Texas A&M University-Commerce Affiliation PLAYER SKILL DECOMPOSITION IN MULTIPLAYER ONLINE BATTLE ARENAS 2 Abstract Successful analysis of player skills in video games has important impacts on the process of enhancing player experience without undermining their continuous skill development. Moreover, player skill analysis becomes more intriguing in team-based video games because such form of study can help discover useful factors in effective team formation. In this paper, we consider the problem of skill decomposition in MOBA (MultiPlayer Online Battle Arena) games, with the goal to understand what player skill factors are essential for the outcome of a game match. To understand the construct of MOBA player skills, we utilize various skill-based predictive models to decompose player skills into interpretative parts, the impact of which are assessed in statistical terms. We apply this analysis approach on two widely known MOBAs, namely League of Legends (LoL) and Defense of the Ancients 2 (DOTA2). The finding is that base skills of in-game avatars, base skills of players, and players' champion-specific skills are three prominent skill components influencing LoL's match outcomes, while those of DOTA2 are mainly impacted by in-game avatars' base skills but not much by the other two. PLAYER SKILL DECOMPOSITION IN MULTIPLAYER ONLINE BATTLE ARENAS 3 Player Skill Decomposition in Multiplayer Online Battle Arenas Introduction Recently a unique type of sports, namely electronic sports (eSports), emerges as a popular genre of computer games, in which human players compete with one another in online, simulated environments governed by rules and regulations similar to those found in traditional forms of sports. A recent report released by SuperData (2016) showed that the worldwide market for eSports, by the end of 2015, has reached approximately 748 million dollars and is expected to grow to 1.9 billion dollars by 2019. Each team consisting of five players has a base to defend and the goal is to attack the opposite teams' champions and ultimately destroy the opponent's base.

Many Collaborative Filtering (CF) algorithms are item-based in the sense that they analyze item-item relations in order to produce item similarities. Recently, several works in the field of Natural Language Processing (NLP) suggested to learn a latent representation of words using neural embedding algorithms. Among them, the Skip-gram with Negative Sampling (SGNS), also known as word2vec, was shown to provide state-of-the-art results on various linguistics tasks. In this paper, we show that item-based CF can be cast in the same framework of neural word embedding. Inspired by SGNS, we describe a method we name item2vec for item-based CF that produces embedding for items in a latent space. The method is capable of inferring item-item relations even when user information is not available. We present experimental results that demonstrate the effectiveness of the item2vec method and show it is competitive with SVD.

Concentration inequalities are indispensable tools for studying the generalization capacity of learning models. Hoeffding's and McDiarmid's inequalities are commonly used, giving bounds independent of the data distribution. Although this makes them widely applicable, a drawback is that the bounds can be too loose in some specific cases. Although efforts have been devoted to improving the bounds, we find that the bounds can be further tightened in some distribution-dependent scenarios and conditions for the inequalities can be relaxed. In particular, we propose four types of conditions for probabilistic boundedness and bounded differences, and derive several distribution-dependent extensions of Hoeffding's and McDiarmid's inequalities. These extensions provide bounds for functions not satisfying the conditions of the existing inequalities, and in some special cases, tighter bounds. Furthermore, we obtain generalization bounds for unbounded and hierarchy-bounded loss functions. Finally we discuss the potential applications of our extensions to learning theory.

We consider i.i.d. samples $x_1, \dots, x_n$ from a measure $\nu$ with density supported on a bounded Euclidean domain $D \subseteq R^d $ where $d\geq3$. A graph on the point cloud is obtained by connecting two points if one of them is among the $k$-nearest neighbors of the other. Our goal is to study consistency of graph based procedures to clustering, classification and dimensionality reduction by studying the variational convergence of the graph total variation associated to such $k$-NN graph. We prove that provided $k:=k_n$ scales like $n \gg k_n \gg \log(n)$, then the $\Gamma$-convergence of the graph total variation towards an appropriate weighted total variation is guaranteed.

We tightly analyze the sample complexity of CCA, provide a learning algorithm that achieves optimal statistical performance in time linear in the required number of samples (up to log factors), as well as a streaming algorithm with similar guarantees.

This paper provides asymptotic theory for Inverse Probability Weighing (IPW) and Locally Robust Estimator (LRE) of Best Linear Predictor where the response missing at random (MAR), but not completely at random (MCAR). We relax previous assumptions in the literature about the first-step nonparametric components, requiring only their mean square convergence. This relaxation allows to use a wider class of machine leaning methods for the first-step, such as lasso. For a generic first-step, IPW incurs a first-order bias unless the model it approximates is truly linear in the predictors. In contrast, LRE remains first-order unbiased provided one can estimate the conditional expectation of the response with sufficient accuracy. An additional novelty is allowing the dimension of Best Linear Predictor to grow with sample size. These relaxations are important for estimation of best linear predictor of teacher-specific and hospital-specific effects with large number of individuals.

This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=||^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of measurements is significantly smaller than the dimension of the signal ($m<

This paper presents an alternative approach to p-values in regression settings. This approach, whose origins can be traced to machine learning, is based on the leave-one-out bootstrap for prediction error. In machine learning this is called the out-of-bag (OOB) error. To obtain the OOB error for a model, one draws a bootstrap sample and fits the model to the in-sample data. The out-of-sample prediction error for the model is obtained by calculating the prediction error for the model using the out-of-sample data. Repeating and averaging yields the OOB error, which represents a robust cross-validated estimate of the accuracy of the underlying model. By a simple modification to the bootstrap data involving "noising up" a variable, the OOB method yields a variable importance (VIMP) index, which directly measures how much a specific variable contributes to the prediction precision of a model. VIMP provides a scientifically interpretable measure of the effect size of a variable, we call the "predictive effect size", that holds whether the researcher's model is correct or not, unlike the p-value whose calculation is based on the assumed correctness of the model. We also discuss a marginal VIMP index, also easily calculated, which measures the marginal effect of a variable, or what we call "the discovery effect". The OOB procedure can be applied to both parametric and nonparametric regression models and requires only that the researcher can repeatedly fit their model to bootstrap and modified bootstrap data. We illustrate this approach on a survival data set involving patients with systolic heart failure and to a simulated survival data set where the model is incorrectly specified to illustrate its robustness to model misspecification.

Behind the scenes, the same call automatically and invisibly decides whether a machine learning classifier is reliable enough to classify the example on its own, or whether human intervention is needed. Models get built automatically, they're continually retrained, and the caller never has to worry whether more data is needed. In the rest of this article, we'll go into more detail on the problems we described above--problems that are common to all efforts to deploy machine learning to solve real-world problems. In order to train any spam classifier, you'll first need a training set of "spam" and "not spam" labels.

Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming data volumes, the scalability of such methods have become more and more important. In this work, we present a method which allows to apply any visualization or embedding algorithm on very large datasets by considering only a fraction of the data as input and then extending the information to all data points using a graph encoding its global similarity. We show that in most cases, using only $\mathcal{O}(\log(N))$ samples is sufficient to diffuse the information to all $N$ data points. In addition, we propose quantitative methods to measure the quality of embeddings and demonstrate the validity of our technique on both synthetic and real-world datasets.