高斯朴素贝叶斯零概率问题

Question

class NaiveBayes():
    def __init__(self):
        self.summaries = dict()

    def fit(self, x_train, y_train):
        self.total_sample = len(x_train)
        classes = self.group_by_class(x_train, y_train)
        for class_value, rows in classes.items():
            rows = np.array(rows)
            std_of_columns = np.std(rows, axis=0)
            mean_of_columns = np.mean(rows, axis=0)
            number_of_instance = len(rows)
            self.summaries[class_value] = (std_of_columns, mean_of_columns, number_of_instance)

    def predict_sample(self, sample_to_be_predicted):
        predictions = np.zeros(len(sample_to_be_predicted))
        for i in range(len(sample_to_be_predicted)):
            predictions[i] = self.predict(sample_to_be_predicted[i])

    def predict(self, instance_to_be_predicted):
        probabilities = self.compute_probabilities(instance_to_be_predicted)
        prediction = self.classify(probabilities)
        return prediction

    def compute_probabilities(self, instance_to_be_predicted):
        probabilities = dict()
        for label in self.summaries:
            std_of_columns, mean_of_columns, number_of_instance = self.summaries[label]
            probabilities[label] = math.log(number_of_instance / self.total_sample)
            for feature, mean, std in zip(instance_to_be_predicted, mean_of_columns, std_of_columns):
                probabilities[label] += math.log(self.calculate_probability(feature, mean, std))
            probabilities[label] = exp(probabilities[label])
        return probabilities

    def classify(self, probabilities):
        best_label = max(probabilities, key=probabilities.get)
        return best_label

    def group_by_class(self, x_train, y_train):
        classes = dict()
        for i, j in zip(y_train, x_train):
            if i not in classes:
                classes[i] = [j]
            else:
                classes[i].append(j)
        return classes

    def calculate_probability(self, feature, mean, stdev):
        exponent = exp(-((feature - mean) ** 2 / (2 * stdev ** 2)))
        return (1 / (sqrt(2 * pi) * stdev)) * exponent

我正在尝试使用在calculate_probability 函数中发生的高斯分布函数来实现朴素贝叶斯。但是，如果正在计算的类的 std 为零，我将获得 NaN 值。如果“-((feature - mean) ** 2 / (2 * stdev ** 2))”（calculate_probability 中表达式的一部分）太大，我得到的概率为 0，因为它导致 (e ^ -huge_number) 评估为 0。我到处钻研，但找不到解决方案。拉普拉斯平滑是不可行的，因为我们正在以一种非常不同的方式进行跟踪。那么，我如何才能在要预测的实例中修复为特征（维度）计算为 0 或 NaN 的概率？