Tracking of Quantized Signals Based on Online Kernel Regression

Kernel-based approaches have achieved noticeable success as non-parametric regression methods under the framework of stochastic optimization. However, most of the kernel-based methods in the literature are not suitable to track sequentially streamed quantized data samples from dynamic environments. This shortcoming occurs mainly for two reasons: first, their poor versatility in tracking variables that may change unpredictably over time, primarily because of their lack of flexibility when choosing a functional cost that best suits the associated regression problem; second, their indifference to the smoothness of the underlying physical signal generating those samples. This work introduces a novel algorithm constituted by an online regression problem that accounts for these two drawbacks and a stochastic proximal method that exploits its structure. In addition, we provide tracking guarantees by analyzing the dynamic regret of our algorithm. Finally, we present some experimental results that support our theoretical analysis and show that our algorithm has a favorable performance compared to the state-of-the-art.