6 research outputs found
A Comprehensive Approach to Universal Piecewise Nonlinear Regression Based on Trees
Cataloged from PDF version of article.In this paper, we investigate adaptive nonlinear
regression and introduce tree based piecewise linear regression
algorithms that are highly efficient and provide significantly
improved performance with guaranteed upper bounds in an
individual sequence manner. We use a tree notion in order to
partition the space of regressors in a nested structure. The introduced
algorithms adapt not only their regression functions but
also the complete tree structure while achieving the performance
of the “best” linear mixture of a doubly exponential number
of partitions, with a computational complexity only polynomial
in the number of nodes of the tree. While constructing these
algorithms, we also avoid using any artificial “weighting” of
models (with highly data dependent parameters) and, instead,
directly minimize the final regression error, which is the ultimate
performance goal. The introduced methods are generic such that
they can readily incorporate different tree construction methods
such as random trees in their framework and can use different
regressor or partitioning functions as demonstrated in the paper
Robust Least Squares Methods Under Bounded Data Uncertainties
Cataloged from PDF version of article.We study the problem of estimating an unknown deterministic signal that is observed through
an unknown deterministic data matrix under additive noise. In particular, we present a minimax
optimization framework to the least squares problems, where the estimator has imperfect data
matrix and output vector information. We define the performance of an estimator relative to the
performance of the optimal least squares (LS) estimator tuned to the underlying unknown data
matrix and output vector, which is defined as the regret of the estimator. We then introduce an
efficient robust LS estimation approach that minimizes this regret for the worst possible data matrix
and output vector, where we refrain from any structural assumptions on the data. We demonstrate
that minimizing this worst-case regret can be cast as a semi-definite programming (SDP) problem.
We then consider the regularized and structured LS problems and present novel robust estimation
methods by demonstrating that these problems can also be cast as SDP problems. We illustrate
the merits of the proposed algorithms with respect to the well-known alternatives in the literature
through our simulations
Optimum Power Allocation for Average Power Constrained Jammers in the Presense of Non-Gaussian Noise
Cataloged from PDF version of article.We study the problem of determining the optimum
power allocation policy for an average power constrained jammer
operating over an arbitrary additive noise channel, where the aim
is to minimize the detection probability of an instantaneously
and fully adaptive receiver employing the Neyman-Pearson (NP)
criterion. We show that the optimum jamming performance
can be achieved via power randomization between at most two
different power levels. We also provide sufficient conditions
for the improvability and nonimprovability of the jamming
performance via power randomization in comparison to a fixed
power jamming scheme. Numerical examples are presented to
illustrate theoretical results