 1.0) / lam\n",
"test_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import List, Tuple, Dict, Optional\n\ncases = [\n (\"lam=0.5 平方根变换手算\", torch.tensor([1.0, 4.0, 9.0, 16.0]), 0.5),\n (\"lam=0.0 对数极限分支\", torch.tensor([1.0, math.e, math.e ** 2]), 0.0),\n (\"lam=1.0 线性平移 x-1\", torch.tensor([2.0, 5.0, 10.0]), 1.0),\n (\"lam=-1.0 倒数变换\", torch.tensor([1.0, 2.0, 4.0]), -1.0),\n]\nfor idx, (name, *args) in enumerate(cases, 1):\n t0 = time.time()\n try:\n exp = ref_obj(*args)\n act = user_obj(*args)\n match, err, max_diff = compare_outputs(act, exp, atol=atol, rtol=rtol)\n passed, msg = match, err\n except Exception as e:\n passed, msg = False, f\"Runtime Exception: {str(e)}\"\n act, exp, max_diff = None, None, None\n cases_results.append({\n \"case_id\": idx, \"case_name\": name, \"passed\": passed,\n \"time_ms\": round((time.time() - t0) * 1000, 2), \"message\": msg,\n \"user_output_summary\": summarize_obj(act) if act is not None else None,\n \"expected_summary\": summarize_obj(exp) if exp is not None else None,\n \"max_diff\": max_diff,\n })\n",
"test_cases": [
{
"name": "lam=0.5 平方根变换手算",
"input_desc": "真实参数契约用例 (x, lam)",
"params": [
{
"name": "x",
"type": "torch.Tensor",
"value": "torch.tensor([1.0, 4.0, 9.0, 16.0], dtype=torch.float32)"
},
{
"name": "lam",
"type": "float",
"value": "0.5"
}
],
"raw_inputs": {
"x": "torch.tensor([1.0, 4.0, 9.0, 16.0], dtype=torch.float32)",
"lam": "0.5"
}
},
{
"name": "lam=0.0 对数极限分支",
"input_desc": "真实参数契约用例 (x, lam)",
"params": [
{
"name": "x",
"type": "torch.Tensor",
"value": "torch.tensor([1.0, 2.7183, 7.3891], dtype=torch.float32)"
},
{
"name": "lam",
"type": "float",
"value": "0.0"
}
],
"raw_inputs": {
"x": "torch.tensor([1.0, 2.7183, 7.3891], dtype=torch.float32)",
"lam": "0.0"
}
},
{
"name": "lam=1.0 线性平移 x-1",
"input_desc": "真实参数契约用例 (x, lam)",
"params": [
{
"name": "x",
"type": "torch.Tensor",
"value": "torch.tensor([2.0, 5.0, 10.0], dtype=torch.float32)"
},
{
"name": "lam",
"type": "float",
"value": "1.0"
}
],
"raw_inputs": {
"x": "torch.tensor([2.0, 5.0, 10.0], dtype=torch.float32)",
"lam": "1.0"
}
}
],
"time_limit": 5.0,
"memory_limit_mb": 512,
"atol": 0.0001,
"rtol": 0.0001,
"forbidden_modules": [
"os",
"sys",
"subprocess",
"socket",
"shutil",
"pathlib",
"ctypes",
"multiprocessing"
],
"forbidden_calls": [
"eval",
"exec",
"compile",
"open",
"__import__",
"input",
"breakpoint"
],
"is_featured": false,
"editorial_md": "#### 💡 核心算法原理与数学推导\n**Box-Cox 幂变换偏态连续特征正态化**（`box_cox_transform`）聚焦于 **Math** 中的关键计算逻辑：\n\n实现统计学中的 Box-Cox 连续幂变换：给定严格为正的张量 `x`（$x_i > 0$）与参数 `lam` ($\\lambda$)：当 $|\\lambda| > 10^{-8}$ 时计算 $\\frac{x^\\lambda - 1}{\\lambda}$；当 $\\lambda = 0$ 时取连续极限 $\\ln(x)$。\n\n在实现中，函数接收参数 `x` (`torch.Tensor`)、`lam` (`float`)，目标是计算出类型与形状严格符合 `torch.Tensor` 契约的结果。\n\n#### 📐 输入输出张量变换与步骤拆解\n- **输入基准规格**：`x` 规格为 `torch.Tensor(shape=[4], dtype=float32)`，`lam` 规格为 `float` (示例值: `0.5`)。\n- **期望输出规格**：`torch.Tensor(shape=[4], dtype=float32)`。\n\n**具体推导与计算步骤如下：**\n1. 条件分支判断 `if abs(lam) < 1e-8`：处理边界条件、掩码过滤或特殊退化情形。\n2. 返回最终结果：输出 `(torch.pow(x, lam) - 1.0) / lam`，严格对齐函数签名要求的返回类型与维度。\n\n#### 📊 复杂度分析\n- **时间复杂度**：$O(N)$（线性于输入张量总元素个数 $\\prod d_i$），所有运算均为向量化逐元素算子或归约计算。\n- **空间复杂度**：$O(N)$，需要与输入或输出张量同规模的显存空间保存计算结果。\n\n#### ⚠️ 关键实现细节与易错点\n- **除零保护与数值平滑 (`eps`)**：在执行分母归一化、标准差缩放或对数运算时，需加上 `eps` 或执行 `clamp_min` 防止除零产生 `NaN` / `Inf`。\n- **边界输入鲁棒性**：注意单样本（`Batch=1`）、零值输入或极端超参数下的计算行为，禁止硬编码特定测试用例常量。\n- **向量化算子优先**：优先使用 PyTorch 原生向量化张量算子，避免低效的逐元素循环。\n\n#### 💻 官方标准参考实现\n```python\nimport torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import List, Tuple, Dict, Optional\n\ndef box_cox_transform(x: torch.Tensor, lam: float = 0.5) -> torch.Tensor:\n if abs(lam) < 1e-8:\n return torch.log(x)\n return (torch.pow(x, lam) - 1.0) / lam\n```"
} |