Related papers: Comparison of continuity equation and Gaussian mix…
Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with the multivariate Gaussian by far the most commonly used.…
The assumption of Gaussian or Gaussian mixture data has been extensively exploited in a long series of precise performance analyses of machine learning (ML) methods, on large datasets having comparably numerous samples and features. To…
This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact…
The mean-field theory for two-layer neural networks considers infinitely wide networks that are linearly parameterized by a probability measure over the parameter space. This nonparametric perspective has significantly advanced both the…
Learning a categorical distribution comes with its own set of challenges. A successful approach taken by state-of-the-art works is to cast the problem in a continuous domain to take advantage of the impressive performance of the generative…
We present two different projects. The first one is related to the development of a semi-analytic model to follow the formation, the evolution and chemical enrichment of cluster galaxies in a hierarchical dark matter model. The second…
A generative diffusion model is used to produce probabilistic ensembles of precipitation intensity maps at the 1-hour 5-km resolution. The generation is conditioned on infrared and microwave radiometric measurements from the GOES and DMSP…
Obtaining high-resolution maps of precipitation data can provide key insights to stakeholders to assess a sustainable access to water resources at urban scale. Mapping a nonstationary, sparse process such as precipitation at very high…
We investigate cosmological density perturbations in a covariant and gauge-invariant formalism, incorporating relativistic causal thermodynamics to give a self-consistent description. The gradient of density inhomogeneities splits…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
Current semi-analytic models (SAMs) of galaxy formation over-predict the fraction of passive small late-type satellite galaxies in dense environments by a factor of two to three. We hypothesize that this is due to inaccurate prescriptions…
Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…
We study the peculiar velocities of density peaks in the presence of primordial non-Gaussianity. Rare, high density peaks in the initial density field can be identified with tracers such as galaxies and clusters in the evolved matter…
We first established the dynamic equations to describe the noisy circling motion of a single particle and the corresponding probability conservation equation in both two dimensions and three dimensions, and then developed the evolution…
A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…
We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a…
We investigate how the consistency relations of large-scale structures are modified when the initial density field is not Gaussian. We consider both scenarios where the primordial density field can be written as a nonlinear functional of a…
Hyperbolic space is increasingly used for hierarchical, tree-like, and network-structured data, but likelihood-based density modeling on hyperbolic space remains relatively limited. This paper develops finite mixture modeling with isotropic…
The emulation of wireless nodes spatial position is a practice used by deployment engineers and network planners to analyze the characteristics of a network. In particular, nodes geolocation will directly impact factors such as…
We present a new semi-analytical model of galaxy formation, GECO (Galaxy Evolution COde), aimed at a better understanding of when and how the two processes of star formation and galaxy assembly have taken place. Our model is structured into…