Related papers: Dynamic relations in sampled processes

We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…

The field of hypothesis generation promises to reduce costs in neuroscience by narrowing the range of interventional studies needed to study various phenomena. Existing machine learning methods can generate scientific hypotheses from…

We model the joint distribution of choice probabilities and decision times in binary choice tasks as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant…

Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…

We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a…

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…

We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering…

The prediction of behavior in dynamical systems, is frequently subject to the design of models. When a time series obtained from observing the system is available, the task can be performed by designing the model from these observations…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…

Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as…

A new class of stochastic processes called independent and periodically identically distributed (i.p.i.d.) processes is defined to capture periodically varying statistical behavior. Algorithms are proposed to detect changes in such i.p.i.d.…

The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs…

The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…