Related papers: Accurate estimates of dynamical statistics using m…
Numerical simulation of continuous-time Markovian processes is an essential and widely applied tool in the investigation of epidemic spreading on complex networks. Due to the high heterogeneity of the connectivity structure through which…
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce an maximum likelihood estimator for constructing such models from data…
Statistical Mechanics deals with ensembles of microstates that are compatible with fixed constraints and that on average define a thermodynamic macrostate. The evolution of a small system is normally subjected to changing constraints and…
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an…
We propose a discrete transition-based reweighting analysis method (dTRAM) for analyzing configuration-space-discretized simulation trajectories produced at different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAM provides…
Markov switching models (MSMs) are probabilistic models that employ multiple sets of parameters to describe different dynamic regimes that a time series may exhibit at different periods of time. The switching mechanism between regimes is…
In this paper, we consider statistical estimation of time-inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi-state life insurance to model the biometric states of an…
Markov jump processes are continuous-time stochastic processes with a wide range of applications in both natural and social sciences. Despite their widespread use, inference in these models is highly non-trivial and typically proceeds via…
Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In…
We present new algorithms for computing and approximating bisimulation metrics in Markov Decision Processes (MDPs). Bisimulation metrics are an elegant formalism that capture behavioral equivalence between states and provide strong…
Markov state models (MSMs) are valuable for studying dynamics of protein conformational changes via statistical analysis of molecular dynamics (MD) simulations. In MSMs, the complex configuration space is coarse-grained into conformational…
Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid.…
We have previously shown that Good-Turing statistics can be applied to molecular dynamics trajectories to estimate the probability of observing completely new (thus far unobserved) biomolecular structures, and showed that the method is…
Transition probability estimation plays a critical role in multi-state modeling, especially in clinical research. This paper investigates the application of semi-Markov and Markov renewal frameworks to the EBMT dataset, focusing on six…
The solution convergence of Markov Decision Processes (MDPs) can be accelerated by prioritized sweeping of states ranked by their potential impacts to other states. In this paper, we present new heuristics to speed up the solution…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
This paper presents a technique for reduced-order Markov modeling for compact representation of time-series data. In this work, symbolic dynamics-based tools have been used to infer an approximate generative Markov model. The time-series…
We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…
In molecular dynamics, statistics of transitions, such as the mean transition time, are macroscopic observables which provide important dynamical information on the underlying microscopic stochastic process. A direct estimation using…
We propose a method for approximating solutions to optimization problems involving the global stability properties of parameter-dependent continuous-time autonomous dynamical systems. The method relies on an approximation of the…