5,506 research outputs found
A new family of high-resolution multivariate spectral estimators
In this paper, we extend the Beta divergence family to multivariate power
spectral densities. Similarly to the scalar case, we show that it smoothly
connects the multivariate Kullback-Leibler divergence with the multivariate
Itakura-Saito distance. We successively study a spectrum approximation problem,
based on the Beta divergence family, which is related to a multivariate
extension of the THREE spectral estimation technique. It is then possible to
characterize a family of solutions to the problem. An upper bound on the
complexity of these solutions will also be provided. Simulations suggest that
the most suitable solution of this family depends on the specific features
required from the estimation problem
A Numerical Method to solve Optimal Transport Problems with Coulomb Cost
In this paper, we present a numerical method, based on iterative Bregman
projections, to solve the optimal transport problem with Coulomb cost. This is
related to the strong interaction limit of Density Functional Theory. The first
idea is to introduce an entropic regularization of the Kantorovich formulation
of the Optimal Transport problem. The regularized problem then corresponds to
the projection of a vector on the intersection of the constraints with respect
to the Kullback-Leibler distance. Iterative Bregman projections on each
marginal constraint are explicit which enables us to approximate the optimal
transport plan. We validate the numerical method against analytical test cases
Thermodynamic assessment of probability distribution divergencies and Bayesian model comparison
Within path sampling framework, we show that probability distribution
divergences, such as the Chernoff information, can be estimated via
thermodynamic integration. The Boltzmann-Gibbs distribution pertaining to
different Hamiltonians is implemented to derive tempered transitions along the
path, linking the distributions of interest at the endpoints. Under this
perspective, a geometric approach is feasible, which prompts intuition and
facilitates tuning the error sources. Additionally, there are direct
applications in Bayesian model evaluation. Existing marginal likelihood and
Bayes factor estimators are reviewed here along with their stepping-stone
sampling analogues. New estimators are presented and the use of compound paths
is introduced
Maximally Divergent Intervals for Anomaly Detection
We present new methods for batch anomaly detection in multivariate time
series. Our methods are based on maximizing the Kullback-Leibler divergence
between the data distribution within and outside an interval of the time
series. An empirical analysis shows the benefits of our algorithms compared to
methods that treat each time step independently from each other without
optimizing with respect to all possible intervals.Comment: ICML Workshop on Anomaly Detectio
- …