Uyarlanır birleşim algoritmalarının kalıcı zaman ve geçici zaman ortalama-karesel analizleri

In this thesis, we analyze adaptive mixture methods that combine outputs of several adaptive filters running in parallel to model an unknown system. We first study three different convex combination methods that combine outputs of two adaptive algorithms and provide their steady-state and transient performances. We next investigate affine and linear combination methods based on Bregman divergences that combine outputs of several adaptive filters and present the mean and the mean-square transient analysis of these adaptive algorithms. In the first part, we investigate convexly constrained mixture methods to adaptively combine outputs of two adaptive filters running in parallel to model a desired unknown system. We compare several algorithms with respect to their mean square error in the steady-state, when the underlying unknown system is nonstationary with a random walk model. We demonstrate that these algorithms are universal such that they achieve the performance of the best constituent filter in the steady-state if certain algorithmic parameters are chosen properly. We also demonstrate that certain mixtures converge to the optimal convex combination filter such that their steady-state performances can be better than the best constituent filter. We also perform the transient analysis of these updates in the mean and mean-square error senses. In the second part, we investigate adaptive mixture methods that linearly combine outputs of m constituent filters running in parallel to model a desired signal. We use Bregman divergences and obtain certain multiplicative updates to train the linear combination weights under an affine constraint or without any constraints. We use unnormalized relative entropy and relative entropy to define two different Bregman divergences that produce an unnormalized exponentiated gradient update and a normalized exponentiated gradient update on the mixture weights, respectively. We then carry out the mean and the mean-square transient analysis of these adaptive algorithms when they are used to combine outputs of $m$ constituent filters. We illustrate the accuracy of our results and demonstrate the effectiveness of these updates for sparse mixture systems.