A comprehensive analysis of the Elo rating algorithm: Stochastic model, convergence characteristics, design guidelines, and experimental results

The Elo algorithm, due to its simplicity, is widely used for rating in sports competitions as well as in other applications where the rating/ranking is a useful tool for predicting future results. However, despite its widespread use, a detailed understanding of the convergence properties of the Elo algorithm is still lacking. Aiming to fill this gap, this paper presents a comprehensive (stochastic) analysis of the Elo algorithm, considering round-robin (one-on-one) competitions. Specifically, analytical expressions are derived characterizing the behavior/evolution of the skills and of important performance metrics. Then, taking into account the relationship between the behavior of the algorithm and the step-size value, which is a hyperparameter that can be controlled, some design guidelines as well as discussions about the performance of the algorithm are provided. To illustrate the applicability of the theoretical findings, experimental results are shown, corroborating the very good match between analytical predictions and those obtained from the algorithm using real-world data (from the Italian SuperLega, Volleyball League).

On the Compression of Neural Networks Using $\ell_0$-Norm Regularization and Weight Pruning

Despite the growing availability of high-capacity computational platforms, implementation complexity still has been a great concern for the real-world deployment of neural networks. This concern is not exclusively due to the huge costs of state-of-the-art network architectures, but also due to the recent push towards edge intelligence and the use of neural networks in embedded applications. In this context, network compression techniques have been gaining interest due to their ability for reducing deployment costs while keeping inference accuracy at satisfactory levels. The present paper is dedicated to the development of a novel compression scheme for neural networks. To this end, a new $\ell_0$-norm-based regularization approach is firstly developed, which is capable of inducing strong sparseness in the network during training. Then, targeting the smaller weights of the trained network with pruning techniques, smaller yet highly effective networks can be obtained. The proposed compression scheme also involves the use of $\ell_2$-norm regularization to avoid overfitting as well as fine tuning to improve the performance of the pruned network. Experimental results are presented aiming to show the effectiveness of the proposed scheme as well as to make comparisons with competing approaches.