127,934 research outputs found
Learning Active Basis Models by EM-Type Algorithms
EM algorithm is a convenient tool for maximum likelihood model fitting when
the data are incomplete or when there are latent variables or hidden states. In
this review article we explain that EM algorithm is a natural computational
scheme for learning image templates of object categories where the learning is
not fully supervised. We represent an image template by an active basis model,
which is a linear composition of a selected set of localized, elongated and
oriented wavelet elements that are allowed to slightly perturb their locations
and orientations to account for the deformations of object shapes. The model
can be easily learned when the objects in the training images are of the same
pose, and appear at the same location and scale. This is often called
supervised learning. In the situation where the objects may appear at different
unknown locations, orientations and scales in the training images, we have to
incorporate the unknown locations, orientations and scales as latent variables
into the image generation process, and learn the template by EM-type
algorithms. The E-step imputes the unknown locations, orientations and scales
based on the currently learned template. This step can be considered
self-supervision, which involves using the current template to recognize the
objects in the training images. The M-step then relearns the template based on
the imputed locations, orientations and scales, and this is essentially the
same as supervised learning. So the EM learning process iterates between
recognition and supervised learning. We illustrate this scheme by several
experiments.Comment: Published in at http://dx.doi.org/10.1214/09-STS281 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Actuarial Applications and Estimation of Extended~CreditRisk
We introduce an additive stochastic mortality model which allows joint
modelling and forecasting of underlying death causes. Parameter families for
mortality trends can be chosen freely. As model settings become high
dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation.
We then link our proposed model to an extended version of the credit risk model
CreditRisk. This allows exact risk aggregation via an efficient numerically
stable Panjer recursion algorithm and provides numerous applications in credit,
life insurance and annuity portfolios to derive P\&L distributions.
Furthermore, the model allows exact (without Monte Carlo simulation error)
calculation of risk measures and their sensitivities with respect to model
parameters for P\&L distributions such as value-at-risk and expected shortfall.
Numerous examples, including an application to partial internal models under
Solvency II, using Austrian and Australian data are shown.Comment: 34 pages, 5 figure
Dispersion relations for
We present a dispersive analysis of the decay amplitude for
that is based on the fundamental principles of analyticity
and unitarity. In this framework, final-state interactions are fully taken into
account. Our dispersive representation relies only on input for the
and scattering phase shifts. Isospin symmetry allows us to describe
both the charged and neutral decay channel in terms of the same function. The
dispersion relation contains subtraction constants that cannot be fixed by
unitarity. We determine these parameters by a fit to Dalitz-plot data from the
VES and BES-III experiments. We study the prediction of a low-energy theorem
and compare the dispersive fit to variants of chiral perturbation theory.Comment: 22 pages, 10 figures; v2: added footnote, version published in EPJ
Multiple testing, uncertainty and realistic pictures
We study statistical detection of grayscale objects in noisy images. The
object of interest is of unknown shape and has an unknown intensity, that can
be varying over the object and can be negative. No boundary shape constraints
are imposed on the object, only a weak bulk condition for the object's interior
is required. We propose an algorithm that can be used to detect grayscale
objects of unknown shapes in the presence of nonparametric noise of unknown
level. Our algorithm is based on a nonparametric multiple testing procedure. We
establish the limit of applicability of our method via an explicit,
closed-form, non-asymptotic and nonparametric consistency bound. This bound is
valid for a wide class of nonparametric noise distributions. We achieve this by
proving an uncertainty principle for percolation on finite lattices.Comment: This paper initially appeared in January 2011 as EURANDOM Report
2011-004. Link to the abstract at EURANDOM Repository:
http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at
EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd
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Subgraph Pattern Matching over Uncertain Graphs with Identity Linkage Uncertainty
There is a growing need for methods which can capture uncertainties and
answer queries over graph-structured data. Two common types of uncertainty are
uncertainty over the attribute values of nodes and uncertainty over the
existence of edges. In this paper, we combine those with identity uncertainty.
Identity uncertainty represents uncertainty over the mapping from objects
mentioned in the data, or references, to the underlying real-world entities. We
propose the notion of a probabilistic entity graph (PEG), a probabilistic graph
model that defines a distribution over possible graphs at the entity level. The
model takes into account node attribute uncertainty, edge existence
uncertainty, and identity uncertainty, and thus enables us to systematically
reason about all three types of uncertainties in a uniform manner. We introduce
a general framework for constructing a PEG given uncertain data at the
reference level and develop highly efficient algorithms to answer subgraph
pattern matching queries in this setting. Our algorithms are based on two novel
ideas: context-aware path indexing and reduction by join-candidates, which
drastically reduce the query search space. A comprehensive experimental
evaluation shows that our approach outperforms baseline implementations by
orders of magnitude
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