Related papers: Risk Model Based on General Compound Hawkes Proces…

We study the asymptotic distribution of the total claim amount for marked Poisson cluster models. The marks determine the size and other characteristics of the individual claims and potentially influence arrival rate of the future claims.…

We are interested in the problem of classifying Multivariate Hawkes Processes (MHP) paths coming from several classes. MHP form a versatile family of point processes that models interactions between connected individuals within a network.…

The Cox proportional hazards model is a canonical method in survival analysis for prediction of the life expectancy of a patient given clinical or genetic covariates -- it is a linear model in its original form. In recent years, several…

The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time,…

With the proliferation of LLM-integrated applications such as GPT-s, millions are deployed, offering valuable services through proprietary instruction prompts. These systems, however, are prone to prompt extraction attacks through…

In this paper, we utilize the framework of Markov processes to attain a more probabilistic perspective on the theory of transfer operators. In doing so, we establish a functional central limit theorem (FLCT) for an $O(N)$ model associated…

This research explores the integration of large language models (LLMs) into scientific data assimilation, focusing on combustion science as a case study. Leveraging foundational models integrated with Retrieval-Augmented Generation (RAG)…

Gaussian process (GP) models provide a powerful tool for prediction but are computationally prohibitive using large data sets. In such scenarios, one has to resort to approximate methods. We derive an approximation based on a composite…

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost…

We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing…

Reinforcement Learning from Human Feedback (RLHF) and related alignment paradigms have become central to steering large language models (LLMs) and multimodal large language models (MLLMs) toward human-preferred behaviors. However, these…

Terrorist activities often exhibit temporal and spatial clustering, making the multivariate Hawkes process (MHP) a useful statistical model for analysing terrorism across different geographic regions. However, terror attack data from the…

In this paper, we study finite-time ruin probabilities for the compound Markov binomial risk model - a discrete-time model where claim sizes are modulated by a finite-state ergodic Markov chain. In the classic (non-modulated) case, the risk…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

Hawkes processes are a class of simple point processes whose intensity depends on the past history, and is in general non-Markovian. Limit theorems for Hawkes processes in various asymptotic regimes have been studied in the literature. In…

Reinforcement Learning from Human Feedback (RLHF) is the prevailing approach to ensure Large Language Models (LLMs) align with human values. However, existing RLHF methods require a high computational cost, one main reason being that RLHF…

The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision…

Interval-censored data solely records the aggregated counts of events during specific time intervals - such as the number of patients admitted to the hospital or the volume of vehicles passing traffic loop detectors - and not the exact…

Given a collection of entities (or nodes) in a network and our intermittent observations of activities from each entity, an important problem is to learn the hidden edges depicting directional relationships among these entities. Here, we…

In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models,…