Game designers can use computer-aided game design methods to quantitatively compare player skill levels, different game variants, and learning rates, for the purpose of modeling how players will likely experience a game. We use Monte-Carlo simulation, hazard functions, and survival analysis to show how difficulty will quantitatively change throughout a game level as we vary skill, game parameters, and learning rates. We give a mathematical overview of survival analysis, present empirical data analyses of our player models for each game variant, and provide theoretical probability distributions for each game. This analysis shows the quantitative reasons why balancing a game for a wide range of player skill can be difficult; our player modeling provides tools for tuning this game balance. We also analyze the score distribution of over 175 million play sessions of a popular online Flappy Bird variant to demonstrate how learning effects can impact scores, implying that learning is crucial aspect of player modeling.

Procedural Content Generation (PCG) using machine learning is a fast growing area of research. Action Role Playing Game (ARPG) levels represent an interesting challenge for PCG due to their multi-tiered structure and nonlinearity. Previous work has used Bayes Nets (BN) to learn properties of the topological structure of levels from The Legend of Zelda. In this paper we describe a method for sampling these learned distributions to generate valid, playable level topologies. We carry this deeper and learn a sampleable representation of the individual rooms using Principal Component Analysis. We combine the two techniques and present a multi-scale machine learned technique for procedurally generating ARPG levels from a corpus of levels from The Legend of Zelda.

We encounter the results of category formation every day, from demographic categories like race and gender, to role-playing-game classes like "fighter" or "mage". Category membership is often not simply based on the possession of discrete properties but instead constructed from and reflect the highly nuanced relationships (gradience) between members and best-example individuals called "prototypes". In this paper, we present The Marginal, an artificial intelligence (AI)-driven game that (1) computationally models the cognitive categories that players develop when customizing videogame avatars and (2) generates challenges for players to use their perception of visual, textual, and numerical data to progress in a game created using these models. We use archetypal analysis, an AI clustering approach for identifying boundary points in data, to generate tasks in The Marginal for its gameplay. It shows how AI can be combined with games to model and evaluate cognitive  categorization phenomena.

In this paper we describe a hierarchical method for procedurally generating 2D game maps using multi-dimensional Markov chains (MdMCs). Our method takes a collection of 2D game maps, breaks them into small chunks and performs clustering to find a set of chunks that correspond to high-level structures (high-level tiles) in the training maps. This set of high-level tiles is then used to re-represent the training maps, and to fit two sets of MdMC models: a high-level model captures the distribution of high-level tiles in the map, and a set of low-level models capture the internal structure of each high-level tile. These two sets of models can then be used to hierarchically generate new maps. We test our approach using two classic games, Super Mario Bros. and Loderunner, and compare the results against other existing map generators.

Behavioral game analytics has predominantly been confined to work on single games, which means that the cross-game applicability of current knowledge remains largely unknown. Here four experiments are presented focusing on the relationship between game ownership, time invested in playing games, and the players themselves, across more than 3000 games distributed by the Steam platform and over 6 million players, covering a total playtime of over 5 billion hours. Experiments are targeted at uncovering high-level patterns in the behavior of players focusing on playtime, using frequent itemset mining on game ownership, cluster analysis to develop playtime-dependent player profiles, correlation between user game rankings and, review scores, playtime and game ownership, as well as cluster analysis on Steam games. Within the context of playtime, the analyses presented provide unique insights into the behavior of game players as they occur across games, for example in how players distribute their time across games.

Clustering is an essential game analysis tool for understanding There are many clustering procedures that could be used player strengths and preferences. For example, clustering to group players based upon their play styles, with k-means techniques have been used to identify player preferences clustering being the most common method. Our use of for using vehicles over direct combat (Drachen et al. 2012), a model-based semi-parametric Bayesian clustering procedure for taking time to solve puzzles over running through content has two important advantages. First, the number of (Drachen, Canossa, and Yannakakis 2009), for understanding clusters (unique player styles) does not have to be prespecified.

Mobile digital games are dominantly released under the freemium business model, but only a small fraction of the players makes any purchases. The ability to predict who will make a purchase enables optimization of marketing efforts, and tailoring customer relationship management to the specific user's profile. Here this challenge is addressed via two models for predicting purchasing players, using a 100,000 player dataset: 1) A classification model focused on predicting whether a purchase will occur or not. 2) a regression model focused on predicting the number of purchases a user will make. Both models are presented within a decision and regression tree framework for building rules that are actionable by companies. To the best of our knowledge, this is the first study investigating purchase decisions in freemium mobile products from a user behavior perspective and adopting behavior-driven learning approaches to this problem.

Counting objects is a fundamental image processisng primitive, and has many scientific, health, surveillance, security, and military applications. Existing supervised computer vision techniques typically require large quantities of labeled training data, and even with that, fail to return accurate results in all but the most stylized settings. Using vanilla crowdsourcing, on the other hand, can lead to significant errors, especially on images with many objects. In this paper, we present our JellyBean suite of algorithms, that combines the best of crowds and computer vision to count objects in images, and uses judicious decomposition of images to greatly improve accuracy at low cost. Our algorithms have several desirable properties: (i) they are theoretically optimal or near-optimal , in that they ask as few questions as possible to humans (under certain intuitively reasonable assumptions that we justify in our paper experimentally); (ii) they operate under stand-alone or hybrid modes, in that they can either work independent of computer vision algorithms, or work in concert with them, depending on whether the computer vision techniques are available or useful for the given setting; (iii) they perform very well in practice, returning accurate counts on images that no individual worker or computer vision algorithm can count correctly, while not incurring a high cost.

The growing need to analyze large collections of documents has led to great developments in topic modeling. Since documents are frequently associated with other related variables, such as labels or ratings, much interest has been placed on supervised topic models. However, the nature of most annotation tasks, prone to ambiguity and noise, often with high volumes of documents, deem learning under a single-annotator assumption unrealistic or unpractical for most real-world applications. In this paper, we propose a supervised topic model that accounts for the heterogeneity and biases among different annotators that are encountered in practice when learning from crowds. We develop an efficient stochastic variational inference algorithm that is able to scale to very large datasets, and we empirically demonstrate the advantages of the proposed model over state of the art approaches.

Models for aggregating contributions by crowd workers have been shown to be challenged by the rise of task-specific biases or errors. Task-dependent errors in assessment may shift the majority opinion of even large numbers of workers to an incorrect answer. We introduce and evaluate probabilistic models that can detect and correct task-dependent bias automatically. First, we show how to build and use probabilistic graphical models for jointly modeling task features, workers' biases, worker contributions and ground truth answers of tasks so that task-dependent bias can be corrected. Second, we show how the approach can perform a type of transfer learning among workers to address the issue of annotation sparsity. We evaluate the models with varying complexity on a large data set collected from a citizen science project and show that the models are effective at correcting the task-dependent worker bias. Finally, we investigate the use of active learning to guide the acquisition of expert assessments to enable automatic detection and correction of worker bias.