Related papers: Large Deviations Properties of Maximum Entropy Mar…
We derive a synaptic weight update rule for learning temporally precise spike train to spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation…
We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates…
We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…
The standard approach to fitting an autoregressive spike train model is to maximize the likelihood for one-step prediction. This maximum likelihood estimation (MLE) often leads to models that perform poorly when generating samples…
This paper proposes a new type of recurrence where we divide the Markov chains into intervals that start when the chain enters into a subset A, then sample another subset B far away from A and end when the chain again return to A. The…
Let $\Xi_n \subset \mathbb R^d$, $n\ge 1$, be a sequence of finite sets and consider a $\Xi_n$-valued, irreducible, reversible, continuous-time Markov chain $(X^{(n)}_t:t\ge 0)$. Denote by $\mathscr P(\mathbb R^d) $ the set of probability…
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of…
Statistical analysis and inferences on spike trains are one of the central topics in neural coding. It is of great interest to understand the underlying distribution and geometric structure of given spike train data. However, a fundamental…
In the last few decades, noise-induced large fluctuations and transition phenomena have garnered significant attention in a variety of scientific contexts. The concept of prehistory probability has been proposed within the framework of…
Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the…
The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…
Estimating the entropy based on data is one of the prototypical problems in distribution property testing and estimation. For estimating the Shannon entropy of a distribution on $S$ elements with independent samples, [Paninski2004] showed…
Most successful applications of deep learning involve similar training and test conditions. However, tasks such as biological sequence design involve searching for sequences that improve desirable properties beyond previously known values,…
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…
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…
The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like…