Related papers: A general approach to sample path generation of in…
This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct…
Consider a non-symmetric generalized diffusion $X(\cdot)$ in ${\bbR}^d$ determined by the differential operator $A(\msx)=-\sum_{ij} \partial_ia_{ij}(\msx)\partial_j +\sum_i b_i(\msx)\partial_i$. In this paper the diffusion process is…
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…
Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has found success by representing the trajectory as a Gaussian process. Gaussian processes can represent a continuous-time trajectory, elegantly handle…
Real-time path tracing increasingly operates under extremely low sampling budgets, often below one sample per pixel, as rendering complexity, resolution, and frame-rate requirements continue to rise. While super-resolution is widely used in…
In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…
We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also…
Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state-space. We develop approximations using jump processes that are time-homogeneous Markov,…
We propose a similarity measure for sparsely sampled time course data in the form of a log-likelihood ratio of Gaussian processes (GP). The proposed GP similarity is similar to a Bayes factor and provides enhanced robustness to noise in…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
Bayesian inference for Markov jump processes (MJPs) where available observations relate to either system states or jumps typically relies on data-augmentation Markov Chain Monte Carlo. State-of-the-art developments involve representing MJP…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing…
We present a unified view of likelihood based Gaussian progress regression for simulation experiments exhibiting input-dependent noise. Replication plays an important role in that context, however previous methods leveraging replicates have…
We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay…
We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…
We introduce Deep Jump Gaussian Processes (DJGP), a novel method for surrogate modeling of a piecewise continuous function on a high-dimensional domain. DJGP addresses the limitations of conventional Jump Gaussian Processes (JGP) in…
The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building…
Diffusion models have emerged as powerful generative techniques for solving inverse problems. Despite their success in a variety of inverse problems in imaging, these models require many steps to converge, leading to slow inference time.…
Continuous-time trajectory estimation is an attractive alternative to discrete-time batch estimation due to the ability to incorporate high-frequency measurements from asynchronous sensors while keeping the number of optimization parameters…