Related papers: Chains with unbounded variable length memory: perf…
In this article we introduce two new perfect simulation algorithms for chains with infinite memory. Both algorithms belong to the coupling of past procedures. The novelty of our approach is that it allows to include unknown states to the…
We establish sufficient conditions for perfect simulation of chains of infinite order on a countable alphabet. The new assumption, localized continuity, is formalized with the help of the notion of context trees, and includes the…
This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…
We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the…
Stochastic chains with memory of variable length constitute an interesting family of stochastic chains of infinite order on a finite alphabet. The idea is that for each past, only a finite suffix of the past, called context, is enough to…
We explicitly construct a coupling attaining Ornstein's $\bar{d}$-distance between ordered pairs of binary chains of infinite order. Our main tool is a representation of the transition probabilities of the coupled bivariate chain of…
In this paper, we study inference for chains of variable order under two distinct contamination regimes. Consider we have a chain of variable memory on a finite alphabet containing zero. At each instant of time an independent coin is…
In the recent publication (arxiv:2007.08063v2 [cs.LG]) a fast prediction algorithm for a single recurrent network (RN) was suggested. In this manuscript we generalize this approach to a chain of RNs and show that it can be implemented in…
We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling…
We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and…
This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length…
We present a perfect simulation algorithm for stationary processes indexed by Z, with summable memory decay. Depending on the decay, we construct the process on finite or semi-infinite intervals, explicitly from an i.i.d. uniform sequence.…
Markov chains with variable length are useful parsimonious stochastic models able to generate most stationary sequence of discrete symbols. The idea is to identify the suffixes of the past, called contexts, that are relevant to predict the…
The Stochastic Context Tree (SCOT) is a useful tool for studying infinite random sequences generated by an m-Markov Chain (m-MC). It captures the phenomenon that the probability distribution of the next state sometimes depends on less than…
We study a class of interacting nonlinear Hawkes point processes on the integer lattice in which each component is reset after its own jumps. The intensity of a component depends on the post-reset activity of its nearest neighbours, which…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
The paper explores the capability of continuous-time recurrent neural networks to store and recall precisely timed scores of spike trains. We show (by numerical experiments) that this is indeed possible: within some range of parameters, any…
Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability…
Recurrent Neural Networks (RNNs), and specifically a variant with Long Short-Term Memory (LSTM), are enjoying renewed interest as a result of successful applications in a wide range of machine learning problems that involve sequential data.…
Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small…