The Winning Solution to the IEEE CIG 2017 Game Data Mining Competition

01/16/2019 ∙ by Anna Guitart, et al. ∙ Yokozuna Data 18

Machine learning competitions such as those organized by Kaggle or KDD represent a useful benchmark for data science research. In this work, we present our winning solution to the Game Data Mining competition hosted at the 2017 IEEE Conference on Computational Intelligence and Games (CIG 2017). The contest consisted of two tracks, and participants (more than 250, belonging to both industry and academia) were to predict which players would stop playing the game, as well as their remaining lifetime. The data were provided by a major worldwide video game company, NCSoft, and came from their successful massively multiplayer online game Blade and Soul. Here, we describe the long short-term memory approach and conditional inference survival ensemble model that made us win both tracks of the contest, as well as the validation procedure that we followed in order to prevent overfitting. In particular, choosing a survival method able to deal with censored data was crucial to accurately predict the moment in which each player would leave the game, as censoring is inherent in churn. The selected models proved to be robust against evolving conditions---since there was a change in the business model of the game (from subscription-based to free-to-play) between the two sample datasets provided---and efficient in terms of time cost. Thanks to these features and also to their a ability to scale to large datasets, our models could be readily implemented in real business settings.

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1 Introduction

In video games, reducing player churn is crucial to increase player engagement and game monetization. By using sophisticated churn prediction models perianez2016churn ; GameBigData , developers can now predict when and where (i.e., in which part of the game) individual players are going to stop playing and take preventive actions to try to retain them. Examples of those actions include sending a particular reward to a player or improving the game following a player-focused data-driven development approach.

Survival analysis focuses on predicting when a certain event will happen, considering censored data. In this case, our event of interest is churn, and highly accurate prediction results can be obtained by combining survival models and ensemble learning techniques. On the other hand, and even though they do not take into account the censoring of churn data, deep learning methods can also be helpful to foresee when a player will quit the game. In particular, long short-term memory (LSTM) networks—recurrent neural networks (RNNs) trained using backpropagation through time—constitute an excellent approach to model sequential problems.

The 2017 IEEE Conference on Computational Intelligence and Games hosted a Game Data Mining competition gamecompetition , in which teams were to accurately predict churn for NCSoft’s game Blade and Soul. In this work, we present the feature engineering and modeling techniques that led us to win both tracks of that contest.

2 Game Data Mining Competition

2.1 The Data

The data to be analyzed came from NCSoft’s Blade and Soul, a massively multiplayer online role-playing game. It consisted of one training dataset and two test datasets, for which results should be evaluated without output information. Each of the datasets covered different periods of time and had information about different users. A summary of the original records is presented in Table 1.

Thirty percent of the players churned in each of the provided data samples. A player was to be labeled as “churned” if he or she did not log in between the fourth and eighth week after the data period, as shown in Figure 1.

Log data were provided in CSV format. Each player’s action log was stored in an individual file, with the user ID as the file name. In log files, every row corresponded to a different action and displayed the time stamp, action type, and detailed information. Table 2

shows a sample log file. There were 82 action types, which represented various in-game player behaviors, such as logging in, leveling up, joining a guild, or buying an item. These 82 action types were classified into 6 categories: connection, character, item, skill, quest, and guild. As shown in Table

2, the detailed information provided depended on the type of action. For example, actions related to earning or losing money included information about the amount of money owned by the character, whereas actions that had to do with battles reflected the outcomes of those battles.

Dataset Data Period Weeks Players Size
Train Apr-01-2017– May-11-2017 6 4000 48 GB
Test 1 July-27-2016– Sep-21-2016 8 3000 30 GB
Test 2 Dec-14-2017– Feb-08-2017 8 3000 30 GB
Table 1: Details of the three datasets.
Time Action Type Details (up to 72 Columns)
2016-04-01 00:09:30.597 Enter world Server ID, character ID, character job, character level, …
2016-04-01 00:12:32.158 Join guild Guild ID, guild level, character data, …
2016-04-01 00:14:50.084 Enter zone Zone ID, character data, …
2016-04-01 00:14:50.084 Save equipped item Item type, item level, equipment score, character data, …
2016-04-01 00:18:54.094 Team duel end Duel ID, duel server, duel point, type of target, …
Table 2: A sample log file.
Figure 1: Between 6 and 8 weeks of data logs were provided (see Table 1). The goal of this competition was to predict churn and survival time from the fourth to the eighth week after the data period.

2.2 Challenge

The aim of this competition gamecompetition was to predict churn and life expectancy during a certain prediction period; see Figure 1. The contest consisted of two tracks:

  • In track 1, participants had to predict whether each player would log in or not during the prediction period and output binary results.

  • In track 2, participants had to predict the survival time (in days) for each player, that is, the number of days between their last action in the provided data and their last predicted action.

2.3 Evaluation

The results of track 1 were evaluated through the score:

(1)

where

(2)
(3)

Here TP stands for true positives, FP for false positives, and FN for false negatives. On the other hand, the root mean squared logarithmic error (RMSLE) was adopted to evaluate the results of track 2:

(4)

where and are the observed and predicted survival times, respectively.

Participants should upload their prediction results for the two test sets to an online submission system, with the number of uploads limited to one every 30 min. After every submission, partial results were calculated and shown on a leader board. For these partial results, only ten percent of the players in each set were considered. The final results—calculated with the full sets—were announced after the submission system was closed.

3 Data Preparation and Feature Engineering

3.1 Time-Oriented Data

More than 3000 variables—including time series information and static inputs—were calculated for each player during the feature engineering process and incorporated into the models. Below we outline some of the computations performed.

  • [leftmargin=2.3em,labelsep=4mm]

  • Actions: Number of times each type of action was performed per day. Some actions were grouped and different statistics were computed. For example, every time a player created, joined, or invited other players to a guild was counted as a “Guild” feature. The way in which actions were grouped is shown in Table 3.

  • Sessions: Different sessions per player and day.

  • Playtime: Total playtime per day.

  • Level: Daily last level and evolution in the game.

  • Target level: Daily highest battle-target level.

  • Number of actors: Number of actors played per day.

  • In-game money: Daily information about money earned and spent.

  • Equipment: Daily equipment score. The higher this score, the better the equipment owned by the player.

  • Static Data: We also calculated some statistics of the time series data (for each player), considering the whole data period.

  • Statistics:

    Different statistics, such as the mean, median, standard deviation, or sum of the time-series features mentioned in Section 

    3.1, were applied depending on the variable. For example, the total amount of money the player got during the data period or the standard deviation of the daily highest battle-target level.

  • Actors information: Number of actors usually played.

  • Guilds: Total number of guilds joined.

  • Information on days of the week: Distribution of actions over different days of the week.

Group Actions
Team Invite a target to a team, join a team, kick out a target from a team, team battle
Guild Create a guild, invite a target to a guild, join a guild
Quest Complete a quest, complete daily challenge, complete weekly challenge
Trade (Get) Get money and item through exchange-window
Trade (Give) Give money and item through exchange-window
Skill Acquire skill, level up skill, use training point, acquire quest skill
Item Repair item, evolve item, exceed item limit
Auction Put item to auction, buy item from auction
Table 3: Groups of actions considered in this work.

3.2 Autoencoders

Autoencoders are unsupervised learning models based on neural networks, which are often applied for dimensionality reduction hinton2006reducing and representation learning bengio2009learning

. Compared to human feature selection, applying autoencoders is less labor-intensive and serves to capture the underlying distribution and factors of the inputs

bengio2013representation .

Autoencoders can be trained employing various kinds of neural networks and are widely used in many machine-learning areas. For example, the authors of stober2015deep

applied convolutional neural networks (CNNs) to train autoencoders for representation learning on electroencephalography recordings. A deep belief network autoencoder was used to encode speech spectrograms in

deng2010binary . LSTM autoencoders were trained to reconstruct natural language paragraphs in li2015hierarchical . And another work larsen2015autoencoding combined generative adversarial networks with autoencoders to encode visual features.

As neural-network-based encoders, the structures of autoencoders are multilayer networks with an input layer, one or several hidden layers, and an output layer. While training autoencoders, the inputs and target outputs are the same

bengio2009learning

. The values of the nodes in a hidden layer are the encoded features. A reconstruction error, which is measured by a cost function such as the mean squared error, is calculated to evaluate the discrepancy between the inputs and their reconstructions, that is, the values in the output layer. As the reconstruction error decreases, the ability of the encoded features to represent and reconstruct the input values increases. This minimization of the reconstruction error is usually accomplished by stochastic gradient descent

bengio2012unsupervised .

4 Feature Selection

As commented in the previous section, there were more than 3000 extracted features after the data preparation. Besides simply adopting all these features, the following three feature selection methods were also tested.

4.1 LSTM Autoencoder

An LSTM autoencoder was employed to derive representative features from the time-series data described in Section 3.1. It comprised five layers: the input layer, a reshape layer, a dense (fully connected) layer, another reshape layer, and the output layer. The values of the nodes in the dense layer are the encoded features. In this work, time-series data were encoded, reducing the dimension of the feature space up to 500 features.

4.2 Feature Value Distribution

In the periods covered by the training and Test 1 datasets, Blade and Soul used a subscription payment system, where players pay a fixed monthly fee. In contrast, in the period corresponding to the Test 2 dataset the game was free-to-play, an approach in which players only pay to purchase in-game items. This change in the business model significantly affected player behavior: for example, most of the players in the Test 2 dataset gained much more experience than players in the training or Test 1 sets.

A feature may become noise if its distribution in the test set is too different from that in the training set. To select only those features distributed over a similar range in both the training and test sets, we calculated the 95% confidence interval for each feature in the training set. After performing experiments with cross-validation, a feature was selected only when more than 70% of its values in the test set were within that 95% confidence interval derived from the training set.

4.3 Feature Importance

A permutation variable importance measure (VIM) based on the area under the curve (AUC) janitza2013auc was chosen in the case of survival ensembles. This method is closely related to the commonly used error-rate-based permutation VIM and is more robust against class imbalance than existing alternatives, because the error rate of a tree is replaced by the AUC.

5 Machine Learning Models

In this section we describe the models that served us to win the competition.

5.1 Tree-Based Ensemble Learning

Decision trees morgan1963problems are nonparametric techniques used for classification and regression problems breiman1984classification ; quinlan2014c4 .

The outcome is modeled by a selection of independent covariates from a pool of variables. The feature space is recursively split to arrange samples with similar characteristics into homogeneous groups and maximize the difference among them. The tree is built starting from a root node, which is recursively split into daughter nodes according to a specific feature and split-point selection method. At each node of the tree, some statistical measure is minimized—commonly the (Gini) impurity breiman1984classification , even though information gain quinlan2014c4

or variance reduction

breiman1984classification can be used as well. The splitting finishes when a certain stopping criterion is met (e.g., early stopping drucker2002effect ), or the full tree can be grown and pruned afterwards bohanec1994trading to reduce overfitting bias.

However, a single tree is sensitive to small changes in the training data. This results into high variance in the predictions, making them not competitive in terms of accuracy breiman1996bagging ; turney1995bias .

Over the past decade, tree-based ensembles have become increasingly popular due to their effectiveness, state-of-the-art results, and applicability to many diverse fields, such as biology li2012identification , chemistry zhang2005boosting ; palmer2007random , telecommunications, or games perianez2016churn ; GameBigData , among others. Tree-based ensemble methods kretowska2014comparison overcome the single-tree instability problem and also improve the accuracy of the results by averaging over the predictions from hundreds or even thousands of trees.

Decision tree ensembles are explicative models, useful to understand the predictive structure of the problem, and provide variable importance scores that can be used for variable selection janitza2013auc .

In this work we focus in two tree-based ensemble approaches: extremely randomized trees and conditional inference survival ensembles.

5.1.1 Extremely Randomized Trees

Extremely randomized trees were first presented in geurts2006extremely and consist of an ensemble of decision trees constructed by introducing random perturbations into the learning procedure from an initial subsample geurts2011learning . In this method, both the variable and the split-point selection are performed randomly based on a given cutting threshold. Totally randomized trees are built with structures independent of the output values of the learning sample. This technique has been previously used in the context of video games ItemPrediction .

Another popular randomization-based ensemble is the classical random forest algorithm

breiman2001random , which differs from the extremely randomized forest in that the split point is not chosen randomly; instead, the best cutting threshold is selected for the feature. Because of this, the extremely randomized forest approach is faster, while producing similarly competitive results—even outperforming the random forest method in some occasions geurts2006extremely .

5.1.2 Conditional Inference Survival Ensembles

Conditional inference trees hothorn2006unbiased are decision trees with recursive binary partitioning zeileis2008model . They differ from other variants in that they are formulated according to a two-step partitioning process: first, the covariate that is more correlated with the output is selected by standardized linear statistics; then, in a second step, the optimal split point is determined by comparing two-sample linear statistics under some splitting criterion. In this way, conditional inference ensembles hothorn2005survival are not biased and do not overfit, contrary to one-step approaches for partitioning (e.g., random forests are biased towards variables with many possible split points hothorn2006unbiased ). Any splitting criterion can be used for the split, and the algorithm stops if a minimal significance is not reached when splitting hothorn2006unbiased .

Conditional inference survival ensembles hothorn2006unbiased ; perianez2016churn

constitute a particular implementation of this method that uses the survival function of the Kaplan–Meier estimator as splitting criterion. Survival approaches were introduced to deal with time-to-event problems or censoring. Problems with censored data (of which churn is a typical example) are characterized by having only partially labeled data: we only have information about users who already churned, not about those who are still playing.

Other survival ensembles such as random survival forests ishwaran2008random do deal with censoring, but they present the same kind of bias as the random forest approach. We refer the reader to bou2011review for a review on different types of survival trees.

5.2 Long Short-Term Memory

An LSTM network hochreiter1997long is a type of RNN graves2013speech

. While conventional RNNs have a vanishing gradient problem that makes the network highly dependent on a limited number of the latest time steps

hochreiter1997long and are not able to remember events that occurred many time steps ago, LSTM networks consist of multiple gates trained to determine what information should be memorized or forgotten at each time step. As a consequence, an LSTM network can learn longer-range sequential dependencies than an RNN network.

LSTM networks have been successfully applied to e.g., machine translation sutskever2014sequence , audio processing graves2013speech , and time-series prediction gers1999learning , achieving state-of-the-art results. They can be further extended to act like an autoencoder li2015hierarchical

, learning without supervision a representation of time-series data to reduce the dimensionality or creating single vector representations of sequences

palangi2016deep . Some other variations are e.g., bidirectional LSTM neworks that process both the beginning and end of the sequence graves2005framewise

and gated recurrent units

chung2014empirical that simplify the LSTM model and are generally more efficient to compute. There are other neural network approaches that have been explored in connection to video game data. For instance, deep belief networks were applied to time series forecasting in guitart2018ficc and deep neural networks (DNNs) and CNNs served to predict customer lifetime value in chen2018ltv .

6 Model Specification

For both tracks and test datasets, multiple models were analyzed, with those based on LSTM, extremely randomized trees, and conditional inference trees providing the best results—and leading us to win the two tracks. The parameters of each model were optimized by cross-validation. (See Section 7.1.)

6.1 Binary Churn Prediction (Track 1)

6.1.1 Extremely Randomized Trees

Extremely randomized trees proved the best model for the Test 1 dataset in this first track. A splitting criterion based on the Gini impurity was applied. After parameter optimization by cross-validation, 50 sample trees were selected and the minimum number of samples required to split an internal node was set to 50.

6.1.2 Lstm

In the first track, an LSTM model produced the best prediction results for the Test 2 dataset. To obtain representative features from the time-oriented data and static data mentioned in Section 3

, a neural network structured with LSTM layers and fully-connected layers was proposed, that is, an LSTM network and a multilayer perceptron network (MLP) were combined. As shown in Figure 

2, the time series input layer was followed by two LSTM layers, while static features were processed with a fully-connected layer. Then, the outputs from both parts were merged into a representative vector. Finally, an MLP network was applied to the representative vector to output the final result, the prediction on whether the user would churn or not.

Figure 2: Neural network structure that provided the best results for the Test 2 dataset in the binary case (track 1). The left part is an LSTM network with the time-series data listed in Section 3.1 as input. The right part is a DNN that takes static features as input. The bottom part is a DNN which merges the outputs of these two networks and provides the final prediction result .

Dropout layers hinton2012improving were inserted in between every two layers to reduce overfitting and perform random feature selection. Since there were many correlated features, such as total playtime and daily playtime, randomly selecting a subset of the input time-series and static features by means of dropout layers prevented the model from depending too much on similar features and improved its generalizability.

6.2 Survival Time Analysis (Track 2)

Conditional Inference Survival Ensembles

Using conditional inference survival ensembles—a censoring approach—provided the best results for both test datasets in the second track. The following optimized parameters and settings were applied: 900 unbiased trees, 30 input features randomly selected from the total input sample, subsampling without replacement, and a stopping criterion based on univariate -values.

The same approach was already used for video game churn prediction in perianez2016churn ; GameBigData . However, in those works, the available data covered the whole player lifetime (since registration until their last login) and the maximum level reached and accumulated playtime up to the moment of leaving the game were also estimated. In contrast, in this competition we were working with partial user data, as previously explained in Section 2.2.

7 Model Validation

Model validation is a major requirement to obtain accurate and unbiased prediction results. It consists in training the model on subsamples of the data and assessing its ability to generalize to larger and independent datasets.

The data used in this study were affected by a business modification: a change in the billing system that shifted the distribution of the data, as explained in Section 4.2. Thus, as the training set consisted entirely of data taken from the subscription model (with free-to-play samples found only in one of the test sets), there was a significant risk of overfitting. For this reason, when performing our model selection, we either focused on methods that are not prone to overfitting (such as conditional inference survival ensembles) or tried to devise a way to avoid it (in the case of LSTM). For the extremely randomized trees approach, data preprocessing and careful feature selection are essential to reduce the prediction variance and bias by training the model on the most relevant features and discarding those that are not so important.

For model validation and estimation, we followed a -fold cross-validation approach stone1974cross with repetition.

Apart from the score and RMSLE mentioned in Section 2.3, additional error estimation methods were applied to evaluate models comprehensively.

7.1 Cross-Validation

In both tracks, we performed five-fold cross-validation for model selection and performance evaluation. The -fold cross-validation stone1974cross method reduces bias—as most of the data is used for the fitting—and also variance—since training data are used as the validation set. This method provides a conservative estimate for the generalizability of the model cawley2010over . We decided to use 5 folds, as shown in Figure 3, so that each of them was large and representative enough, also making sure that they had similar distributions of the target data.

After partitioning the whole training sample into training and validation splits (consisting of 80% and 20% of the data, respectively), we performed the five-fold cross-validation for parameter tuning. With the best set of parameters, we applied the models to the validation split and selected only those that produced top scores.

Once the cross-validation process was finished, we trained the most promising models (using the adjusted parameters) on the whole training dataset and submitted our predictions for the Test 1 and 2 sets. After checking the partial results displayed in the leader board, we kept using only the models that were exhibiting the best performance. Tables 4 and 5 show our main results in the two tracks.

However, let us recall that the scores shown in the leader board were computed using only 10% of the total test sample. Thus, focusing too much in increasing those scores might have led to an overfitting problem, where the model would yield accurate predictions for that 10% subsample while failing to generalize to the remaining 90% of the data. This is precisely what we wanted to avoid by performing an exhaustive cross-validation of the models prior to the submissions.

Figure 3: Five-fold cross-validation was performed after dividing the training data into training and validation splits.
Test Set Model Features Score Accuracy (%) Validation TP TN FP FN
Test 1 ERT A 0.6096 73.23 0.650 627 1570 530 273
ERT C 0.6073 73.10 0.633 624 1569 531 276
C. Ensembles B 0.6055 74.33 0.636 591 1639 461 309
LSTM C 0.5999 72.43 0.661 620 1553 547 280
LSTM A 0.5980 73.07 0.663 601 1591 509 299
Test 2 LSTM A 0.6377 75.07 0.659 683 1654 446 330
C. Ensembles B 0.6173 75.00 0.638 605 1645 455 295
LSTM C 0.6162 74.33 0.661 618 1612 488 282
ERT A 0.6159 75.13 0.639 598 1656 444 302
ERT C 0.6108 75.07 0.630 587 1665 435 313
Table 4: Track 1 results. (ERT: Extremely ranzomized trees, C. Ensembles: Conditional inference survival ensembles, LSTM: Combination of long short-term memory and multilayer perceptron networks, A: Feature value distribution, B: Feature importance, C: All features without feature selection, Validation: -score on the training set, TP: True positive, TN: True negative, FP: False positive, FN: False negative, Accuracy: .)
Test Set RMSLE RMSE MAE Validation
Test 1 1.0478 127.0 104.9 0.9142
Test 2 0.8621 60.9 45.3 0.9153
Table 5: Track 2 results. (RMSLE: Root mean squared logarithmic error, RMSE: Root mean squared error, MAE: Mean absolute error, Validation: RMSLE on the training set.)

7.2 Results

Table 4 lists the track 1 results for the different models and feature selection methods (described in Section 4.3) that we explored. For the Test 1 dataset, the best results were achieved when using extremely randomized trees (ERT) and feature value distribution to perform feature selection. For the Test 2 dataset, the higher -score was obtained with the model that combined LSTM and DNN networks and the same feature selection method as in the previous case.

In Table 5, we show the track 2 results. Here, we used a model based on conditional inference survival ensembles, and features were selected through the feature importance method.

It is interesting to note that, in both tracks, the Test 2 dataset yielded better results (higher  scores in Table 4 and lower errors in Table 5) for all the models and feature selection methods tested—a trend also observed in the results obtained by other teams. Recalling that the Test 1 dataset covered a period in which the game followed a subscription-based business model, whereas for Test 2 the game was already free-to-play, this suggest that machine learning models learn player patterns more easily in games that employ a freemium scheme.

From these observations, it is apparent that the ability of the models to generalize and adapt to evolving data, namely to learn from different data distributions, was essential in this competition. Due to this, we devoted much effort to perform a careful model selection and validation, which allowed us to clearly outperform all the other groups at the end—when the full test sample was used to obtain the final scores for each model—even if we were not at the top of the leader board.

7.3 Binary Churn Prediction (Track 1)

Besides the score, we also used the receiver operating characteristic (ROC) curve and the AUC measure to provide a more exhaustive validation.

The ROC curve is constructed by representing the true positive (accurately predicted positive samples) and false positive (misclassified negative samples) rates, and the AUC is just the area under the ROC curve bradley1997use .

7.4 Survival Time Analysis (Track 2)

In the case of track 2, the outcome is the overall survival time of the player in the game. In addition to the measure, we evaluated the mean absolute error (MAE), root mean squared error (RMSE) and integrated Brier score (IBS). The MAE describes the average deviation of the predicted value with respect to the actual value. The RMSE has the same expression as the RMSLE (see Equation (4)) but without taking logarithms. Finally, the IBS is an evaluation measure specifically formulated for survival analysis graf1999assessment ; mogensen2012evaluating that provides a final score for the error estimation of the survival time outputs.

8 Discussion and Conclusions

The models that led us to win both tracks of the Game Data Mining competition hosted at the 2017 IEEE Conference on Computational Intelligence and Games were based on long short-term memory networks, extremely randomized trees, and conditional inference survival ensembles. Model selection was certainly key to our success in track 2, which involved predicting the time for each player to churn (i.e., leave the game), as we were the only group that employed a model well-suited to deal with censored data. Since censoring is inherent in churn, adopting a survival model gave us a decisive advantage.

All the selected models proved to be robust against evolving conditions, managing to adapt to the change in the game’s business model that took place between the two provided datasets. In addition, they were efficient in terms of time cost: in both tracks, it took less than one hour to train each model on the 4000 user training set and apply it to the 6000 testing users. (As cross-validation and intensive parameter optimization were performed, the full experimental procedure actually took longer.) Thanks to these properties—and also to their ability to scale to large datasets—our models could be readily implemented in real business settings.

There were some factors that made this competition particularly challenging. First, only 10% of the test data were available for validation, which forced us to perform an exhaustive and careful training in order to prevent overfitting. Moreover, the fact that the provided datasets contained information on just a small subsample of all players of this title and covered a short period of time (6–8 weeks) made this prediction problem particularly ambitious. Knowing the characteristics of the selected players (e.g., whether all of them were paying users or even VIP users) or the full data history of each player—since they registered until their last login—could have served to achieve even better results, as those obtained in perianez2016churn ; GameBigData for a model based on conditional inference survival ensembles.

Computing additional features could also have helped to improve accuracy. Concerning the machine learning models, it would be interesting to apply other advanced DNN techniques, such as CNNs, which were already used in chen2018ltv to predict the lifetime value of video game players from time series data.

On the whole, by winning this competition we showed that the proposed models are able to accurately predict churn in a real game, pinpointing which players will leave the game and estimating when they will do it. Moreover, the accuracy of the results should be even higher in real situations in which some of the limitations discussed above are removed—in particular, once larger datasets that include more users and span longer periods of time are available. Thanks to this accuracy and also to their adaptability to evolving conditions, time-efficiency, and scalability, we expect these machine learning models to play an important role in the video game industry in the forthcoming future, allowing studios to increase monetization and to provide a personalized game experience.

Conceptualization, A.G., P.P.C. and Á.P.; Methodology, A.G., P.P.C. and Á.P.; Software, A.G., P.P.C. and Á.P.; Validation, A.G. and P.P.C.; Formal Analysis, A.G., P.P.C. and Á.P.; Investigation, A.G., P.P.C. and Á.P.; Resources, Á.P.; Data Curation, P.P.C.; Writing—Original Draft Preparation, A.G., P.P.C. and Á.P.; Writing—Review & Editing, A.G. and Á.P.; Visualization, A.G. and P.P.C.; Supervision, Á.P.; Project Administration, Á.P.This research received no external funding.

Acknowledgements.
We thank Javier Grande for his careful review of the manuscript and Vitor Santos for his support. The authors declare no conflict of interest. References

References

  • (1) Periá nez, Á.; Saas, A.; Guitart, A.; Magne, C. Churn Prediction in Mobile Social Games: Towards a Complete Assessment Using Survival Ensembles. In Proceedings of the 2016 IEEE International Conference on Data Science and Advanced Analytics (DSAA), Montreal, QC, Canada, 17–19 October 2016; pp. 564–573.
  • (2) Bertens, P.; Guitart, A.; Periá nez, Á. Games and Big Data: A Scalable Multi-Dimensional Churn Prediction Model. In Proceedings of the IEEE Conference on Computational Intelligence and Games (CIG), New York, NY, USA, 22–25 August 2017; pp. 33–36.
  • (3) Game Data Mining Competition 2017. Available online: https://cilab.sejong.ac.kr/gdmc2017/ (accessed on 10 December 2018).
  • (4) Hinton, G.E.; Salakhutdinov, R.R. Reducing the dimensionality of data with neural networks. Science 2006313, 504–507. [CrossRef]
  • (5) Bengio, Y. Learning deep architectures for ai. Found. Trends Mach. Learn. 2009, 2, 1–127. [CrossRef]
  • (6) Bengio, Y.; Courville, A.; Vincent, P. Representation learning: A review and new perspectives. IEEE Trans. Pattern Anal. Mach. Intell. 2013, 35, 1798–1828. [CrossRef] [PubMed]
  • (7) Stober, S.; Sternin, A.; Owen, A.M.; Grahn, J.A. Deep feature learning for EGG recordings. arXiv 2015, arXiv:1511.04306.
  • (8) Deng, L.; Seltzer, M.L.; Yu, D.; Acero, A.; Mohamed, A.-R.; Hinton, G. Binary coding of speech spectrograms using a deep auto-encoder. In Proceedings of the Eleventh Annual Conference of the International Speech Communication Association, Graz, Austria, 15–19 September 2010.
  • (9) Li, J.; Luong, M.-T.; Jurafsky, D. A hierarchical neural autoencoder for paragraphs and documents.

    In Proceedings of the 7th International Joint Conference on Natural Language Processing, Taipei, Taiwan, 27 November–1 December 2015; Volume 1, pp. 1106–1115.

  • (10) Larsen, A.B.L.; Sønderby, S.K.; Larochelle, H.; Winther, O. Autoencoding beyond pixels using a learned similarity metric. In Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, 19–24 June 2015; Volume 48, pp. 1558–1566.
  • (11) Bengio, Y.; Courville, A.C.; Vincent, P. Unsupervised feature learning and deep learning: A review and new perspectives. Avaible online: https://pdfs.semanticscholar.org/f8c8/619ea7d68e604e40b814b40c72888a755e95.pdf (accessed on 15 December 2018).
  • (12) Janitza, S.; Strobl, C.; Boulesteix, A.-L. An auc-based permutation variable importance measure for random forests. BMC Bioinform. 2013, 14, 119. [CrossRef] [PubMed]
  • (13) Morgan, J.N.; Sonquist, J.A. Problems in the analysis of survey data, and a proposal. J. Am. Stat. Assoc. 196358, 415–434. [CrossRef]
  • (14) Breiman, L.; Friedman, J.; Stone, C.J.; Olshen, R.A. Classification and Regression Trees; CRC Press: Boca Raton, FL, USA, 1984.
  • (15) Quinlan, J.R. C4. 5: Programs for Machine Learning; Elsevier: Amsterdam, The Netherlands, 2014.
  • (16) Drucker, H. Effect of pruning and early stopping on performance of a boosting ensemble. Comput. Stat. Data Anal. 2002, 38, 393–406. [CrossRef]
  • (17) Bohanec, M.; Bratko, I. Trading accuracy for simplicity in decision trees. Mach. Learn. 1994, 15, 223–250. [CrossRef]
  • (18) Breiman, L. Bagging predictors. Mach. Learn. 1996, 24, 123–140. [CrossRef]
  • (19) Turney, P. Bias and the quantification of stability. Mach. Learn. 1995, 20, 23–33. [CrossRef]
  • (20) Li, Z.-C.; Lai, Y.-H.; Chen, L.-L.; Zhou, X.; Dai, Z.; Zou, X.-Y. Identification of human protein complexes from local sub-graphs of protein–protein interaction network based on random forest with topological structure features. Anal. Chim. Acta 2012, 718, 32–41. [CrossRef]
  • (21) Zhang, M.; Xu, Q.; Massart, D. Boosting partial least squares. Anal. Chem. 2005, 77, 1423–1431. [CrossRef] [PubMed]
  • (22) Palmer, D.S.; O’Boyle, N.M.; Glen, R.C.; Mitchell, J.B. Random forest models to predict aqueous solubility. J. Chem. Iinf. Model. 2007, 47, 150–158. [CrossRef] [PubMed]
  • (23) Kretowska, M. Comparison of tree-based ensembles in application to censored data.

    In Proceedings of the International Conference on Artificial Intelligence and Soft Computing, Zakopane, Poland, 13–17 June 2014.

  • (24) Geurts, P.; Ernst, D.; Wehenkel, L. Extremely randomized trees. Mach. Learn. 2006, 63, 3–42. [CrossRef]
  • (25) Geurts, P.; Louppe, G. Learning to rank with extremely randomized trees. In Proceedings of the JMLR: Workshop and Conference Proceedings, Fort Lauderdale, FL, USA, 11–13 April 2011; Volume 14, pp. 49–61.
  • (26) Bertens, P.; Guitart, A.; Periá nez, Á. A Machine-Learning Item Recommendation System for Video Games. arXiv 2004, arXiv: 1806.04900.
  • (27) Breiman, L. Random forests. Mach. Learn. 2001, 45, 5–32. [CrossRef]
  • (28) Hothorn, T.; Hornik, K.; Zeileis, A. Unbiased recursive partitioning: A conditional inference framework. J. Comput. Graph. Stat. 2006, 15, 651–674. [CrossRef]
  • (29) Zeileis, A.; Hothorn, T.; Hornik, K. Model-based recursive partitioning. J. Comput. Graph. Stat. 2008, 17, 492–514. [CrossRef]
  • (30) Hothorn, T.; Bühlmann, P.; Dudoit, S.; Molinaro, A.; van der Laan, M.J. Survival ensembles. Biostatistics 20057, 355–373. [CrossRef]
  • (31) Ishwaran, H.; Kogalur, U.B.; Blackstone, E.H.; Lauer, M.S. Random survival forests. Ann. Appl. Stat 2008, 2, 841–860. [CrossRef]
  • (32) Bou-Hamad, I.; Larocque, D.; Ben-Ameur, H. A review of survival trees. Stat. Surv. 2011, 5, 44–71. [CrossRef]
  • (33) Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput. 1997, 9, 1735–1780. [CrossRef] [PubMed]
  • (34) Graves, A.; Mohamed, A.-R.; Hinton, G. Speech recognition with deep recurrent neural networks. In Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (Icassp), Vancouver, British, 26–31 May 2013; pp. 6645–6649.
  • (35) Sutskever, I.; Vinyals, O.; Le, Q.V. Sequence to sequence learning with neural networks. In Advances in Neural Information Processing Systems; Mit Press: Cambridge, MA, USA, 2014; pp. 3104–3112.
  • (36) Gers, F.A.; Schmidhuber, J.; Cummins, F. Learning to forget: Continual prediction with LSTM. In Proceedings of the 9th International Conference on Artificial Neural Networks: ICANN ’99, Edinburgh, UK, 7–10 September 1999.
  • (37) Palangi, H.; Deng, L.; Shen, Y.; Gao, J.; He, X.; Chen, J.; Song, X.; Ward, R. Deep sentence embedding using long short-term memory networks: Analysis and application to information retrieval. IEEE/ACM Trans. Audio Speech Lang. Process. (TASLP) 2016, 24, 694–707. [CrossRef]
  • (38) Graves, A.; Schmidhuber, J. Framewise phoneme classification with bidirectional LSTM and other neural network architectures. Neural Netw. 2005, 18, 602–610. [CrossRef] [PubMed]
  • (39) Chung, J.; Gulcehre, C.; Cho, K.; Bengio, Y. Empirical evaluation of gated recurrent neural networks on sequence modeling. NIPS 2014 Workshop on Deep Learning. arXiv 2014, arXiv:1412.3555.
  • (40) Guitart, A.; Chen, P.P.; Bertens, P.; Periáñez, Á. Forecasting Player Behavioral Data and Simulating In-Game Events. In Advances in Information and Communication Networks. Future of Information and Communication Conference (FICC). Advances in Intelligent Systems and Computing; Arai K., Kapoor S., Bhatia R., Eds.; Springer: Cham, Swizzland, 2018; Volume 886.
  • (41) Chen, P.P.; Guitart, A.; Periá nez, Á.; Fernández del Río, A.

    Customer lifetime value in video games using deep learning and parametric models.

    In Proceedings of the IEEE International Conference on Big Data, Seattle, WA, USA, 10–13 December 2018.
  • (42) Hinton, G.E.; Srivastava, N.; Krizhevsky, A.; Sutskever, I.; Salakhutdinov, R.R. Improving neural networks by preventing co-adaptation of feature detectors. arXiv 2012, arXiv:1207.0580.
  • (43) Stone, M. Cross-validatory choice and assessment of statistical predictions. J. R. Stat. Soc. Ser. B (Methodol.) 1974, 36, 111–147. [CrossRef]
  • (44) Cawley, G.C.; Talbot, N.L. On over-fitting in model selection and subsequent selection bias in performance evaluation. J. Mach. Learn. Res. 2010, 11, 2079–2107.
  • (45) Bradley, A.P. The use of the area under the roc curve in the evaluation of machine learning algorithms. Pattern Recognit. 1997, 30, 1145–1159. [CrossRef]
  • (46) Graf, E.; Schmoor, C.; Sauerbrei, W.; Schumacher, M. Assessment and comparison of prognostic classification schemes for survival data. Stat. Med. 1999, 18, 2529–2545. [CrossRef]
  • (47) Mogensen, U.B.; Ishwaran, H.; Gerds, T.A. Evaluating random forests for survival analysis using prediction error curves. J. Stat. Softw. 2012, 50, 1. [CrossRef]