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Active learning is relevant and challenging for high-dimensional regression models when the annotation of the samples is expensive. Yet most of the existing sampling methods cannot be applied to large-scale problems, consuming too much time…

Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in…

In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…

A successful deep learning network is highly dependent not only on the training dataset, but the training algorithm used to condition the network for a given task. The loss function, dataset, and tuning of hyperparameters all play an…

Molecular dynamics is a powerful tool for studying the thermodynamics and kinetics of complex molecular events. However, these simulations can rarely sample the required time scales in practice. Transition path sampling overcomes this…

The sensitivity analysis of biological system models can significantly contribute to identifying and explaining influences of internal or external changes on model and its elements. We propose here a comprehensive framework to study…

We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows to write such PDEs in terms of two potentials: the free energy and the dissipation potential.…

In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an…

We develop an approach to efficiently grow neural networks, within which parameterization and optimization strategies are designed by considering their effects on the training dynamics. Unlike existing growing methods, which follow simple…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Finding collective variables to describe some important coarse-grained information on physical systems, in particular metastable states, remains a key issue in molecular dynamics. Recently, machine learning techniques have been intensively…

Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly…

Differential-algebraic equations (DAEs) with state-dependent events arise in systems whose continuous dynamics are constrained by algebraic equations and interrupted by mode changes, switching logic, impacts, or state reinitializations.…

The vector autoregressive (VAR) model has been used to describe the dependence within and across multiple time series. This is a model for stationary time series which can be extended to allow the presence of a deterministic trend in each…

This paper introduces a novel approach for modelling time-varying connectivity in neuroimaging data, focusing on the slow fluctuations in synaptic efficacy that mediate neuronal dynamics. Building on the framework of Dynamic Causal…

Deep Learning has the hierarchical network architecture to represent the complicated features of input patterns. Such architecture is well known to represent higher learning capability compared with some conventional models if the best set…

Recent efforts on combining deep models with probabilistic graphical models are promising in providing flexible models that are also easy to interpret. We propose a variational message-passing algorithm for variational inference in such…

Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed…

We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm is…

This paper introduces a new framework for recovering causal graphs from observational data, leveraging the observation that the distribution of an effect, conditioned on its causes, remains invariant to changes in the prior distribution of…