示例#1
0
def test_scaler_without_centering():
    rng = np.random.RandomState(42)
    X = rng.randn(4, 5)
    X[:, 0] = 0.0  # first feature is always of zero
    X_csr = sparse.csr_matrix(X)
    X_csc = sparse.csc_matrix(X)

    assert_raises(ValueError, StandardScaler().fit, X_csr)

    null_transform = StandardScaler(with_mean=False, with_std=False, copy=True)
    X_null = null_transform.fit_transform(X_csr)
    assert_array_equal(X_null.data, X_csr.data)
    X_orig = null_transform.inverse_transform(X_null)
    assert_array_equal(X_orig.data, X_csr.data)

    scaler = StandardScaler(with_mean=False).fit(X)
    X_scaled = scaler.transform(X, copy=True)
    assert_false(np.any(np.isnan(X_scaled)))

    scaler_csr = StandardScaler(with_mean=False).fit(X_csr)
    X_csr_scaled = scaler_csr.transform(X_csr, copy=True)
    assert_false(np.any(np.isnan(X_csr_scaled.data)))

    scaler_csc = StandardScaler(with_mean=False).fit(X_csc)
    X_csc_scaled = scaler_csr.transform(X_csc, copy=True)
    assert_false(np.any(np.isnan(X_csc_scaled.data)))

    assert_equal(scaler.mean_, scaler_csr.mean_)
    assert_array_almost_equal(scaler.std_, scaler_csr.std_)

    assert_equal(scaler.mean_, scaler_csc.mean_)
    assert_array_almost_equal(scaler.std_, scaler_csc.std_)

    assert_array_almost_equal(X_scaled.mean(axis=0),
                              [0., -0.01, 2.24, -0.35, -0.78], 2)
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])

    X_csr_scaled_mean, X_csr_scaled_std = mean_variance_axis0(X_csr_scaled)
    assert_array_almost_equal(X_csr_scaled_mean, X_scaled.mean(axis=0))
    assert_array_almost_equal(X_csr_scaled_std, X_scaled.std(axis=0))

    # Check that X has not been modified (copy)
    assert_true(X_scaled is not X)
    assert_true(X_csr_scaled is not X_csr)

    X_scaled_back = scaler.inverse_transform(X_scaled)
    assert_true(X_scaled_back is not X)
    assert_true(X_scaled_back is not X_scaled)
    assert_array_almost_equal(X_scaled_back, X)

    X_csr_scaled_back = scaler_csr.inverse_transform(X_csr_scaled)
    assert_true(X_csr_scaled_back is not X_csr)
    assert_true(X_csr_scaled_back is not X_csr_scaled)
    assert_array_almost_equal(X_csr_scaled_back.toarray(), X)

    X_csc_scaled_back = scaler_csr.inverse_transform(X_csc_scaled.tocsc())
    assert_true(X_csc_scaled_back is not X_csc)
    assert_true(X_csc_scaled_back is not X_csc_scaled)
    assert_array_almost_equal(X_csc_scaled_back.toarray(), X)
示例#2
0
def test_scaler_without_centering():
    rng = np.random.RandomState(42)
    X = rng.randn(4, 5)
    X[:, 0] = 0.0  # first feature is always of zero
    X_csr = sparse.csr_matrix(X)
    X_csc = sparse.csc_matrix(X)

    assert_raises(ValueError, StandardScaler().fit, X_csr)

    null_transform = StandardScaler(with_mean=False, with_std=False, copy=True)
    X_null = null_transform.fit_transform(X_csr)
    assert_array_equal(X_null.data, X_csr.data)
    X_orig = null_transform.inverse_transform(X_null)
    assert_array_equal(X_orig.data, X_csr.data)

    scaler = StandardScaler(with_mean=False).fit(X)
    X_scaled = scaler.transform(X, copy=True)
    assert_false(np.any(np.isnan(X_scaled)))

    scaler_csr = StandardScaler(with_mean=False).fit(X_csr)
    X_csr_scaled = scaler_csr.transform(X_csr, copy=True)
    assert_false(np.any(np.isnan(X_csr_scaled.data)))

    scaler_csc = StandardScaler(with_mean=False).fit(X_csc)
    X_csc_scaled = scaler_csr.transform(X_csc, copy=True)
    assert_false(np.any(np.isnan(X_csc_scaled.data)))

    assert_equal(scaler.mean_, scaler_csr.mean_)
    assert_array_almost_equal(scaler.std_, scaler_csr.std_)

    assert_equal(scaler.mean_, scaler_csc.mean_)
    assert_array_almost_equal(scaler.std_, scaler_csc.std_)

    assert_array_almost_equal(
        X_scaled.mean(axis=0), [0., -0.01, 2.24, -0.35, -0.78], 2)
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])

    X_csr_scaled_mean, X_csr_scaled_std = mean_variance_axis0(X_csr_scaled)
    assert_array_almost_equal(X_csr_scaled_mean, X_scaled.mean(axis=0))
    assert_array_almost_equal(X_csr_scaled_std, X_scaled.std(axis=0))

    # Check that X has not been modified (copy)
    assert_true(X_scaled is not X)
    assert_true(X_csr_scaled is not X_csr)

    X_scaled_back = scaler.inverse_transform(X_scaled)
    assert_true(X_scaled_back is not X)
    assert_true(X_scaled_back is not X_scaled)
    assert_array_almost_equal(X_scaled_back, X)

    X_csr_scaled_back = scaler_csr.inverse_transform(X_csr_scaled)
    assert_true(X_csr_scaled_back is not X_csr)
    assert_true(X_csr_scaled_back is not X_csr_scaled)
    assert_array_almost_equal(X_csr_scaled_back.toarray(), X)

    X_csc_scaled_back = scaler_csr.inverse_transform(X_csc_scaled.tocsc())
    assert_true(X_csc_scaled_back is not X_csc)
    assert_true(X_csc_scaled_back is not X_csc_scaled)
    assert_array_almost_equal(X_csc_scaled_back.toarray(), X)
示例#3
0
def test_scaler_1d():
    """Test scaling of dataset along single axis"""
    rng = np.random.RandomState(0)
    X = rng.randn(5)
    X_orig_copy = X.copy()

    scaler = StandardScaler()
    X_scaled = scaler.fit(X).transform(X, copy=False)
    assert_array_almost_equal(X_scaled.mean(axis=0), 0.0)
    assert_array_almost_equal(X_scaled.std(axis=0), 1.0)

    # check inverse transform
    X_scaled_back = scaler.inverse_transform(X_scaled)
    assert_array_almost_equal(X_scaled_back, X_orig_copy)

    # Test with 1D list
    X = [0., 1., 2, 0.4, 1.]
    scaler = StandardScaler()
    X_scaled = scaler.fit(X).transform(X, copy=False)
    assert_array_almost_equal(X_scaled.mean(axis=0), 0.0)
    assert_array_almost_equal(X_scaled.std(axis=0), 1.0)

    X_scaled = scale(X)
    assert_array_almost_equal(X_scaled.mean(axis=0), 0.0)
    assert_array_almost_equal(X_scaled.std(axis=0), 1.0)
示例#4
0
def test_scaler_1d():
    """Test scaling of dataset along single axis"""
    rng = np.random.RandomState(0)
    X = rng.randn(5)
    X_orig_copy = X.copy()

    scaler = StandardScaler()
    X_scaled = scaler.fit(X).transform(X, copy=False)
    assert_array_almost_equal(X_scaled.mean(axis=0), 0.0)
    assert_array_almost_equal(X_scaled.std(axis=0), 1.0)

    # check inverse transform
    X_scaled_back = scaler.inverse_transform(X_scaled)
    assert_array_almost_equal(X_scaled_back, X_orig_copy)

    # Test with 1D list
    X = [0., 1., 2, 0.4, 1.]
    scaler = StandardScaler()
    X_scaled = scaler.fit(X).transform(X, copy=False)
    assert_array_almost_equal(X_scaled.mean(axis=0), 0.0)
    assert_array_almost_equal(X_scaled.std(axis=0), 1.0)

    X_scaled = scale(X)
    assert_array_almost_equal(X_scaled.mean(axis=0), 0.0)
    assert_array_almost_equal(X_scaled.std(axis=0), 1.0)

    X = np.ones(5)
    assert_array_equal(scale(X, with_mean=False), X)
示例#5
0
def evalOne(parameters):
    all_obs = []
    all_pred = []
    for location in locations:
        trainX, testX, trainY, testY = splitDataForXValidation(location, "location", data, all_features, "target")
        normalizer_X = StandardScaler()
        trainX = normalizer_X.fit_transform(trainX)
        testX = normalizer_X.transform(testX)
        normalizer_Y = StandardScaler()
        trainY = normalizer_Y.fit_transform(trainY)
        testY = normalizer_Y.transform(testY)
        model = BaggingRegressor(base_estimator=SVR(kernel='rbf', C=parameters["C"], cache_size=5000), max_samples=parameters["max_samples"],n_estimators=parameters["n_estimators"], verbose=0, n_jobs=-1)
        model.fit(trainX, trainY)
        prediction = model.predict(testX)
        prediction = normalizer_Y.inverse_transform(prediction)
        testY = normalizer_Y.inverse_transform(testY)
        all_obs.extend(testY)
        all_pred.extend(prediction)
        
    return rmseEval(all_obs, all_pred)[1]
示例#6
0
def evalOne(parameters):
    all_obs = []
    all_pred = []
    for location in locations:
        trainX, testX, trainY, testY = splitDataForXValidation(
            location, "location", data, all_features, "target")
        normalizer_X = StandardScaler()
        trainX = normalizer_X.fit_transform(trainX)
        testX = normalizer_X.transform(testX)
        normalizer_Y = StandardScaler()
        trainY = normalizer_Y.fit_transform(trainY)
        testY = normalizer_Y.transform(testY)

        layers = []
        for _ in range(0, parameters["hidden_layers"]):
            layers.append(
                Layer(parameters["hidden_type"],
                      units=parameters["hidden_neurons"]))
        layers.append(Layer("Linear"))
        model = Regressor(layers=layers,
                          learning_rate=parameters["learning_rate"],
                          n_iter=parameters["iteration"],
                          random_state=42)

        X = np.array(trainX)
        y = np.array(trainY)

        model.fit(X, y)

        model.fit(trainX, trainY)
        prediction = model.predict(testX)
        prediction = normalizer_Y.inverse_transform(prediction)
        testY = normalizer_Y.inverse_transform(testY)

        print("location: " + str(location) + " -> " +
              str(rmseEval(prediction, testY)[1]))

        all_obs.extend(testY)
        all_pred.extend(prediction)

    return rmseEval(all_obs, all_pred)[1]
示例#7
0
def test_scaler_2d_arrays():
    """Test scaling of 2d array along first axis"""
    rng = np.random.RandomState(0)
    X = rng.randn(4, 5)
    X[:, 0] = 0.0  # first feature is always of zero

    scaler = StandardScaler()
    X_scaled = scaler.fit(X).transform(X, copy=True)
    assert_false(np.any(np.isnan(X_scaled)))

    assert_array_almost_equal(X_scaled.mean(axis=0), 5 * [0.0])
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
    # Check that X has been copied
    assert_true(X_scaled is not X)

    # check inverse transform
    X_scaled_back = scaler.inverse_transform(X_scaled)
    assert_true(X_scaled_back is not X)
    assert_true(X_scaled_back is not X_scaled)
    assert_array_almost_equal(X_scaled_back, X)

    X_scaled = scale(X, axis=1, with_std=False)
    assert_false(np.any(np.isnan(X_scaled)))
    assert_array_almost_equal(X_scaled.mean(axis=1), 4 * [0.0])
    X_scaled = scale(X, axis=1, with_std=True)
    assert_false(np.any(np.isnan(X_scaled)))
    assert_array_almost_equal(X_scaled.mean(axis=1), 4 * [0.0])
    assert_array_almost_equal(X_scaled.std(axis=1), 4 * [1.0])
    # Check that the data hasn't been modified
    assert_true(X_scaled is not X)

    X_scaled = scaler.fit(X).transform(X, copy=False)
    assert_false(np.any(np.isnan(X_scaled)))
    assert_array_almost_equal(X_scaled.mean(axis=0), 5 * [0.0])
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
    # Check that X has not been copied
    assert_true(X_scaled is X)

    X = rng.randn(4, 5)
    X[:, 0] = 1.0  # first feature is a constant, non zero feature
    scaler = StandardScaler()
    X_scaled = scaler.fit(X).transform(X, copy=True)
    assert_false(np.any(np.isnan(X_scaled)))
    assert_array_almost_equal(X_scaled.mean(axis=0), 5 * [0.0])
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
    # Check that X has not been copied
    assert_true(X_scaled is not X)
示例#8
0
def test_scaler_2d_arrays():
    """Test scaling of 2d array along first axis"""
    rng = np.random.RandomState(0)
    X = rng.randn(4, 5)
    X[:, 0] = 0.0  # first feature is always of zero

    scaler = StandardScaler()
    X_scaled = scaler.fit(X).transform(X, copy=True)
    assert_false(np.any(np.isnan(X_scaled)))

    assert_array_almost_equal(X_scaled.mean(axis=0), 5 * [0.0])
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
    # Check that X has been copied
    assert_true(X_scaled is not X)

    # check inverse transform
    X_scaled_back = scaler.inverse_transform(X_scaled)
    assert_true(X_scaled_back is not X)
    assert_true(X_scaled_back is not X_scaled)
    assert_array_almost_equal(X_scaled_back, X)

    X_scaled = scale(X, axis=1, with_std=False)
    assert_false(np.any(np.isnan(X_scaled)))
    assert_array_almost_equal(X_scaled.mean(axis=1), 4 * [0.0])
    X_scaled = scale(X, axis=1, with_std=True)
    assert_false(np.any(np.isnan(X_scaled)))
    assert_array_almost_equal(X_scaled.mean(axis=1), 4 * [0.0])
    assert_array_almost_equal(X_scaled.std(axis=1), 4 * [1.0])
    # Check that the data hasn't been modified
    assert_true(X_scaled is not X)

    X_scaled = scaler.fit(X).transform(X, copy=False)
    assert_false(np.any(np.isnan(X_scaled)))
    assert_array_almost_equal(X_scaled.mean(axis=0), 5 * [0.0])
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
    # Check that X has not been copied
    assert_true(X_scaled is X)

    X = rng.randn(4, 5)
    X[:, 0] = 1.0  # first feature is a constant, non zero feature
    scaler = StandardScaler()
    X_scaled = scaler.fit(X).transform(X, copy=True)
    assert_false(np.any(np.isnan(X_scaled)))
    assert_array_almost_equal(X_scaled.mean(axis=0), 5 * [0.0])
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])
    # Check that X has not been copied
    assert_true(X_scaled is not X)
示例#9
0
def predict(model: nn.Module,
            data: MoleculeDataset,
            batch_size: int,
            scaler: StandardScaler = None) -> List[List[float]]:
    """
    Makes predictions on a dataset using an ensemble of models.

    :param model: A model.
    :param data: A MoleculeDataset.
    :param batch_size: Batch size.
    :param scaler: A StandardScaler object fit on the training targets.
    :return: A list of lists of predictions. The outer list is examples
    while the inner list is tasks.
    """
    model.eval()

    preds = []

    num_iters, iter_step = len(data), batch_size

    for i in range(0, num_iters, iter_step):
        # Prepare batch
        mol_batch = MoleculeDataset(data[i:i + batch_size])
        smiles_batch, features_batch = mol_batch.smiles(), mol_batch.features()

        # Run model
        batch = smiles_batch

        with torch.no_grad():
            batch_preds = model(batch, features_batch)

        batch_preds = batch_preds.data.cpu().numpy()

        # Inverse scale if regression
        if scaler is not None:
            batch_preds = scaler.inverse_transform(batch_preds)

        # Collect vectors
        batch_preds = batch_preds.tolist()
        preds.extend(batch_preds)

    return preds
示例#10
0
def test_scaler_int():
    # test that scaler converts integer input to floating
    # for both sparse and dense matrices
    rng = np.random.RandomState(42)
    X = rng.randint(20, size=(4, 5))
    X[:, 0] = 0  # first feature is always of zero
    X_csr = sparse.csr_matrix(X)
    X_csc = sparse.csc_matrix(X)

    null_transform = StandardScaler(with_mean=False, with_std=False, copy=True)
    with warnings.catch_warnings(record=True):
        X_null = null_transform.fit_transform(X_csr)
    assert_array_equal(X_null.data, X_csr.data)
    X_orig = null_transform.inverse_transform(X_null)
    assert_array_equal(X_orig.data, X_csr.data)

    with warnings.catch_warnings(record=True):
        scaler = StandardScaler(with_mean=False).fit(X)
        X_scaled = scaler.transform(X, copy=True)
    assert_false(np.any(np.isnan(X_scaled)))

    with warnings.catch_warnings(record=True):
        scaler_csr = StandardScaler(with_mean=False).fit(X_csr)
        X_csr_scaled = scaler_csr.transform(X_csr, copy=True)
    assert_false(np.any(np.isnan(X_csr_scaled.data)))

    with warnings.catch_warnings(record=True):
        scaler_csc = StandardScaler(with_mean=False).fit(X_csc)
        X_csc_scaled = scaler_csr.transform(X_csc, copy=True)
    assert_false(np.any(np.isnan(X_csc_scaled.data)))

    assert_equal(scaler.mean_, scaler_csr.mean_)
    assert_array_almost_equal(scaler.std_, scaler_csr.std_)

    assert_equal(scaler.mean_, scaler_csc.mean_)
    assert_array_almost_equal(scaler.std_, scaler_csc.std_)

    assert_array_almost_equal(X_scaled.mean(axis=0),
                              [0., 1.109, 1.856, 21., 1.559], 2)
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])

    X_csr_scaled_mean, X_csr_scaled_std = mean_variance_axis0(
        X_csr_scaled.astype(np.float))
    assert_array_almost_equal(X_csr_scaled_mean, X_scaled.mean(axis=0))
    assert_array_almost_equal(X_csr_scaled_std, X_scaled.std(axis=0))

    # Check that X has not been modified (copy)
    assert_true(X_scaled is not X)
    assert_true(X_csr_scaled is not X_csr)

    X_scaled_back = scaler.inverse_transform(X_scaled)
    assert_true(X_scaled_back is not X)
    assert_true(X_scaled_back is not X_scaled)
    assert_array_almost_equal(X_scaled_back, X)

    X_csr_scaled_back = scaler_csr.inverse_transform(X_csr_scaled)
    assert_true(X_csr_scaled_back is not X_csr)
    assert_true(X_csr_scaled_back is not X_csr_scaled)
    assert_array_almost_equal(X_csr_scaled_back.toarray(), X)

    X_csc_scaled_back = scaler_csr.inverse_transform(X_csc_scaled.tocsc())
    assert_true(X_csc_scaled_back is not X_csc)
    assert_true(X_csc_scaled_back is not X_csc_scaled)
    assert_array_almost_equal(X_csc_scaled_back.toarray(), X)
示例#11
0
def test_scaler_int():
    # test that scaler converts integer input to floating
    # for both sparse and dense matrices
    rng = np.random.RandomState(42)
    X = rng.randint(20, size=(4, 5))
    X[:, 0] = 0  # first feature is always of zero
    X_csr = sparse.csr_matrix(X)
    X_csc = sparse.csc_matrix(X)

    null_transform = StandardScaler(with_mean=False, with_std=False, copy=True)
    with warnings.catch_warnings(record=True):
        X_null = null_transform.fit_transform(X_csr)
    assert_array_equal(X_null.data, X_csr.data)
    X_orig = null_transform.inverse_transform(X_null)
    assert_array_equal(X_orig.data, X_csr.data)

    with warnings.catch_warnings(record=True):
        scaler = StandardScaler(with_mean=False).fit(X)
        X_scaled = scaler.transform(X, copy=True)
    assert_false(np.any(np.isnan(X_scaled)))

    with warnings.catch_warnings(record=True):
        scaler_csr = StandardScaler(with_mean=False).fit(X_csr)
        X_csr_scaled = scaler_csr.transform(X_csr, copy=True)
    assert_false(np.any(np.isnan(X_csr_scaled.data)))

    with warnings.catch_warnings(record=True):
        scaler_csc = StandardScaler(with_mean=False).fit(X_csc)
        X_csc_scaled = scaler_csr.transform(X_csc, copy=True)
    assert_false(np.any(np.isnan(X_csc_scaled.data)))

    assert_equal(scaler.mean_, scaler_csr.mean_)
    assert_array_almost_equal(scaler.std_, scaler_csr.std_)

    assert_equal(scaler.mean_, scaler_csc.mean_)
    assert_array_almost_equal(scaler.std_, scaler_csc.std_)

    assert_array_almost_equal(
        X_scaled.mean(axis=0),
        [0., 1.109, 1.856, 21., 1.559], 2)
    assert_array_almost_equal(X_scaled.std(axis=0), [0., 1., 1., 1., 1.])

    X_csr_scaled_mean, X_csr_scaled_std = mean_variance_axis0(
        X_csr_scaled.astype(np.float))
    assert_array_almost_equal(X_csr_scaled_mean, X_scaled.mean(axis=0))
    assert_array_almost_equal(X_csr_scaled_std, X_scaled.std(axis=0))

    # Check that X has not been modified (copy)
    assert_true(X_scaled is not X)
    assert_true(X_csr_scaled is not X_csr)

    X_scaled_back = scaler.inverse_transform(X_scaled)
    assert_true(X_scaled_back is not X)
    assert_true(X_scaled_back is not X_scaled)
    assert_array_almost_equal(X_scaled_back, X)

    X_csr_scaled_back = scaler_csr.inverse_transform(X_csr_scaled)
    assert_true(X_csr_scaled_back is not X_csr)
    assert_true(X_csr_scaled_back is not X_csr_scaled)
    assert_array_almost_equal(X_csr_scaled_back.toarray(), X)

    X_csc_scaled_back = scaler_csr.inverse_transform(X_csc_scaled.tocsc())
    assert_true(X_csc_scaled_back is not X_csc)
    assert_true(X_csc_scaled_back is not X_csc_scaled)
    assert_array_almost_equal(X_csc_scaled_back.toarray(), X)
示例#12
0
    print(str(location))
    trainX, testX, trainY, testY = splitDataForXValidation(
        location, "location", data, all_features, "target")
    normalizer_X = StandardScaler()
    trainX = normalizer_X.fit_transform(trainX)
    testX = normalizer_X.transform(testX)
    normalizer_Y = StandardScaler()
    trainY = normalizer_Y.fit_transform(trainY)
    testY = normalizer_Y.transform(testY)
    model = BaggingRegressor(base_estimator=SVR(kernel='rbf',
                                                C=40,
                                                cache_size=5000),
                             max_samples=4200,
                             n_estimators=10,
                             verbose=0,
                             n_jobs=-1)
    model.fit(trainX, trainY)
    prediction = model.predict(testX)
    prediction = normalizer_Y.inverse_transform(prediction)
    testY = normalizer_Y.inverse_transform(testY)

    for i in range(0, len(testY)):
        output.write(str(location))
        output.write(",")
        output.write(str(testY[i]))
        output.write(",")
        output.write(str(prediction[i]))
        output.write("\n")

output.close()
示例#13
0
X2 = [[float(x) / 10.0, float(x) / 10.0,
       float(x) / 10.0] for x in range(0, 231)]

layers = []
layers.append(Layer("Rectifier", units=100))
layers.append(Layer("Rectifier", units=100))
layers.append(Layer("Rectifier", units=100))
layers.append(Layer("Linear"))

model = Regressor(layers=layers,
                  learning_rate=0.001,
                  n_iter=5000,
                  random_state=42)

normalizer_X = StandardScaler()
trainX = normalizer_X.fit_transform(X)
trainX2 = normalizer_X.fit_transform(X2)
normalizer_Y = StandardScaler()
trainY = normalizer_Y.fit_transform(Y)

model.fit(np.array(trainX), np.array(trainY))
Y_pred = model.predict(np.array(trainX2))
Y_pred = normalizer_Y.inverse_transform(Y_pred)

Y_pred = [y[0] for y in Y_pred]

print(str(Y_pred))

plot2(Y, Y_pred, OUTPUT_PNG_FILE, "Observed pollution concentration levels",
      "Predicted pollution concentration levels by ANR")