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Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…
Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…
This paper is concerned with elucidating a relationship between two common coupling methods for the continuous time Markov chain models utilized in the cell biology literature. The couplings considered here are primarily used in a…
We consider estimating the transition probability matrix of a finite-state finite-observation alphabet hidden Markov model with known observation probabilities. The main contribution is a two-step algorithm; a method of moments estimator…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
In this paper, we consider the problem of estimating parameters of a linear regression model. Using a hybrid systems framework, a hybrid algorithm is proposed allowing the estimate to converge to the exact value of the unknown parameters in…
We demonstrate that centered likelihood ratio estimators for the sensitivity indices of complex stochastic dynamics are highly efficient with low, constant in time variance and consequently they are suitable for sensitivity analysis in…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate…
We consider the problem of performing inference with imprecise continuous-time hidden Markov chains, that is, imprecise continuous-time Markov chains that are augmented with random output variables whose distribution depends on the hidden…
In this paper we propose a new class of coupling methods for the sensitivity analysis of high dimensional stochastic systems and in particular for lattice Kinetic Monte Carlo. Sensitivity analysis for stochastic systems is typically based…
We consider the important problem of estimating parameter sensitivities for stochastic models of reaction networks that describe the dynamics as a continuous-time Markov process over a discrete lattice. These sensitivity values are useful…
We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest these systems are analytically intractable, and one has to resort to computational methods to…
Stochastic optimization techniques are standard in variational inference algorithms. These methods estimate gradients by approximating expectations with independent Monte Carlo samples. In this paper, we explore a technique that uses…
A random walk-based method is proposed to efficiently compute the solution of a large class of fractional in time linear systems of differential equations (linear F-ODE systems), along with the derivatives with respect to the system…
We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is…
We propose a method to approximate continuous-time, continuous-state stochastic processes by a discrete-time Markov chain defined on a nonuniform grid. Our method provides exact moment matching for processes whose first and second moments…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
This study introduces a novel approach for learning mixtures of Markov chains, a critical process applicable to various fields, including healthcare and the analysis of web users. Existing research has identified a clear divide in…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…