The APSM family of algorithms was introduced in Chapter 8, as one among the most popular techniques for online/adaptive learning. As pointed out there, a major advantage of this algorithmic family is that one can readily incorporate convex constraints. In Chapter 8, APSM was used as an alternative to methods that build around the LS loss function, such as the LMS and the RLS. The rationale behind APSM is that because our data are assumed to be generated by a regression model, then the unknown vector could be estimated by finding a point in the intersection of a sequence of hyperslabs that are defined by the data points, that is, ${S}_{n}[\u03f5]:\; =\left\{\mathit{\theta}\in {\mathbb{R}}^{l}:\left|{y}_{n}-{\mathit{x}}_{n}^{\text{T}}\mathit{\theta}\right|\le \u03f5\right\}$. Also, it was pointed out that ...

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