44,505 research outputs found
Robust Hypothesis Testing with a Relative Entropy Tolerance
This paper considers the design of a minimax test for two hypotheses where
the actual probability densities of the observations are located in
neighborhoods obtained by placing a bound on the relative entropy between
actual and nominal densities. The minimax problem admits a saddle point which
is characterized. The robust test applies a nonlinear transformation which
flattens the nominal likelihood ratio in the vicinity of one. Results are
illustrated by considering the transmission of binary data in the presence of
additive noise.Comment: 14 pages, 5 figures, submitted to the IEEE Transactions on
Information Theory, July 2007, revised April 200
A Contraction Analysis of the Convergence of Risk-Sensitive Filters
A contraction analysis of risk-sensitive Riccati equations is proposed. When
the state-space model is reachable and observable, a block-update
implementation of the risk-sensitive filter is used to show that the N-fold
composition of the Riccati map is strictly contractive with respect to the
Riemannian metric of positive definite matrices, when N is larger than the
number of states. The range of values of the risk-sensitivity parameter for
which the map remains contractive can be estimated a priori. It is also found
that a second condition must be imposed on the risk-sensitivity parameter and
on the initial error variance to ensure that the solution of the risk-sensitive
Riccati equation remains positive definite at all times. The two conditions
obtained can be viewed as extending to the multivariable case an earlier
analysis of Whittle for the scalar case.Comment: 22 pages, 6 figure
Robust Kalman Filtering: Asymptotic Analysis of the Least Favorable Model
We consider a robust filtering problem where the robust filter is designed
according to the least favorable model belonging to a ball about the nominal
model. In this approach, the ball radius specifies the modeling error tolerance
and the least favorable model is computed by performing a Riccati-like backward
recursion. We show that this recursion converges provided that the tolerance is
sufficiently small
Robust State Space Filtering under Incremental Model Perturbations Subject to a Relative Entropy Tolerance
This paper considers robust filtering for a nominal Gaussian state-space
model, when a relative entropy tolerance is applied to each time increment of a
dynamical model. The problem is formulated as a dynamic minimax game where the
maximizer adopts a myopic strategy. This game is shown to admit a saddle point
whose structure is characterized by applying and extending results presented
earlier in [1] for static least-squares estimation. The resulting minimax
filter takes the form of a risk-sensitive filter with a time varying risk
sensitivity parameter, which depends on the tolerance bound applied to the
model dynamics and observations at the corresponding time index. The
least-favorable model is constructed and used to evaluate the performance of
alternative filters. Simulations comparing the proposed risk-sensitive filter
to a standard Kalman filter show a significant performance advantage when
applied to the least-favorable model, and only a small performance loss for the
nominal model
Spectral action on noncommutative torus
The spectral action on noncommutative torus is obtained, using a
Chamseddine--Connes formula via computations of zeta functions. The importance
of a Diophantine condition is outlined. Several results on holomorphic
continuation of series of holomorphic functions are obtained in this context.Comment: 57 page
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