@article{MalemShinitskiOjedaOpper2022,
author = {Malem-Shinitski, Noa and Ojeda, Cesar and Opper, Manfred},
title = {Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects},
series = {Entropy},
volume = {24},
journal = {Entropy},
number = {3},
publisher = {MDPI},
address = {Basel},
issn = {1099-4300},
doi = {10.3390/e24030356},
pages = {22},
year = {2022},
abstract = {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.},
language = {en}
}
@phdthesis{MalemShinitski2023,
author = {Malem-Shinitski, Noa},
title = {Bayesian inference and modeling for point processes with applications from neuronal activity to scene viewing},
doi = {10.25932/publishup-61495},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-614952},
school = {Universit{\"a}t Potsdam},
pages = {vii, 129},
year = {2023},
abstract = {Point processes are a common methodology to model sets of events. From earthquakes to social media posts, from the arrival times of neuronal spikes to the timing of crimes, from stock prices to disease spreading -- these phenomena can be reduced to the occurrences of events concentrated in points. Often, these events happen one after the other defining a time--series. Models of point processes can be used to deepen our understanding of such events and for classification and prediction. Such models include an underlying random process that generates the events. This work uses Bayesian methodology to infer the underlying generative process from observed data. Our contribution is twofold -- we develop new models and new inference methods for these processes. We propose a model that extends the family of point processes where the occurrence of an event depends on the previous events. This family is known as Hawkes processes. Whereas in most existing models of such processes, past events are assumed to have only an excitatory effect on future events, we focus on the newly developed nonlinear Hawkes process, where past events could have excitatory and inhibitory effects. After defining the model, we present its inference method and apply it to data from different fields, among others, to neuronal activity. The second model described in the thesis concerns a specific instance of point processes --- the decision process underlying human gaze control. This process results in a series of fixated locations in an image. We developed a new model to describe this process, motivated by the known Exploration--Exploitation dilemma. Alongside the model, we present a Bayesian inference algorithm to infer the model parameters. Remaining in the realm of human scene viewing, we identify the lack of best practices for Bayesian inference in this field. We survey four popular algorithms and compare their performances for parameter inference in two scan path models. The novel models and inference algorithms presented in this dissertation enrich the understanding of point process data and allow us to uncover meaningful insights.},
language = {en}
}
@article{SeeligRabeMalemShinitskietal.2020,
author = {Seelig, Stefan A. and Rabe, Maximilian Michael and Malem-Shinitski, Noa and Risse, Sarah and Reich, Sebastian and Engbert, Ralf},
title = {Bayesian parameter estimation for the SWIFT model of eye-movement control during reading},
series = {Journal of mathematical psychology},
volume = {95},
journal = {Journal of mathematical psychology},
publisher = {Elsevier},
address = {San Diego},
issn = {0022-2496},
doi = {10.1016/j.jmp.2019.102313},
pages = {32},
year = {2020},
abstract = {Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.},
language = {en}
}
@article{MalemShinitskiOpperReichetal.2020,
author = {Malem-Shinitski, Noa and Opper, Manfred and Reich, Sebastian and Schwetlick, Lisa and Seelig, Stefan A. and Engbert, Ralf},
title = {A mathematical model of local and global attention in natural scene viewing},
series = {PLoS Computational Biology : a new community journal},
volume = {16},
journal = {PLoS Computational Biology : a new community journal},
number = {12},
publisher = {PLoS},
address = {San Fransisco},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1007880},
pages = {21},
year = {2020},
abstract = {Author summary
Switching between local and global attention is a general strategy in human information processing. We investigate whether this strategy is a viable approach to model sequences of fixations generated by a human observer in a free viewing task with natural scenes. Variants of the basic model are used to predict the experimental data based on Bayesian inference. Results indicate a high predictive power for both aggregated data and individual differences across observers. The combination of a novel model with state-of-the-art Bayesian methods lends support to our two-state model using local and global internal attention states for controlling eye movements.
Understanding the decision process underlying gaze control is an important question in cognitive neuroscience with applications in diverse fields ranging from psychology to computer vision. The decision for choosing an upcoming saccade target can be framed as a selection process between two states: Should the observer further inspect the information near the current gaze position (local attention) or continue with exploration of other patches of the given scene (global attention)? Here we propose and investigate a mathematical model motivated by switching between these two attentional states during scene viewing. The model is derived from a minimal set of assumptions that generates realistic eye movement behavior. We implemented a Bayesian approach for model parameter inference based on the model's likelihood function. In order to simplify the inference, we applied data augmentation methods that allowed the use of conjugate priors and the construction of an efficient Gibbs sampler. This approach turned out to be numerically efficient and permitted fitting interindividual differences in saccade statistics. Thus, the main contribution of our modeling approach is two-fold; first, we propose a new model for saccade generation in scene viewing. Second, we demonstrate the use of novel methods from Bayesian inference in the field of scan path modeling.},
language = {en}
}