Related papers: Markovletics: Methods and A Novel Application for …
Rough volatility models have recently been empirically shown to provide a good fit to historical volatility time series and implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility…
Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world…
As datasets capturing human choices grow in richness and scale -- particularly in online domains -- there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity,…
Verifying quantum systems has attracted a lot of interest in the last decades.In this paper, we study the quantitative model-checking of quantum continuous-time Markov chains (quantum CTMCs). The branching-time properties of quantum CTMCs…
In this paper, we consider the Markov-Chain Monte Carlo (MCMC) approach for random sampling of combinatorial objects. The running time of such an algorithm depends on the total mixing time of the underlying Markov chain and is unknown in…
We develop clustering procedures for longitudinal trajectories based on a continuous-time hidden Markov model (CTHMM) and a generalized linear observation model. Specifically in this paper, we carry out finite and infinite mixture…
Most successful applications of deep learning involve similar training and test conditions. However, tasks such as biological sequence design involve searching for sequences that improve desirable properties beyond previously known values,…
Markov models have been widely used to represent and analyse user web navigation data. In previous work we have proposed a method to dynamically extend the order of a Markov chain model and a complimentary method for assessing the…
Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and…
We discuss a Monte Carlo Markov Chain (MCMC) procedure for the random sampling of some one-dimensional lattice paths with constraints, for various constraints. We show that an approach inspired by optimal transport allows us to bound…
Inference for continuous-time Markov chains (CTMCs) becomes challenging when the process is only observed at discrete time points. The exact likelihood is intractable, and existing methods often struggle even in medium-dimensional…
We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments…
We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…
We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a…
We demonstrate that a number of sociology models for social network dynamics can be viewed as continuous time Bayesian networks (CTBNs). A sampling-based approximate inference method for CTBNs can be used as the basis of an…
In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive…
In this paper we present the concept of description of random processes in complex systems with the discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Continuous normalizing flows (CNFs) learn the probability path between a reference distribution and a target distribution by modeling the vector field generating said path using neural networks. Recently, Lipman et al. (2022) introduced a…
In this paper we study asymptotic properties of different data-augmentation-type Markov chain Monte Carlo algorithms sampling from mixture models comprising discrete as well as continuous random variables. Of particular interest to us is…