Related papers: Finding Acceptable Parameter Regions of Stochastic…
In biochemical networks, reactions often occur on disparate timescales and can be characterized as either "fast" or "slow." The quasi-steady state approximation (QSSA) utilizes timescale separation to project models of biochemical networks…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
This paper concerns quasi-stochastic approximation (QSA) to solve root finding problems commonly found in applications to optimization and reinforcement learning. The general constant gain algorithm may be expressed as the…
Parameter sensitivity analysis is a powerful tool in the building and analysis of biochemical network models. For stochastic simulations, parameter sensitivity analysis can be computationally expensive, requiring multiple simulations for…
In this work, we investigate Batch Normalization technique and propose its probabilistic interpretation. We propose a probabilistic model and show that Batch Normalization maximazes the lower bound of its marginalized log-likelihood. Then,…
The problem we consider is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
We study the sample complexity of stochastic convex optimization when problem parameters, e.g., the distance to optimality, are unknown. We pursue two strategies. First, we develop a reliable model selection method that avoids overfitting…
Classical molecular dynamics (MD) simulations enable modeling of materials and examination of microscopic details that are not accessible experimentally. The predictive capability of MD relies on the force field (FF) used to describe…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
In particle physics, as in many areas of science, parameter inference relies on simulations to bridge the gap between theory and experiment. Recent developments in simulation-based inference have boosted the sensitivity of analyses;…
This paper deals with the construction of a metamodel (i.e. a simplified mathematical model) for a stochastic computer code (also called stochastic numerical model or stochastic simulator), where stochastic means that the code maps the…
This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of…
Inferring parameters of models of biochemical kinetics from single-cell data remains challenging because of the uncertainty arising from the intractability of the likelihood function of stochastic reaction networks. Such uncertainty falls…
Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…
Regulatory networks describe the interactions between molecular or cellular regulators, like transcription factors and genes in gene regulatory networks, kinases and their receptors in signalling networks, or neurons in neural networks. A…
A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the…
Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…