TY  - JOUR
A1  - Malem-Shinitski, Noa
A1  - Ojeda, Cesar
A1  - Opper, Manfred
T1  - Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects
JF  - Entropy
N2  - Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.
KW  - Bayesian inference
KW  - point process
KW  - Gaussian process
Y1  - 2022
U6  - https://doi.org/10.3390/e24030356
SN  - 1099-4300
VL  - 24
IS  - 3
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Rosenblum, Michael
A1  - Frühwirth, Martha
A1  - Moser, Maximilian
A1  - Pikovskij, Arkadij
T1  - Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia
JF  - Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences
N2  - We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.
KW  - phase dynamics
KW  - point process
KW  - vagal sympathetic activity
KW  - autonomic nervous system
Y1  - 2019
U6  - https://doi.org/10.1098/rsta.2019.0045
SN  - 1364-503X
SN  - 1471-2962
VL  - 377
IS  - 2160
PB  - Royal Society
CY  - London
ER  - 
TY  - JOUR
A1  - Barthelme, Simon
A1  - Trukenbrod, Hans Arne
A1  - Engbert, Ralf
A1  - Wichmann, Felix A.
T1  - Modeling fixation locations using spatial point processes
JF  - Journal of vision
N2  - Whenever eye movements are measured, a central part of the analysis has to do with where subjects fixate and why they fixated where they fixated. To a first approximation, a set of fixations can be viewed as a set of points in space; this implies that fixations are spatial data and that the analysis of fixation locations can be beneficially thought of as a spatial statistics problem. We argue that thinking of fixation locations as arising from point processes is a very fruitful framework for eye-movement data, helping turn qualitative questions into quantitative ones. We provide a tutorial introduction to some of the main ideas of the field of spatial statistics, focusing especially on spatial Poisson processes. We show how point processes help relate image properties to fixation locations. In particular we show how point processes naturally express the idea that image features' predictability for fixations may vary from one image to another. We review other methods of analysis used in the literature, show how they relate to point process theory, and argue that thinking in terms of point processes substantially extends the range of analyses that can be performed and clarify their interpretation.
KW  - eye movements
KW  - fixation locations
KW  - saliency
KW  - modeling
KW  - point process
KW  - spatial statistics
Y1  - 2013
U6  - https://doi.org/10.1167/13.12.1
SN  - 1534-7362
VL  - 13
IS  - 12
PB  - Association for Research in Vision and Opthalmology
CY  - Rockville
ER  -