Related papers: Markov Chain Neural Networks
We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our…
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…
We consider a class of small-sample distribution estimators over noisy channels. Our estimators are designed for repetition channels, and rely on properties of the runs of the observed sequences. These runs are modeled via a special type of…
The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms of three parameters which control the probability of,…
We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g.…
Tensor networks and circuits are widely used data structures to represent pseudo-Boolean functions. These two formalisms have been studied primarily in separate communities, and this paper aims to establish equivalences between them. We…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
Continuous-time Markov chains on non-negative integers can be used for modeling biological systems, population dynamics, and queueing models. Qualitative behaviors of birth-and-death models, typical examples of such one-dimensional…
We introduce a generalization of temporal-difference (TD) learning to networks of interrelated predictions. Rather than relating a single prediction to itself at a later time, as in conventional TD methods, a TD network relates each…
In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…
Graph neural networks trained to predict observable dynamics can be used to decompose the temporal activity of complex heterogeneous systems into simple, interpretable representations. Here we apply this framework to simulated neural…
We present a scheme for sequential decision making with a risk-sensitive objective and constraints in a dynamic environment. A neural network is trained as an approximator of the mapping from parameter space to space of risk and policy with…
This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…
Dynamic networks are used in a variety of fields to represent the structure and evolution of the relationships between entities. We present a model which embeds longitudinal network data as trajectories in a latent Euclidean space. A Markov…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
This article describes a method for computing limits of a class of non-stationary Markov chains motivated by healthcare sojourn-time cycles. A mathematical validation of the computation method is also given. Applications are described that…
The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking…