25,849 research outputs found
Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
An infinite projected entangled pair state (iPEPS) is a tensor network ansatz
to represent a quantum state on an infinite 2D lattice whose accuracy is
controlled by the bond dimension . Its real, Lindbladian or imaginary time
evolution can be split into small time steps. Every time step generates a new
iPEPS with an enlarged bond dimension , which is approximated by an
iPEPS with the original . In Phys. Rev. B 98, 045110 (2018) an algorithm was
introduced to optimize the approximate iPEPS by maximizing directly its
fidelity to the one with the enlarged bond dimension . In this work we
implement a more efficient optimization employing a local estimator of the
fidelity. For imaginary time evolution of a thermal state's purification, we
also consider using unitary disentangling gates acting on ancillas to reduce
the required . We test the algorithm simulating Lindbladian evolution and
unitary evolution after a sudden quench of transverse field in the 2D
quantum Ising model. Furthermore, we simulate thermal states of this model and
estimate the critical temperature with good accuracy: for and
for the more challenging case of close to the quantum
critical point at .Comment: published version, presentation improve
Population Synthesis via k-Nearest Neighbor Crossover Kernel
The recent development of multi-agent simulations brings about a need for
population synthesis. It is a task of reconstructing the entire population from
a sampling survey of limited size (1% or so), supplying the initial conditions
from which simulations begin. This paper presents a new kernel density
estimator for this task. Our method is an analogue of the classical
Breiman-Meisel-Purcell estimator, but employs novel techniques that harness the
huge degree of freedom which is required to model high-dimensional nonlinearly
correlated datasets: the crossover kernel, the k-nearest neighbor restriction
of the kernel construction set and the bagging of kernels. The performance as a
statistical estimator is examined through real and synthetic datasets. We
provide an "optimization-free" parameter selection rule for our method, a
theory of how our method works and a computational cost analysis. To
demonstrate the usefulness as a population synthesizer, our method is applied
to a household synthesis task for an urban micro-simulator.Comment: 10 pages, 4 figures, IEEE International Conference on Data Mining
(ICDM) 201
A Latent Source Model for Patch-Based Image Segmentation
Despite the popularity and empirical success of patch-based nearest-neighbor
and weighted majority voting approaches to medical image segmentation, there
has been no theoretical development on when, why, and how well these
nonparametric methods work. We bridge this gap by providing a theoretical
performance guarantee for nearest-neighbor and weighted majority voting
segmentation under a new probabilistic model for patch-based image
segmentation. Our analysis relies on a new local property for how similar
nearby patches are, and fuses existing lines of work on modeling natural
imagery patches and theory for nonparametric classification. We use the model
to derive a new patch-based segmentation algorithm that iterates between
inferring local label patches and merging these local segmentations to produce
a globally consistent image segmentation. Many existing patch-based algorithms
arise as special cases of the new algorithm.Comment: International Conference on Medical Image Computing and Computer
Assisted Interventions 201
The random link approximation for the Euclidean traveling salesman problem
The traveling salesman problem (TSP) consists of finding the length of the
shortest closed tour visiting N ``cities''. We consider the Euclidean TSP where
the cities are distributed randomly and independently in a d-dimensional unit
hypercube. Working with periodic boundary conditions and inspired by a
remarkable universality in the kth nearest neighbor distribution, we find for
the average optimum tour length = beta_E(d) N^{1-1/d} [1+O(1/N)] with
beta_E(2) = 0.7120 +- 0.0002 and beta_E(3) = 0.6979 +- 0.0002. We then derive
analytical predictions for these quantities using the random link
approximation, where the lengths between cities are taken as independent random
variables. From the ``cavity'' equations developed by Krauth, Mezard and
Parisi, we calculate the associated random link values beta_RL(d). For d=1,2,3,
numerical results show that the random link approximation is a good one, with a
discrepancy of less than 2.1% between beta_E(d) and beta_RL(d). For large d, we
argue that the approximation is exact up to O(1/d^2) and give a conjecture for
beta_E(d), in terms of a power series in 1/d, specifying both leading and
subleading coefficients.Comment: 29 pages, 6 figures; formatting and typos correcte
A note on the evaluation of generative models
Probabilistic generative models can be used for compression, denoising,
inpainting, texture synthesis, semi-supervised learning, unsupervised feature
learning, and other tasks. Given this wide range of applications, it is not
surprising that a lot of heterogeneity exists in the way these models are
formulated, trained, and evaluated. As a consequence, direct comparison between
models is often difficult. This article reviews mostly known but often
underappreciated properties relating to the evaluation and interpretation of
generative models with a focus on image models. In particular, we show that
three of the currently most commonly used criteria---average log-likelihood,
Parzen window estimates, and visual fidelity of samples---are largely
independent of each other when the data is high-dimensional. Good performance
with respect to one criterion therefore need not imply good performance with
respect to the other criteria. Our results show that extrapolation from one
criterion to another is not warranted and generative models need to be
evaluated directly with respect to the application(s) they were intended for.
In addition, we provide examples demonstrating that Parzen window estimates
should generally be avoided
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