Related papers: Risk Model Based on General Compound Hawkes Proces…
Large Language Models (LLMs), such as ChatGPT, have achieved impressive milestones in natural language processing (NLP). Despite their impressive performance, the models are known to pose important risks. As these models are deployed in…
We prove that the long-run behavior of Hawkes processes is fully determined by the average number and the dispersion of child events. For subcritical processes we provide FLLNs and FCLTs under minimal conditions on the kernel of the process…
Model selection is basically a process of finding the best model from the subset of models in which the explanatory variables are effective on the response variable. The log likelihood function for the lack of fit term and a specified…
Generalized evolutionary point processes offer a class of point process models that allows for either excitation or inhibition based upon the history of the process. In this regard, we propose modeling which comprises generalization of the…
Event data consisting of time of occurrence of the events arises in several real-world applications. Recent works have introduced neural network based point processes for modeling event-times, and were shown to provide state-of-the-art…
The performance of Large Language Models (LLMs) in reasoning tasks depends heavily on prompt design, with Chain-of-Thought (CoT) and self-consistency being critical methods that enhance this ability. However, these methods do not fully…
A popular Bayesian nonparametric approach to survival analysis consists in modeling hazard rates as kernel mixtures driven by a completely random measure. In this paper we derive asymptotic results for linear and quadratic functionals of…
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…
For two nonstandard renewal risk models, we investigate the precise large deviations of the finite-time ruin probability and a random sum of the net-loss process, and the asymptotics of the random-time ruin probability. Notably, in one of…
Recently, a marked Poisson process (MPP) model for life catastrophe risk was proposed in [6]. We provide a justification and further support for the model by considering more general Poisson point processes in the context of extreme value…
Hazards can be exposed by HAZOP as text information, and studying their classification is of great significance to the development of industrial informatics, which is conducive to safety early warning, decision support, policy evaluation,…
We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…
Large Language Models (LLMs) have been applied to Math Word Problems (MWPs) with transformative impacts, revolutionizing how these complex problems are approached and solved in various domains including educational settings. However, the…
Generalization of the Lorden's inequality is an excellent tool for obtaining strong upper bounds for the convergence rate for various complicated stochastic models. This paper demonstrates a method for obtaining such bounds for some…
We consider the learning of multi-agent Hawkes processes, a model containing multiple Hawkes processes with shared endogenous impact functions and different exogenous intensities. In the framework of stochastic maximum likelihood…
In this paper we propose a procedure for robust estimation in the context of generalized linear models based on the maximum Lq-likelihood method. Alongside this, an estimation algorithm that represents a natural extension of the usual…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…
This study addresses construction site hazard identification by proposing a retrieval-augmented framework that enhances large language models (LLMs) without requiring fine-tuning. Current LLM-based approaches face limitations: image-text…
The paper investigates a discrete time Binomial risk model with different types of polices and shock events may influence some of the claim sizes. It is shown that this model can be considered as a particular case of the classical compound…