6 research outputs found
On the Equivalence of f-Divergence Balls and Density Bands in Robust Detection
The paper deals with minimax optimal statistical tests for two composite
hypotheses, where each hypothesis is defined by a non-parametric uncertainty
set of feasible distributions. It is shown that for every pair of uncertainty
sets of the f-divergence ball type, a pair of uncertainty sets of the density
band type can be constructed, which is equivalent in the sense that it admits
the same pair of least favorable distributions. This result implies that robust
tests under -divergence ball uncertainty, which are typically only minimax
optimal for the single sample case, are also fixed sample size minimax optimal
with respect to the equivalent density band uncertainty sets.Comment: 5 pages, 1 figure, accepted for publication in the Proceedings of the
IEEE International Conference on Acoustics, Speech, and Signal Processing
(ICASSP) 201
On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints
The problem of minimizing convex functionals of probability distributions is
solved under the assumption that the density of every distribution is bounded
from above and below. A system of sufficient and necessary first-order
optimality conditions as well as a bound on the optimality gap of feasible
candidate solutions are derived. Based on these results, two numerical
algorithms are proposed that iteratively solve the system of optimality
conditions on a grid of discrete points. Both algorithms use a block coordinate
descent strategy and terminate once the optimality gap falls below the desired
tolerance. While the first algorithm is conceptually simpler and more
efficient, it is not guaranteed to converge for objective functions that are
not strictly convex. This shortcoming is overcome in the second algorithm,
which uses an additional outer proximal iteration, and, which is proven to
converge under mild assumptions. Two examples are given to demonstrate the
theoretical usefulness of the optimality conditions as well as the high
efficiency and accuracy of the proposed numerical algorithms.Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on
Signal Processing. In previous versions, the example in Section VI.B
contained some mistakes and inaccuracies, which have been fixed in this
versio
Robust Sequential Detection in Distributed Sensor Networks
We consider the problem of sequential binary hypothesis testing with a
distributed sensor network in a non-Gaussian noise environment. To this end, we
present a general formulation of the Consensus + Innovations Sequential
Probability Ratio Test (CISPRT). Furthermore, we introduce two different
concepts for robustifying the CISPRT and propose four different algorithms,
namely, the Least-Favorable-Density-CISPRT, the Median-CISPRT, the M-CISPRT,
and the Myriad-CISPRT. Subsequently, we analyze their suitability for different
binary hypothesis tests before verifying and evaluating their performance in a
shift-in-mean and a shift-in-variance scenario.Comment: 13 pages, 5 figure