November 29th 2023
Prof. Florian Frommlet, opens an external URL in a new window, Medical University of Vienna
Flexible Bayesian Model Selection
Abstract: Linear or simple parametric models are often not sufficient to describe complex relationships between input variables and a response. Such relationships can be better described through more flexible approaches like neural networks, but these result typically in less interpretable models and tend to suffer from potential overfitting. Alternatively, specific parametric nonlinear functions can be used, but the specification of such functions is in general complicated. We will introduce an approach to construct highly flexible nonlinear parametric regression models, where nonlinear features are generated iteratively. Combined with variable selection, this allows us to find a small set of important features and thereby more interpretable models. Within the space of possible functions, a Bayesian approach, introducing priors for features based on their complexity, is considered. A genetically modified mode jumping Markov chain Monte Carlo algorithm is adopted to perform Bayesian inference and estimate posterior probabilities for model averaging.
The family of non-linear features which can be generated is vast and includes several well known families for non-linear modeling as special cases, including for example classical neural networks, fractional polynomials, or logic regression. For high-dimensional data our algorithm can also be used to fit only linear models or perhaps linear models including interactions. Apart from introducing our general methodology this talk will include also several examples which illustrate how our method can be used to obtain meaningful nonlinear models in practical applications. We are currently working on a CRAN version of our algorithm which will provide a user-friendly implementation for this powerful tool.
November 29th 2023
Prof. Peter Rousseeuw, opens an external URL in a new window, KU Leuven
Dr. Jakob Raymaekers, opens an external URL in a new window, Maastricht University
Challenges of Cellwise Outliers
Abstract: It is well-known that real data often contain outliers. The term outlier typically refers to a case, that is, a row of the n × d data matrix. In recent times a different type has come into focus, the cellwise outliers. These are suspicious cells (entries) that can occur anywhere in the data matrix. Even a relatively small proportion of outlying cells can contaminate over half the rows, which is a problem for rowwise robust methods. This article discusses the challenges posed by cellwise outliers, and some methods developed so far to deal with them. New results are obtained on cellwise breakdown values for loca- tion, covariance and regression. A cellwise robust method is proposed for correspondence analysis, with real data illustrations. The paper concludes by formulating some points for debate.
October 23rd, 2023
Prof. Gregor Kastner, opens an external URL in a new window, University of Klagenfurt
Posterior predictive model assessment using formal methods in a spatio-temporal model
Abstract: We propose an interdisciplinary framework, Bayesian formal predictive model assessment. It combines Bayesian predictive inference, a well established tool in statistics, with formal verification methods rooting in the computer science community. Bayesian predictive inference allows for coherently incorporating uncertainty about unknown quantities by making use of methods or models that produce predictive distributions, which in turn inform decision problems. By formalizing these problems and the corresponding properties, we can use spatio-temporal reach and escape logic to formulate and probabilistically assess their satisfaction. This way, competing models can directly be compared based on their ability to predict the property satisfaction a posteriori. The approach is illustrated on an urban mobility application, where the crowdedness in the center of Milan is proxied by aggregated mobile phone traffic data. We specify several desirable spatio-temporal properties related to city crowdedness such as a fault-tolerant network or the reachability of hospitals. After verifying these properties on draws from the posterior predictive distributions, we compare several spatio-temporal Bayesian models based on their overall and property-based predictive performance. This is based on joint work with Laura Vana, Ennio Visconti, Laura Nenzi, Annalisa Cadonna.
June 7th, 2023
Prof. Lexin Li, opens an external URL in a new window, University of California, Berkeley School of Public Health
Statistical Neuroimaging Analysis: An Overview
Abstract: Understanding the inner workings of human brains, as well as their connections with neurological disorders, is one of the most intriguing scientific questions. Studies in neuroscience are greatly facilitated by a variety of neuroimaging technologies, including anatomical magnetic resonance imaging (MRI), functional magnetic resonance imaging (fMRI), electroencephalography (EEG), diffusion tensor imaging, positron emission tomography (PET), among many others. The size and complexity of medical imaging data, however, pose numerous challenges, and call for constant development of new statistical methods. In this talk, I give an overview of a range of neuroimaging topics our group has been investigating, including imaging tensor analysis, brain connectivity network analysis, multimodality analysis, and imaging causal analysis. I also illustrate with a number of specific case studies.