A Unified Bayesian Perspective for Conventional and Robust Adaptive Filters

In this work, we present a new perspective on the origin and interpretation of adaptive filters. By applying Bayesian principles of recursive inference from the state-space model and using a series of simplifications regarding the structure of the solution, we can present, in a unified framework, derivations of many adaptive filters which depend on the probabilistic model of the observational noise. In particular, under a Gaussian model, we obtain solutions well-known in the literature (such as LMS, NLMS, or Kalman filter), while using non-Gaussian noise, we obtain new families of adaptive filter. Notably, under assumption of Laplacian noise, we obtain a family of robust filters of which the signed-error algorithm is a well-known member, while other algorithms, derived effortlessly in the proposed framework, are entirely new. Numerical examples are shown to illustrate the properties and provide a better insight into the performance of the derived adaptive filters.

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).