Wordle预测：美赛C题技术解析

2023 美赛C题：Wordle结果预测（上）技术分析

问题背景与核心目标

2023年美赛C题聚焦于预测游戏Wordle的玩家结果分布。Wordle是一款每日限猜一次的单词猜测游戏，玩家需在六次尝试内猜出目标单词。题目要求建立模型预测未来日期的结果分布（如1/2/3/4/5/6次猜测成功或失败的比例），并分析模型对单词属性（如字母频率、词性）的敏感性。

数据预处理与特征工程

原始数据包含2022年1月7日至12月31日的玩家结果分布（1-6次猜测的成功率及失败率）。需提取以下特征：

• 单词属性：词长、字母重复性、元音/辅音比例、词频（基于语料库统计）。
• 字母特征：首字母频率、特定位置字母出现概率（如E在第二位的频率）。
• 日期信息：星期几、节假日标志（可能影响玩家活跃度）。

示例代码（Python特征提取）：

from collections import Counter

def extract_word_features(word):
    vowels = {'a', 'e', 'i', 'o', 'u'}
    letter_counts = Counter(word)
    return {
        'length': len(word),
        'unique_letters': len(letter_counts),
        'vowel_ratio': sum(c in vowels for c in word) / len(word),
        'first_letter_freq': corpus_first_letter_freq[word[0]]  # 预计算的语料库统计
    }

统计分析与基线模型

1. 时间序列分析：观察结果分布的周期性（如周末效应），使用ARIMA或Prophet模型捕捉趋势。
2. 单词难度量化：定义难度系数为失败率与平均尝试次数的加权组合：
   [ \text{Difficulty} = \alpha \cdot \text{Fail Rate} + (1-\alpha) \cdot \mathbb{E}[\text{Attempts}] ]
3. 回归模型：将每日结果分布作为因变量，单词特征为自变量，采用多元线性回归或分位数回归建模。

机器学习模型构建

• 树模型应用：XGBoost或Random Forest处理非线性关系，特征重要性分析可识别关键单词属性（如字母重复性对难度的影响）。
• 集成方法：结合时间序列预测与单词特征模型，通过加权融合提升鲁棒性。

示例代码（XGBoost训练）：

import xgboost as xgb

model = xgb.XGBRegressor(objective='reg:squarederror')
model.fit(X_train, y_train)
feature_importances = model.feature_importances_

模型验证与敏感性分析

• 交叉验证：按时间划分训练/验证集，避免数据泄露。
• 敏感性测试：扰动单词特征（如修改词频），观察预测分布变化，使用Sobol指数量化特征影响。

（下篇将深入讨论动态建模、玩家行为模拟及优化策略）

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