1,195 research outputs found

    A State-Space Perspective on Modelling and Inference for Online Skill Rating

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    This paper offers a comprehensive review of the main methodologies used for skill rating in competitive sports. We advocate for a state-space model perspective, wherein players' skills are represented as time-varying, and match results serve as the sole observed quantities. The state-space model perspective facilitates the decoupling of modeling and inference, enabling a more focused approach highlighting model assumptions, while also fostering the development of general-purpose inference tools. We explore the essential steps involved in constructing a state-space model for skill rating before turning to a discussion on the three stages of inference: filtering, smoothing and parameter estimation. Throughout, we examine the computational challenges of scaling up to high-dimensional scenarios involving numerous players and matches, highlighting approximations and reductions used to address these challenges effectively. We provide concise summaries of popular methods documented in the literature, along with their inferential paradigms and introduce new approaches to skill rating inference based on sequential Monte Carlo and finite state-spaces. We close with numerical experiments demonstrating a practical workflow on real data across different sports

    Eye quietness and quiet eye in expert and novice golf performance: an electrooculographic analysis

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    Quiet eye (QE) is the final ocular fixation on the target of an action (e.g., the ball in golf putting). Camerabased eye-tracking studies have consistently found longer QE durations in experts than novices; however, mechanisms underlying QE are not known. To offer a new perspective we examined the feasibility of measuring the QE using electrooculography (EOG) and developed an index to assess ocular activity across time: eye quietness (EQ). Ten expert and ten novice golfers putted 60 balls to a 2.4 m distant hole. Horizontal EOG (2ms resolution) was recorded from two electrodes placed on the outer sides of the eyes. QE duration was measured using a EOG voltage threshold and comprised the sum of the pre-movement and post-movement initiation components. EQ was computed as the standard deviation of the EOG in 0.5 s bins from –4 to +2 s, relative to backswing initiation: lower values indicate less movement of the eyes, hence greater quietness. Finally, we measured club-ball address and swing durations. T-tests showed that total QE did not differ between groups (p = .31); however, experts had marginally shorter pre-movement QE (p = .08) and longer post-movement QE (p < .001) than novices. A group × time ANOVA revealed that experts had less EQ before backswing initiation and greater EQ after backswing initiation (p = .002). QE durations were inversely correlated with EQ from –1.5 to 1 s (rs = –.48 - –.90, ps = .03 - .001). Experts had longer swing durations than novices (p = .01) and, importantly, swing durations correlated positively with post-movement QE (r = .52, p = .02) and negatively with EQ from 0.5 to 1s (r = –.63, p = .003). This study demonstrates the feasibility of measuring ocular activity using EOG and validates EQ as an index of ocular activity. Its findings challenge the dominant perspective on QE and provide new evidence that expert-novice differences in ocular activity may reflect differences in the kinematics of how experts and novices execute skills

    March madness prediction using machine learning techniques

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    Project Work presented as the partial requirement for obtaining a Master's degree in Information Management, specialization in Knowledge Management and Business IntelligenceMarch Madness describes the final tournament of the college basketball championship, considered by many as the biggest sporting event in the United States - moving every year tons of dollars in both bets and television. Besides that, there are 60 million Americans who fill out their tournament bracket every year, and anything is more likely than hit all 68 games. After collecting and transforming data from Sports-Reference.com, the experimental part consists of preprocess the data, evaluate the features to consider in the models and train the data. In this study, based on tournament data over the last 20 years, Machine Learning algorithms like Decision Trees Classifier, K-Nearest Neighbors Classifier, Stochastic Gradient Descent Classifier and others were applied to measure the accuracy of the predictions and to be compared with some benchmarks. Despite of the most important variables seemed to be those related to seeds, shooting and the number of participations in the tournament, it was not possible to define exactly which ones should be used in the modeling and all ended up being used. Regarding the results, when training the entire dataset, the accuracy ranges from 65 to 70%, where Support Vector Classification yields the best results. When compared with picking the highest seed, these results are slightly lower. On the other hand, when predicting the Tournament of 2017, the Support Vector Classification and the Multi-Layer Perceptron Classifier reach 85 and 79% of accuracy, respectively. In this sense, they surpass the previous benchmark and the most respected websites and statistics in the field. Given some existing constraints, it is quite possible that these results could be improved and deepened in other ways. Meanwhile, this project can be referenced and serve as a basis for the future work

    Score-Based Bayesian Skill Learning

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    We extend the Bayesian skill rating system of TrueSkill to accommodate score-based match outcomes. TrueSkill has proven to be a very effective algorithm for matchmaking - the process of pairing competitors based on similar skill-level - in competitive online gaming. However, for the case of two teams/players, TrueSkill only learns from win, lose, or draw outcomes and cannot use additional match outcome information such as scores. To address this deficiency, we propose novel Bayesian graphical models as extensions of TrueSkill that (1) model player's offence and defence skills separately and (2) model how these offence and defence skills interact to generate score-based match outcomes. We derive efficient (approximate) Bayesian inference methods for inferring latent skills in these new models and evaluate them on three real data sets including Halo 2 XBox Live matches. Empirical evaluations demonstrate that the new score-based models (a) provide more accurate win/loss probability estimates than TrueSkill when training data is limited, (b) provide competitive and often better win/loss classification performance than TrueSkill, and (c) provide reasonable score outcome predictions with an appropriate choice of likelihood - prediction for which TrueSkill was not designed, but which can be useful in many applications. © 2012 Springer-Verlag

    Efficient Learning from Comparisons

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    Humans are comparison machines: comparing and choosing an item among a set of alternatives (such as objects or concepts) is arguably one of the most natural ways for us to express our preferences and opinions. In many applications, the analysis of data consisting of comparisons enables finding valuable information. But datasets often contain inconsistent comparison outcomes, because human preferences shift and observations are tainted by noise. A principled approach to dealing with intransitive data is to posit a probabilistic model of comparisons. In this thesis, we revisit Luce's choice model, the study of which began almost a century ago, in the context of large-scale online data collection. We set out to learn a ranking over a set of items from comparisons in a computationally, statistically and data efficient way. First, we consider the algorithmic problem of estimating model parameters from choice data, and we seek to improve upon the computational and statistical efficiency of existing methods. Our contribution is to show that it is possible to express the maximizer of the model's likelihood function as the stationary distribution of a Markov chain. This enables the use of fast linear solvers or well-studied iterative methods for Markov chains for parameter inference in Luce's model. Second, we develop a data-efficient method for learning a ranking, by adaptively choosing pairs of items to compare, based on previous comparison outcomes. We begin by showing that Quicksort, a widely-known sorting algorithm, works well even if comparison outcomes are noisy. Under distributional assumptions on model parameters, we provide asymptotic bounds on the quality of the ranking it recovers. Building on this result, we use sorting algorithms as a basis for a simple, practical active-learning method that performs well on real-world datasets, at a small fraction of the computational cost of competing methods. Third, we focus on structured choices in a network. In particular, we study a model where users navigate in a network (e.g., following links on the Web) and set out to estimate transition probabilities along the edges of the network from limited observations. We show that if transitions follow Luce's axiom, their probability can be inferred using only data consisting of the (marginal) traffic at each node of the network. We propose a robust inference algorithm that admits a computationally-efficient implementation. Our method scales to networks with billions of nodes and achieves good predictive performance on clickstream data. Beyond human preferences, probabilistic models of pairwise comparisons can also be applied to sports. Consider football: two teams are compared against each other, and the better one wins. In the last part of this thesis, we look at a concrete application of pairwise comparison models and tackle the task of predicting outcomes of matches between national football teams. These teams play only a few matches every year, hence it is difficult to accurately assess their strength. Noting that national team players also compete against each other in clubs, we propose a way to overcome this challenge by taking into account outcomes of matches between clubs, of which there are plenty. We do so by embedding all matches in player space, and devise a computationally-efficient inference procedure. The resulting model predicts international tournament results more accurately than those using only national team results
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