基于样条的多元分位数回归实现及predict方法报错问题咨询

我想用带样条的多元分位数回归分析数据，数据包含3个自变量和1个因变量。我将数据划分为训练集与验证集，计划在训练集拟合模型后用验证集验证。采用statsmodels.formula.api的quantreg()及patsy的bs()实现，但调用predict()时出现报错。现存在两个疑问：

1. 当前实现思路是否正确？
2. 该场景下如何正确使用predict()？

原代码 #

import pandas as pd
import statsmodels.formula.api as smf
import patsy    
from sklearn.model_selection import train_test_split

train_x, valid_x, train_y, valid_y = train_test_split(data.iloc[:,:3], 
data.total, test_size=0.1, random_state = 1)

train=train_x.join(train_y) 
vel = train['vel']
salmean = train['salmean']
em = train['em']
total = train['total']

model = smf.quantreg('total ~ bs(vel, df=3, degree=3) + bs(salmean, df=3, 
degree=3) + bs(em, df=3, degree=3) ', train).fit(0.9)

y_pre =model.predict(valid_x)

报错信息 #

PatsyError: predict requires that you use a DataFrame when predicting from a model that was created using the formula api.
The original error message returned by patsy is:
Error evaluating factor: NotImplementedError: some data points fall outside the outermost knots, and I'm not sure how to handle them. (Patches accepted!)
total ~ bs(vel, df=3, degree=3) + bs(salmean, df=3, degree=3) + bs(em, df=3, degree=3)

问题分析与解答 #

1. 实现思路的正确性 #

整体思路没问题：拆分训练/验证集、用样条拓展自变量维度、拟合分位数回归，这个流程是分位数回归建模的标准做法。但报错暴露了两个细节疏漏：

• 验证集中部分自变量值超出了训练集生成样条时的边界节点范围，而patsy的bs()默认不支持外推计算
• 外层提示的"需要DataFrame"是patsy内部报错后的附加提示，核心问题是样条外推的限制

2. 正确使用predict()的方法 #

需要从固定样条节点和允许外推两个核心点调整，同时保证预测数据的变量名一致性：

修正后的代码

import pandas as pd
import statsmodels.formula.api as smf
from patsy import bs
from sklearn.model_selection import train_test_split

# 拆分数据集
train_x, valid_x, train_y, valid_y = train_test_split(data.iloc[:,:3], 
                                                      data.total, test_size=0.1, random_state=1)
train = train_x.join(train_y)

# 基于训练集提前计算每个自变量的样条节点
knots_vel = bs(train['vel'], df=3, degree=3).knots
knots_salmean = bs(train['salmean'], df=3, degree=3).knots
knots_em = bs(train['em'], df=3, degree=3).knots

# 用固定节点拟合模型，开启extrapolate允许外推
model = smf.quantreg(
    'total ~ bs(vel, knots=knots_vel, degree=3, extrapolate=True) + '
    'bs(salmean, knots=knots_salmean, degree=3, extrapolate=True) + '
    'bs(em, knots=knots_em, degree=3, extrapolate=True)',
    data=train
).fit(0.9)

# 直接传入验证集DataFrame进行预测
y_pre = model.predict(valid_x)

关键调整说明

• 固定样条节点：基于训练集生成节点，确保训练和预测阶段使用完全一致的样条分段规则，避免因数据分布差异导致的节点偏移
• 开启外推：extrapolate=True参数让patsy允许对超出节点范围的验证集数据进行外推计算，解决核心报错
• 变量名一致性：确保valid_x包含vel、salmean、em三个变量名，与公式中的变量名严格对应

内容的提问来源于stack exchange，提问作者Sharon