4,677 research outputs found
Latent tree models
Latent tree models are graphical models defined on trees, in which only a
subset of variables is observed. They were first discussed by Judea Pearl as
tree-decomposable distributions to generalise star-decomposable distributions
such as the latent class model. Latent tree models, or their submodels, are
widely used in: phylogenetic analysis, network tomography, computer vision,
causal modeling, and data clustering. They also contain other well-known
classes of models like hidden Markov models, Brownian motion tree model, the
Ising model on a tree, and many popular models used in phylogenetics. This
article offers a concise introduction to the theory of latent tree models. We
emphasise the role of tree metrics in the structural description of this model
class, in designing learning algorithms, and in understanding fundamental
limits of what and when can be learned
Multilinear Wavelets: A Statistical Shape Space for Human Faces
We present a statistical model for D human faces in varying expression,
which decomposes the surface of the face using a wavelet transform, and learns
many localized, decorrelated multilinear models on the resulting coefficients.
Using this model we are able to reconstruct faces from noisy and occluded D
face scans, and facial motion sequences. Accurate reconstruction of face shape
is important for applications such as tele-presence and gaming. The localized
and multi-scale nature of our model allows for recovery of fine-scale detail
while retaining robustness to severe noise and occlusion, and is
computationally efficient and scalable. We validate these properties
experimentally on challenging data in the form of static scans and motion
sequences. We show that in comparison to a global multilinear model, our model
better preserves fine detail and is computationally faster, while in comparison
to a localized PCA model, our model better handles variation in expression, is
faster, and allows us to fix identity parameters for a given subject.Comment: 10 pages, 7 figures; accepted to ECCV 201
Bayesian modelling and quantification of Raman spectroscopy
Raman spectroscopy can be used to identify molecules such as DNA by the
characteristic scattering of light from a laser. It is sensitive at very low
concentrations and can accurately quantify the amount of a given molecule in a
sample. The presence of a large, nonuniform background presents a major
challenge to analysis of these spectra. To overcome this challenge, we
introduce a sequential Monte Carlo (SMC) algorithm to separate each observed
spectrum into a series of peaks plus a smoothly-varying baseline, corrupted by
additive white noise. The peaks are modelled as Lorentzian, Gaussian, or
pseudo-Voigt functions, while the baseline is estimated using a penalised cubic
spline. This latent continuous representation accounts for differences in
resolution between measurements. The posterior distribution can be
incrementally updated as more data becomes available, resulting in a scalable
algorithm that is robust to local maxima. By incorporating this representation
in a Bayesian hierarchical regression model, we can quantify the relationship
between molecular concentration and peak intensity, thereby providing an
improved estimate of the limit of detection, which is of major importance to
analytical chemistry
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