Coalition Feature Interpretation and Attribution in Algorithmic Trading Models

Abstract

The ability to correctly interpret a prediction model’s output is critically important in many problem spheres. Accurate interpretation generates user trust in the model, provides insight into how a model may be improved, and supports understanding of the process being modeled. Absence of this capability has constrained algorithmic trading from making use of more powerful predictive models, such as XGBoost and Random Forests. Recently, the adaptation of coalitional game theory has led to the development of consistent methods of determining feature importance for these models (SHAP).This study designs and tests a novel method of integrating the capabilities of SHAP into predictive models for algorithmic trading.

Appendix

Random Forests was selected for this study because it is much easier to tune parameters than with XGBoost. Random Forests contain adjustable hyperparameters whose values can dramatically affect performance. This flexibility contributes to their robustness. Common hyperparameters include the number of trees used in the forest, the maximum depth of each tree, and the minimum number or proportion of samples in a leaf. Random search for the best hyperparameter values avoids the exhaustive enumeration of grid search and replaces it with selecting random subsets of hyperparameter combinations. Random Forests are also harder to overfit than XGBoost.

A Random Forest is an ensemble of unpruned classification or regression trees induced from bootstrap samples of the training data, using random feature selection in the tree induction process. Prediction is made by aggregating (majority vote for classification or averaging for regression) the predictions of the ensemble. Formally an ensemble of $k$ trees is an estimator comprised of a collection of randomized trees $\{ h\left( {x, \theta_{k} } \right), k = 1, \ldots , K$ }, where the $\theta_{k}$ are independent identically distributed random vectors, and $x$ is an input vector. Letting $\theta$ represent the generic random vector $\theta_{k}$ having the same distribution as $k$, as $K$ goes to infinity, the mean-squared generalization error of the random forest goes almost surely to that of $E\left[ {h\left( {x, \theta_{k} } \right)} \right]$, thus mitigating the possibility of overfitting the model.

Random forests increase diversity among the classifiers by altering the feature sets over the different tree induction processes and resampling the data. The procedure to build a forest with K trees is as follows:

The italicized part of the algorithm is where random forests depart from the normal bagging procedure. Specifically, when building a decision tree using traditional bagging, the best feature is selected from a given set of features $F$ in each node and the set of features does not change over the different runs of the induction procedure. Conversely, with random forests a different random subset of size $g\left( {\left| F \right|} \right)$ is evaluated at each node (e.g., $g\left( x \right) = 0.15x \;or\; g\left( x \right) = \surd x, \,etc.$) with the best feature selected from this subset. This has been shown to increase variability.