Related papers: Interpretation and approximation tools for big, de…
We investigate the potential of supervised machine learning to propagate a quantum system in time. While Markovian dynamics can be learned easily, given a sufficient amount of data, non-Markovian systems are non-trivial and their…
We investigate absorption, i.e., almost sure convergence to an absorbing state, in time-varying (non-homogeneous) discrete-time Markov chains with finite state space. We consider systems that can switch among a finite set of transition…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small…
Convolutional neural networks have become the main tools for processing two-dimensional data. They work well for images, yet convolutions have a limited receptive field that prevents its applications to more complex 2D tasks. We propose a…
We propose a new approach for estimating the finite dimensional transition matrix of a Markov chain using a large number of independent sample paths observed at random times. The sample paths may be observed as few as two times, and the…
Real-world complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in…
This work introduces a new abstraction technique for reducing the state space of large, discrete-time labelled Markov chains. The abstraction leverages the semantics of interval Markov decision processes and the existing notion of…
One of the most frequently used models for understanding human navigation on the Web is the Markov chain model, where Web pages are represented as states and hyperlinks as probabilities of navigating from one page to another. Predominantly,…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…
The evolution processes of complex systems carry key information in the systems' functional properties. Applying machine learning algorithms, we demonstrate that the historical formation process of various networked complex systems can be…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
We studied how to obtain a distribution for the number of ancestors in species of sexual reproduction. Present models concentrate on the estimation of distributions repetitions of ancestors in genealogical trees. It has been shown that is…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically…
Most real-world networks contain well-defined community structures where nodes are densely connected internally within communities. To learn from these networks, we develop MarkovGNN that captures the formation and evolution of communities…
Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…
Reversibility is a key property of Markov chains, central to algorithms such as Metropolis-Hastings and other MCMC methods. Yet many applications yield non-reversible chains, motivating the problem of approximating them by reversible ones…