Related papers: The Wreath Process: A totally generative model of …

Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…

This paper presents a statistical model for stationary ergodic point processes, estimated from a single realization observed in a square window. With existing approaches in stochastic geometry, it is very difficult to model processes with…

Deep generative models produce data according to a learned representation, e.g. diffusion models, through a process of approximation computing possible samples. Approximation can be understood as reconstruction and the large datasets used…

Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…

We present methods of calculating statistics generating functions over the colored permutation groups, and generalizing known theorems from the symmetric groups to general colored permutations groups.

A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…

The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network…

Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for…

This study deals with two-dimensional (2D) signal processing using the wavelet packet transform. When the basis is unknown the candidate of basis increases in exponential order with respect to the signal size. Previous studies do not…

A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by…

We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…

A common practice to account for psychophysical biases in vision is to frame them as consequences of a dynamic process relying on optimal inference with respect to a generative model. The present study details the complete formulation of…

Generative modeling provides a powerful framework for learning data distributions. These models initially relied on probabilistic methods such as Gaussian Processes (GP) for uncertainty-aware predictions and shifted towards larger trainable…

Recent studies show increasing demands and interests in automatically generating layouts, while there is still much room for improving the plausibility and robustness. In this paper, we present a data-driven layout framework without model…

This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance,…

We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…

Numerous methods have been proposed for probabilistic generative modelling of 3D objects. However, none of these is able to produce textured objects, which renders them of limited use for practical tasks. In this work, we present the first…

This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…