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We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the…
Biochemical reactions involving three or more reactants, called higher-molecular reactions, play an important role in theoretical systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical…
This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…
In an experimental study of single enzyme reactions, it has been proposed that the rate constants of the enzymatic reactions fluctuate randomly, according to a given distribution. To quantify the uncertainty arising from random rate…
Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…
We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…
Bilevel learning has gained prominence in machine learning, inverse problems, and imaging applications, including hyperparameter optimization, learning data-adaptive regularizers, and optimizing forward operators. The large-scale nature of…
Stochastic optimization in learning and inference often relies on Markov chain Monte Carlo (MCMC) to approximate gradients when exact computation is intractable. However, finite-time MCMC estimators are biased, and reducing this bias…
Motivated by the widespread use of temporal-difference (TD-) and Q-learning algorithms in reinforcement learning, this paper studies a class of biased stochastic approximation (SA) procedures under a mild "ergodic-like" assumption on the…
In this work, we consider the problem of estimating summary statistics to characterise biochemical reaction networks of interest. Such networks are often described using the framework of the Chemical Master Equation (CME). For…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
Researchers have employed stochastic simulations to determine the validity of their theoretical findings and to study analytically intractable spreading dynamics. In both cases, the correctness and efficiency of the simulation algorithm are…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
Stochastic minimax optimization on Riemannian manifolds has recently attracted significant attention due to its broad range of applications, such as robust training of neural networks and robust maximum likelihood estimation. Existing…
Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…
Motivation: Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortu-nately, in all but simplest models the resulting discrete…
A large number of application problems involve two levels of optimization, where one optimization task is nested inside the other. These problems are known as bilevel optimization problems and have been studied by both classical…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…