Related papers: Diffusion method in Random Matrix Theory
We present a new integral transform called the Generalized Borel Transform (GBT) and show how to use it to compute some distribution functions used to describe the statistico-mechanical behavior of macromolecules. For this purpose, we…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
Nonnegative Boltzmann machines (NNBMs) are recurrent probabilistic neural network models that can describe multi-modal nonnegative data. NNBMs form rectified Gaussian distributions that appear in biological neural network models, positive…
Dyson's integration theorem is widely used in the computation of eigenvalue correlation functions in Random Matrix Theory. Here we focus on the variant of the theorem for determinants, relevant for the unitary ensembles with Dyson index…
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly…
The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed…
While Bayesian inference provides a principled framework for reasoning under uncertainty, its widespread adoption is limited by the intractability of exact posterior computation, necessitating the use of approximate inference. However,…
In this paper we consider parameter estimation for discretely observed diffusion processes. In particular, we focus on data that are observed at low frequency and methodology that can estimate parameters with uncertainty quantification.…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…
Random Sample Consensus (RANSAC) is a fundamental approach for robustly estimating parametric models from noisy data. Existing learning-based RANSAC methods utilize deep learning to enhance the robustness of RANSAC against outliers.…
We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…
We introduce the functions included in the R Packet distdichoR for the implementation of the distributional method for the dichotomisation of continuous outcomes. While recalling the principle of the method for the distributions for which…
Recent theoretical modeling offers a unified picture for the description of stochastic processes characterized by a crossover from anomalous to normal behavior. This is particularly welcome, as a growing number of experiments suggest the…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
We use the Random Matrix Theory (RMT) to study the probability distribution function and moments of the wave power transmitted inside systems with ergodic wave motion. The results describe either open multichannel systems or their closed…
Diffusion generative models have demonstrated remarkable success in visual domains such as image and video generation. They have also recently emerged as a promising approach in robotics, especially in robot manipulations. Diffusion models…
We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for…