Related papers: Moment-Based Variational Inference for Markov Jump…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
Hidden Markov Models (HMMs) comprise a powerful generative approach for modeling sequential data and time-series in general. However, the commonly employed assumption of the dependence of the current time frame to a single or multiple…
Markovian diffusion processes yield a system of conservation laws which couple various conditional expectation values (local moments). Solutions of that closed system of deterministic partial differential equations stand for a regular…
A stable-like process is a Feller process $(X_t)_{t\geq 0}$ taking values in $\mathbb{R}^d$ and whose generator behaves, locally, like an $\alpha$-stable L\'evy process, but the index $\alpha$ and all other characteristics may depend on the…
We consider a latent space model for dynamic networks, where our objective is to estimate the pairwise inner products plus the intercept of the latent positions. To balance posterior inference and computational scalability, we consider a…
This paper is concerned with combined inference for point processes on the real line observed in a broken interval. For such processes, the classic history-based approach cannot be used. Instead, we adapt tools from sequential spatial point…
We consider the problem of time series forecasting in an adaptive setting. We focus on the inference of state-space models under unknown and potentially time-varying noise variances. We introduce an augmented model in which the variances…
For Markov jump processes on irreducible networks with finite number of sites, we derive a general and explicit expression of the squared coefficient of variation for the net number of transitions from one site to a connected site in a…
A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting…
We provide a new estimation method for conditional moment models via the martingale difference divergence (MDD).Our MDD-based estimation method is formed in the framework of a continuum of unconditional moment restrictions. Unlike the…
We are interested in the rate of convergence of a subordinate Markov process to its invariant measure. Given a subordinator and the corresponding Bernstein function (Laplace exponent) we characterize the convergence rate of the subordinate…
L\'{e}vy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on L\'{e}vy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse…
The barren plateau phenomenon, characterized by loss gradients that vanish exponentially with system size, poses a challenge to scaling variational quantum algorithms. Here we explore the potential of warm starts, whereby one initializes…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
While short-range dependence is widely assumed in the literature for its simplicity, long-range dependence is a feature that has been observed in data from finance, hydrology, geophysics and economics. In this paper, we extend a…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of…
Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…
In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…
In this paper, we establish optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal processing, image processing, and computer vision, among…