Related papers: Analyzing neural responses to natural signals: Max…
Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high…
The quality of an estimated nonlinear model highly depends on the data quality that was used for the system identification. By using a Gaussian Process-based optimal input design approach, a so-called space-filling dataset can be generated…
Advances in large-scale neural recordings have expanded our ability to describe the activity of distributed brain circuits. However, understanding how neural population dynamics differ across regions and behavioral contexts remains…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
In recent years, the study of coupled excitable oscillators has largely benefited from a new analytical technique developed by Ott and Antonsen. This technique allows to express the dynamics of certain macroscopic observable in the ensemble…
In many areas of science and engineering, discovering the governing differential equations from the noisy experimental data is an essential challenge. It is also a critical step in understanding the physical phenomena and prediction of the…
Our understanding of neural computation is founded on the assumption that neurons fire in response to a linear summation of inputs. Yet experiments demonstrate that some neurons are capable of complex functions that require interactions…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…
Recent efforts to understand intermediate representations in deep neural networks have commonly attempted to label individual neurons and combinations of neurons that make up linear directions in the latent space by examining extremal…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally,…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
In general, comprehension of any type of complex system depends on the resolution used to examine the phenomena occurring within it. However, identifying a priori, for example, the best time frequencies/scales to study a certain system…
Research showed that, the information transmitted in biological neurons is encoded in the instants of successive action potentials or their firing rate. In addition to that, in-vivo operation of the neuron makes measurement difficult and…
Detecting shared neural activity from functional magnetic resonance imaging (fMRI) across individuals exposed to the same stimulus can reveal synchronous brain responses, functional roles of regions, and potential clinical biomarkers.…
The rate coding response of a single peripheral sensory neuron in the asymptotic, near-equilibrium limit can be derived using information theory, asymptotic Bayesian statistics and a theory of complex systems. Almost no biological knowledge…
Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer…
Neural networks exhibit a remarkable degree of representational convergence across diverse architectures, training objectives, and even data modalities. This convergence is predictive of alignment with brain representation. A recent…
Functional neuroimaging measures how the brain responds to complex stimuli. However, sample sizes are modest, noise is substantial, and stimuli are high dimensional. Hence, direct estimates are inherently imprecise and call for…