Project Details
Projekt
Amortized Bayesian Inference for Multilevel Models
Subject Area
Image and Language Processing, Computer Graphics and Visualisation, Human Computer Interaction, Ubiquitous and Wearable Computing
Term
since 2022
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 508399956
Probabilistic multilevel models (MLMs) are a central building block in the Bayesian toolkit for data analysis and have found widespread application across the quantitative sciences. They not only enable joint, interpretable modeling of data gathered on different hierarchical levels but also allow for fully probabilistic quantification of uncertainty. Despite their widely acknowledged advantages, MLMs remain challenging and often even intractable to estimate and evaluate. Recent developments in generative deep learning and simulation-based inference have shown promising results in tackling complex stochastic models. Deep learning approaches employ powerful neural density estimators to learn intractable (posterior) distributions over high dimensional parameter spaces. However, the utility of deep learning methods for learning Bayesian MLMs remains largely unexplored.In this project, we propose to develop a general and efficient neural inference framework for estimating and evaluating complex Bayesian MLMs. Our framework will substantially extend previous work on simulation-based Bayesian inference for single-level models. For MLMs of arbitrary complexity, we propose to train a specialized hierarchical network that is aligned to the probabilistic structure of the model. During training, the model serves as an instructor, which, by means of simulation, trains the network to become an expert in recovering the parameters of interest for any actually observed data set. Once trained, the network can be stored and used for efficient inference and validation, such as posterior predictions, probabilistic calibration, or cross-validation. This way, the training effort amortizes over subsequent applications of the network and covers not only the inference phase of a Bayesian workflow but also the model evaluation steps, which usually comprise a computational bottleneck with standard (non-amortized) Bayesian methods. Thus, the proposed project has the potential to greatly enhance model-based inference and understanding of complex processes across the quantitative sciences.The project is structured into four work packages: First, we will derive the theoretical basis of our framework and perform extensive validation and comparison studies on widely used two-level models. Second, we will extend our framework to arbitrary MLMs, accompanied by further validation and benchmarking. Third, we will apply our framework to solve a challenging real-world problem involving model families from the popular ACT-R cognitive architecture. Finally, we will develop a user-friendly open-source library to make the developed methods available to the public, thus ensuring its widespread application in research and practice.
DFG Programme
Research Grants
