Machine learning tree methods
Learn how to use tree-based machine learning models to predict future values of a stock’s price, as well as how to use forest-based machine learning methods for regression and feature selection.
Feature engineering from volume
We’re going to use non-linear models to make more accurate predictions. With linear models, features must be linearly correlated to the target. Other machine learning models can combine features in non-linear ways. For example, what if the price goes up when the moving average of price is going up, and the moving average of volume is going down? The only way to capture those interactions is to either multiply the features, or to use a machine learning algorithm that can handle non-linearity (e.g. random forests).
To incorporate more information that may interact with other features, we can add in weakly-correlated features. First we will add volume data, which we have in the lng_df as the Adj_Volume column.
Tabit 是python的一個金融指數處理庫.
SMA： simple moving average 簡單移動平均
基礎函數： talib.SMA(價格,週期）
pct_change() 用來計算同列兩個相鄰數字的變化率.
# Create 2 new volume features, 1-day % change and 5-day SMA of the % change
new_features = ['Adj_Volume_1d_change', 'Adj_Volume_1d_change_SMA']
feature_names.extend(new_features)
lng_df['Adj_Volume_1d_change'] = lng_df['Adj_Volume'].pct_change()
lng_df['Adj_Volume_1d_change_SMA'] = talib.SMA(lng_df['Adj_Volume_1d_change'].values,
timeperiod=5)
# Plot histogram of volume % change data
lng_df[new_features].plot(kind='hist', sharex=False, bins=50)
plt.show()
We can see the moving average of volume changes has a much smaller range than the raw data.
Create day-of-week features
We can engineer datetime features to add even more information for our non-linear models. Most financial data has datetimes, which have lots of information in them – year, month, day, and sometimes hour, minute, and second. But we can also get the day of the week, and things like the quarter of the year, or the elapsed time since some event (e.g. earnings reports).
We are only going to get the day of the week here, since our dataset doesn’t go back very far in time. The dayofweek property from the pandas datetime index will help us get the day of the week. Then we will dummy dayofweek with pandas’ get_dummies(). This creates columns for each day of the week with binary values (0 or 1). We drop the first column because it can be inferred from the others.
# Use pandas' get_dummies function to get dummies for day of the week
days_of_week = pd.get_dummies(lng_df.index.dayofweek,
prefix='weekday',
drop_first=True)
# Set the index as the original DataFrame index for merging
days_of_week.index = lng_df.index
# Join the dataframe with the days of week DataFrame
lng_df = pd.concat([lng_df, days_of_week], axis=1)
# Add days of week to feature names
feature_names.extend(['weekday_' + str(i) for i in range(1, 5)])
lng_df.dropna(inplace=True) # drop missing values in-place
print(lng_df.head())
Examine correlations of the new features
# Add the weekday labels to the new_features list
new_features.extend(['weekday_' + str(i) for i in range(1, 5)])
# Plot the correlations between the new features and the targets
sns.heatmap(lng_df[new_features + ['5d_close_future_pct']].corr(), annot=True)
plt.yticks(rotation=0) # ensure y-axis ticklabels are horizontal
plt.xticks(rotation=90) # ensure x-axis ticklabels are vertical
plt.tight_layout()
plt.show()
Examine correlations of the new features
# Add the weekday labels to the new_features list
new_features.extend(['weekday_' + str(i) for i in range(1, 5)])
# Plot the correlations between the new features and the targets
sns.heatmap(lng_df[new_features + ['5d_close_future_pct']].corr(), annot=True)
plt.yticks(rotation=0) # ensure y-axis ticklabels are horizontal
plt.xticks(rotation=90) # ensure x-axis ticklabels are vertical
plt.tight_layout()
plt.show()
Fit a decision tree
Random forests are a go-to model for predictions; they work well out of the box. But we’ll first learn the building block of random forests – decision trees.
Decision trees split the data into groups based on the features. Decision trees start with a root node, and split the data down until we reach leaf nodes.
We can use sklearn to fit a decision tree with DecisionTreeRegressor and .fit(features, targets).
Without limiting the tree’s depth (or height), it will keep splitting the data until each leaf has 1 sample in it, which is the epitome of overfitting.
from sklearn.tree import DecisionTreeRegressor
# Create a decision tree regression model with default arguments
decision_tree = DecisionTreeRegressor()
# Fit the model to the training features and targets
decision_tree.fit(train_features, train_targets)
# Check the score on train and test
print(decision_tree.score(train_features, train_targets))
print(decision_tree.score(test_features, test_targets))
Try different max depths
We always want to optimize our machine learning models to make the best predictions possible. We can do this by tuning hyperparameters, which are settings for our models. We will see in more detail how these are useful in future chapters, but for now think of them as knobs we can turn to tune our predictions to be as good as possible.
For regular decision trees, probably the most important hyperparameter is max_depth. This limits the number of splits in a decision tree. Let’s find the best value of max_depth based on the R2
score of our model on the test set, which we can obtain using the score() method of our decision tree models.
# Loop through a few different max depths and check the performance
for d in [3, 5, 10]:
# Create the tree and fit it
decision_tree = DecisionTreeRegressor(max_depth=d)
decision_tree.fit(train_features, train_targets)
# Print out the scores on train and test
print('max_depth=', str(d))
print(decision_tree.score(train_features, train_targets))
print(decision_tree.score(test_features, test_targets), '\n')
Check our results
Once we have an optimized model, we want to check how it is performing in more detail. We already saw the R2 score, but it can be helpful to see the predictions plotted vs actual values. We can use the .predict() method of our decision tree model to get predictions on the train and test sets.
Ideally, we want to see diagonal lines from the lower left to the upper right. However, due to the simplicity of decisions trees, our model is not going to do well on the test set. But it will do well on the train set.
# Use the best max_depth of 3 from last exercise to fit a decision tree
decision_tree = DecisionTreeRegressor(max_depth=3)
decision_tree.fit(train_features, train_targets)
# Predict values for train and test
train_predictions = decision_tree.predict(train_features)
test_predictions = decision_tree.predict(test_features)
# Scatter the predictions vs actual values
plt.scatter(train_predictions, train_targets, label='train')
plt.scatter(test_predictions, test_targets, label='test')
plt.show()
The predictions group into lines because our depth is limited.
Fit a random forest
Data scientists often use random forest models. They perform well out of the box, and have lots of settings to optimize performance. Random forests can be used for classification or regression; we’ll use it for regression to predict the future price change of LNG.
from sklearn.ensemble import RandomForestRegressor
# Create the random forest model and fit to the training data
rfr = RandomForestRegressor(n_estimators=200)
rfr.fit(train_features, train_targets)
# Look at the R^2 scores on train and test
print(rfr.score(train_features, train_targets))
print(rfr.score(test_features, test_targets))
Tune random forest hyperparameters
As with all models, we want to optimize performance by tuning hyperparameters. We have many hyperparameters for random forests, but the most important is often the number of features we sample at each split, or max_features in RandomForestRegressor from the sklearn library. For models like random forests that have randomness built-in, we also want to set the random_state. This is set for our results to be reproducible.
Usually, we can use sklearn’s GridSearchCV() method to search hyperparameters, but with a financial time series, we don’t want to do cross-validation due to data mixing. We want to fit our models on the oldest data and evaluate on the newest data. So we’ll use sklearn’s ParameterGrid to create combinations of hyperparameters to search.
from sklearn.model_selection import ParameterGrid
# Create a dictionary of hyperparameters to search
grid = {'n_estimators': [200], 'max_depth': [3], 'max_features': [4, 8], 'random_state': [42]}
test_scores = []
# Loop through the parameter grid, set the hyperparameters, and save the scores
for g in ParameterGrid(grid):
rfr.set_params(**g) # ** is "unpacking" the dictionary
rfr.fit(train_features, train_targets)
test_scores.append(rfr.score(test_features, test_targets))
# Find best hyperparameters from the test score and print
best_idx = np.argmax(test_scores)
print(test_scores[best_idx], ParameterGrid(grid)[best_idx])
Evaluate performance
Lastly, and as always, we want to evaluate performance of our best model to check how well or poorly we are doing. Ideally it’s best to do back-testing, but that’s an involved process we don’t have room to cover in this course.
We’ve already seen the R2 scores, but let’s take a look at the scatter plot of predictions vs actual results using matplotlib. Perfect predictions would be a diagonal line from the lower left to the upper right.
# Use the best hyperparameters from before to fit a random forest model
rfr = RandomForestRegressor(n_estimators=200, max_depth=3, max_features=4, random_state=42)
rfr.fit(train_features, train_targets)
# Make predictions with our model
train_predictions = rfr.predict(train_features)
test_predictions = rfr.predict(test_features)
# Create a scatter plot with train and test actual vs predictions
plt.scatter(train_targets, train_predictions, label='train')
plt.scatter(test_targets, test_predictions, label='test')
plt.legend()
plt.show()
Random forest feature importances
One useful aspect of tree-based methods is the ability to extract feature importances. This is a quantitative way to measure how much each feature contributes to our predictions. It can help us focus on our best features, possibly enhancing or tuning them, and can also help us get rid of useless features that may be cluttering up our model.
Tree models in sklearn have a .feature_importances_ property that’s accessible after fitting the model. This stores the feature importance scores. We need to get the indices of the sorted feature importances using np.argsort() in order to make a nice-looking bar plot of feature importances (sorted from greatest to least importance).
# Get feature importances from our random forest model
importances = rfr.feature_importances_
# Get the index of importances from greatest importance to least
sorted_index = np.argsort(importances)[::-1]
x = range(len(importances))
# Create tick labels
labels = np.array(feature_names)[sorted_index]
plt.bar(x, importances[sorted_index], tick_label=labels)
# Rotate tick labels to vertical
plt.xticks(rotation=90)
plt.show()
A gradient boosting model
Now we’ll fit a gradient boosting (GB) model. It’s been said a linear model is like a Toyota Camry, and GB is like a Black Hawk helicopter. GB has potential to outperform random forests, but doesn’t always do so. This is called the no free lunch theorem, meaning we should always try lots of different models for each problem.
GB is similar to random forest models, but the difference is that trees are built successively. With each iteration, the next tree fits the residual errors from the previous tree in order to improve the fit.
For now we won’t search our hyperparameters – they’ve been searched for you.
from sklearn.ensemble import GradientBoostingRegressor
# Create GB model -- hyperparameters have already been searched for you
gbr = GradientBoostingRegressor(max_features=4,
learning_rate=0.01,
n_estimators=200,
subsample=0.6,
random_state=42)
gbr.fit(train_features, train_targets)
print(gbr.score(train_features, train_targets))
print(gbr.score(test_features, test_targets))
Gradient boosting feature importances
As with random forests, we can extract feature importances from gradient boosting models to understand which features are the best predictors. Sometimes it’s nice to try different tree-based models and look at the feature importances from all of them. This can help average out any peculiarities that may arise from one particular model.
The feature importances are stored as a numpy array in the .feature_importances_ property of the gradient boosting model. We’ll need to get the sorted indices of the feature importances, using np.argsort(), in order to make a nice plot. We want the features from largest to smallest, so we will use Python’s indexing to reverse the sorted importances like feat_importances[::-1].
# Extract feature importances from the fitted gradient boosting model
feature_importances = gbr.feature_importances_
# Get the indices of the largest to smallest feature importances
sorted_index = np.argsort(feature_importances)[::-1]
x = range(features.shape[1])
# Create tick labels
labels = np.array(feature_names)[sorted_index]
plt.bar(x, feature_importances[sorted_index], tick_label=labels)
# Set the tick lables to be the feature names, according to the sorted feature_idx
plt.xticks(rotation=90)
plt.show()
