Related papers: A Direct Prediction of the Shape Parameter -- a pu…

Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the…

One of the most popular methods of the machine learning prediction explanation is the SHapley Additive exPlanations method (SHAP). An imprecise SHAP as a modification of the original SHAP is proposed for cases when the class probability…

Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

This work presents a novel and effective method for fitting multidimensional ellipsoids to scattered data in the contamination of noise and outliers. We approach the problem as a Bayesian parameter estimate process and maximize the…

A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

We develop a framework for extracting a concise representation of the shape information available from diffuse shading in a small image patch. This produces a mid-level scene descriptor, comprised of local shape distributions that are…

We present alphaPDE, a new multivariate analysis technique for parameter estimation. The method is based on a direct construction of joint probability densities of known variables and the parameters to be estimated. We show how posterior…

Position representation is crucial for building position-aware representations in Transformers. Existing position representations suffer from a lack of generalization to test data with unseen lengths or high computational cost. We…

The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most…

In this paper we provide a new linear sampling method based on the same data but a different definition of the data operator for two inverse problems: the multi-frequency inverse source problem for a fixed observation direction and the Born…

The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…

We propose a simple formula for multichannel resonant scattering with parameters related to physical resonant properties. It can be used to predict residue phase from other resonant parameters and describe the shape of scattering amplitudes…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

We introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for…

In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…

In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…

A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…