1,304 research outputs found
Entanglement, quantum phase transitions, and density matrix renormalization
We investigate the role of entanglement in quantum phase transitions, and
show that the success of the density matrix renormalization group (DMRG) in
understanding such phase transitions is due to the way it preserves
entanglement under renormalization. We provide a reinterpretation of the DMRG
in terms of the language and tools of quantum information science which allows
us to rederive the DMRG in a physically transparent way. Motivated by our
reinterpretation we suggest a modification of the DMRG which manifestly takes
account of the entanglement in a quantum system. This modified renormalization
scheme is shown,in certain special cases, to preserve more entanglement in a
quantum system than traditional numerical renormalization methods.Comment: 5 pages, 1 eps figure, revtex4; added reference and qualifying
remark
Practical Bayesian Optimization for Variable Cost Objectives
We propose a novel Bayesian Optimization approach for black-box functions
with an environmental variable whose value determines the tradeoff between
evaluation cost and the fidelity of the evaluations. Further, we use a novel
approach to sampling support points, allowing faster construction of the
acquisition function. This allows us to achieve optimization with lower
overheads than previous approaches and is implemented for a more general class
of problem. We show this approach to be effective on synthetic and real world
benchmark problems.Comment: 8 pages, 7 figure
Efficient Bayesian Nonparametric Modelling of Structured Point Processes
This paper presents a Bayesian generative model for dependent Cox point
processes, alongside an efficient inference scheme which scales as if the point
processes were modelled independently. We can handle missing data naturally,
infer latent structure, and cope with large numbers of observed processes. A
further novel contribution enables the model to work effectively in higher
dimensional spaces. Using this method, we achieve vastly improved predictive
performance on both 2D and 1D real data, validating our structured approach.Comment: Presented at UAI 2014. Bibtex: @inproceedings{structcoxpp14_UAI,
Author = {Tom Gunter and Chris Lloyd and Michael A. Osborne and Stephen J.
Roberts}, Title = {Efficient Bayesian Nonparametric Modelling of Structured
Point Processes}, Booktitle = {Uncertainty in Artificial Intelligence (UAI)},
Year = {2014}
Distribution of Gaussian Process Arc Lengths
We present the first treatment of the arc length of the Gaussian Process (GP)
with more than a single output dimension. GPs are commonly used for tasks such
as trajectory modelling, where path length is a crucial quantity of interest.
Previously, only paths in one dimension have been considered, with no
theoretical consideration of higher dimensional problems. We fill the gap in
the existing literature by deriving the moments of the arc length for a
stationary GP with multiple output dimensions. A new method is used to derive
the mean of a one-dimensional GP over a finite interval, by considering the
distribution of the arc length integrand. This technique is used to derive an
approximate distribution over the arc length of a vector valued GP in
by moment matching the distribution. Numerical simulations
confirm our theoretical derivations.Comment: 10 pages, 4 figures, Accepted to The 20th International Conference on
Artificial Intelligence and Statistics (AISTATS
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