相关论文: UNIPoint: Universally Approximating Point Processe…

The intensity of a Gibbs point process is usually an intractable function of the model parameters. For repulsive pairwise interaction point processes, this intensity can be expressed as the Laplace transform of some particular function.…

Neural operators, serving as physics surrogate models, have recently gained increased interest. With ever increasing problem complexity, the natural question arises: what is an efficient way to scale neural operators to larger and more…

We propose a novel framework for modeling multiple multivariate point processes, each with heterogeneous event types that share an underlying space and obey the same generative mechanism. Focusing on Hawkes processes and their variants that…

Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the…

This article derives quantitative limit theorems for multivariate Poisson and Poisson process approximations. Employing the solution of Stein's equation for Poisson random variables, we obtain an explicit bound for the multivariate Poisson…

Uncertainty estimation is an important research area to make deep neural networks (DNNs) more trustworthy. While extensive research on uncertainty estimation has been conducted with unimodal data, uncertainty estimation for multimodal data…

Predicting fine-grained interests of users with temporal behavior is important to personalization and information filtering applications. However, existing interest prediction methods are incapable of capturing the subtle degreed user…

Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…

Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…

Many scientific fields, from medicine to seismology, rely on analyzing sequences of events over time to understand complex systems. Traditionally, machine learning models must be built and trained from scratch for each new dataset, which is…

The statistical analysis of structured spatial point process data where the event locations are determined by an underlying spatially embedded relational system has become a vivid field of research. Despite a growing literature on different…

A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…

We analyze several aspects of a class of simple counting processes, that can emerge in some fields of applications where the presence of a change-point occurs. Under simple conditions we, in particular, prove a significant inequality for…

.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…

Artificial neural networks (ANNs), despite their universal function approximation capability and practical success, are subject to catastrophic forgetting. Catastrophic forgetting refers to the abrupt unlearning of a previous task when a…

The estimation of viewpoints and keypoints effectively enhance object detection methods by extracting valuable traits of the object instances. While the output of both processes differ, i.e., angles vs. list of characteristic points, they…

We develop nonparametric Bayesian modelling approaches for Poisson processes, using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, such as the unit square,…

We focus on the estimation of the intensity of a Poisson process in the presence of a uniform noise. We propose a kernel-based procedure fully calibrated in theory and practice. We show that our adaptive estimator is optimal from the oracle…

A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given by the sum of a baseline intensity and another term that depends on the entire past history…

In this paper, we develop a wavelet-based theoretical framework for analyzing the universal approximation capabilities of neural networks over a wide range of activation functions. Leveraging wavelet frame theory on the spaces of…