84 research outputs found
Multiple-copy state discrimination: Thinking globally, acting locally
We theoretically investigate schemes to discriminate between two
nonorthogonal quantum states given multiple copies. We consider a number of
state discrimination schemes as applied to nonorthogonal, mixed states of a
qubit. In particular, we examine the difference that local and global
optimization of local measurements makes to the probability of obtaining an
erroneous result, in the regime of finite numbers of copies , and in the
asymptotic limit as . Five schemes are considered:
optimal collective measurements over all copies, locally optimal local
measurements in a fixed single-qubit measurement basis, globally optimal fixed
local measurements, locally optimal adaptive local measurements, and globally
optimal adaptive local measurements. Here, adaptive measurements are those for
which the measurement basis can depend on prior measurement results. For each
of these measurement schemes we determine the probability of error (for finite
) and scaling of this error in the asymptotic limit. In the asymptotic
limit, adaptive schemes have no advantage over the optimal fixed local scheme,
and except for states with less than 2% mixture, the most naive scheme (locally
optimal fixed local measurements) is as good as any noncollective scheme. For
finite , however, the most sophisticated local scheme (globally optimal
adaptive local measurements) is better than any other noncollective scheme, for
any degree of mixture.Comment: 11 pages, 14 figure
New prioritized value iteration for Markov decision processes
The problem of solving large Markov decision processes accurately and quickly is challenging. Since the computational effort incurred is considerable, current research focuses on finding superior acceleration techniques. For instance, the convergence properties of current solution methods depend, to a great extent, on the order of backup operations. On one hand, algorithms such as topological sorting are able to find good orderings but their overhead is usually high. On the other hand, shortest path methods, such as Dijkstra's algorithm which is based on priority queues, have been applied successfully to the solution of deterministic shortest-path Markov decision processes. Here, we propose an improved value iteration algorithm based on Dijkstra's algorithm for solving shortest path Markov decision processes. The experimental results on a stochastic shortest-path problem show the feasibility of our approach. © Springer Science+Business Media B.V. 2011.García Hernández, MDG.; Ruiz Pinales, J.; Onaindia De La Rivaherrera, E.; Aviña Cervantes, JG.; Ledesma Orozco, S.; Alvarado Mendez, E.; Reyes Ballesteros, A. (2012). New prioritized value iteration for Markov decision processes. Artificial Intelligence Review. 37(2):157-167. doi:10.1007/s10462-011-9224-zS157167372Agrawal S, Roth D (2002) Learning a sparse representation for object detection. In: Proceedings of the 7th European conference on computer vision. Copenhagen, Denmark, pp 1–15Bellman RE (1954) The theory of dynamic programming. Bull Amer Math Soc 60: 503–516Bellman RE (1957) Dynamic programming. Princeton University Press, New JerseyBertsekas DP (1995) Dynamic programming and optimal control. Athena Scientific, MassachusettsBhuma K, Goldsmith J (2003) Bidirectional LAO* algorithm. 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Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
Shape description and matching using integral invariants on eccentricity transformed images
Matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision. To keep track of changes inside the breast, for example, it is important for a computer aided detection system to establish correspondences between regions of interest. Shape transformations, computed both with integral invariants (II) and with geodesic distance, yield signatures that are invariant to isometric deformations, such as bending and articulations. Integral invariants describe the boundaries of planar shapes. However, they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure. Conversely, eccentricity transforms (Ecc) can match shapes by signatures of geodesic distance histograms based on information from inside the shape; but they ignore the boundary information. We describe a method that combines the boundary signature of a shape obtained from II and structural information from the Ecc to yield results that improve on them separately
Dynamic Programming: an overview
Dynamic programing is one of the major problem-solving methodologies in a number of disciplines such as operations research and computer science. It is also a very important and powerful tool of thought. But not all is well on the dynamic programming front. There is definitely lack of commercial software support and the situation in the classroom is not as good as it should be. In this paper we take a bird's view of dynamic programming so as to identify ways to make it more accessible to students, academics and practitioners alike
Wald's maximin model: a treasure in disguise!
Purpose
The purpose of this paper is to illustrate the expressive power of Wald's maximin model and the mathematical modeling effort requisite in its application in decision under severe uncertainty.
Design/methodology/approach
Decision making under severe uncertainty is art as well as science. This fact is manifested in the insight and ingenuity that the modeller/analyst is required to inject into the mathematical modeling of decision problems subject to severe uncertainty. The paper elucidates this point in a brief discussion on the mathematical modeling of Wald's maximin paradigm.
Findings
The apparent simplicity of the maximin paradigm implies that modeling it successfully requires a considerable mathematical modeling effort.
Practical implications
The paper illustrates the importance of mastering the art of mathematical modeling especially in the application of Wald's maximin model.
Originality/value
This paper sheds new light on some of the modeling aspects of Wald's maximin paradigm.28
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