我试图将一个关于房价的Keras教程改编用于评估棋盘游戏的位置。然而，问题在于棋盘游戏的位置是二维的，这让Keras报错。

以下是一些基于教程的代码，用于处理从线性方程生成的虚拟数据。

import numpy as npfrom keras.models import Sequentialfrom keras.layers import Densefrom keras.wrappers.scikit_learn import KerasRegressorfrom sklearn.model_selection import cross_val_scorefrom sklearn.model_selection import KFold# fix random seed for reproducibilityseed = 1np.random.seed(seed)# Generate dataset with linear outputs.sample_count = 1000column_count = 5X = np.random.uniform(size=sample_count * column_count)X.shape = (sample_count, column_count)Y = 2*X[:, 0] + X[:, 1] + X[:, 2] + 11*X[:, 3] + 3*X[:, 4]# define base modeldef baseline_model():    # create model    model = Sequential()    model.add(Dense(column_count * 2,                    input_dim=column_count,                    kernel_initializer='normal',                    activation='relu'))    model.add(Dense(1, kernel_initializer='normal'))    # Compile model    model.compile(loss='mean_squared_error', optimizer='adam')    return model# evaluate model with standardized datasetestimator = KerasRegressor(build_fn=baseline_model, epochs=100, batch_size=5, verbose=0)kfold = KFold(n_splits=10, random_state=seed)results = cross_val_score(estimator, X, Y, cv=kfold)print("Results: %.2f (%.2f) MSE" % (results.mean(), results.std()))estimator.fit(X, Y)test_samples = np.identity(column_count)predictions = estimator.predict(test_samples)print(predictions)

这些代码运行得很好，但在尝试使用等效的二维数据时就出现了问题。以下是二维数据的代码：

当我运行这段代码时，得到以下错误：

Traceback (most recent call last):  File "/home/don/PycharmProjects/ml_tutorial/ml_tutorial/run_linear2.py", line 40, in <module>    results = cross_val_score(estimator, X, Y, cv=kfold)  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/model_selection/_validation.py", line 402, in cross_val_score    error_score=error_score)  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/model_selection/_validation.py", line 240, in cross_validate    for train, test in cv.split(X, y, groups))  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/externals/joblib/parallel.py", line 917, in __call__    if self.dispatch_one_batch(iterator):  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/externals/joblib/parallel.py", line 759, in dispatch_one_batch    self._dispatch(tasks)  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/externals/joblib/parallel.py", line 716, in _dispatch    job = self._backend.apply_async(batch, callback=cb)  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/externals/joblib/_parallel_backends.py", line 182, in apply_async    result = ImmediateResult(func)  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/externals/joblib/_parallel_backends.py", line 549, in __init__    self.results = batch()  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/externals/joblib/parallel.py", line 225, in __call__    for func, args, kwargs in self.items]  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/externals/joblib/parallel.py", line 225, in <listcomp>    for func, args, kwargs in self.items]  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/sklearn/model_selection/_validation.py", line 528, in _fit_and_score    estimator.fit(X_train, y_train, **fit_params)  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/keras/wrappers/scikit_learn.py", line 152, in fit    history = self.model.fit(x, y, **fit_args)  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/keras/engine/training.py", line 952, in fit    batch_size=batch_size)  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/keras/engine/training.py", line 789, in _standardize_user_data    exception_prefix='target')  File "/home/don/.local/share/virtualenvs/ml_tutorial-3a_885qf/lib/python3.6/site-packages/keras/engine/training_utils.py", line 128, in standardize_input_data    'with shape ' + str(data_shape))ValueError: Error when checking target: expected dense_2 to have 3 dimensions, but got array with shape (900, 1)

我该如何说服模型接受二维输入呢？

回答：

根据一个类似的讨论在GitHub问题中，你可以简单地添加一个Flatten()层来降低输入维度。

我想我可能还需要使用其他层，比如Conv2D，来真正利用二维关系，但这已经让我避免了错误。