使用SHAP时如何解释多类分类问题的base_value? [英] How to interpret base_value of multi-class classification problem when using SHAP?

问题描述

我正在使用shap库进行ML解释，以更好地理解k均值分割算法簇.简而言之，我制作了一些博客，使用k-means对它们进行聚类，然后将这些聚类作为标签，并使用xgboost尝试预测它们.我有5个聚类，所以这是一个信号标签多类分类问题.

 将numpy导入为np从sklearn.datasets导入make_blobs将熊猫作为pd导入从sklearn.preprocessing导入StandardScaler从sklearn.cluster导入KMeans将xgboost导入为xgb进口杂货X，y = make_blobs(n_samples = 500，centers = 5，n_features = 5，random_state = 0)数据= pd.DataFrame(np.concatenate((X，y.reshape(500,1))，轴= 1)，列= ['var_1'，'var_2'，'var_3'，'var_4'，'var_5'，'cluster_id'])data ['cluster_id'] = data ['cluster_id'].astype(int).astype(str)定标器= StandardScaler()scaled_features = scaler.fit_transform(data.iloc [:，:-1])kmeans = KMeans(n_clusters = 5，** kmeans_kwargs)kmeans.fit(scaled_features)数据['predicted_cluster_id'] = kmeans.labels_.astype(int).astype(str)clf = xgb.XGBClassifier()clf.fit(scaled_data.iloc [:，:-1]，scaled_data ['predicted_cluster_id'])shap.initjs()解释器= shap.TreeExplainer(clf)shap_values = explorer.shap_values(scaled_data.iloc [0，:-1] .values.reshape(1，-1))shap.force_plot(explainer.expected_value [0]，shap_values [0]，link ='logit')#为范围(0，5)中的i重复更改0 

由于类别为'3'，因此上面的图片有意义.但是为什么这个base_value不应该是1/5?我前段时间问自己

解决方案

link ="logit" 似乎不适用于多类，因为它仅适用于二进制输出.这就是为什么看不到总计为1的概率的原因.

让我们简化您的代码:

 将numpy导入为np从sklearn.datasets导入make_blobs将熊猫作为pd导入从sklearn.preprocessing导入StandardScaler从sklearn.cluster导入KMeans将xgboost导入为xgb进口杂货从scipy.special导入softmax，logit，expitnp.random.seed(42)X，y_true = make_blobs(n_samples = 500，中心= 5，n_features = 3，random_state = 0)定标器= StandardScaler()X_scaled = scaler.fit_transform(X)kmeans = KMeans(n_clusters = 5)y_predicted = kmeans.fit_predict(X_scaled，)clf = xgb.XGBClassifier()clf.fit(X_scaled，y_predicted)shap.initjs() 

然后，您在以下位置看到的期望值:

  explainer = shap.TreeExplainer(clf)说明器.expected_value数组([0.67111245、0.60223354、0.53357694、0.50821152、0.50145331]) 

是原始空间中的基本分数.

可以使用 softmax 将多类原始分数转换为概率:

  softmax(explainer.expected_value)数组([0.22229282，0.20749694，0.19372895，0.18887673，0.18760457]) 

shap.force_plot(...，link ="logit")对于多类而言没有意义，并且似乎无法从原始切​​换为概率，并且仍然保持可加性(因为softmax(x + y)≠softmax(x)+ softmax(y)).

如果您想分析概率空间中的数据，请尝试 KernelExplainer :

 从shap导入KernelExplainermasker = shap.maskers.Independent(X_scaled，100)ke = KernelExplainer(clf.predict_proba，data = masker.data)ke.expected_value#array([0.18976762，0.1900516，0.20042894，0.19995041，0.21980143])shap_values = ke.shap_values(masker.data)shap.force_plot(ke.expected_value [0]，shap_values [0] [0]) 

或摘要图:

从导入

 shap.waterfall_plot(说明(shap_values [0] [0]，ke.expected_value [0])) 

现在可以添加概率空间中的shap值，并且与第0个数据点的基本概率(请参见上文)和预测概率都很好地吻合:

  clf.predict_proba(masker.data [0] .reshape(1，-1))数组([[2.2844513e-04，8.1287889e-04，6.5225776e-04，9.9737883e-01，9.2762709e-04]]，dtype = float32) 

I am using shap library for ML interpretability to better understand k-means segmentation algorithm clusters. In a nutshell I make some blogs, use k-means to cluster them and then take the clusters as label and xgboost to try to predict them. I have 5 clusters so it is a signle-label multi-class classification problem.

import numpy as np
from sklearn.datasets import make_blobs
import pandas as pd
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import KMeans 
import xgboost as xgb
import shap

X, y = make_blobs(n_samples=500, centers=5, n_features=5, random_state=0)
data = pd.DataFrame(np.concatenate((X, y.reshape(500,1)), axis=1), columns=['var_1', 'var_2', 'var_3', 'var_4', 'var_5', 'cluster_id'])
data['cluster_id'] = data['cluster_id'].astype(int).astype(str)
scaler = StandardScaler()
scaled_features = scaler.fit_transform(data.iloc[:,:-1])
kmeans = KMeans(n_clusters=5, **kmeans_kwargs)
kmeans.fit(scaled_features)
data['predicted_cluster_id'] = kmeans.labels_.astype(int).astype(str)
clf = xgb.XGBClassifier()
clf.fit(scaled_data.iloc[:,:-1], scaled_data['predicted_cluster_id'])
shap.initjs()
explainer = shap.TreeExplainer(clf)
shap_values = explainer.shap_values(scaled_data.iloc[0,:-1].values.reshape(1,-1))
shap.force_plot(explainer.expected_value[0], shap_values[0], link='logit')  # repeat changing 0 for i in range(0, 5)

The pictures above make sense as the class is '3'. But why this base_value, shouldn't it be 1/5? I asked myself a while ago a similar question but this time I set already link='logit'.

解决方案

link="logit" does not seem right for multiclass, as it's only suitable for binary output. This is why you do not see probabilities summing up to 1.

Let's streamline your code:

import numpy as np
from sklearn.datasets import make_blobs
import pandas as pd
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import KMeans 
import xgboost as xgb
import shap
from scipy.special import softmax, logit, expit
np.random.seed(42)

X, y_true = make_blobs(n_samples=500, centers=5, n_features=3, random_state=0)
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)
kmeans = KMeans(n_clusters=5)
y_predicted = kmeans.fit_predict(X_scaled, )

clf = xgb.XGBClassifier()
clf.fit(X_scaled, y_predicted)
shap.initjs()

Then, what you see as expected values in:

explainer = shap.TreeExplainer(clf)
explainer.expected_value
array([0.67111245, 0.60223354, 0.53357694, 0.50821152, 0.50145331])

are base scores in raw space.

The multi-class raw scores can be converted to probabilities with softmax:

softmax(explainer.expected_value)
array([0.22229282, 0.20749694, 0.19372895, 0.18887673, 0.18760457])

shap.force_plot(..., link="logit") doesn't make sense for multiclass, and it seems impossible to switch from raw to probability and still maintain additivity (because softmax(x+y) ≠ softmax(x) + softmax(y)).

Should you wish to analyze your data in probability space try KernelExplainer:

from shap import KernelExplainer
masker = shap.maskers.Independent(X_scaled, 100)
ke = KernelExplainer(clf.predict_proba, data=masker.data)
ke.expected_value
# array([0.18976762, 0.1900516 , 0.20042894, 0.19995041, 0.21980143])
shap_values=ke.shap_values(masker.data)
shap.force_plot(ke.expected_value[0], shap_values[0][0])

or summary plot:

from shap import Explanation
shap.waterfall_plot(Explanation(shap_values[0][0],ke.expected_value[0]))

which are now additive for shap values in probability space and align well with both base probabilities (see above) and predicted probabilities for 0th datapoint:

clf.predict_proba(masker.data[0].reshape(1,-1))
array([[2.2844513e-04, 8.1287889e-04, 6.5225776e-04, 9.9737883e-01,
        9.2762709e-04]], dtype=float32)

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