14,745 research outputs found
Bayesian Nonparametric Feature and Policy Learning for Decision-Making
Learning from demonstrations has gained increasing interest in the recent
past, enabling an agent to learn how to make decisions by observing an
experienced teacher. While many approaches have been proposed to solve this
problem, there is only little work that focuses on reasoning about the observed
behavior. We assume that, in many practical problems, an agent makes its
decision based on latent features, indicating a certain action. Therefore, we
propose a generative model for the states and actions. Inference reveals the
number of features, the features, and the policies, allowing us to learn and to
analyze the underlying structure of the observed behavior. Further, our
approach enables prediction of actions for new states. Simulations are used to
assess the performance of the algorithm based upon this model. Moreover, the
problem of learning a driver's behavior is investigated, demonstrating the
performance of the proposed model in a real-world scenario
Bayesian Nonparametric Unmixing of Hyperspectral Images
Hyperspectral imaging is an important tool in remote sensing, allowing for
accurate analysis of vast areas. Due to a low spatial resolution, a pixel of a
hyperspectral image rarely represents a single material, but rather a mixture
of different spectra. HSU aims at estimating the pure spectra present in the
scene of interest, referred to as endmembers, and their fractions in each
pixel, referred to as abundances. Today, many HSU algorithms have been
proposed, based either on a geometrical or statistical model. While most
methods assume that the number of endmembers present in the scene is known,
there is only little work about estimating this number from the observed data.
In this work, we propose a Bayesian nonparametric framework that jointly
estimates the number of endmembers, the endmembers itself, and their
abundances, by making use of the Indian Buffet Process as a prior for the
endmembers. Simulation results and experiments on real data demonstrate the
effectiveness of the proposed algorithm, yielding results comparable with
state-of-the-art methods while being able to reliably infer the number of
endmembers. In scenarios with strong noise, where other algorithms provide only
poor results, the proposed approach tends to overestimate the number of
endmembers slightly. The additional endmembers, however, often simply represent
noisy replicas of present endmembers and could easily be merged in a
post-processing step
Realization spaces of 4-polytopes are universal
Let be a -dimensional polytope. The {\em realization space}
of~ is the space of all polytopes that are combinatorially
equivalent to~, modulo affine transformations. We report on work by the
first author, which shows that realization spaces of \mbox{4-dimensional}
polytopes can be ``arbitrarily bad'': namely, for every primary semialgebraic
set~ defined over~, there is a -polytope whose realization
space is ``stably equivalent'' to~. This implies that the realization space
of a -polytope can have the homotopy type of an arbitrary finite simplicial
complex, and that all algebraic numbers are needed to realize all -
polytopes. The proof is constructive. These results sharply contrast the
-dimensional case, where realization spaces are contractible and all
polytopes are realizable with integral coordinates (Steinitz's Theorem). No
similar universality result was previously known in any fixed dimension.Comment: 10 page
Unit Root in Unemployment - New Evidence from Nonparametric Tests
We apply range unit-root tests to OECD unemployment rates and compare the results to conventional tests. By simulations, we nd that unemployment is represented adequately by a new nonlinear transformation of a serially-correlated I(1) process.
From the Jordan product to Riemannian geometries on classical and quantum states
The Jordan product on the self-adjoint part of a finite-dimensional
-algebra is shown to give rise to Riemannian metric
tensors on suitable manifolds of states on , and the covariant
derivative, the geodesics, the Riemann tensor, and the sectional curvature of
all these metric tensors are explicitly computed. In particular, it is proved
that the Fisher--Rao metric tensor is recovered in the Abelian case, that the
Fubini--Study metric tensor is recovered when we consider pure states on the
algebra of linear operators on a finite-dimensional
Hilbert space , and that the Bures--Helstrom metric tensors is
recovered when we consider faithful states on .
Moreover, an alternative derivation of these Riemannian metric tensors in terms
of the GNS construction associated to a state is presented. In the case of pure
and faithful states on , this alternative geometrical
description clarifies the analogy between the Fubini--Study and the
Bures--Helstrom metric tensor.Comment: 32 pages. Minor improvements. References added. Comments are welcome
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