Fabian Hadiji

Predicting player churn in the wild

Free-to-Play or “freemium” games represent a fundamental shift in the business models of the game industry, facilitated by the increasing use of online distribution platforms and the introduction of increasingly powerful mobile platforms. The ability of a game development company to analyze and derive insights from behavioral telemetry is crucial to the success of these games which rely on in-game purchases and in-game advertising to generate revenue, and for the company to remain competitive in a global marketplace. The ability to model, understand and predict future player behavior has a crucial value, allowing developers to obtain data-driven insights to inform design, development and marketing strategies. One of the key challenges is modeling and predicting player churn. This paper presents the first cross-game study of churn prediction in Free-to-Play games. Churn in games is discussed and thoroughly defined as a formal problem, aligning with industry standards. Furthermore, a range of features which are generic to games are defined and evaluated for their usefulness in predicting player churn, e.g. playtime, session length and session intervals. Using these behavioral features, combined with the individual retention model for each game in the dataset used, we develop a broadly applicable churn prediction model, which does not rely on game-design specific features. The presented classifiers are applied on a dataset covering five free-to-play games resulting in high accuracy churn prediction.

Poisson Dependency Networks: Gradient Boosted Models for Multivariate Count Data

Although count data are increasingly ubiquitous, surprisingly little work has employed probabilistic graphical models for modeling count data. Indeed the univariate case has been well studied, however, in many situations counts influence each other and should not be considered independently. Standard graphical models such as multinomial or Gaussian ones are also often ill-suited, too, since they disregard either the infinite range over the natural numbers or the potentially asymmetric shape of the distribution of count variables. Existing classes of Poisson graphical models can only model negative conditional dependencies or neglect the prediction of counts or do not scale well. To ease the modeling of multivariate count data, we therefore introduce a novel family of Poisson graphical models, called Poisson Dependency Networks (PDNs). A PDN consists of a set of local conditional Poisson distributions, each representing the probability of a single count variable given the others, that naturally facilitates a simple Gibbs sampling inference. In contrast to existing Poisson graphical models, PDNs are non-parametric and trained using functional gradient ascent, i.e., boosting. The particularly simple form of the Poisson distribution allows us to develop the first multiplicative boosting approach: starting from an initial constant value, alternatively a log-linear Poisson model, or a Poisson regression tree, a PDN is represented as products of regression models grown in a stage-wise optimization. We demonstrate on several real world datasets that PDNs can model positive and negative dependencies and scale well while often outperforming state-of-the-art, in particular when using multiplicative updates.

Beyond heatmaps: Spatio-temporal clustering using behavior-based partitioning of game levels

Evaluating the spatial behavior of players allows for comparing design intent with emergent behavior. However, spatial analytics for game development is still in its infancy and current analysis mostly relies on aggregate visualizations such as heatmaps. In this paper, we propose the use of advanced spatial clustering techniques to evaluate player behavior. In particular, we consider the use of DEDICOM and DESICOM, two techniques that operate on asymmetric spatial similarity matrices and can simultaneously uncover preferred locations and likely transitions between them. Our results highlight the ability of asymmetric techniques to partition game maps into meaningful areas and to retain information about player movements between these areas.

Statistical Relational Learning of Grammar Rules for 3D Building Reconstruction

The automatic interpretation of 3D point clouds for building reconstruction is a challenging task. The interpretation process requires highly structured models representing semantics. Formal grammars can describe structures as well as the parameters of buildings and their parts. We propose a novel approach for the automatic learning of weighted attributed context-free grammar rules for 3D building reconstruction, supporting the laborious manual design of rules. We separate structure from parameter learning. Specific Support Vector Machines (SVMs) are used to generate a weighted context-free grammar and predict structured outputs such as parse trees. The grammar is extended by parameters and constraints, which are learned based on a statistical relational learning method using Markov Logic Networks (MLNs). MLNs enforce the topological and geometric constraints. MLNs address uncertainty explicitly and provide probabilistic inference. They are able to deal with partial observations caused by occlusions. Uncertain projective geometry is used to deal with the uncertainty of the observations. Learning is based on a large building database covering different building styles and facade structures. In particular, a treebank that has been derived from the database is employed for structure learning.

Efficient sequential clamping for lifted message passing

Lifted message passing approaches can be extremely fast at computing approximate marginal probability distributions over single variables and neighboring ones in the underlying graphical model. They do, however, not prescribe a way to solve more complex inference tasks such as computing joint marginals for k-tuples of distant random variables or satisfying assignments of CNFs. A popular solution in these cases is the idea of turning the complex inference task into a sequence of simpler ones by selecting and clamping variables one at a time and running lifted message passing again after each selection. This naive solution, however, recomputes the lifted network in each step from scratch, therefore often canceling the benefits of lifted inference. We show how to avoid this by efficiently computing the lifted network for each conditioning directly from the one already known for the single node marginals. Our experiments show that significant efficiency gains are possible for lifted message passing guided decimation for SAT and sampling.

LTE Connectivity and Vehicular Traffic Prediction Based on Machine Learning Approaches

The prediction of both, vehicular traffic and communication connectivity are important research topics. In this paper, we propose the usage of innovative machine learning approaches for these objectives. For this purpose, Poisson Dependency Networks (PDNs) are introduced to enhance the prediction quality of vehicular traffic flows. The machine learning model is fitted based on empirical vehicular traffic data. The results show that PDNs enable a significantly better short-term prediction in comparison to a prediction based on the physics of traffic. To combine vehicular traffic with cellular communication networks, a correlation between connectivity indicators and vehicular traffic flow is shown based on measurement results. This relationship is leveraged by means of Poisson regression trees in both directions, and hence, enabling the prediction of both types of network utilization.

Modeling heart procedures from EHRs: An application of exponential families

In order to facilitate better estimations on coronary artery disease conditions of a patient, we aim to predict the number of Angioplasty (a coronary artery procedure) by taking into account all the information from his/her Electronic Health Record (EHR) data. For this purpose, two exponential family members—multinomial distribution and Poisson distribution models—are considered, which treat the target variable as categorical-valued and count-valued respectively. From the perspective of exponential family, we derive the functional gradient boosting approach for these two distributions and analyze their assumptions with real EHR data. Our empirical results show that Poisson models appear to be more faithful for modeling the number of this procedure.