Related papers: Capturing the dynamical repertoire of single neuro…
Neural Processes (NPs; Garnelo et al., 2018a,b) are a rich class of models for meta-learning that map data sets directly to predictive stochastic processes. We provide a rigorous analysis of the standard maximum-likelihood objective used to…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…
Inferring the biophysical parameters of conductance-based models (CBMs) from experimentally accessible recordings remains a central challenge in computational neuroscience. Spike times are the most widely available data, yet they reveal…
Spiking neural networks (SNNs) are distributed trainable systems whose computing elements, or neurons, are characterized by internal analog dynamics and by digital and sparse synaptic communications. The sparsity of the synaptic spiking…
In this paper we consider Poisson loglinear models with linear constraints (LMLC) on the expected table counts. Multinomial and product multinomial loglinear models can be obtained by considering that some marginal totals (linear…
The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While nonlinear computations can be implemented successfully in spiking neural networks, this…
Spiking neural networks, also often referred to as the third generation of neural networks, carry the potential for a massive reduction in memory and energy consumption over traditional, second-generation neural networks. Inspired by the…
The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in…
GMRES is a powerful numerical solver used to find solutions to extremely large systems of linear equations. These systems of equations appear in many applications in science and engineering. Here we demonstrate a real-time machine learning…
This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct…
Neurons communicate with downstream systems via sparse and incredibly brief electrical pulses, or spikes. Using these events, they control various targets such as neuromuscular units, neurosecretory systems, and other neurons in connected…
Multivariate count models are often justified by their ability to capture latent dependence, but researchers receive little guidance on when this added structure improves on simpler penalized marginal Poisson regression. We study this…
Inspired by the operation of biological brains, Spiking Neural Networks (SNNs) have the unique ability to detect information encoded in spatio-temporal patterns of spiking signals. Examples of data types requiring spatio-temporal processing…
Information coding by precise timing of spikes can be faster and more energy-efficient than traditional rate coding. However, spike-timing codes are often brittle, which has limited their use in theoretical neuroscience and computing…
We consider a stochastic model describing the spiking activity of a countable set of neurons spatially organized into a homogeneous tree of degree $d$, $d \geq 2$; the degree of a neuron is just the number of connections it has. Roughly,…
Repeating spatiotemporal spike patterns exist and carry information. Here we investigated how a single spiking neuron can optimally respond to one given pattern (localist coding), or to either one of several patterns (distributed coding,…
Gaussian processes (GPs) are powerful probabilistic models that define flexible priors over functions, offering strong interpretability and uncertainty quantification. However, GP models often rely on simple, stationary kernels which can…