Related papers: Perfect simulation for interacting Hawkes processe…
The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological and economic systems. By expressing the probability for the next event per unit time…
We study associative memory neural networks based on the Hodgkin-Huxley type of spiking neurons. We introduce the spike-timing-dependent learning rule, in which the time window with the negative part as well as the positive part is used to…
Recent computational experiments have demonstrated the spontaneous emergence of self-replicating programs across universal automata, artificial chemistries, and self-modifying code systems. Remarkably, these results arise without explicit…
In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their…
Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such…
In classical Hawkes process, the baseline intensity and triggering kernel are assumed to be a constant and parametric function respectively, which limits the model flexibility. To generalize it, we present a fully Bayesian nonparametric…
When the sample path of a Hawkes process is observed discretely, such that only the total event counts in disjoint time intervals are known, the likelihood function becomes intractable. To overcome the challenge of likelihood-based…
The theory community has proposed several new heap variants in the recent past which have remained largely untested experimentally. We take the field back to the drawing board, with straightforward implementations of both classic and novel…
Many real-world applications require robust algorithms to learn point processes based on a type of incomplete data --- the so-called short doubly-censored (SDC) event sequences. We study this critical problem of quantitative asynchronous…
We propose a new Kalikow decomposition for continuous time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation…
We investigate a recently proposed model for cortical computation which performs relational inference. It consists of several interconnected, structurally equivalent populations of leaky integrate-and-fire (LIF) neurons, which are trained…
Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic…
We introduce a stochastic principal-agent model. A principal and an agent interact in a stochastic environment, each privy to observations about the state not available to the other. The principal has the power of commitment, both to elicit…
Hawkes Processes are a type of point process which models self-excitement among time events. It has been used in a myriad of applications, ranging from finance and earthquakes to crime rates and social network activity analysis.Recently, a…
While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates.…
In this paper a general approach for the perfect simulation of a stationary process with at most countable state space is outlined. The process is specified through a kernel, prescribing the probability of each state conditional to the…
Motivated by applications in reinforcement learning (RL), we study a nonlinear stochastic approximation (SA) algorithm under Markovian noise, and establish its finite-sample convergence bounds under various stepsizes. Specifically, we show…
We consider a population of Hawkes processes modeling the activity of $N$ interacting neurons. The neurons are regularly positioned on the circle $[-\pi, \pi]$, and the connectivity between neurons is given by a cosine kernel. The firing…
We present a sound and complete method for the verification of qualitative liveness properties of replicated systems under stochastic scheduling. These are systems consisting of a finite-state program, executed by an unknown number of…
We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the mean-field of the afferent edges and nodes. The flipping of…