24,916 research outputs found
Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images
We present a novel kernel regression framework for smoothing scalar surface
data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel
constructed from the eigenfunctions, we formulate a new bivariate kernel
regression framework as a weighted eigenfunction expansion with the heat kernel
as the weights. The new kernel regression is mathematically equivalent to
isotropic heat diffusion, kernel smoothing and recently popular diffusion
wavelets. Unlike many previous partial differential equation based approaches
involving diffusion, our approach represents the solution of diffusion
analytically, reducing numerical inaccuracy and slow convergence. The numerical
implementation is validated on a unit sphere using spherical harmonics. As an
illustration, we have applied the method in characterizing the localized growth
pattern of mandible surfaces obtained in CT images from subjects between ages 0
and 20 years by regressing the length of displacement vectors with respect to
the template surface.Comment: Accepted in Medical Image Analysi
Coupled non-parametric shape and moment-based inter-shape pose priors for multiple basal ganglia structure segmentation
This paper presents a new active contour-based, statistical method for simultaneous volumetric segmentation of multiple subcortical structures in the brain. In biological tissues, such as the human brain, neighboring structures exhibit co-dependencies which can aid in segmentation, if properly analyzed and modeled. Motivated by this observation, we formulate the segmentation problem as a maximum a posteriori estimation problem, in which we incorporate statistical prior models on the shapes and inter-shape (relative) poses of the structures of interest. This provides a principled mechanism to bring high level information about the shapes and the relationships of anatomical structures into the segmentation problem. For learning the prior densities we use a nonparametric multivariate kernel density estimation framework. We combine these priors with data in a variational framework and develop an active contour-based iterative segmentation algorithm.
We test our method on the problem of volumetric segmentation of basal ganglia structures in magnetic resonance (MR) images.
We present a set of 2D and 3D experiments as well as a quantitative performance analysis. In addition, we perform a comparison to several existent segmentation methods and demonstrate the improvements provided by our approach in terms of segmentation accuracy
Improving Parametric Mortgage Prepayment Models with Non-parametric Kernel Regression
Developing a good prepayment model is a central task in the valuation of mortgages and mortgage-backed securities but conventional parametric models often have bad out-of-sample predictive ability. A likely explanation is the highly non-linear nature of the prepayment function. Non-parametric techniques are much better at detecting non-linearity and multivariate interaction. This article discusses how non-parametric kernel regression may be applied to loan level event histories to produce a better parametric model. By utilizing a parsimonious specification, a model can be produced that practitioners can use in valuation routines based on Monte Carlo interest rate simulation.
mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data
We present the R-package mgm for the estimation of k-order Mixed Graphical
Models (MGMs) and mixed Vector Autoregressive (mVAR) models in high-dimensional
data. These are a useful extensions of graphical models for only one variable
type, since data sets consisting of mixed types of variables (continuous,
count, categorical) are ubiquitous. In addition, we allow to relax the
stationarity assumption of both models by introducing time-varying versions
MGMs and mVAR models based on a kernel weighting approach. Time-varying models
offer a rich description of temporally evolving systems and allow to identify
external influences on the model structure such as the impact of interventions.
We provide the background of all implemented methods and provide fully
reproducible examples that illustrate how to use the package
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