1,774 research outputs found
Quantum learning: optimal classification of qubit states
Pattern recognition is a central topic in Learning Theory with numerous
applications such as voice and text recognition, image analysis, computer
diagnosis. The statistical set-up in classification is the following: we are
given an i.i.d. training set where
represents a feature and is a label attached to that
feature. The underlying joint distribution of is unknown, but we can
learn about it from the training set and we aim at devising low error
classifiers used to predict the label of new incoming features.
Here we solve a quantum analogue of this problem, namely the classification
of two arbitrary unknown qubit states. Given a number of `training' copies from
each of the states, we would like to `learn' about them by performing a
measurement on the training set. The outcome is then used to design mesurements
for the classification of future systems with unknown labels. We find the
asymptotically optimal classification strategy and show that typically, it
performs strictly better than a plug-in strategy based on state estimation.
The figure of merit is the excess risk which is the difference between the
probability of error and the probability of error of the optimal measurement
when the states are known, that is the Helstrom measurement. We show that the
excess risk has rate and compute the exact constant of the rate.Comment: 24 pages, 4 figure
A flexible space-variant anisotropic regularisation for image restoration with automated parameter selection
We propose a new space-variant anisotropic regularisation term for
variational image restoration, based on the statistical assumption that the
gradients of the target image distribute locally according to a bivariate
generalised Gaussian distribution. The highly flexible variational structure of
the corresponding regulariser encodes several free parameters which hold the
potential for faithfully modelling the local geometry in the image and
describing local orientation preferences. For an automatic estimation of such
parameters, we design a robust maximum likelihood approach and report results
on its reliability on synthetic data and natural images. For the numerical
solution of the corresponding image restoration model, we use an iterative
algorithm based on the Alternating Direction Method of Multipliers (ADMM). A
suitable preliminary variable splitting together with a novel result in
multivariate non-convex proximal calculus yield a very efficient minimisation
algorithm. Several numerical results showing significant quality-improvement of
the proposed model with respect to some related state-of-the-art competitors
are reported, in particular in terms of texture and detail preservation
Bayesian inverse problems with partial observations
We study a nonparametric Bayesian approach to linear inverse problems under
discrete observations. We use the discrete Fourier transform to convert our
model into a truncated Gaussian sequence model, that is closely related to the
classical Gaussian sequence model. Upon placing the truncated series prior on
the unknown parameter, we show that as the number of observations
the corresponding posterior distribution contracts around
the true parameter at a rate depending on the smoothness of the true parameter
and the prior, and the ill-posedness degree of the problem. Correct
combinations of these values lead to optimal posterior contraction rates (up to
logarithmic factors). Similarly, the frequentist coverage of Bayesian credible
sets is shown to be dependent on a combination of smoothness of the true
parameter and the prior, and the ill-posedness of the problem. Oversmoothing
priors lead to zero coverage, while undersmoothing priors produce highly
conservative results. Finally, we illustrate our theoretical results by
numerical examples.Comment: 22 pages, 2 figure
Contents lists available at ScienceDirect Pattern Recognition
journal homepage: www.elsevier.com/locate/pr Edge-preserving smoothing using a similarity measure in adaptive geodesi
A general approach to posterior contraction in nonparametric inverse problems
In this paper we propose a general method to derive an upper bound for the
contraction rate of the posterior distribution for nonparametric inverse
problems. We present a general theorem that allows us to derive con- traction
rates for the parameter of interest from contraction rates of the related
direct problem of estimating transformed parameter of interest. An interesting
aspect of this approach is that it allows us to derive con- traction rates for
priors that are not related to the singular value decomposition of the
operator. We apply our result to several examples of linear inverse problems,
both in the white noise sequence model and the nonparametric regression model,
using priors based on the singular value decomposition of the operator,
location-mixture priors and splines prior, and recover minimax adaptive
contraction rates
Random Matrices with Slow Correlation Decay
We consider large random matrices with a general slowly decaying correlation
among its entries. We prove universality of the local eigenvalue statistics and
optimal local laws for the resolvent away from the spectral edges, generalizing
the recent result of [arXiv:1604.08188] to allow slow correlation decay and
arbitrary expectation. The main novel tool is a systematic diagrammatic control
of a multivariate cumulant expansion.Comment: 41 pages, 1 figure. We corrected a typo in (4.1b
Biomimetic Design for Efficient Robotic Performance in Dynamic Aquatic Environments - Survey
This manuscript is a review over the published articles on edge detection. At first, it provides theoretical background, and then reviews wide range of methods of edge detection in different categorizes. The review also studies the relationship between categories, and presents evaluations regarding to their application, performance, and implementation. It was stated that the edge detection methods structurally are a combination of image smoothing and image differentiation plus a post-processing for edge labelling. The image smoothing involves filters that reduce the noise, regularize the numerical computation, and provide a parametric representation of the image that works as a mathematical microscope to analyze it in different scales and increase the accuracy and reliability of edge detection. The image differentiation provides information of intensity transition in the image that is necessary to represent the position and strength of the edges and their orientation. The edge labelling calls for post-processing to suppress the false edges, link the dispread ones, and produce a uniform contour of objects
Applying Evolutionary Optimisation to Robot Obstacle Avoidance
This paper presents an artificial evolutionbased method for stereo image
analysis and its application to real-time obstacle detection and avoidance for
a mobile robot. It uses the Parisian approach, which consists here in splitting
the representation of the robot's environment into a large number of simple
primitives, the "flies", which are evolved following a biologically inspired
scheme and give a fast, low-cost solution to the obstacle detection problem in
mobile robotics
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