示例#1
0
def forward_selection(max_features, X_train, y_train):
    ordered_features = []
    ordered_scores = []
    # Start with no features.
    selected_features = []
    learner = TemporalRegressionAlgorithms()
    eval = RegressionEvaluation()
    prev_best_perf = sys.float_info.max

    # Select the appropriate number of features.
    for i in range(0, max_features):
        print i
        #Determine the features left to select.
        features_left = list(set(X_train.columns) - set(selected_features))
        best_perf = sys.float_info.max
        best_feature = ''

        # For all features we can still select...
        for f in features_left:
            temp_selected_features = copy.deepcopy(selected_features)
            temp_selected_features.append(f)
            # Determine the mse of a decision tree learner if we were to add
            # the feature.
            regr_train_y, regr_test_y = learner.recurrent_neural_network(
                X_train, y_train, X_train, y_train, gridsearch=False)

            perf, std_tr = eval.mean_squared_error_with_std(
                train_y.ix[10:, ], regr_train_y.ix[10:, ])

            # If the performance is better than what we have seen so far (we aim for low mse)
            # we set the current feature to the best feature and the same for the best performance.
            if perf < best_perf:
                best_perf = perf
                best_feature = f
    # We select the feature with the best performance.
        selected_features.append(best_feature)
        prev_best_perf = best_perf
        ordered_features.append(best_feature)
        ordered_scores.append(best_perf)
    return selected_features, ordered_features, ordered_scores
def main():
    # Read the result from the previous chapter and convert the index to datetime
    try:
        dataset = pd.read_csv(DATA_PATH / DATASET_FILENAME, index_col=0)
        dataset.index = pd.to_datetime(dataset.index)
    except IOError as e:
        print('File not found, try to run previous crowdsignals scripts first!')
        raise e

    # Create an instance of visualization class to plot the results
    DataViz = VisualizeDataset(__file__)

    # Consider the second task, namely the prediction of the heart rate. Therefore create a dataset with the heart
    # rate as target and split using timestamps, because this is considered as a temporal task.
    print('\n- - - Loading dataset - - -')
    prepare = PrepareDatasetForLearning()
    learner = RegressionAlgorithms()
    evaluation = RegressionEvaluation()
    train_X, test_X, train_y, test_y = prepare.split_single_dataset_regression_by_time(dataset, 'hr_watch_rate',
                                                                                       '2016-02-08 18:28:56',
                                                                                       '2016-02-08 19:34:07',
                                                                                       '2016-02-08 20:07:50')
    print('Training set length is: ', len(train_X.index))
    print('Test set length is: ', len(test_X.index))

    # Select subsets of the features
    print('- - - Selecting subsets - - -')
    basic_features = ['acc_phone_x', 'acc_phone_y', 'acc_phone_z', 'acc_watch_x', 'acc_watch_y', 'acc_watch_z',
                      'gyr_phone_x', 'gyr_phone_y', 'gyr_phone_z', 'gyr_watch_x', 'gyr_watch_y', 'gyr_watch_z',
                      'labelOnTable', 'labelSitting', 'labelWashingHands', 'labelWalking', 'labelStanding',
                      'labelDriving',
                      'labelEating', 'labelRunning', 'light_phone_lux', 'mag_phone_x', 'mag_phone_y', 'mag_phone_z',
                      'mag_watch_x', 'mag_watch_y', 'mag_watch_z', 'press_phone_pressure']
    pca_features = ['pca_1', 'pca_2', 'pca_3', 'pca_4', 'pca_5', 'pca_6', 'pca_7']
    time_features = [name for name in dataset.columns if ('temp_' in name and 'hr_watch' not in name)]
    freq_features = [name for name in dataset.columns if (('_freq' in name) or ('_pse' in name))]
    cluster_features = ['cluster']
    print('#basic features: ', len(basic_features))
    print('#PCA features: ', len(pca_features))
    print('#time features: ', len(time_features))
    print('#frequency features: ', len(freq_features))
    print('#cluster features: ', len(cluster_features))
    features_after_chapter_3 = list(set().union(basic_features, pca_features))
    features_after_chapter_4 = list(set().union(features_after_chapter_3, time_features, freq_features))
    features_after_chapter_5 = list(set().union(features_after_chapter_4, cluster_features))

    if FLAGS.mode == 'selection' or FLAGS.mode == 'all':
        # First, consider the Pearson correlations and see whether features can be selected based on them
        fs = FeatureSelectionRegression()
        print('\n- - - Running feature selection - - -')
        features, correlations = fs.pearson_selection(10, train_X[features_after_chapter_5], train_y)
        util.print_pearson_correlations(correlations)

    # Select the 10 features with the highest correlation
    selected_features = ['temp_pattern_labelOnTable', 'labelOnTable', 'temp_pattern_labelOnTable(b)labelOnTable',
                         'pca_2_temp_mean_ws_120', 'pca_1_temp_mean_ws_120', 'acc_watch_y_temp_mean_ws_120', 'pca_2',
                         'acc_phone_z_temp_mean_ws_120', 'gyr_watch_y_pse', 'gyr_watch_x_pse']
    possible_feature_sets = [basic_features, features_after_chapter_3, features_after_chapter_4,
                             features_after_chapter_5, selected_features]
    feature_names = ['initial set', 'Chapter 3', 'Chapter 4', 'Chapter 5', 'Selected features']

    if FLAGS.mode == 'overall' or FLAGS.mode == 'all':
        print('\n- - - Running test of all different regression algorithms - - -')
        # First study the importance of the parameter settings. Therefore repeat the experiment a number of times to get
        # a bit more robust data as the initialization of e.g. the NN is random
        REPEATS = FLAGS.repeats
        scores_over_all_algs = []

        for i in range(0, len(possible_feature_sets)):
            selected_train_X = train_X[possible_feature_sets[i]]
            selected_test_X = test_X[possible_feature_sets[i]]

            performance_tr_nn, performance_tr_nn_std = 0, 0
            performance_tr_rf, performance_tr_rf_std = 0, 0
            performance_te_nn, performance_te_nn_std = 0, 0
            performance_te_rf, performance_te_rf_std = 0, 0

            # First run non deterministic classifiers a number of times to average their score
            for repeat in range(0, REPEATS):
                print(f'Training NeuralNetwork run {repeat + 1}/{REPEATS} ... ')
                regr_train_y, regr_test_y = learner.\
                    feedforward_neural_network(selected_train_X, train_y, selected_test_X, gridsearch=True)
                mean_tr, std_tr = evaluation.mean_squared_error_with_std(train_y, regr_train_y)
                mean_te, std_te = evaluation.mean_squared_error_with_std(test_y, regr_test_y)
                performance_tr_nn += mean_tr
                performance_tr_nn_std += std_tr
                performance_te_nn += mean_te
                performance_te_nn_std += std_te

                print(f'Training RandomForest run {repeat + 1}/{REPEATS} ... ')
                regr_train_y, regr_test_y = learner.random_forest(selected_train_X, train_y, selected_test_X,
                                                                  gridsearch=True)
                mean_tr, std_tr = evaluation.mean_squared_error_with_std(train_y, regr_train_y)
                mean_te, std_te = evaluation.mean_squared_error_with_std(test_y, regr_test_y)
                performance_tr_rf += mean_tr
                performance_tr_rf_std += std_tr
                performance_te_rf += mean_te
                performance_te_rf_std += std_te

            overall_performance_tr_nn = performance_tr_nn / REPEATS
            overall_performance_tr_nn_std = performance_tr_nn_std / REPEATS
            overall_performance_te_nn = performance_te_nn / REPEATS
            overall_performance_te_nn_std = performance_te_nn_std / REPEATS
            overall_performance_tr_rf = performance_tr_rf / REPEATS
            overall_performance_tr_rf_std = performance_tr_rf_std / REPEATS
            overall_performance_te_rf = performance_te_rf / REPEATS
            overall_performance_te_rf_std = performance_te_rf_std / REPEATS

            # Run deterministic algorithms:
            print("Support Vector Regressor run 1/1 ... ")
            # Convergence of the SVR does not always occur (even adjusting tolerance and iterations does not help)
            regr_train_y, regr_test_y = learner.\
                support_vector_regression_without_kernel(selected_train_X, train_y, selected_test_X, gridsearch=False)
            mean_tr, std_tr = evaluation.mean_squared_error_with_std(train_y, regr_train_y)
            mean_te, std_te = evaluation.mean_squared_error_with_std(test_y, regr_test_y)
            performance_tr_svm = mean_tr
            performance_tr_svm_std = std_tr
            performance_te_svm = mean_te
            performance_te_svm_std = std_te

            print("Training Nearest Neighbor run 1/1 ... ")
            regr_train_y, regr_test_y = learner.k_nearest_neighbor(selected_train_X, train_y, selected_test_X,
                                                                   gridsearch=True)
            mean_tr, std_tr = evaluation.mean_squared_error_with_std(train_y, regr_train_y)
            mean_te, std_te = evaluation.mean_squared_error_with_std(test_y, regr_test_y)
            performance_tr_knn = mean_tr
            performance_tr_knn_std = std_tr
            performance_te_knn = mean_te
            performance_te_knn_std = std_te

            print("Training Decision Tree run 1/1 ... ")
            regr_train_y, regr_test_y = learner.\
                decision_tree(selected_train_X, train_y, selected_test_X, gridsearch=True,
                              export_tree_path=EXPORT_TREE_PATH)
            mean_tr, std_tr = evaluation.mean_squared_error_with_std(train_y, regr_train_y)
            mean_te, std_te = evaluation.mean_squared_error_with_std(test_y, regr_test_y)
            performance_tr_dt = mean_tr
            performance_tr_dt_std = std_tr
            performance_te_dt = mean_te
            performance_te_dt_std = std_te

            scores_with_sd = [(overall_performance_tr_nn, overall_performance_tr_nn_std, overall_performance_te_nn,
                               overall_performance_te_nn_std),
                              (overall_performance_tr_rf, overall_performance_tr_rf_std, overall_performance_te_rf,
                               overall_performance_te_rf_std),
                              (performance_tr_svm, performance_tr_svm_std, performance_te_svm, performance_te_svm_std),
                              (performance_tr_knn, performance_tr_knn_std, performance_te_knn, performance_te_knn_std),
                              (performance_tr_dt, performance_tr_dt_std, performance_te_dt, performance_te_dt_std)]
            util.print_table_row_performances_regression(feature_names[i], scores_with_sd)
            scores_over_all_algs.append(scores_with_sd)

        # Plot the results
        DataViz.plot_performances_regression(['NN', 'RF', 'SVM', 'KNN', 'DT'], feature_names, scores_over_all_algs)

    if FLAGS.mode == 'detail' or FLAGS.mode == 'all':
        print('\n- - - Running visualization of results - - -')
        regr_train_y, regr_test_y = learner.random_forest(train_X[features_after_chapter_5], train_y,
                                                          test_X[features_after_chapter_5], gridsearch=False,
                                                          print_model_details=True)
        DataViz.plot_numerical_prediction_versus_real(train_X.index, train_y, regr_train_y, test_X.index, test_y,
                                                      regr_test_y, 'heart rate')
示例#3
0
    performance_tr_rnn = 0
    performance_tr_rnn_std = 0
    performance_te_rnn = 0
    performance_te_rnn_std = 0

    for repeat in range(0, repeats):
        print '----', repeat
        regr_train_y, regr_test_y = learner.reservoir_computing(
            selected_train_X,
            train_y,
            selected_test_X,
            test_y,
            gridsearch=True,
            per_time_step=False)

        mean_tr, std_tr = eval.mean_squared_error_with_std(
            train_y.ix[washout_time:, ], regr_train_y.ix[washout_time:, ])
        mean_te, std_te = eval.mean_squared_error_with_std(
            test_y.ix[washout_time:, ], regr_test_y.ix[washout_time:, ])

        performance_tr_res += mean_tr
        performance_tr_res_std += std_tr
        performance_te_res += mean_te
        performance_te_res_std += std_te

        regr_train_y, regr_test_y = learner.recurrent_neural_network(
            selected_train_X,
            train_y,
            selected_test_X,
            test_y,
            gridsearch=True)
    performance_tr_rf = 0
    performance_tr_rf_std = 0
    performance_tr_svm = 0
    performance_tr_svm_std = 0
    performance_te_nn = 0
    performance_te_nn_std = 0
    performance_te_rf = 0
    performance_te_rf_std = 0
    performance_te_svm = 0
    performance_te_svm_std = 0

    for repeat in range(0, repeats):
        regr_train_y, regr_test_y = learner.feedforward_neural_network(
            selected_train_X, train_y, selected_test_X, gridsearch=True)

        mean_tr, std_tr = eval.mean_squared_error_with_std(
            train_y, regr_train_y)
        mean_te, std_te = eval.mean_squared_error_with_std(test_y, regr_test_y)
        mean_training = eval.mean_squared_error(train_y, regr_train_y)
        performance_tr_nn += mean_tr
        performance_tr_nn_std += std_tr
        performance_te_nn += mean_te
        performance_te_nn_std += std_te

        regr_train_y, regr_test_y = learner.random_forest(selected_train_X,
                                                          train_y,
                                                          selected_test_X,
                                                          gridsearch=True)
        mean_tr, std_tr = eval.mean_squared_error_with_std(
            train_y, regr_train_y)
        mean_te, std_te = eval.mean_squared_error_with_std(test_y, regr_test_y)
        performance_tr_rf += mean_tr
示例#5
0
def main():
    # Read the result from the previous chapter and convert the index to datetime
    try:
        dataset = pd.read_csv(DATA_PATH / DATASET_FNAME, index_col=0)
        dataset.index = pd.to_datetime(dataset.index)
    except IOError as e:
        print(
            'File not found, try to run previous crowdsignals scripts first!')
        raise e

    # Create an instance of visualization class to plot the results
    DataViz = VisualizeDataset(__file__)

    # Consider the second task, namely the prediction of the heart rate. Therefore create a dataset with the heart
    # rate as target and split using timestamps, because this is considered as a temporal task
    print('\n- - - Loading dataset - - -')
    prepare = PrepareDatasetForLearning()
    train_X, test_X, train_y, test_y = prepare.split_single_dataset_regression_by_time(
        dataset, 'hr_watch_rate', '2016-02-08 18:29:56', '2016-02-08 19:34:07',
        '2016-02-08 20:07:50')
    print('Training set length is: ', len(train_X.index))
    print('Test set length is: ', len(test_X.index))

    # Select subsets of the features
    print('\n- - - Selecting subsets - - -')
    basic_features = [
        'acc_phone_x', 'acc_phone_y', 'acc_phone_z', 'acc_watch_x',
        'acc_watch_y', 'acc_watch_z', 'gyr_phone_x', 'gyr_phone_y',
        'gyr_phone_z', 'gyr_watch_x', 'gyr_watch_y', 'gyr_watch_z',
        'labelOnTable', 'labelSitting', 'labelWashingHands', 'labelWalking',
        'labelStanding', 'labelDriving', 'labelEating', 'labelRunning',
        'light_phone_lux', 'mag_phone_x', 'mag_phone_y', 'mag_phone_z',
        'mag_watch_x', 'mag_watch_y', 'mag_watch_z', 'press_phone_pressure'
    ]
    pca_features = [
        'pca_1', 'pca_2', 'pca_3', 'pca_4', 'pca_5', 'pca_6', 'pca_7'
    ]
    time_features = [
        name for name in dataset.columns
        if ('temp_' in name and 'hr_watch' not in name)
    ]
    freq_features = [
        name for name in dataset.columns
        if (('_freq' in name) or ('_pse' in name))
    ]
    cluster_features = ['cluster']
    print('#basic features: ', len(basic_features))
    print('#PCA features: ', len(pca_features))
    print('#time features: ', len(time_features))
    print('#frequency features: ', len(freq_features))
    print('#cluster features: ', len(cluster_features))
    features_after_chapter_3 = list(set().union(basic_features, pca_features))
    features_after_chapter_4 = list(set().union(features_after_chapter_3,
                                                time_features, freq_features))
    features_after_chapter_5 = list(set().union(features_after_chapter_4,
                                                cluster_features))

    selected_features = [
        'temp_pattern_labelOnTable', 'labelOnTable',
        'temp_pattern_labelOnTable(b)labelOnTable', 'cluster',
        'pca_1_temp_mean_ws_120', 'pca_2_temp_mean_ws_120', 'pca_2',
        'acc_watch_y_temp_mean_ws_120', 'gyr_watch_y_pse', 'gyr_watch_x_pse'
    ]
    possible_feature_sets = [
        basic_features, features_after_chapter_3, features_after_chapter_4,
        features_after_chapter_5, selected_features
    ]
    feature_names = [
        'initial set', 'Chapter 3', 'Chapter 4', 'Chapter 5',
        'Selected features'
    ]

    if FLAGS.mode == 'correlation' or FLAGS.mode == 'all':
        # First study whether the time series is stationary and what the autocorrelations are
        adfuller(dataset['hr_watch_rate'], autolag='AIC')
        plt.Figure()
        autocorrelation_plot(dataset['hr_watch_rate'])
        DataViz.save(plt)
        plt.show()

    # Now focus on the learning part
    learner = TemporalRegressionAlgorithms()
    evaluate = RegressionEvaluation()

    if FLAGS.mode == 'overall' or FLAGS.mode == 'all':
        # Repeat the experiment a number of times to get a bit more robust data as the initialization of e.g. the NN is
        # random
        repeats = FLAGS.repeats

        # Set a washout time to give the NN's the time to stabilize (so don't compute the error during the washout time)
        washout_time = FLAGS.washout
        scores_over_all_algs = []

        for i in range(0, len(possible_feature_sets)):
            print(f'Evaluating for features {possible_feature_sets[i]}')
            selected_train_X = train_X[possible_feature_sets[i]]
            selected_test_X = test_X[possible_feature_sets[i]]

            # First run non deterministic classifiers a number of times to average their score
            performance_tr_res, performance_tr_res_std = 0, 0
            performance_te_res, performance_te_res_std = 0, 0
            performance_tr_rnn, performance_tr_rnn_std = 0, 0
            performance_te_rnn, performance_te_rnn_std = 0, 0

            for repeat in range(0, repeats):
                print(f'--- run {repeat} ---')
                regr_train_y, regr_test_y = learner.reservoir_computing(
                    selected_train_X,
                    train_y,
                    selected_test_X,
                    test_y,
                    gridsearch=True,
                    per_time_step=False)

                mean_tr, std_tr = evaluate.mean_squared_error_with_std(
                    train_y.iloc[washout_time:, ],
                    regr_train_y.iloc[washout_time:, ])
                mean_te, std_te = evaluate.mean_squared_error_with_std(
                    test_y.iloc[washout_time:, ],
                    regr_test_y.iloc[washout_time:, ])

                performance_tr_res += mean_tr
                performance_tr_res_std += std_tr
                performance_te_res += mean_te
                performance_te_res_std += std_te

                regr_train_y, regr_test_y = learner.recurrent_neural_network(
                    selected_train_X,
                    train_y,
                    selected_test_X,
                    test_y,
                    gridsearch=True)

                mean_tr, std_tr = evaluate.mean_squared_error_with_std(
                    train_y.iloc[washout_time:, ],
                    regr_train_y.iloc[washout_time:, ])
                mean_te, std_te = evaluate.mean_squared_error_with_std(
                    test_y.iloc[washout_time:, ],
                    regr_test_y.iloc[washout_time:, ])

                performance_tr_rnn += mean_tr
                performance_tr_rnn_std += std_tr
                performance_te_rnn += mean_te
                performance_te_rnn_std += std_te

            # Only apply the time series in case of the basis features
            if feature_names[i] == 'initial set':
                regr_train_y, regr_test_y = learner.time_series(
                    selected_train_X,
                    train_y,
                    selected_test_X,
                    test_y,
                    gridsearch=True)

                mean_tr, std_tr = evaluate.mean_squared_error_with_std(
                    train_y.iloc[washout_time:, ],
                    regr_train_y.iloc[washout_time:, ])
                mean_te, std_te = evaluate.mean_squared_error_with_std(
                    test_y.iloc[washout_time:, ],
                    regr_test_y.iloc[washout_time:, ])

                overall_performance_tr_ts = mean_tr
                overall_performance_tr_ts_std = std_tr
                overall_performance_te_ts = mean_te
                overall_performance_te_ts_std = std_te
            else:
                overall_performance_tr_ts = 0
                overall_performance_tr_ts_std = 0
                overall_performance_te_ts = 0
                overall_performance_te_ts_std = 0

            overall_performance_tr_res = performance_tr_res / repeats
            overall_performance_tr_res_std = performance_tr_res_std / repeats
            overall_performance_te_res = performance_te_res / repeats
            overall_performance_te_res_std = performance_te_res_std / repeats
            overall_performance_tr_rnn = performance_tr_rnn / repeats
            overall_performance_tr_rnn_std = performance_tr_rnn_std / repeats
            overall_performance_te_rnn = performance_te_rnn / repeats
            overall_performance_te_rnn_std = performance_te_rnn_std / repeats

            scores_with_sd = [
                (overall_performance_tr_res, overall_performance_tr_res_std,
                 overall_performance_te_res, overall_performance_te_res_std),
                (overall_performance_tr_rnn, overall_performance_tr_rnn_std,
                 overall_performance_te_rnn, overall_performance_te_rnn_std),
                (overall_performance_tr_ts, overall_performance_tr_ts_std,
                 overall_performance_te_ts, overall_performance_te_ts_std)
            ]
            util.print_table_row_performances_regression(
                feature_names[i], scores_with_sd)
            scores_over_all_algs.append(scores_with_sd)

        DataViz.plot_performances_regression(
            ['Reservoir', 'RNN', 'Time series'], feature_names,
            scores_over_all_algs)

    if FLAGS.mode == 'detail' or FLAGS.mode == 'all':
        regr_train_y, regr_test_y = learner.reservoir_computing(
            train_X[features_after_chapter_5],
            train_y,
            test_X[features_after_chapter_5],
            test_y,
            gridsearch=False)
        DataViz.plot_numerical_prediction_versus_real(
            train_X.index, train_y, regr_train_y['hr_watch_rate'],
            test_X.index, test_y, regr_test_y['hr_watch_rate'], 'heart rate')

        regr_train_y, regr_test_y = learner.recurrent_neural_network(
            train_X[basic_features],
            train_y,
            test_X[basic_features],
            test_y,
            gridsearch=True)
        DataViz.plot_numerical_prediction_versus_real(
            train_X.index, train_y, regr_train_y['hr_watch_rate'],
            test_X.index, test_y, regr_test_y['hr_watch_rate'], 'heart rate')

        regr_train_y, regr_test_y = learner.time_series(
            train_X[basic_features],
            train_y,
            test_X[basic_features],
            test_y,
            gridsearch=True)
        DataViz.plot_numerical_prediction_versus_real(
            train_X.index, train_y, regr_train_y['hr_watch_rate'],
            test_X.index, test_y, regr_test_y['hr_watch_rate'], 'heart rate')

    if FLAGS.mode == 'dynamical' or FLAGS.mode == 'all':
        # And now some example code for using the dynamical systems model with parameter tuning (note: focus on
        # predicting accelerometer data):
        train_X, test_X, train_y, test_y = prepare.split_single_dataset_regression(
            copy.deepcopy(dataset), ['acc_phone_x', 'acc_phone_y'],
            0.9,
            filter_data=False,
            temporal=True)
        output_sets = learner. \
            dynamical_systems_model_nsga_2(train_X, train_y, test_X, test_y,
                                           ['self.acc_phone_x', 'self.acc_phone_y', 'self.acc_phone_z'],
                                           ['self.a * self.acc_phone_x + self.b * self.acc_phone_y',
                                            'self.c * self.acc_phone_y + self.d * self.acc_phone_z',
                                            'self.e * self.acc_phone_x + self.f * self.acc_phone_z'],
                                           ['self.acc_phone_x', 'self.acc_phone_y'],
                                           ['self.a', 'self.b', 'self.c', 'self.d', 'self.e', 'self.f'],
                                           pop_size=10, max_generations=10, per_time_step=True)
        DataViz.plot_pareto_front(output_sets)

        DataViz.plot_numerical_prediction_versus_real_dynsys_mo(
            train_X.index, train_y, test_X.index, test_y, output_sets, 0,
            'acc_phone_x')

        regr_train_y, regr_test_y = learner. \
            dynamical_systems_model_ga(train_X, train_y, test_X, test_y,
                                       ['self.acc_phone_x', 'self.acc_phone_y', 'self.acc_phone_z'],
                                       ['self.a * self.acc_phone_x + self.b * self.acc_phone_y',
                                        'self.c * self.acc_phone_y + self.d * self.acc_phone_z',
                                        'self.e * self.acc_phone_x + self.f * self.acc_phone_z'],
                                       ['self.acc_phone_x', 'self.acc_phone_y'],
                                       ['self.a', 'self.b', 'self.c', 'self.d', 'self.e', 'self.f'],
                                       pop_size=5, max_generations=10, per_time_step=True)

        DataViz.plot_numerical_prediction_versus_real(
            train_X.index, train_y['acc_phone_x'], regr_train_y['acc_phone_x'],
            test_X.index, test_y['acc_phone_x'], regr_test_y['acc_phone_x'],
            'acc_phone_x')

        regr_train_y, regr_test_y = learner. \
            dynamical_systems_model_sa(train_X, train_y, test_X, test_y,
                                       ['self.acc_phone_x', 'self.acc_phone_y', 'self.acc_phone_z'],
                                       ['self.a * self.acc_phone_x + self.b * self.acc_phone_y',
                                        'self.c * self.acc_phone_y + self.d * self.acc_phone_z',
                                        'self.e * self.acc_phone_x + self.f * self.acc_phone_z'],
                                       ['self.acc_phone_x', 'self.acc_phone_y'],
                                       ['self.a', 'self.b', 'self.c', 'self.d', 'self.e', 'self.f'],
                                       max_generations=10, per_time_step=True)

        DataViz.plot_numerical_prediction_versus_real(
            train_X.index, train_y['acc_phone_x'], regr_train_y['acc_phone_x'],
            test_X.index, test_y['acc_phone_x'], regr_test_y['acc_phone_x'],
            'acc_phone_x')