如何让 SGDClassifier 反映不确定性

Question

您如何让sklearn 的SGDClassifier预测显示不确定性？

我试图确认SGDClassifier将报告 50% 的输入数据的概率，这些数据不严格对应于任何标签。但是，我发现分类器始终是 100% 确定的。

我正在使用以下脚本对此进行测试：

from sklearn.linear_model import SGDClassifier

c = SGDClassifier(loss="log")
#c = SGDClassifier(loss="modified_huber")

X = [
    # always -1
    [1,0,0],
    [1,0,0],
    [1,0,0],
    [1,0,0],

    # always +1
    [0,0,1],
    [0,0,1],
    [0,0,1],
    [0,0,1],

    # uncertain
    [0,1,0],
    [0,1,0],
    [0,1,0],
    [0,1,0],
    [0,1,0],
    [0,1,0],
    [0,1,0],
    [0,1,0],
]
y = [
    -1,
    -1,
    -1,
    -1,
    +1,
    +1,
    +1,
    +1,

    -1,
    +1,
    -1,
    +1,
    -1,
    +1,
    -1,
    +1,
]

def lookup_prob_class(c, dist):
    a = sorted(zip(dist, c.classes_))
    best_prob, best_class = a[-1]
    return best_prob, best_class

c.fit(X, y)

probs = c.predict_proba(X)
print 'probs:'
for dist, true_value in zip(probs, y):
    prob, value = lookup_prob_class(c, dist)
    print '%.02f'%prob, value, true_value

如您所见，我的训练数据总是将 -1 与输入数据 [1,0,0]、+1 与 [0,0,1] 和 50/50 与 [0,1,0] 相关联。

因此，我希望结果 frompredict_proba()为输入 [0,1,0] 返回 0.5。但相反，它报告的概率为 100%。这是为什么，我该如何解决？

有趣的是，换出SGDClassifier的DecisionTreeClassifier或RandomForestClassifier不生产我期望的输出。

Answer 1

它确实显示出一些不确定性：

>>> c.predict_proba(X)
array([[  9.97254333e-01,   2.74566740e-03],
       [  9.97254333e-01,   2.74566740e-03],
       [  9.97254333e-01,   2.74566740e-03],
       [  9.97254333e-01,   2.74566740e-03],
       [  1.61231111e-06,   9.99998388e-01],
       [  1.61231111e-06,   9.99998388e-01],
       [  1.61231111e-06,   9.99998388e-01],
       [  1.61231111e-06,   9.99998388e-01],
       [  1.24171982e-04,   9.99875828e-01],
       [  1.24171982e-04,   9.99875828e-01],
       [  1.24171982e-04,   9.99875828e-01],
       [  1.24171982e-04,   9.99875828e-01],
       [  1.24171982e-04,   9.99875828e-01],
       [  1.24171982e-04,   9.99875828e-01],
       [  1.24171982e-04,   9.99875828e-01],
       [  1.24171982e-04,   9.99875828e-01]])

如果您希望模型更不确定，则必须对其进行更强的正则化。这是通过调整alpha参数来完成的：

>>> c = SGDClassifier(loss="log", alpha=1)
>>> c.fit(X, y)
SGDClassifier(alpha=1, class_weight=None, epsilon=0.1, eta0=0.0,
       fit_intercept=True, l1_ratio=0.15, learning_rate='optimal',
       loss='log', n_iter=5, n_jobs=1, penalty='l2', power_t=0.5,
       random_state=None, shuffle=False, verbose=0, warm_start=False)
>>> c.predict_proba(X)
array([[ 0.58782817,  0.41217183],
       [ 0.58782817,  0.41217183],
       [ 0.58782817,  0.41217183],
       [ 0.58782817,  0.41217183],
       [ 0.53000442,  0.46999558],
       [ 0.53000442,  0.46999558],
       [ 0.53000442,  0.46999558],
       [ 0.53000442,  0.46999558],
       [ 0.55579239,  0.44420761],
       [ 0.55579239,  0.44420761],
       [ 0.55579239,  0.44420761],
       [ 0.55579239,  0.44420761],
       [ 0.55579239,  0.44420761],
       [ 0.55579239,  0.44420761],
       [ 0.55579239,  0.44420761],
       [ 0.55579239,  0.44420761]])

alpha是对高特征权重的惩罚，因此 越高alpha，允许权重增长越少，线性模型值变得越不极端，逻辑概率估计越接近 ½。通常，此参数使用交叉验证进行调整。