Related papers: Trajectory stratification of stochastic dynamics

We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…

Complex systems may often be characterized by their hierarchical dynamics. In this paper do we present a method and an operational algorithm that automatically infer this property in a broad range of systems; discrete stochastic processes.…

Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…

The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…

Calculating transition probabilities between different states of multistable climate tipping systems is computationally challenging in high-dimensional models. Targeted algorithms, such as the Trajectory-Adaptive Multilevel Splitting (TAMS)…

Random walks are a fundamental model in applied mathematics and are a common example of a Markov chain. The limiting stationary distribution of the Markov chain represents the fraction of the time spent in each state during the stochastic…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories:…

Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…

Recently, researchers proposed various low-precision gradient compression, for efficient communication in large-scale distributed optimization. Based on these work, we try to reduce the communication complexity from a new direction. We…

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…

Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…

We introduce a novel semi-supervised video segmentation approach based on an efficient video representation, called as "super-trajectory". Each super-trajectory corresponds to a group of compact trajectories that exhibit consistent motion…

Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental…

Increasing and massive volumes of trajectory data are being accumulated that may serve a variety of applications, such as mining popular routes or identifying ridesharing candidates. As storing and querying massive trajectory data is…

Robots are still poor at traversing cluttered large obstacles required for important applications like search and rescue. By contrast, animals are excellent at doing so, often using direct physical interaction with obstacles rather than…

Detecting rare events, those defined to give rise to high impact but have a low probability of occurring, is a challenge in a number of domains including meteorological, environmental, financial and economic. The use of machine learning to…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Many rare weather events, including hurricanes, droughts, and floods, dramatically impact human life. To accurately forecast these events and characterize their climatology requires specialized mathematical techniques to fully leverage the…