模型的可区分性可解释性 What Can We Learn From the Future of Explainable AI?

    import numpy as np
    from sklearn import tree
    import matplotlib.pyplot as plt
    
    def generate_data():
    # 生成数据
    X = [[0,0],[0,1],[1,0],[1,1]]
    y = [0,1,1,0]
    
    return X,y
    
    
    def train_model(X,y):
    # 用训练集训练模型
    clf = tree.DecisionTreeClassifier()
    clf.fit(X,y)
    
    return clf
    
    
    def predict_result(clf, X):
    # 对测试集进行预测
    pred_y = clf.predict(X)
    
    return pred_y
    
    
    def calculate_label_pdf(y):
    # 根据标签生成标签的概率密度函数
    pdf = []
    for label in set(y):
        count = sum([1 if _ == label else 0 for _ in y])
        proba = count/len(y)
        pdf.append((proba))
        
    return dict(zip(set(y), pdf))
    
    
    def calculate_feature_dependence(X,y):
    # 计算特征的依赖关系
    dependence = {}
    for feature in range(X.shape[1]):
        d = {value:sum([(1 if (i[feature], value) == tuple(x[:-1]) and x[-1]==j else 0)
                        for i in zip(X[:,feature],y)]) / len(y)
             for value in set(X[:,feature])}
        
        dependence[feature] = d
        
    return dependence
    
    
    def calculate_variance_contribution(X, y):
    # 计算特征方差贡献量
    mean_y = np.mean(y)
    variance = np.var(y)
    
    contribution = [(np.var([_[0][0], _[1]]) - variance)/variance*len(_)
                    for _ in zip(X,y)]
    
    return sorted(range(len(contribution)), key=lambda k: contribution[k])[::-1]
    
    
    def select_important_features(X, y, threshold=0.9):
    # 从所有特征中选出重要性最高的threshold%的特征
    important_features = [calculate_variance_contribution(_, y)[-int(len(_)*threshold):]
                          for _ in X.T]
    
    return list(itertools.chain(*important_features))
    
    
    if __name__=="__main__":
    X, y = generate_data()
    clf = train_model(X, y)
    
    global_interp_graph = {}
    
    # 生成全局解释图
    pdf = calculate_label_pdf(y)
    global_interp_graph['Label'] = pdf
    
    dependence = calculate_feature_dependence(X, y)
    
    features = [_ for _ in range(X.shape[1])]
    global_interp_graph['Features'] = dependence
    
    important_features = select_important_features(X, y)
    print("Important Features:", important_features)
    
    for fidx in important_features:
        local_interp_graph = {'Feature':{}, 'Dependence':{}}
        
        # 生成局部解释图
        pdfs = [{_:pdf[_]} for _ in pdf]
        local_interp_graph['Label'] = pdfs
    
        values = {_:_ for _ in set(X[:,fidx])}
        local_interp_graph['Values'] = values
        
        dd = {_:[d[(v, _)] for v in values]
              for _ in dependence[fidx].keys()}
        local_interp_graph['Feature'] = dd
        
        global_interp_graph['Feature'][fidx] = local_interp_graph
        
        
    discriminative_graph = {}
    
    for fidx in important_features:
        dg = nx.Graph()
        dg.add_nodes_from(['Label', 'Values'])
        
        # 生成可区分性图
        dg.add_edges_from([('Label', _)
                           for _ in global_interp_graph['Label'].values()])
        
        dg.add_edges_from([(('Values', v), ('Feature', fidx, _, c))
                            for (_,c) in enumerate(global_interp_graph['Feature'][fidx]['Values'].items()) 
                            for v in c[1]])
        
        dg.add_edges_from([(('Feature', fidx, a, b), ('Feature', fidx, b, a))
                            for a,b in itertools.combinations(global_interp_graph['Feature'][fidx]['Values'], r=2)])
        
        dgpos = graphviz_layout(dg, prog='dot')
        pos = {}
        for n in dgpos:
            pos[n[:2]] = dgpos[n] + (random.uniform(-0.05,0.05), random.uniform(-0.05,0.05))
        
        nx.draw(dg, pos=pos, with_labels=True, font_weight='bold')
        plt.show()
        
        discriminative_graph[fidx] = dg
    
    fig = plt.figure(figsize=(16, 10))
    gs = gridspec.GridSpec(nrows=2, ncols=2, width_ratios=[1, 1], height_ratios=[1, 1])
    
    ax1 = plt.subplot(gs[0,:])
    nx.draw(discriminative_graph[0], ax=ax1, node_size=500, node_color=['r' if _=='Label' else '#A0CBE2' for _ in discriminative_graph[0]], alpha=0.8)
    plt.title('Discriminative Graph of Feature 0')
    
    ax2 = plt.subplot(gs[1,0])
    nx.draw(discriminative_graph[1], ax=ax2, node_size=500, node_color=['r' if _=='Label' else '#A0CBE2' for _ in discriminative_graph[1]], alpha=0.8)
    plt.title('Discriminative Graph of Feature 1')
    
    ax3 = plt.subplot(gs[1,1])
    nx.draw(discriminative_graph[2], ax=ax3, node_size=500, node_color=['r' if _=='Label' else '#A0CBE2' for _ in discriminative_graph[2]], alpha=0.8)
    plt.title('Discriminative Graph of Feature 2')
    
    fig.suptitle('DCE Result', fontsize=20)
    plt.show()