# Winning the Kaggle Algorithmic Trading Challenge with the Composition of Many Models and Feature Engineering

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1 IEICE Transactions on Information and Systems, vol.e96-d, no.3, pp , Winning the Kaggle Algorithmic Trading Challenge with the Composition of Many Models and Feature Engineering Ildefons Magrans de Abril Tokyo Institute of Technology, Japan. Masashi Sugiyama Tokyo Institute of Technology, Japan. sugi Abstract This letter presents the ideas and methods of the winning solution 2 for the Kaggle Algorithmic Trading Challenge. This analysis challenge took place between 11th November 2011 and 8th January 2012, and 264 competitors submitted solutions. The objective of this competition was to develop empirical predictive models to explain stock market prices following a liquidity shock. The winning system builds upon the optimal composition of several models and a feature extraction and selection strategy. We used Random Forest as a modeling technique to train all sub-models as a function of an optimal feature set. The modeling approach can cope with highly complex data having low Maximal Information Coefficients between the dependent variable and the feature set and provides a feature ranking metric which we used in our feature selection algorithm. Keywords Kaggle Challenge, Model Architecture, Boosting, Feature Selection, High Frequency Trading, Liquidity Shock, Maximal Information Coefficient 1 Introduction The goal of the Kaggle Algorithmic Trading Challenge was to encourage the development of empirical models to predict the short term response of Order-Driven Markets (ODM) following large liquidity shocks [1]. A liquidity shock is defined as any trade that changes the best bid or ask price. Liquidity shocks occur when a large trade (or series of smaller trades) consumes all available volume at the best price. 2 Solution designed and implemented by Ildefons Magrans de Abril.

3 Winning the Kaggle Algorithmic Trading Challenge 3 Algorithm 1 Time interval partitioning algorithm 1: b e 52; P NULL; i 1 2: while b < 100 do 3: C i NULL; e b + length(c i ); besterror 4: repeat 5: C i createtimeinterval(b,e) 6: C all createtimeinterval(e+1,100) 7: error evaluatemodel(p,c i,c all ) 8: if besterror > error then 9: besterror error 10: end if 11: e e : until besterror error 13: addtimeinterval(p, C i ) 14: i i + 1; b e 15: end while specific future time intervals between 52 and 100. The set P consists of K disjoint time intervals and its union is the full interval : K K M bid (t) = a i,t M bid,i (t), M ask (t) = a i,t M ask,i (t), i=1{ where a i,t = 1 if t C i, 0 otherwise, i=1 t [52, 100]. C i represents the i-th K post-liquidity shock time interval and M bid/ask,i (t) is the submodel responsible for predicting the constant price on the interval C i. Dividing the future time interval into the set of intervals P should avoid mixing the low signal-to-noise-ratio of far-away prices with the more predictable prices close to the liquidity shock. An additional model feature is that time intervals should have an increasing length (i.e., length(c i+1 ) length(c i )). This feature is a consequence of the main hypothesis because an always increasing prediction error may require averaging longer price time series to obtain a constant price prediction with an acceptable error. Algorithm 1 is responsible for dividing the future time interval into disjoint and consecutive sub-intervals of increasing length (line 3). It is implemented as a greedy algorithm and it is able to partition the post-liquidity shock time interval with O(n) time complexity. 2.2 Feature Engineering Our feature engineering strategy is, together with the model architecture, one of the relevant contributions of this letter and an important piece of our success. The following

6 Winning the Kaggle Algorithmic Trading Challenge 6 Algorithm 2 Feature selection algorithm 1: Train a single piece model using all S features 2: Compute model performance against the test set 3: Rank features importance (RF importance method) 4: for each subset size S i =S, S 1,..., 1 : do 5: Retrain the model with only S i most important features 6: Re-compute individual variable importance and re-rank 7: Fit the model to S f features and rank individual features 8: end for 9: Determine which S i yielded the smallest RMSE. Call this S f 10: repeat 11: Choose a set of semantically similar features from S f 12: Select the feature with less rank not selected before 13: Evaluate the model performance 14: If smaller RMSE, then remove the feature 15: until no improvement 16: repeat 17: Choose a feature set among the already removed in Steps 1)-9) considering only those semantically orthogonal with the already selected in Steps 1)-15) 18: If smaller RMSE, then we add the feature to S f 19: until no improvement 3 Validation The first step to validate the model ideas was to select a suitable feature subset. We applied the feature selection algorithm described in Section 2.4 to the same sample dataset used in the same section to evaluate the suitability of different modeling approaches. According to the discussion in Section 2.2.2, we should have applied our feature selection algorithm separately to single piece bid and ask models defined in the full time interval However, due to time constraints, we only optimized one side F b. F a was estimated from F b by just taking the ask side of price features. The selected feature sets F b and F a were used by all bid and ask sub-models respectively as suggested by the optimization problem relaxation described in Section The following step was to learn the optimal set P of time intervals. We used again the same sample dataset used in Section 2.3 to evaluate the suitability of different modeling approaches and computed the F b feature subset found in the previous step. The application of the partitioning algorithm (Section 2.1) on the bid model (i.e., M bid (t)) delivered the following set of time intervals: {52 52, 53 53, 54 55, 56 58, 59 64, 65 73, }. Our final model fitting setup consisted of three datasets of samples each randomly sampled from the training dataset and with the same security id proportions as the test dataset. We computed F b and F a for each sample and trained a complete model with each training dataset. Finally, the models were applied to the test dataset and the

7 Winning the Kaggle Algorithmic Trading Challenge 7 Evolution of Public and Private Scores RMSE submissions Figure 1: Evolution of public (dashed line) and private (solid line) scores. Feature extraction, selection, model partitioning and final prediction average were performed sequentially as indicated in the plot. three predictions from each sub-model were averaged. Fig. 1 shows the evolution of the public and private scores during the two months of the competition. The private score is the RMSE on the full test set. The private score was only made public after finishing the competition. The public score is the RMSE calculated on approximately 30% of the test data. The public score was available in real time to all competitors. Public and private scores are more correlated during the initial process of adding new features than during the second process of selecting the optimal feature subset. This lack of correlation could be due to a methodological bug during the execution of the feature selection algorithm: During this step the authors used a single dataset of samples instead of the three datasets used in the other validations stages. This could have biased our feature selection towards those features that better explain this particular dataset. Finally, the best solution was obtained by averaging the predictions obtained from each of three models fitted respectively with the three sample datasets (last three submissions). In order to test the main hypothesis, we also submitted an additional solution based on a single-piece model (4 th and 5 th last submissions). The many-piece model solution clearly provided the final edge to win. Therefore, we consider that this is a strong positive indicator for the model hypothesis discussed in Section 2. It is worth mentioning that, according to information disclosed in the challenge forums, a common modeling choice among most competitors was to use a single time interval with constant post liquidity shock bid and ask prices. This is an additional clue that points to the suitable implementation of our main hypothesis as a key component of our solution.

8 Winning the Kaggle Algorithmic Trading Challenge 8 4 Conclusions This letter presented our solution for the Kaggle Algorithmic Trading Challenge. Our main design hypothesis was that the predictive potential close to the liquidity shock should be higher and it should be degraded with the distance. This hypothesis guided the design of our model architecture and it required a complex feature extraction and selection strategy. An additional self-imposed constraint on this strategy was to uniquely generate semantically meaningful features. This self-imposed constraint was motivated by the authors will to generate a predictive model with the highest explanatory potential, but it also helped to identify features which had not been initially selected using a simple backward feature elimination method. Acknowledgments: The authors were partially supported by the FIRST program. References [1] Kaggle Algorithmic Trading Challenge, AlgorithmicTradingChallenge/data [2] F. Lillo, J. D.Farmer and R. N. Mantegna, Master curve for price-impact function, Nature, vol.421, pp , [3] T. Foucault, O. Kadan and E. Kandel, Limit Order Book as a Market for Liquidity, Review of Financial Studies, vol.18, no.4, pp , [4] J. Ulrich, Package TTR: Technical trading Rules, CRAN Repository: cran.r-project.org/web/packages/ttr/ttr.pdf [5] D. Reshef, Y. Reshef, H. Finucane, S. Grossman, G. McVean, P. Turnbaugh, E. Lander, M. Mitzenmacher, P. Sabeti, Detecting novel associations in large datasets, Science 334, vol.334, no. 6062, pp , [6] A. Liaw, Package randomforest: Breiman and Cutler s Random Forest for Classification and Regression, CRAN Repository: packages/randomforest/randomforest.pdf [7] G. Ridgeway, Package gbm, CRAN Repository: web/packages/gbm/gbm.pdf [8] Heritage Provider Network, Health Prize, Site: com/c/hhp [9] T. Van Nguyen, B. Mishra, Modeling Hospitalization Outcomes with Random Decision Trees and Bayesian Feature Selection, Unpublished, Site: nyu.edu/mishra/publications/mypub.html

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