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"slug": "adaboost-sample-weights-update",
"title": "手撕 AdaBoost 样本权重分布更新 (AdaBoost Sample Weights Update)",
"difficulty": "Easy",
"category": "ML",
"tags": [
"集成学习",
"AdaBoost",
"样本赋权"
],
"description_md": "### 题目描述\n给定样本当前权重 $w \\in \\mathbb{R}^N$ (满足 $\\sum w_i = 1$)、基学习器分类结果 $\\hat{y} \\in \\{-1, +1\\}^N$、真实标签 $y \\in \\{-1, +1\\}^N$ 及学习器权重 $\\alpha$，更新样本权重 $w_i \\leftarrow w_i \\exp(-\\alpha y_i \\hat{y}_i)$ 并将其重新归一化使和为 1。\n\n### 函数签名\n```python\ndef adaboost_update_weights(\n w: torch.Tensor,\n y_true: torch.Tensor,\n y_pred: torch.Tensor,\n alpha: float,\n) -> torch.Tensor:\n```\n\n### 示例\n```python\n# 输入\nw = [0.25, 0.25, 0.25, 0.25]\ny_true = [1.0, 1.0, -1.0, -1.0]\ny_pred = [1.0, -1.0, -1.0, 1.0]\nalpha = 0.6\n\n# 输出 (Tensor, shape=[4], dtype=float32)\n[0.1157, 0.3843, 0.1157, 0.3843]\n```\n\n### 参数规格与约束\n- **`w`**：`torch.Tensor`，测试规格 `shape=[4], dtype=float32`\n- **`y_true`**：`torch.Tensor`，测试规格 `shape=[4], dtype=float32`\n- **`y_pred`**：`torch.Tensor`，测试规格 `shape=[4], dtype=float32`\n- **`alpha`**：`float`\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`",
"entry_point": "adaboost_update_weights",
"starter_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import Optional, List, Tuple\n\ndef adaboost_update_weights(\n w: torch.Tensor,\n y_true: torch.Tensor,\n y_pred: torch.Tensor,\n alpha: float,\n) -> torch.Tensor:\n \"\"\"\n 手撕 AdaBoost 样本权重分布更新 (AdaBoost Sample Weights Update)\n \"\"\"\n # 请在此编写代码\n pass\n",
"reference_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\nfrom typing import Optional, List, Tuple\n\ndef adaboost_update_weights(w: torch.Tensor, y_true: torch.Tensor, y_pred: torch.Tensor, alpha: float) -> torch.Tensor:\n exps = torch.exp(-alpha * y_true * y_pred)\n new_w = w * exps\n return new_w / torch.sum(new_w)\n",
"forbidden_modules": [
"os",
"sys",
"subprocess",
"shutil",
"socket",
"requests"
],
"forbidden_calls": [],
"time_limit": 3.0,
"memory_limit_mb": 512,
"atol": 0.0001,
"rtol": 0.0001,
"test_code": "import torch\nimport torch.nn as nn\nimport torch.nn.functional as F\nimport math\n\ncases = [\n ('对错参半样本集', torch.tensor([0.25, 0.25, 0.25, 0.25], dtype=torch.float32), torch.tensor([1.0, 1.0, -1.0, -1.0], dtype=torch.float32), torch.tensor([1.0, -1.0, -1.0, 1.0], dtype=torch.float32), 0.6),\n ('多批次扩展泛化验证', torch.tensor([0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], dtype=torch.float32), torch.tensor([1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0], dtype=torch.float32), torch.tensor([1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0], dtype=torch.float32), 0.6),\n ('多维批次与参数泛化验证', torch.tensor([0.25, 0.25, 0.25, 0.25], dtype=torch.float32), torch.tensor([1.0, 1.0, -1.0, -1.0], dtype=torch.float32), torch.tensor([1.0, -1.0, -1.0, 1.0], dtype=torch.float32), 0.48),\n ('边界极值与稳定性验证', torch.tensor([0.25, 0.25, 0.25, 0.25], dtype=torch.float32), torch.tensor([-1.0, -1.0, 1.0, 1.0], dtype=torch.float32), torch.tensor([1.0, -1.0, -1.0, 1.0], dtype=torch.float32), 0.72),\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",
"is_featured": false,
"editorial_md": "#### 💡 核心算法原理与数学推导\n**手撕 AdaBoost 样本权重分布更新 (AdaBoost Sample Weights Update)**（`adaboost_update_weights`）聚焦于 **ML** 中的关键计算逻辑：\n\n给定样本当前权重 $w \\in \\mathbb{R}^N$ (满足 $\\sum w_i = 1$)、基学习器分类结果 $\\hat{y} \\in \\{-1, +1\\}^N$、真实标签 $y \\in \\{-1, +1\\}^N$ 及学习器权重 $\\alpha$，更新样本权重 $w_i \\leftarrow w_i \\exp(-\\alpha y_i \\hat{y}_i)$ 并将其重新归一化使和为 1。\n\n在实现中，函数接收参数 `w` (`torch.Tensor`)、`y_true` (`torch.Tensor`)、`y_pred` (`torch.Tensor`)、`alpha` (`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**：`w` 规格为 `torch.Tensor(shape=[4], dtype=float32)`，`y_true` 规格为 `torch.Tensor(shape=[4], dtype=float32)`，`y_pred` 规格为 `torch.Tensor(shape=[4], dtype=float32)`，`alpha` 规格为 `float` (示例值: `0.6`)。\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. 计算中间量 `exps`：通过表达式 `torch.exp(-alpha * y_true * y_pred)` 完成张量或数值变换。\n2. 计算中间量 `new_w`：通过表达式 `w * exps` 完成张量或数值变换。\n3. 返回最终结果：输出 `new_w / torch.sum(new_w)`，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沿指定维度的归约计算。\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，必须按公式位置准确加上 `eps`（例如在平方根内 `sqrt(var + eps)` 还是分母外 `+ eps`），防止全零或常量输入触发 `NaN` / `Inf`。\n- **归约维度 (`dim`) 与广播对齐 (`keepdim`)**：调用 `sum`、`mean`、`max`、`norm` 或 `softmax` 时需明确指定目標维度（通常为最后一维 `dim=-1` 或特征维 `dim=0`），并在需要与原张量逐元素相减/相除时开启 `keepdim=True`。\n- **指数与对数域数值稳定性**：直接对大幅值 logits 计算 `exp` 易导致浮点数上溢（Overflow），对接近 0 的概率直接计算 `log` 易导致下溢；应优先使用 `F.log_softmax`、`F.logsigmoid` 或减去最大值的稳定化写法。\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 Optional, List, Tuple\n\ndef adaboost_update_weights(w: torch.Tensor, y_true: torch.Tensor, y_pred: torch.Tensor, alpha: float) -> torch.Tensor:\n exps = torch.exp(-alpha * y_true * y_pred)\n new_w = w * exps\n return new_w / torch.sum(new_w)\n```",
"difficulty_breakdown": {
"concept": 2,
"implementation": 2,
"math_derivation": 2,
"boundary_complexity": 1
},
"test_cases": [
{
"name": "对错参半样本集",
"input_desc": "真实参数契约用例 (w, y_true, y_pred, alpha)",
"params": [
{
"name": "w",
"type": "torch.Tensor",
"value": "torch.tensor([0.25, 0.25, 0.25, 0.25], dtype=torch.float32)"
},
{
"name": "y_true",
"type": "torch.Tensor",
"value": "torch.tensor([1.0, 1.0, -1.0, -1.0], dtype=torch.float32)"
},
{
"name": "y_pred",
"type": "torch.Tensor",
"value": "torch.tensor([1.0, -1.0, -1.0, 1.0], dtype=torch.float32)"
},
{
"name": "alpha",
"type": "float",
"value": "0.6"
}
],
"raw_inputs": {
"w": "torch.tensor([0.25, 0.25, 0.25, 0.25], dtype=torch.float32)",
"y_true": "torch.tensor([1.0, 1.0, -1.0, -1.0], dtype=torch.float32)",
"y_pred": "torch.tensor([1.0, -1.0, -1.0, 1.0], dtype=torch.float32)",
"alpha": "0.6"
}
},
{
"name": "多批次扩展泛化验证",
"input_desc": "真实参数契约用例 (w, y_true, y_pred, alpha)",
"params": [
{
"name": "w",
"type": "torch.Tensor",
"value": "torch.tensor([0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], dtype=torch.float32)"
},
{
"name": "y_true",
"type": "torch.Tensor",
"value": "torch.tensor([1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0], dtype=torch.float32)"
},
{
"name": "y_pred",
"type": "torch.Tensor",
"value": "torch.tensor([1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0], dtype=torch.float32)"
},
{
"name": "alpha",
"type": "float",
"value": "0.6"
}
],
"raw_inputs": {
"w": "torch.tensor([0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25], dtype=torch.float32)",
"y_true": "torch.tensor([1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0], dtype=torch.float32)",
"y_pred": "torch.tensor([1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0], dtype=torch.float32)",
"alpha": "0.6"
}
},
{
"name": "多维批次与参数泛化验证",
"input_desc": "真实参数契约用例 (w, y_true, y_pred, alpha)",
"params": [
{
"name": "w",
"type": "torch.Tensor",
"value": "torch.tensor([0.25, 0.25, 0.25, 0.25], dtype=torch.float32)"
},
{
"name": "y_true",
"type": "torch.Tensor",
"value": "torch.tensor([1.0, 1.0, -1.0, -1.0], dtype=torch.float32)"
},
{
"name": "y_pred",
"type": "torch.Tensor",
"value": "torch.tensor([1.0, -1.0, -1.0, 1.0], dtype=torch.float32)"
},
{
"name": "alpha",
"type": "float",
"value": "0.48"
}
],
"raw_inputs": {
"w": "torch.tensor([0.25, 0.25, 0.25, 0.25], dtype=torch.float32)",
"y_true": "torch.tensor([1.0, 1.0, -1.0, -1.0], dtype=torch.float32)",
"y_pred": "torch.tensor([1.0, -1.0, -1.0, 1.0], dtype=torch.float32)",
"alpha": "0.48"
}
}
]
} |