Research projects Fall 2023
The deadline for applications is June 30th, 2023.
This round will consist of the following projects:
- ELLIS Excellence Fellowship 2023_01 - Surface Watermarking for Large Language Models
- ELLIS Excellence Fellowship 2023_02 - Translating the experiment into physics
- ELLIS Excellence Fellowship 2023_03 - Supporting the energy transition with AI: estimate the power direction and power factor from current measurements
- ELLIS Excellence Fellowship 2023_04 - Safely transferring reinforcement learning agents under adversarial attacks
- ELLIS Excellence Fellowship 2023_05 - Robust neural network controllers in uncertain environments
- ELLIS Excellence Fellowship 2023_06 - Towards Biologically-Inspired Network Pruning: Predictive Coding and Covariance Reduction in Artificial Neural Networks
- ELLIS Excellence Fellowship 2023_07 - Robust (causal) inference using mathematical models of dynamical systems in biology
- ELLIS Excellence Fellowship 2023_08 - Dynamic brain connectivity: Changepoint detection in Wishart processes
Surface Watermarking for Large Language Models
Supervisor: Prof. Dr. Martha Larson
ELLIS Excellence Fellowship 2023_01
Project description
Large Language Models (LLMs), such as ChatGPT, require enormous amounts of training data collected from online sources and must be frequently updated to keep up with current events. As the use of LLMs increases, more of the text online will have been automatically generated rather than written by a human author. With this trend, the danger increases that LLMs will be trained using text that they themselves have generated. LLMs feeding back into themselves in this way can give rise to unintended adverse effects, such as reinforcing hallucination or creating echo chambers.
Proposals have been made as how ChatGPT could embed a `watermark' into the text it generates [1], which would make it possible to detect automatically generated text. Such a watermark would also help to control the spread of LLM-generated disinformation, by making automatically generated text identifiable. However, the drawback of standard watermarks is that they cannot be discerned without insider knowledge: effectively a secret key.
In this project, we develop a "surface watermark" that is easily detected by the human reader, but is not distracting. Such a watermark serves to make it readily evident to a reader that a text has been automatically generated, without requiring knowledge of the secret key. In this project, you will develop approaches to creating text with a surface watermark. You will test the approaches for both accuracy and the usefulness and acceptability of the watermarked text to human readers.
The fundamental machine learning challenge is to design a neural approach that is capable of precisely controlling word and/or character counts. You will have the opportunity to explore a variety of approaches to creating watermarks, such as adversarial text (e.g., "HotFlip") and neural style transfer.
Requirements
Basic knowledge of deep learning, interest in language/linguistics and in human interpretation of generative AI.
How to apply
If you are interested in applying for this position please send your one page CV, motivation letter and a list of your obtained grades to: ellis-fellowships@ru.nl with the header containing the title and number of the project and your s-number.
References:
Translating the experiment into physics
Supervisor: Dr. Sascha Caron
ELLIS Excellence Fellowship 2023_02
Project description
This task is about reconstructing particle trajectories in a particle physics experiment, e.g. in the ATLAS experiment at the Large Hadron Collider at CERN or in astroparticle experiments like the KM3NeT/Icecube experiments. This is one of the most important experimental algorithms in particle physics. So far, conventional algorithms have generally been used, but Deep Learning is likely to take over trajectory reconstruction in the future. However, the question arises: what is the best approach and algorithm for reconstructing these particles with neural networks? Several approaches based on graph networks have been explored. We would like to try different approaches in this challenge, e.g., sequence to sequence / transformers (i.e., translating hits to tracks, see below).
When particles collide in a particle detector, the collision creates a large number of secondary particles. These particles can travel through the detector and leave signals called "hits" as they interact with the detector material. The hits are recorded by various detector components such as track detectors.
By reconstructing the particle tracks from the detector hits (x,y,z coordinates), scientists can determine the properties of the particles, such as their momentum, charge, and type, which allows for further analysis and identification of specific particles such as Higgs bosons or other exotic particles. The process of track reconstruction plays a crucial role in deciphering the physics of particle collisions in experiments such as the Large Hadron Collider.
The process of reconstructing particle tracks from these detector hits is essential to understanding the paths and properties of the particles produced in the collision. In summary, the main idea of this project is to develop a kind of TrackGPT that can translate hits into tracks (and perhaps vice versa). In a second step, we would measure the performance of this algorithm in terms of energy and speed and compare it with other approaches. Finally, we will work with a large company (not HAL) to see if we can apply the transformer architecture to specialized computing hardware (called neuromorphic computing).
The student involved in this project will be part of an interdisciplinary team comprising physicists, computer scientists, and industry partners. The project offers a unique opportunity to contribute to cutting-edge research at the intersection of particle physics and Deep Learning, with the potential for significant advancements in trajectory reconstruction and its practical applications.
Requirements
Basic knowledge in deep learning, interest in physics, interest in large language models and transformers
How to apply
If you are interested in applying for this position please send your one page CV, motivation letter and a list of your obtained grades to: ellis-fellowships@ru.nl with the header containing the title and number of the project and your s-number.
Supporting the energy transition with AI: estimate the power direction and power factor from current measurements
Supervisors: Yuliya Shapolavola (Radboud University) and Jacco Heres (Alliander)
ELLIS Excellence Fellowship 2023_03
Project description
Alliander aims to play a decisive role in the energy transition to a more sustainable future. The company seeks new technologies and responds to new developments in the energy sector with the goal to use the grid more efficiently and boost productivity. It allows us to connect as many renewables, electric vehicles, heat pumps and new customers to the grid as possible.
Alliander has measurements at various locations in its electricity network, to get insights in the currents, voltages and active/reactive powers in the grid (https://en.wikipedia.org/wiki/AC_power). Most of these measurements only measure the absolute value of the current (I), because these measurements are cheaper and more reliable then measurements of the active and reactive powers (P & Q). The latter, however, provide more insight in the behavior of the grid and different loads, and are much more suitable to do e.g. load forecasting and State-Estimation. Is it possible to estimate the direction of the power flow or even the fraction between P and Q (called the power factor: https://en.wikipedia.org/wiki/Power_factor) from absolute current measurements?
There is data from locations/substations where we do measure all the different quantities, which can be used to train a machine learning model, but there are also physical laws that constraint the solution space. For example there is Kirchhoff's current law that states that all incoming and outgoing (complex) currents or powers should add up to zero. This problem therefore lends itself very well to a Bayesian approach where physical knowledge and knowledge from data is combined.
Other features that might be helpful can be found in the timeseries of a single measurement itself: when the sign of the active power changes, this usually means that there is also a clearly visible change in the sign of the derivative of the absolute current. A third way for a model to gain insight are spatial features, e.g. the approximated generated solar power in a certain area that is powered via the location/substation in question.
There might be various directions to try to solve this problem, e.g. Conditional Variational Auto-Encoders, Physical Informed Machine Learning or Gaussian Processes
What do we offer you?
This is a challenging and highly varied internship in an organization that is at the center of the energy transition. Alliander is at the forefront of applying Data Science in a technical environment. Obviously, this includes a good internship allowance and we support you with all means to perform your work well. We have more than enough data available and ready to perform this project.
You will work 2 days per week at Alliander (location Arnhem close to the main station), and 3 days per week at the Radboud University with the other Ellis Excellence Fellowship students.
Requirements
You are MSc student with an artificial intelligence and/or computer science background. You are also interested in modeling complex systems and working with large amounts of data.
You also have:
- Programming experience with regard to modeling and machine learning, in Python or R.
- Interest in the energy system and the challenges of the energy transition.
Additionally, knowledge and experience about Bayesian Machine Learning (e.g. Gaussian Processes, Bayesian Networks, Conditional Variational Auto-Encoders) and/or machine learning models on timeseries is desirable.
About Alliander
Alliander is a large Dutch distribution system operator (DSO) that ensures that millions of customers have access to electricity and gas every day for living, working, transport and recreation. We stand for an energy supply that gives everyone access to reliable, affordable and sustainable energy under the same conditions. Now and in the future. That is what we work on together every day. We offer our professionals an environment for innovative and smart ideas. An environment for your energy.
You will work the AI for Energy Grids Lab within the Research Centre for Digital Technologies. This team is researching smart and innovative technologies that help us do our job better and faster in the field and in the office. We are researching which digital innovations will bring real value to Alliander and which should therefore be implemented on a large scale in (digitalization) teams.
The AI for Energy Grids lab is an ICAI lab focused on developing methods and tools that use grid data to improve the efficiency, sustainability, and reliability of the medium-low voltage grid. It combines the expertise of Alliander data scientists, electrical engineers, and the latest digitalization programs for grid data, with academic expertise on methods from artificial intelligence. The lab is a collaboration Alliander Delft University of Technology, Radboud University, the University of Twente and the HAN University of Applied Sciences.
How to apply: If you are interested in applying for this position please send your one page CV, motivation letter and a list of your obtained grades to: ellis-fellowships@ru.nl with the header containing the title and number of the project and your s-number.
References
- Gámez Medina, J. M., de la Torre y Ramos, J., López Monteagudo, F. E., Ríos Rodríguez, L. D. C., Esparza, D., Rivas, J. M., ... & Romero Moyano, A. A. (2022). Power Factor Prediction in Three Phase Electrical Power Systems Using Machine Learning. Sustainability, 14(15), 9113.
- Wang, Chenguang, Simon H. Tindemans, and Peter Palensky. "Generating Contextual Load Profiles Using a Conditional Variational Autoencoder." 2022 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe). IEEE, 2022.
- Misyris, George S., Andreas Venzke, and Spyros Chatzivasileiadis. "Physics-informed neural networks for power systems." 2020 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2020.
- Pilar, Philipp, et al. "Incorporating Sum Constraints into Multitask Gaussian Processes." arXiv preprint arXiv:2202.01793 (2022).
Safely transferring reinforcement learning agents under adversarial attacks
Supervisors: Dr. Nils Jansen and Dr. Thiago Dias Simão
ELLIS Excellence Fellowship 2023_04
Motivation
Safety is a paramount challenge for the deployment of autonomous agents. In particular, ensuring safety while an agent is still learning may require considerable prior knowledge (Carr et al., 2023; Simão et al., 2021). A workaround is to pre-train the agent in a similar environment, called the source task (⋄), where it can behave unsafely, and deploy it in the actual environment, called the target task (⊙), once it has learned how to act safely. Such situations are common when we train the agent on a simulator or laboratory before deploying it into the real world.
Challenge
Previous work has shown that it is possible to safely transfer an reinforcement learning (RL) agent from a source task that preserves the safety dynamics of the target task (Yang et al., 2022). However, this assumption may be too strong for real-world applications. Building high-fidelity simulators require extensive and meticulous engineering. Furthermore, small differences in the dynamics of the source and target tasks can be amplified as the agent interacts multiple times with the environment, leading to performance degradation in the target task.
Goal
This project investigates how to transfer an agent from a source task to a different target task while maintaining the same safety guarantees. In other words, this project investigates how to robustly perform safe transfers.
Overview
A potential approach is to train the agent in the source task under adversarial attacks to increase the robustness of the transfer. The project builds on the results from a previous ELLIS fellowship project (Hogewind et al., 2023) and the resulting codebase (https://github.com/LAVA-LAB/safe-slac).
The main tasks are:
- Literature review and formulation of the problem statement.
- Training Safe RL agents, such as SAC-Lagrangian.
- Implement new methods to improve the robustness of the safe RL agents after the transfer.
- Designing experiments to evaluate the safety of the transfer.
Requirements
Basic knowledge in reinforcement learning.
Learn more
Access http://lava-lab.org/projects/safetransfer/ for more details.
How to apply
If you are interested in applying for this position please send your one page CV, motivation letter and a list of your obtained grades to: ellis-fellowships@ru.nl with the header containing the title and number of the project and your s-number.
References
- Carr, S., Jansen, N., Junges, S., & Topcu, U. (2023). Safe Reinforcement Learning via Shielding under Partial Observability. AAAI.
- Simão, T. D., Jansen, N., & Spaan, M. T. J. (2021). AlwaysSafe: Reinforcement Learning without Safety Constraint Violations during Training. AAMAS, 1226–1235.
- Yang, Q., Simão, T. D., Jansen, N., Tindemans, S. H., & Spaan, M. T. J. (2022). Training and transferring safe policies in reinforcement learning. AAMAS 2022 Workshop on Adaptive Learning Agents.
- Hogewind, Y., Simão, T. D., Kachman, T., & Jansen, N. (2023). Safe Reinforcement Learning From Pixels Using a Stochastic Latent Representation. ICLR.
Robust neural network controllers in uncertain environments
Supervisors: Dr. Nils Jansen and Dr. Sebastian Junges
ELLIS Excellence Fellowship 2023_05
Project description
This project concerns the robustness of neural networks in complex environments under uncertainty. Think of a delivery drone navigating through a crowded urban environment, as depicted in the two examples in Figure 1. An effective and safe controller for this drone needs to take into account, for instance, sensor imprecision, restricted views, unexpected wind gusts, or other air traffic participants.
Decision-making under uncertainty. In artificial intelligence, such decision-making problems under uncertainty [Kochenderfer, 2015] are commonly modeled by Markov decision processes (MDPs) or their various extensions. Reinforcement learning is a prominent machine learning technique to create a decision-making policy for such problems, with deep reinforcement learning employing neural networks as policy representations. Effective means to prove the robustness of such neural network policies have been proposed, for instance, in [Carr et al., 2021]. Yet, these policies are usually trained for one specific environment and are thus prone to overfitting. In the real world, problems are subject to slight changes or distributional shifts. Consequently, the robustness of such neural network controllers remains an open challenge to real-world applicability.
Goal of this fellowship
We propose the following approach towards increased robustness of controllers. Instead of training the neural network based on a single model, we employ a so-called family of MDPs [Ceska et al., 2019]. In a nutshell, such a family contains a potentially infinite number of environments that share certain similarities, such as joint feature spaces. Intuitively, the two drone scenarios depicted in Figure 1 can be modeled by two MDPs that belong to the same family. The goal is to find a single, robust controller that performs well in both environments [van der Vegt et al., 2023].
Approach
(1) We train the neural network controller for a randomly chosen subset of MDPs from the family.
(2) We formally verify the performance of the neural network Robust Neural Network Controllers to assess its robustness regarding the whole family. We will use the Python-based interface of the model checker Storm [Hensel et al., 2022] (www.stormchecker.org).
(3) In case the performance is not satisfactory, we generate so-called diagnostic data to generate new training data. As a baseline, we will employ an actor-critic architecture [Konda and Tsitsiklis, 1999], but we will expect the student to provide a broad set of experiments that investigate the appropriate neural network architecture.
Embedding of the fellowship
The student working on this project will, besides ELLIS, be embedded in the daily activities of the research groups of the supervisors Nils Jansen and Sebastian Junges. The topic is part of the ERC starting grant “DEUCE: Data-Driven Verification and Learning Under Uncertainty”, and the student would directly join the ongoing discussions with two Ph.D. students. We conduct weekly meetings with the whole team, and facilitate an open and cooperative research culture, where also students are directly involved. There will be the possibility and funding to visit at least one workshop or conference on related topics to interact with the top researchers in the field.
Requirements
Basic knowledge in machine learning or formal verification.
How to apply
If you are interested in applying for this position please send your one page CV, motivation letter and a list of your obtained grades to: ellis-fellowships@ru.nl with the header containing the title and number of the project and your s-number.
References
- S. Carr, N. Jansen, and U. Topcu. Task-aware verifiable rnn-based policies for partially observable markov decision processes. J. Artif. Intell. Res., 72:819–847, 2021.
- M. Ceska, N. Jansen, S. Junges, and J. Katoen. Shepherding hordes of markov chains. In TACAS (2), volume 11428 of Lecture Notes in Computer Science, pages 172–190. Springer, 2019.
- C. Hensel, S. Junges, J. Katoen, T. Quatmann, and M. Volk. The probabilistic model checker storm. volume 24, pages 589–610, 2022.
- M. J. Kochenderfer. Decision Making Under Uncertainty: Theory and Application. MIT press, 2015.
- V. R. Konda and J. N. Tsitsiklis. Actor-critic algorithms. In NIPS, pages 1008–1014. The MIT Press, 1999.
- M. van der Vegt, N. Jansen, and S. Junges. Robust almost-sure reachability in multi-environment MDPs. In TACAS (1), volume 13993 of Lecture Notes in Computer Science, pages 508–526. Springer, 2023.2
Towards Biologically-Inspired Network Pruning: Predictive Coding and Covariance Reduction in Artificial Neural Networks
Supervisor: Dr. Nasir Ahmad
ELLIS Excellence Fellowship 2023_06
Project description
Neuroscience proposes predictive coding as a principle, suggesting that units attenuate each other's activity by predicting the activity of their neighbours and inhibiting them. This is hypothesised to be a mechanism for energy reduction and efficient encoding of information. This project aims to make Artificial Neural Networks (ANNs) more energy and computation efficient by using this principle to allow efficient pruning of ANN nodes.
In previous work [1], we demonstrated that the neural architecture typically used to describe predictive coding simply emerges when a network is constrained to minimise the amount of activity it generates. Recently, we further developed ideas fusing the principle of predictive coding with the idea of active decorrelation between the activities of units in a deep neural network. Within this project, we aim to extend this research line to develop a method for ranking units such that each unit in a neural network layer is constrained to have minimum correlation with the preceding units of that layer. One intriguing aspect of this approach is that this ranking translates into ranked feature restriction, where each subsequent unit is more restricted in its representation than those that preceded it.
Following the training of networks (with this layer-wise ranking), we can systematically prune networks from the most highly restricted units in a layer towards the least. This presents a method for network node pruning that is both principled and inspired by neural function. This approach holds significant potential to flexibly and on-the-fly reduce the number of parameters and the amount of computation needed to execute an artificial neural network model with minimal loss in accuracy.
Our preliminary results indicate that such an arrangement permits node pruning of deep neural networks in a manner that is both functional, innovative, and biologically inspired. Consequently, we propose the following research questions for this project:
- Can the principles of predictive coding and covariance reduction be effectively combined to develop novel, biologically inspired neural network models with ranked feature restriction?
- How effectively can we prune deep neural networks with ranked feature restriction, and what is the impact on network performance and efficiency?
- What other computational efficiency gains can be translated from principles of efficient coding in computational neuroscience for brain-inspired AI?
The project necessitates an interdisciplinary approach, bridging neuroscience and machine learning. The student will become a vital part of the research group in addition to participating in the ELLIS network. They will also have the opportunity to directly join ongoing collaborations with PhD students within the host lab.
Requirements/what we are looking for in a student
- Experience in a deep learning framework (Pytorch, Jax, or Tensorflow)
- Firm grasp of linear algebra and calculus principles
- Interest or inclination toward neuro-inspired AI
How to apply
If you are interested in applying for this position please send your one page CV, motivation letter and a list of your obtained grades to: ellis-fellowships@ru.nl with the header containing the title and number of the project and your s-number.
References
[1] Ali, A., Ahmad, N., de Groot, E., Johannes van Gerven, M. A., & Kietzmann, T. C. (2022). Predictive coding is a consequence of energy efficiency in recurrent neural networks. Patterns (New York, N.Y.), 3(12), 100639. https://doi.org/10.1016/j.patter.2022.100639
Robust (causal) inference using mathematical models of dynamical systems in biology
Supervisors: Dr. Tom Claassen and Dr. Inge Wortel
ELLIS Excellence Fellowship 2023_07
Project description
In this interdisciplinary project, you will combine elements of causal inference theory and mathematical biology to help improve our understanding of dynamical systems.
From physics and engineering to ecology, virology, epidemiology, and biochemistry: many scientific fields use mathematical models to reason about dynamical processes. This is especially important for systems in which multiple entities interact. Such systems rapidly become too complex for us to intuit outcomes based on qualitative assumptions alone; and good models are crucial to develop hypotheses, make predictions, or reliably calculate key system parameters from available data. A good example can be found in the models of viral dynamics developed in the 1990s and 2000s [1]. These models, which are similar to the familiar predator-prey models in biology, were incredibly impactful because they helped understand the complex interplay between HIV and the immune system, explained why HIV patients rapidly became resistant to drugs and why they needed life-long therapy, and inspired better treatment strategies.
But despite the benefits of this approach, it also has its limitations. One important problem was discovered about ten years ago, when it was shown that seemingly minor extensions to some models could completely flip their (causal) implications. This has raised concerns about the validity of our interpretations: if very similar models can lead to opposite conclusions, how do we know which of our modelling predictions are actually true (or rather ‘robust’) [2]?
In this project we want to tackle this issue by building on promising recent work [3], which proposed ways to detect cases where model extensions are robust in their predictions – and tools to select the best model in cases where they are not. Specifically, you will use available models for viral dynamics to simulate data and try to answer one or more of the following research questions:
- Can we use the insights from [3] to select between different infection models based on data?
- Can we recognize when our (causal) model interpretations are robust?
- Given a dataset and a set of models with competing predictions, to what extent can we reduce uncertainty in predictions?
Requirements
We search for MSc students in computer science, artificial intelligence, mathematics, or a related discipline with a strong interest in multi-disciplinary research. You are highly motivated, open-minded and interested in pursuing an academic career.
How to apply
If you are interested in applying for this position please send your one page CV, motivation letter and a list of your obtained grades to: ellis-fellowships@ru.nl with the header containing the title and number of the project and your s-number.
References
- [1] Perelson (2002). Modelling viral and immune system dynamics. Nature Reviews Immunology, https://www.nature.com/articles/nri700
- [2] de Boer (2012). Which of our modeling predictions are robust? PLOS Computational Biology, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002593#s7
- [3] Blom and Mooij (2022). Robustness of model predictions under extension. Conference on Uncertainty in Artificial Intelligence, https://arxiv.org/pdf/2012.04723v2.pdf
Dynamic brain connectivity: Changepoint detection in Wishart processes
Supervisor: Dr. Max Hinne
ELLIS Excellence Fellowship 2023_08
Project description
The human brain comprises a vast network of spatially segregated regions that integrate and process information from sensory input to behavioural output. Neuroscience has identified functional connectivity, where network weights are determined by the co-activation of pairs of brain regions. as one of the fundamental lenses through which this network can be studied. Recent results show that time-varying functional connectivity provides a sensitive predictor of cognition and mental disorder, and better predicts task-related phenotypes such as processing speed and fluid intelligence scores than static networks [1]. By modelling this time-varying functional connectivity, we aim to understand (and eventually treat) psychiatric or neurological diseases, gain insight in the effects of ageing on the brain, and to learn how brain connectivity influences cognition.
As a crucial first step into this direction, we have recently developed a Bayesian nonparametric regression framework based on Wishart processes [2] that can capture dynamic functional connectivity. Our preliminary results show that this approach outperforms the prevailing baseline approaches. It also quantifies its estimation uncertainty. Simultaneously, we have formulated a Bayesian regression discontinuity approach capable of detecting and quantifying the impact of interventions on a dynamic system [3].
The project aims to merge these two active research lines, which brings us to the following research questions:
- How can we adapt our regression discontinuity design framework to detect an arbitrary number of changes in a univariate time series?
- Can we incorporate this univariate approach into our Wishart process model for dynamic functional connectivity?
- How does the proposed system perform in comparison to common baselines like the infinite hidden Markov model?
Given that we do not know specific parametric forms for the time series of dynamic connectivity, nor do we know the potential number of changes they might undergo, we turn to the adaptability of Bayesian nonparametric modelling. This requires efficient approximate inference, for which we leverage the algorithms implemented in the Blackjax framework [4].
The selected student will have the opportunity to become an integral part of the Uncertainty in Complex Systems group. They will work closely with the PhD students involved in the related projects mentioned above.
Requirements
Approximate Bayesian inference, basic understanding of Gaussian processes, interest in Bayesian nonparametric and neuroscience
How to apply
If you are interested in applying for this position please send your one page CV, motivation letter and a list of your obtained grades to: ellis-fellowships@ru.nl with the header containing the title and number of the project and your s-number.
References
- Lurie, D. J., Kessler, D., Bassett, D. S., Betzel, R. F., Breakspear, M., Keilholz, S., Kucyi, A., Liégeois, R., Lindquist, M. A., McIntosh, A. R., Poldrack, R. A., Shine, J. M., Thompson, W. H., Bielczyk, N. Z., Douw, L., Kraft, D., Miller, R. L., Muthuraman, M., Pasquini, L., … Calhoun, V. D. (2020). Questions and controversies in the study of time-varying functional connectivity in resting fMRI. Network Neuroscience, 4(1), 30–69.
- Wilson, A. G., & Ghahramani, Z. (2011). Generalised Wishart processes. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, 736–744. http://arxiv.org/abs/1101.0240
- Hinne, M., Leeftink, D., van Gerven, M. A. J., & Ambrogioni, L. (2022). Bayesian model averaging for nonparametric discontinuity design. PLOS ONE, 17(6), e0270310. https://doi.org/10.1371/journal.pone.0270310
- Junpeng, L., & Louf, R. (2020). Blackjax: A sampling library for JAX. http://github.com/blackjax-devs/blackjax