A quick gamma approximation speeds up Bayesian inference.
problem Inconvenient gamma shape parameter conjugate priors in Bayesian models.
method Introduced an easy algorithm to approximate gamma shape parameter full conditional by another gamma distribution.
result The approximation is accurate and fast, even for small sample sizes.
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of t…
Piecewise Linear-Quadratic (PLQ) penalties are widely used to develop models in statistical inference, signal processing, and machine learning. Common examples of PLQ penalties include least squares, Huber, Vapnik, 1-norm, and their asymmetric generalizations. Properties of these estimators depend on the choice of pena…
BézierGAN generates smooth curves from low-dimensional parameters.
problem Designing smooth curves for aerodynamic and hydrodynamic shapes.
method Generative model that maps low-dimensional latent representation to Bézier curve points.
result Generates diverse and realistic curves with consistent shape variation.
Optimizes shapes in uncertain Navier-Stokes flow problems.
problem Optimizing shapes with geometric constraints and physical uncertainty.
method Multi-shape calculus and stochastic augmented Lagrangian method.
result Successfully optimized shapes in uncertain Navier-Stokes flow.
A new method for pricing options with flexible volatility shapes.
problem Parameterizing risk-neutral distributions for accurate option pricing.
method Parsimonious and interpretable parameters for direct control over implied volatility curves.
result Accurate calibration across a large dataset of option curves.
Bayesian analysis of geological shapes for improved oil prediction.
problem Simplistic classifications of geological shapes hinder accurate oil prediction.
method Deriving integrated likelihood for cross-sectional shapes given class parameters using Bayesian statistics.
result First coherent statistical analysis of geological shapes.
Study examines heart and football-shaped metrics, verifying geometric structure.
problem Analyzing reducible spherical conical metrics and their geometric properties.
method Examined 1-parameter heart shape and 3-parameter football shape families, verified structure theorem, used explicit metric and geodesic calculations.
result Naturally arise from Abelian differentials of the third kind, offer new evidence for spherical geometry and complex analytic structure interaction.
Divides state space into regions with identical term structure shapes.
problem Classifying term structure shapes in the two-factor Vasicek model.
method Using envelopes and winding numbers to divide and classify the state space.
result Nearly complete classification of parameter space regarding term structure shapes.
The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.
problem Generalizing convex and star-shaped concepts to symplectic vector spaces.
method Study of variational problems for symplectically convex and star-shaped curves.
result Extremal points of the variational problem are rigid multiply traversed conics for a range of parameters.
Optimizing full likelihoods adapts loss scales and shapes for robust modeling.
problem Rigid loss functions limit model adaptability and robustness.
method Optimize full likelihoods with adjustable parameters.
result Adaptive tuning of loss scales and shapes improves model robustness.
Introduces a new stationary GE-process for gold price analysis.
problem Analyzing gold price data with a flexible stationary process.
method Developed a new stationary GE-process with three parameters. Analyzed synthetic and real gold price data.
result Maximum likelihood estimators can be obtained for the unknown parameters.
Optimizes expensive shape models using Gaussian processes in reduced eigenbases.
problem Optimizing expensive numerical simulators with many parameters.
method High-dimensional shape mapping, eigenshape coordinate system, regularized likelihood maximization, critical dimensions focus, random embedding, manifold replication.
result More accurate and faster optimization with reduced parameter space.
Paper simplifies transforms for elastic metrics on curve shapes.
problem Improving the performance of shape analysis algorithms.
method Extending coordinate transformations to a family of isometries.
result Existence of optimal matchings over the diffeomorphism group.
New method identifies causal parameters in tree-shaped linear models using cycles.
problem Identifying causal parameters from correlations in tree-shaped linear models.
method Investigates tree-shaped linear models, uses missing cycles to identify causal parameters, solves quadratic equations.
result Shows how missing cycles can be combined to obtain a unique solution for causal parameters.
Classifies shapes of yield curves in the Svensson family.
problem Classifying shapes of yield curves in the Svensson family.
method Complete classification of shapes using mathematical analysis.
result Certain complex shapes cannot appear after a deterministic time horizon.
Efficiently estimates material parameter space with multifidelity Gaussian process modeling.
problem Estimating a region of material parameter space with similar precipitate shapes.
method Multifidelity Gaussian process modeling to reduce computational cost.
result Significant reduction in sampling cost for accurate LER estimation.
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance of the estimation of the shape parameter of generalized Pareto distributed using …
Study shows one-dimensional location-scale-shape models are flat in Wasserstein geometry.
problem Investigating curvature in location-scale-shape models under Wasserstein metric.
method Introduced location-scale-shape model and investigated its geometry.
result Location-scale-shape model is intrinsically flat but extrinsically curved in Wasserstein geometry.
Generative model combines shape and intensity priors for left atrium segmentation.
problem Challenges in segmenting left atrium MRI images due to shape variation and multimodality.
method Generative image model with mixture of Gaussians for shape priors and autoencoders for intensity priors.
result Maximizes posterior probability using a mixture of Gaussians for shape priors and autoencoders for intensity priors.
Paper develops formulas for shape derivatives in wave scattering.
problem Computing high order shape derivatives for wave scattering is challenging.
method Introduces elegant recurrence formulas using differential forms and Lie derivatives.
result Unified framework for computing high order shape perturbations in scattering problems.
New shape representation for airfoils improves design and manufacturing.
problem Designing and manufacturing airfoils efficiently and accurately.
method Combining physics-based and data-driven techniques on a Grassmannian manifold.
result Rich set of novel 2D airfoil deformations not previously captured.
Unified treatment of elastic metrics for curves in any dimension.
problem Defining metrics on spaces of Euclidean curves for statistical analysis.
method Developing a unified approach to elastic metrics, extending results on existence of solutions and algorithms for computing distances and geodesics.
result Unified treatment of elastic metrics for all parameter choices, extending previous work.
Paper optimizes fiber optic communication constellations using machine learning.
problem Improving fiber optic communication performance through better constellation shaping.
method An unsupervised learning approach embedding a fiber channel model into neural networks.
result Improved performance up to 0.13 bit/4D in simulation and experimentally up to 0.12 bit/4D.
Deep neural network predicts cardiac shape from MRI images and patient data.
problem Automatic 3D cardiac shape analysis for large-scale studies.
method Uses deep neural networks combining MRI images and patient metadata.
result Significant agreement with reference shapes in cardiac parameters.
Adaptive RBF-KAN improves KANs by dynamically adjusting kernel parameters.
problem Efficiently approximating multivariate functions using learnable univariate edge functions.
method Integrates LOOCV-based kernel scale estimation with adaptive kernel learning.
result Adaptive RBF-KAN outperforms fixed kernel KANs on various benchmark functions.
3D-PRNN generates shapes from depth images using recurrent neural networks.
problem Representing 3D shapes from limited sensor data.
method Generative Recurrent Neural Network (3D-PRNN) with Gaussian Fields.
result 3D-PRNN synthesizes plausible shapes from primitives, outperforming nearest-neighbor methods.
Unsupervised clustering of curves according to their shapes is an important problem with broad scientific applications. The existing model-based clustering techniques either rely on simple probability models (e.g., Gaussian) that are not generally valid for shape analysis or assume the number of clusters. We develop an…
The study classifies term structure shapes in the two-factor Vasicek model using total positivity.
problem Classifying all possible term structure shapes in the two-factor Vasicek model of interest rates.
method Total positivity theory pioneered by Samuel Karlin.
result Four additional shapes can be produced in certain parameter regimes.
Develops a framework for debiased machine learning with shape constraints.
problem Identifying and estimating parameters in high-dimensional models with endogeneity.
method General framework of identification and estimation, incorporating shape constraints.
result Identification and estimation of the Riesz representer α0 under shape constraints. Generates tubular and membranous shapes using curvature functionals.
problem Difficult analysis of tubular and membranous shapes.
method Modeling as curvature optimization problem, phase-field formulation, GPU algorithm.
result Wide continuum of shape textures discovered.
Bayesian optimization outperforms other methods in nano-optical shape optimization and parameter reconstruction.
problem Optimizing nano-optical structures with non-convex objective functions.
method Benchmarked five global optimization methods including Bayesian optimization.
result Bayesian optimization yields significantly better results in a fraction of the time.
New method uses KL-divergence to create non-informative priors for multivariate Gaussian.
problem Handling hyperparameters for non-informative limits in multivariate Gaussian conjugate priors.
method Using scaled KL-divergence between multivariate Gaussians to construct Wishart and normal-Wishart conjugate priors.
result Forming non-informative priors without violating Wishart shape parameter restrictions.
Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping we demonstrate that the steady parameters associated with the physical environment det…
EPD method accurately captures parameter distributions from RCS data.
problem Limitations of traditional methods in estimating parameter distributions from RCS data.
method EPD method generates synthetic trajectories, estimates parameters, and selects parameters based on discrepancy.
result EPD provides accurate distribution of parameters without data loss.
A new method for analyzing shapes and forms using additive models on manifolds.
problem Analyzing shapes and forms under geometric transformations.
method Extending generalized additive regression to models for shapes/forms using squared geodesic distance and Riemannian L2-Boosting algorithm. result Automated model selection and intuitive visualization of covariate effects in shape/form space.
SVarM uses varifold representations for shape classification and regression.
problem Challenges in analyzing geometric data due to non-Euclidean shape spaces.
method Develops a neural network-based framework for varifold representations of shapes.
result Demonstrates strong performance and robustness in shape classification and regression.
A new method for analyzing shapes using FDA techniques.
problem Statistical shape analysis of deformed contours.
method Functional Data Analysis (FDA) with basis expansion and principal component analysis.
result Successfully identifies deformation parameters and captures contour distributions.
Study fully augmented links using algebraic equations from link diagrams.
problem Understanding the geometry and commensurability of fully augmented links.
method Extend Thistlethwaite and Tsvietkova's method to fully augmented links, define algebraic equations, and relate solutions to cusp shapes.
result Solutions to algebraic equations are linked to cusp shapes of fully augmented link complements.
The paper uses 3D shapes to reveal sundial design adjustments based on latitude.
problem Identifying sundial design adjustments based on installation location.
method Shape analysis in a high-dimensional space, regression in shape space.
result Sundial design adjustments were latitude-dependent.
The paper introduces flat-topped PDFs for better fitting machine learning models.
problem Improving goodness of fit in machine learning models.
method Developed a new PDF based on the Fermi-Dirac or logistic function for adaptability.
result Flat-topped PDFs enhance model simplicity and fit quality.
New framework classifies high-dimensional shapes using ray intersections, establishing data requirements.
problem Classifying high-dimensional shapes in real-world data.
method Ray-based classification (RBC) framework using intersections of one-dimensional representations (rays) with shape boundaries.
result Established bounds on the number of rays necessary for shape classification, defined by key angular metrics.
New connection found between shape reconstruction methods and persistent homology.
problem Connecting shape reconstruction methods with persistent homology.
method Wrap complexes and lexicographic optimal homologous cycles.
result Lexicographically optimal homologous cycles are supported on Wrap complexes.
New method uses cluster shapes to improve track finding in particle collisions.
problem Combining timing and additional detector information for efficient track finding.
method Neural networks to analyze cluster shapes for track seeding.
result Cluster shapes reduce fake combinatorial backgrounds while maintaining high track efficiency.
Machine learning shapes bodies via inverse scattering.
problem Generating 3D human bodies with customizable characteristics.
method Combining inverse scattering with machine learning.
result Generates geometric bodies from characteristic parameters.
Cardiac motion modeling using LDDMM and shape splines.
problem Difficulties in probing cardiac function due to shape and deformation interactions.
method LDDMM framework, parallel transport, normalization, shape splines.
result Significant differences in model parameters between pathologies, revealing insights into disease dynamics.
Differentiable pipeline replaces non-differentiable CAE components for shape optimization.
problem Gradient-based optimization is limited by non-differentiable components in CAE workflows.
method Surrogate models replace non-differentiable pipeline components, enabling gradient-based optimization.
result Gradient-based shape optimization possible without differentiable solvers.
SCAMP clusters data by selecting candidate clusters that follow shape constraints, avoiding the need for tuning parameters.
problem Clustering data in high-dimensional space with unknown number of clusters.
method SCAMP formulates clustering as a search and selection problem, using shape constraints and preference functions to select clusters.
result SCAMP can be run multiple times to assess clustering uncertainty, providing a robust method for data annotation.