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Multivariate orthogonal polynomials in $D$ real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials,…
Finding appropriate low dimensional representations of high-dimensional multi-modal data can be challenging, since each modality embodies unique deformations and interferences. In this paper, we address the problem using manifold learning,…
Successful video analysis relies on accurate recognition of pixels across frames, and frame reconstruction methods based on video correspondence learning are popular due to their efficiency. Existing frame reconstruction methods, while…
In this note, we propose a variational framework in which the minimization of the acceleration on the group of diffeomorphisms endowed with a right-invariant metric is well-posed. It relies on constraining the acceleration to belong to a…
Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…
Multi-Objective Evolutionary Algorithms (MOEAs) have been proved efficient to deal with Multi-objective Optimization Problems (MOPs). Until now tens of MOEAs have been proposed. The unified mode would provide a more systematic approach to…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
This paper discusses the generation of multivariate $C^\infty$ functions with compact small supports by subdivision schemes. Following the construction of such a univariate function, called \emph{Up-function}, by a non-stationary scheme…
Disentanglement learning is central to understanding and reusing learned representations in variational autoencoders (VAEs). Although equivariance has been explored in this context, effectively exploiting it for disentanglement remains…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
Multi-view learning has become a popular research topic in recent years, but research on the cross-application of classic multi-label classification and multi-view learning is still in its early stages. In this paper, we focus on the…
The increasing use of multivariate methods, and in particular the Matrix Element Method (MEM), represents a revolution in experimental particle physics. With continued exponential growth in computing capabilities, the use of sophisticated…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
A multi-modal multi-objective optimization problem is a special kind of multi-objective optimization problem with multiple Pareto subsets. In this paper, we propose an efficient multi-modal multi-objective optimization algorithm based on…
We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions…
Multimodal VAEs seek to model the joint distribution over heterogeneous data (e.g.\ vision, language), whilst also capturing a shared representation across such modalities. Prior work has typically combined information from the modalities…
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient…
The design and implementation of a multiplexed spiral phase mask in an experimental optical tweezer setup are presented. This diffractive optical element allows the generation of multiple concentric vortex beams with independent topological…
We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
In this paper we propose a multivariate ordinal regression model which allows the joint modeling of three-dimensional panel data containing both repeated and multiple measurements for a collection of subjects. This is achieved by a…