Related papers: A general approach to sample path generation of in…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
This work presents an efficient framework to generate a motion plan of a robot with high degrees of freedom (e.g., a humanoid robot). High-dimensionality of the robot configuration space often leads to difficulties in utilizing the…
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by L\'evy processes with infinite activity. These schemes combine a compound Poisson approximation for the jump part of the…
This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…
We consider simulation of spatially one-dimensional space-time fractional diffusion. Whereas in an earlier paper of ours we have developed the basic theory of what we call parametric subordination via three-fold splitting applied to…
Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…
In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…
Large-scale Gaussian process models are becoming increasingly important and widely used in many areas, such as, computer experiments, stochastic optimization via simulation, and machine learning using Gaussian processes. The standard…
Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…
Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability…
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched…
The indeterminate nature of human motion requires trajectory prediction systems to use a probabilistic model to formulate the multi-modality phenomenon and infer a finite set of future trajectories. However, the inference processes of most…
In this paper, we revisit batch state estimation through the lens of Gaussian process (GP) regression. We consider continuous-discrete estimation problems wherein a trajectory is viewed as a one-dimensional GP, with time as the independent…
Denoising Probabilistic Models (DPMs) represent an emerging domain of generative models that excel in generating diverse and high-quality images. However, most current training methods for DPMs often neglect the correlation between…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
A major obstacle to the wide-spread adoption of neural retrieval models is that they require large supervised training sets to surpass traditional term-based techniques, which are constructed from raw corpora. In this paper, we propose an…
By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions and…