Related papers: Multivariate $\alpha$-molecules
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of…
In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multiresolution analysis with directional components. We will do so by constructing subdivision schemes which…
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate functions. The theory of Chebyshev (uniform) approximation for univariate functions is very elegant. The optimality conditions are based on the notion…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
Neural networks have emerged as a promising paradigm for quantum information processing, yet they confront the challenge of generating training datasets with sufficient size and rich diversity, which is particularly acute when dealing with…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
Detecting visual relationships, i.e. <Subject, Predicate, Object> triplets, is a challenging Scene Understanding task approached in the past via linguistic priors or spatial information in a single feature branch. We introduce a new deeply…
Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two…
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
Molecule inverse folding has been a long-standing challenge in chemistry and biology, with the potential to revolutionize drug discovery and material science. Despite specified models have been proposed for different small- or…
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
Video prediction is a pixel-wise dense prediction task to infer future frames based on past frames. Missing appearance details and motion blur are still two major problems for current predictive models, which lead to image distortion and…
Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual…
We show the potential for classifying images of mixtures of aggregate, based themselves on varying, albeit well-defined, sizes and shapes, in order to provide a far more effective approach compared to the classification of individual sizes…
Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization and robustness. Most existing function approximation…
We introduce continuous indexed points for improved multivariate volume visualization. Indexed points represent linear structures in parallel coordinates and can be used to encode local correlation of multivariate (including multifield,…
A method of {\it topological grammars} is proposed for multidimensional data approximation. For data with complex topology we define a {\it principal cubic complex} of low dimension and given complexity that gives the best approximation for…
Clustering multivariate binary data is of interest in many scientific fields, including ecology, biomedicine, and social policy. Beyond heuristic clustering algorithms, such data can be modelled using multivariate Bernoulli mixture models.…