Online Regression with Controlled Label Noise Rate.

Many online regression (and adaptive filtering) algorithms are linear, use additive update and designed for the noise-free setting. We consider the practical setting where the algorithm's feedback is noisy, rather than a clean label. We propose a new family of algorithms which modifies the learning rate based on the noise-variance of the feedback (labels), by shrinking both inputs and feedbacks, based on the amount of noise per input instance. We consider both settings, where the noise is either given or estimated. Empirical study with both synthetic and real-world speech data shows that our algorithms improve the overall performance of the regressor, even when there is no additional explicit information (i.e. amount of noise). We also consider a more general setting where an algorithm can sample more than single (noisy) label, yet there is a total (or average) budget for the feedback. We propose a few strategies how to effectively spend the given budget, which are based on noise-variance estimation and our shrinkage rule. We show empirically that our approach outperforms other naive approaches.