现在我们已经有了多个 ALS 模型，每个模型使用了一组不同的超参数。我们可以在 msd 数据集的训练集部分上进行交叉验证训练，然后在测试集上运行并用之前介绍的 ROEM 函数评估每个模型的表现。不幸的是，这个过程在本练习中会花费太多时间，因此我们已为您单独完成。作为参考，您可以使用下面的循环来评估您的 model_list（这里使用的是 msd 数据集）：

# Split the data into training and test sets
(training, test) = msd.randomSplit([0.8, 0.2])

#Building 5 folds within the training set.
train1, train2, train3, train4, train5 = training.randomSplit([0.2, 0.2, 0.2, 0.2, 0.2], seed = 1)
fold1 = train2.union(train3).union(train4).union(train5)
fold2 = train3.union(train4).union(train5).union(train1)
fold3 = train4.union(train5).union(train1).union(train2)
fold4 = train5.union(train1).union(train2).union(train3)
fold5 = train1.union(train2).union(train3).union(train4)

foldlist = [(fold1, train1), (fold2, train2), (fold3, train3), (fold4, train4), (fold5, train5)]

# Empty list to fill with ROEMs from each model
ROEMS = []

# Loops through all models and all folds
for model in model_list:
    for ft_pair in foldlist:

        # Fits model to fold within training data
        fitted_model = model.fit(ft_pair[0])

        # Generates predictions using fitted_model on respective CV test data
        predictions = fitted_model.transform(ft_pair[1])

        # Generates and prints a ROEM metric CV test data
        r = ROEM(predictions)
        print ("ROEM: ", r)

    # Fits model to all of training data and generates preds for test data
    v_fitted_model = model.fit(training)
    v_predictions = v_fitted_model.transform(test)
    v_ROEM = ROEM(v_predictions)

    # Adds validation ROEM to ROEM list
    ROEMS.append(v_ROEM)
    print ("Validation ROEM: ", v_ROEM)

为便于演示步骤，我们已经为 192 个模型生成了测试集预测，并计算了各自的 ROEM。这些结果已放在提供的 ROEMS 列表中。由于列表并非 Pyspark 独有结构，而 numpy 处理列表非常方便，我们这里将使用 numpy。请按照下方说明，找出最佳的 ROEM 以及对应的模型索引。

Million Songs 数据集简介

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