Abstract For a Hilbert space-valued martingale $$(f_{n})$$ ( f n ) and an adapted sequence of positive random variables $$(w_{n})$$ w , we show the weighted Davis-type inequality $$\begin{aligned}...

In this paper, we consider a least square semidefinite programming problem under ellipsoidal data uncertainty. We show that the robustification of this uncertain problem can be reformulated as a semidefinite linear programming problem with an additional second-order cone constraint. We then provide an explicit quantitative sensitivity analysis on how the solution under the robustification depen...

An efficient algorithm is derived for the recursive computation of the filtering and all types of linear leastsquare prediction estimates (fixed-point, fixed-interval, and fixed-lead predictors) of a nonstationary signal vector. It is assumed that the signal is observed in the presence of an additive white noise which can be correlated with the signal. The methodology employed only requires tha...

The demand for increased capacity in wireless communication networks has motivated recent research activities toward wireless systems that exploit the concept of smart antenna and space selectivity. Efficient utilization of limited radio frequency spectrum is only possible to use smart/adaptive antenna system. Smart antenna radiates not only narrow beam towards desired users exploiting signal p...

Statistical inference subject to nonnegativity constraints is a frequently occurring problem in signal processing. The nonnegative least-mean-square (NNLMS) algorithm was derived to address such problems in an online way. This algorithm builds on a fixed-point iteration strategy driven by the Karush-Kuhn-Tucker conditions. It was shown to provide low variance estimates, but it however suffers f...

In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions. Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder. Variational auto enocders make better approximaiton than MCMC. The VAE defines a generative process in terms of ancestral sampling through a cascade of hidde...

In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability. The kernel method is a powerful nonparametric modeling tool for pattern analysis and statistical signal processing. Through a nonlinear mapping, kernel methods...