TY - JOUR
T1 - Adaptive multiregression in reproducing kernel hilbert spaces
T2 - The multiaccess MIMO channel case
AU - Slavakis, Konstantinos
AU - Bouboulis, Pantelis
AU - Theodoridis, Sergios
PY - 2012/12/1
Y1 - 2012/12/1
N2 - This paper introduces a wide framework for online, i.e., time-adaptive, supervised multiregression tasks. The problem is formulated in a general infinite-dimensional reproducing kernel Hilbert space (RKHS). In this context, a fairly large number of nonlinear multiregression models fall as special cases, including the linear case. Any convex, continuous, and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. To this end, we demonstrate a way to calculate the subgradients of robust loss functions, suitable for the multiregression task. As it is by now well documented, when dealing with online schemes in RKHS, the memory keeps increasing with each iteration step. To attack this problem, a simple sparsification strategy is utilized, which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters. A convergence analysis of the technique, based on arguments of convex analysis, is also provided. To demonstrate the capacity of the proposed method, the multiregressor is applied to the multiaccess multiple-input multiple-output channel equalization task for a setting with poor resources and nonavailable channel information. Numerical results verify the potential of the method, when its performance is compared with those of the state-of-the-art linear techniques, which, in contrast, use space-time coding, more antenna elements, as well as full channel information.
AB - This paper introduces a wide framework for online, i.e., time-adaptive, supervised multiregression tasks. The problem is formulated in a general infinite-dimensional reproducing kernel Hilbert space (RKHS). In this context, a fairly large number of nonlinear multiregression models fall as special cases, including the linear case. Any convex, continuous, and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. To this end, we demonstrate a way to calculate the subgradients of robust loss functions, suitable for the multiregression task. As it is by now well documented, when dealing with online schemes in RKHS, the memory keeps increasing with each iteration step. To attack this problem, a simple sparsification strategy is utilized, which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters. A convergence analysis of the technique, based on arguments of convex analysis, is also provided. To demonstrate the capacity of the proposed method, the multiregressor is applied to the multiaccess multiple-input multiple-output channel equalization task for a setting with poor resources and nonavailable channel information. Numerical results verify the potential of the method, when its performance is compared with those of the state-of-the-art linear techniques, which, in contrast, use space-time coding, more antenna elements, as well as full channel information.
KW - Adaptive kernel learning
KW - convex analysis
KW - multiple-input multiple-output channel equalization
KW - projection
KW - regression
KW - subgradient
UR - http://www.scopus.com/inward/record.url?scp=84875880314&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84875880314&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2011.2178321
DO - 10.1109/TNNLS.2011.2178321
M3 - Article
C2 - 24808505
AN - SCOPUS:84875880314
SN - 2162-237X
VL - 23
SP - 260
EP - 276
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 2
M1 - 6117088
ER -