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Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation…
Following on from a general observation in an earlier paper, we consider the continuous symmetries of a certain class of conformal field theories constructed from lattices and their reflection-twisted orbifolds. It is shown that the naive…
We aim at estimating in a non-parametric way the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$, for $d \ge 2$, from the discrete observations of a finite sample…
Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…
The attracting set and the inverse limit set are important objects associated to a self-map on a set. We call \emph{stable set} of the self-map the projection of the inverse limit set. It is included in the attracting set, but is not equal…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
In a series of papers Tsirelson constructed from measure types of random sets and generalised random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying…
Model sets are always Meyer sets, but not vice-versa. This article is about characterizing model sets (general and regular) amongst the Meyer sets in terms of two associated dynamical systems. These two dynamical systems describe two very…
The inversion of a gravitational lens system is, as is well known, plagued by the so-called mass-sheet degeneracy: one can always rescale the density distribution of the lens and add a constant-density mass-sheet such that the, also…
Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…
A class of spectral subgrid models based on a self-similar and reversible closure is studied with the aim to minimize the impact of subgrid scales on the inertial range of fully developed turbulence. In this manner, we improve the scale…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…
Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some regularity conditions. Unlike the univariate case, the converse also requires regularity…
Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying…
Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…