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Adaptive Graph Neural Networks for Cosmological Data Generalization: Acknowledgements and Disclosure

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Andrea Roncoli, Department of Computer, Science (University of Pisa);
(2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago);
(3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory);
(4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute);
(5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Data and Methods Results Conclusions Acknowledgments and Disclosure of Funding, and References Additional Plots 4 Conclusions We propose and demonstrate a method for unsupervised DA for cosmological inference with GNNs. We use an MMD-based loss to enable the domain-invariant encoding of features by the GNN. This approach enhances cross-domain robustness: compared to previous methods, DA-GNNs reduce prediction error and improve uncertainty estimates. Limitations The cross-domain accuracy remains worse when compared to single-domain performance. Although reaching the same accuracy might not be possible, more flexible approaches such as adversarial-based DA techniques [20, 36], instead of distance-based ones such as MMD, might yield better results. Moreover, due to computational and time constraints, our models have been trained and tested only on two of the four available CAMELS simulation suites. Using more suites would yield better cross-domain efficacy and reliability at assessment time. These limitations will be addressed in future work. This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Abstract and Intro Data and Methods Data and Methods Results Results Conclusions Conclusions Acknowledgments and Disclosure of Funding, and References Acknowledgments and Disclosure of Funding, and References Additional Plots Additional Plots 4 Conclusions We propose and demonstrate a method for unsupervised DA for cosmological inference with GNNs. We use an MMD-based loss to enable the domain-invariant encoding of features by the GNN. This approach enhances cross-domain robustness: compared to previous methods, DA-GNNs reduce prediction error and improve uncertainty estimates. Limitations The cross-domain accuracy remains worse when compared to single-domain performance. Although reaching the same accuracy might not be possible, more flexible approaches such as adversarial-based DA techniques [20, 36], instead of distance-based ones such as MMD, might yield better results. Moreover, due to computational and time constraints, our models have been trained and tested only on two of the four available CAMELS simulation suites. Using more suites would yield better cross-domain efficacy and reliability at assessment time. These limitations will be addressed in future work. Limitations

Adaptive Graph Neural Networks for Cosmological Data Generalization: Conclusions

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Andrea Roncoli, Department of Computer, Science (University of Pisa);
(2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago);
(3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory);
(4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute);
(5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Data and Methods Results Conclusions Acknowledgments and Disclosure of Funding, and References Additional Plots 3 Results Latent space organization Isomaps are two-dimensional projections of the multi-dimensional latent space [35]. Figure 1 shows the difference in the latent space structure without (top row) and with (bottom row) DA. Ellipses in the top right isomap highlight how the two distributions are encoded in different regions of the latent space. Without the MMD loss, the model encodes samples with very different values of Ωm close to each other, if they originate from different simulations (circles and triangles of different colors are overlapping). This scenario leads to the fragility of the regressor, which cannot learn to output different values for the same latent space encodings. On the contrary, the DA-GNN (bottom right plot) correctly encodes the samples in a domain-invariant way. Visually, circle and triangle distributions are overlapping, which indicates domain mixing. Furthermore, the direction in the color gradient shows that the DA-GNN encodes information such that the regressor can now more correctly predict cosmological parameters based on the encodings of both simulations. [5] In [41], authors get slightly better results for the same domain, and slightly worse for the cross-domain tests. We impute these differences to choices such as batch sizes and optimization techniques we took due to computational and time constraints. [6] In Appendix A, the IllustrisTNG counterpart of this plot is presented. This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Abstract and Intro Data and Methods Data and Methods Results Results Conclusions Conclusions Acknowledgments and Disclosure of Funding, and References Acknowledgments and Disclosure of Funding, and References Additional Plots Additional Plots 3 Results Latent space organization Isomaps are two-dimensional projections of the multi-dimensional latent space [35]. Figure 1 shows the difference in the latent space structure without (top row) and with (bottom row) DA. Ellipses in the top right isomap highlight how the two distributions are encoded in different regions of the latent space. Without the MMD loss, the model encodes samples with very different values of Ωm close to each other, if they originate from different simulations (circles and triangles of different colors are overlapping). This scenario leads to the fragility of the regressor, which cannot learn to output different values for the same latent space encodings. On the contrary, the DA-GNN (bottom right plot) correctly encodes the samples in a domain-invariant way. Visually, circle and triangle distributions are overlapping, which indicates domain mixing. Furthermore, the direction in the color gradient shows that the DA-GNN encodes information such that the regressor can now more correctly predict cosmological parameters based on the encodings of both simulations. [5] In [41], authors get slightly better results for the same domain, and slightly worse for the cross-domain tests. We impute these differences to choices such as batch sizes and optimization techniques we took due to computational and time constraints. [6] In Appendix A, the IllustrisTNG counterpart of this plot is presented.

Adaptive Graph Neural Networks for Cosmological Data Generalization: Results

Industrial robots have been helping manufacture products and facilitate logistics for more than 60 years. Traditionally, these robots are very good at a specific function — for instance, going from A to B. Throw an obstacle into their work environment however — be it a physical object or a human collaborator — and severe safety hazards arise. Technology is progressing such that today’s industrial robots are being designed to be “adaptive,” meaning that they’re ​​capable of adapting to and learning from their environment, including human interactions. The big vision is that humans and automated robots will be able to interact with one another on a machine shop floor, reducing the risk involved with having humans work side by side with giant machines. In Europe, industrial robots are becoming more commonplace. Data published in 2021 from The International Federation of Robotics showed European industrial robot installations up 24% compared to 2020. And while Europe still trails the United States and China in terms of industrial robot use, the growth of EU industrial production — up 8% in 2021 and another 5% in 2022 — could drive robot adoption in factories. In order to better ensure that the industrial robots of the future can readily adapt to changing environments, while maintaining safe and trustworthy collaboration with humans, a group of universities, tech accelerators and private research labs from the European Union (EU) have established RoboSAPIENS. The project, which is funded by the European Union’s Horizon Europe 2021-2027 research and innovation programme, will develop and implement safety mechanisms that will empower robots to — at a high level — safely adapt to unexpected changes. In an interview with TheNextWeb’s Ioanna Lykiardopoulou, consortium partner Ana Cavalcanti, a professor at the University of York, said that the project aims to include a trustworthiness checker in the current Monitor-Analyze-Plan-Execute-Knowledge (MAPE-K) framework for self adaptive systems. “What is missing here is the inclusion in the loop of a step that verifies whether certified guarantees, of safety or trustworthiness, are kept when plans change,” Cavalcanti told TheNextWeb. By adding this step, researchers hope that if a robot encounters an obstacle, it will consult if its originally programmed plan is still valid with the introduction of the obstacle. If it is not, the system will self update and a “trustworthiness checker” will validate the changes for safety issues. The researchers will use a combination of Deep Learning (DL) and Digital Twin (DT) — or a virtual representation of a physical object — techniques to generate the new control settings. “As the EU advances its industrial robotics capabilities, it’s imperative that measures be taken to ensure the safety and trustworthiness of the next generation of robots working alongside humans in a collaborative environment,” said Peter Gorm Larsen, a Professor in the Department of Electrical and Computer Engineering at Aarhus University, and the coordinator of the RoboSAPIENS project. “With RoboSAPIENS, we will prepare Europe’s industrial robotics industry for rapid and unforeseen adaptability in system structure and environment, assuring trustworthy collaboration with humans by changing behavior while maintaining and even enhancing performance and safety,” he added. According to a statement from the consortium, the project is already working on industrial use studies. The first empowers robots to disassemble electronic consumer waste, another aims to improve navigation predictability of autonomous water vessels. A third looks to help Autonomous Mobile Robots (AMRs) adapt to anomalies on machine shop floors, and a fourth will automatically assess risks in human-robot collaboration (cobot) situations. Consortium partners include Denmark’s Aarhus University; Aristotle University of Thessaloniki, AUTH (Greece); Danish Technological Institute, DTI (Denmark); Fraunhofer IFF, Fraunhofer (Germany); University of York, UoY (United Kingdom); University of Antwerp, UA (Belgium); Norwegian University of Science and Technology, NTNU (Norway); PAL Robotics, PAL (Spain); ISDI Accelerator, ISDI (Spain); Simula Research Lab, SRL (Norway). The RoboSAPIENS consortium isn’t the only entity working on marketing self adaptive robots safer and more efficient. Earlier this year, Google’s Deep Mind announced a series of releases related to industrial robots, including Self-Adaptive Robust Attention for Robotics Transformers (SARA-RT) which helps robots learn and perform new tasks at more efficient speeds. And last year, a team of Japanese researchers developed a learning framework to train robots to “sense” their surrounding environment, making it safer for human-robot collaboration. Industrial robots have been helping manufacture products and facilitate logistics for more than 60 years. Traditionally, these robots are very good at a specific function — for instance, going from A to B. Throw an obstacle into their work environment however — be it a physical object or a human collaborator — and severe safety hazards arise. Technology is progressing such that today’s industrial robots are being designed to be “adaptive,” meaning that they’re ​​capable of adapting to and learning from their environment, including human interactions. The big vision is that humans and automated robots will be able to interact with one another on a machine shop floor, reducing the risk involved with having humans work side by side with giant machines. In Europe, industrial robots are becoming more commonplace. Data published in 2021 from The International Federation of Robotics showed European industrial robot installations up 24% compared to 2020. And while Europe still trails the United States and China in terms of industrial robot use, the growth of EU industrial production — up 8% in 2021 and another 5% in 2022 — could drive robot adoption in factories. published growth of EU industrial production In order to better ensure that the industrial robots of the future can readily adapt to changing environments, while maintaining safe and trustworthy collaboration with humans, a group of universities, tech accelerators and private research labs from the European Union (EU) have established RoboSAPIENS . RoboSAPIENS The project, which is funded by the European Union’s Horizon Europe 2021-2027 research and innovation programme, will develop and implement safety mechanisms that will empower robots to — at a high level — safely adapt to unexpected changes. In an interview with TheNextWeb ’s Ioanna Lykiardopoulou, consortium partner Ana Cavalcanti, a professor at the University of York, said that the project aims to include a trustworthiness checker in the current Monitor-Analyze-Plan-Execute-Knowledge (MAPE-K) framework for self adaptive systems. interview TheNextWeb “What is missing here is the inclusion in the loop of a step that verifies whether certified guarantees, of safety or trustworthiness, are kept when plans change,” Cavalcanti told TheNextWeb . TheNextWeb By adding this step, researchers hope that if a robot encounters an obstacle, it will consult if its originally programmed plan is still valid with the introduction of the obstacle. If it is not, the system will self update and a “trustworthiness checker” will validate the changes for safety issues. The researchers will use a combination of Deep Learning (DL) and Digital Twin (DT) — or a virtual representation of a physical object — techniques to generate the new control settings. “As the EU advances its industrial robotics capabilities, it’s imperative that measures be taken to ensure the safety and trustworthiness of the next generation of robots working alongside humans in a collaborative environment,” said Peter Gorm Larsen, a Professor in the Department of Electrical and Computer Engineering at Aarhus University, and the coordinator of the RoboSAPIENS project. “With RoboSAPIENS, we will prepare Europe’s industrial robotics industry for rapid and unforeseen adaptability in system structure and environment, assuring trustworthy collaboration with humans by changing behavior while maintaining and even enhancing performance and safety,” he added. According to a statement from the consortium, the project is already working on industrial use studies. The first empowers robots to disassemble electronic consumer waste, another aims to improve navigation predictability of autonomous water vessels. A third looks to help Autonomous Mobile Robots (AMRs) adapt to anomalies on machine shop floors, and a fourth will automatically assess risks in human-robot collaboration (cobot) situations. Consortium partners include Denmark’s Aarhus University; Aristotle University of Thessaloniki, AUTH (Greece); Danish Technological Institute, DTI (Denmark); Fraunhofer IFF, Fraunhofer (Germany); University of York, UoY (United Kingdom); University of Antwerp, UA (Belgium); Norwegian University of Science and Technology, NTNU (Norway); PAL Robotics, PAL (Spain); ISDI Accelerator, ISDI (Spain); Simula Research Lab, SRL (Norway). The RoboSAPIENS consortium isn’t the only entity working on marketing self adaptive robots safer and more efficient. Earlier this year, Google’s Deep Mind announced a series of releases related to industrial robots, including Self-Adaptive Robust Attention for Robotics Transformers (SARA-RT) which helps robots learn and perform new tasks at more efficient speeds. And last year, a team of Japanese researchers developed a learning framework to train robots to “sense” their surrounding environment, making it safer for human-robot collaboration. announced developed

European Researchers Enhance Human-Robot Collaboration with Self-Adaptive Industrial Robots

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Andrea Roncoli, Department of Computer, Science (University of Pisa);
(2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago);
(3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory);
(4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute);
(5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Data and Methods Results Conclusions Acknowledgments and Disclosure of Funding, and References Additional Plots 2 Data and Methods 2.1 Domain Adaptation Optimization and Computing Resources We performed experiments on NVIDIA A100 40GB GPU. For each of the models, implemented using PyTorch Geometric [19], we perform a hyperparameter search using the Optuna library [1], with 50 trials per model. More details on code performance, model implementations, and selected hyperparameters can be found in the publicly available code[4]. 2.2 Evaluation [1] https://arepo-code.org/ [2] http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html [3] CAMELS dataset documentation: https://camels.readthedocs.io/en/latest/index.html [4] GitHub repository will be added after the anonymous review stage. This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Abstract and Intro Data and Methods Data and Methods Results Results Conclusions Conclusions Acknowledgments and Disclosure of Funding, and References Acknowledgments and Disclosure of Funding, and References Additional Plots Additional Plots 2 Data and Methods 2.1 Domain Adaptation Optimization and Computing Resources We performed experiments on NVIDIA A100 40GB GPU. For each of the models, implemented using PyTorch Geometric [19], we perform a hyperparameter search using the Optuna library [1], with 50 trials per model. More details on code performance, model implementations, and selected hyperparameters can be found in the publicly available code[4]. Optimization and Computing Resources 2.2 Evaluation [1] https://arepo-code.org/ [2] http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html [3] CAMELS dataset documentation: https://camels.readthedocs.io/en/latest/index.html [4] GitHub repository will be added after the anonymous review stage.

Adaptive Graph Neural Networks for Cosmological Data Generalization: Data and Methods

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Andrea Roncoli, Department of Computer, Science (University of Pisa);
(2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago);
(3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory);
(4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute);
(5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Data and Methods Results Conclusions Acknowledgments and Disclosure of Funding, and References Additional Plots Abstract 1 Introduction Accurate determination of cosmological parameters using big data from astronomical surveys is a task of paramount importance in modern science. Historically, the extraction of valuable cosmological information has relied on computing summary statistics [31, 16, 15]. More recently, deep learning methods, such as 2D and 3D Convolutional Neural Networks (CNNs), showed great promise in extracting rich non-linear information that summary statistics struggle to capture [32, 39, 29]. However, CNNs lack scale-invariance, as their analysis is firmly anchored to the grid size of the convolutional kernels, while any information on scales below that is lost. Choosing a superfine grid to avoid information loss, though, would simply yield almost entirely zeros in case of sparse and irregular data, such as galaxy clusterings. Thus, CNNs result in an inadequate method for structured sparse data. In contrast, Graph Neural Networks (GNNs) [23, 4, 49, 46] can handle structured cosmic web data in a scale-free manner [41, 14]. As with any other model, the typical procedure is to train GNNs on labeled data (like simulations) and then infer cosmological parameters from unlabeled data (like observations). However, there is a significant risk of these models not generalizing in the presence of the domain shift between simulations and observations. Systematic biases have been demonstrated even in experiments that train and test on simulations with different subgrid physics [41]. Domain adaptation (DA) techniques [11, 43, 18, 27] can be used to increase model robustness to this type of domain shift. Here we propose the use of Domain Adaptive Graph Neural Networks (DA-GNNs) and investigate the utility of distance-based DA losses i.e., Maximum Mean Discrepancy (MMD) [6]. MMD is an unsupervised DA technique because it does not require labeled data, which is paramount for future applications on observations. We show that our domain-adaptive models achieve stronger generalization across datasets than regular GNN models. Our work is a significant step towards building future models trained on simulations, yet robust enough to work on observational data. Related Work GNNs have shown great potential for extracting information from large sparse datasets, such as the distribution of galaxies, galaxy clusters, and cosmic large-scale structures [25, 28, 41, 33, 42, 14]. Unfortunately, due to the complexity of most deep learning models, they often learn dataset-specific features, which renders them useless when testing on a different dataset (different simulations or astronomical observations). In astronomy, it has been shown that DA techniques applied to different types of CNNs can substantially improve model performance in cross-dataset applications [8, 10, 9, 37, 21, 2]. Recently, it has been shown that DA can be used on other types of deep learning algorithms such as GNNs [12, 24, 45, 47, 7, 44, 17]. However, DA on GNNs has not been used for any astrophysics or cosmology applications. This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). This paper is available on arxiv under CC 4.0 license. available on arxiv Authors: Authors: (1) Andrea Roncoli, Department of Computer, Science (University of Pisa); (2) Aleksandra Ciprijanovi´c´, Computational Science and AI Directorate (Fermi National Accelerator Laboratory) and Department of Astronomy and Astrophysics (University of Chicago); (3) Maggie Voetberg, Computational Science and AI Directorate, (Fermi National Accelerator Laboratory); (4) Francisco Villaescusa-Navarro, Center for Computational Astrophysics (Flatiron Institute); (5) Brian Nord, Computational Science and AI Directorate, Fermi National Accelerator Laboratory, Department of Astronomy and Astrophysics (University of Chicago) and Kavli Institute for Cosmological Physics (University of Chicago). Table of Links Abstract and Intro Abstract and Intro Data and Methods Data and Methods Results Results Conclusions Conclusions Acknowledgments and Disclosure of Funding, and References Acknowledgments and Disclosure of Funding, and References Additional Plots Additional Plots Abstract 1 Introduction Accurate determination of cosmological parameters using big data from astronomical surveys is a task of paramount importance in modern science. Historically, the extraction of valuable cosmological information has relied on computing summary statistics [31, 16, 15]. More recently, deep learning methods, such as 2D and 3D Convolutional Neural Networks (CNNs), showed great promise in extracting rich non-linear information that summary statistics struggle to capture [32, 39, 29]. However, CNNs lack scale-invariance, as their analysis is firmly anchored to the grid size of the convolutional kernels, while any information on scales below that is lost. Choosing a superfine grid to avoid information loss, though, would simply yield almost entirely zeros in case of sparse and irregular data, such as galaxy clusterings. Thus, CNNs result in an inadequate method for structured sparse data. In contrast, Graph Neural Networks (GNNs) [23, 4, 49, 46] can handle structured cosmic web data in a scale-free manner [41, 14]. As with any other model, the typical procedure is to train GNNs on labeled data (like simulations) and then infer cosmological parameters from unlabeled data (like observations). However, there is a significant risk of these models not generalizing in the presence of the domain shift between simulations and observations. Systematic biases have been demonstrated even in experiments that train and test on simulations with different subgrid physics [41]. Domain adaptation (DA) techniques [11, 43, 18, 27] can be used to increase model robustness to this type of domain shift. Here we propose the use of Domain Adaptive Graph Neural Networks (DA-GNNs) and investigate the utility of distance-based DA losses i.e., Maximum Mean Discrepancy (MMD) [6]. MMD is an unsupervised DA technique because it does not require labeled data, which is paramount for future applications on observations. We show that our domain-adaptive models achieve stronger generalization across datasets than regular GNN models. Our work is a significant step towards building future models trained on simulations, yet robust enough to work on observational data. Related Work GNNs have shown great potential for extracting information from large sparse datasets, such as the distribution of galaxies, galaxy clusters, and cosmic large-scale structures [25, 28, 41, 33, 42, 14]. Unfortunately, due to the complexity of most deep learning models, they often learn dataset-specific features, which renders them useless when testing on a different dataset (different simulations or astronomical observations). In astronomy, it has been shown that DA techniques applied to different types of CNNs can substantially improve model performance in cross-dataset applications [8, 10, 9, 37, 21, 2]. Recently, it has been shown that DA can be used on other types of deep learning algorithms such as GNNs [12, 24, 45, 47, 7, 44, 17]. However, DA on GNNs has not been used for any astrophysics or cosmology applications. Related Work

Adaptive Graph Neural Networks for Cosmological Data Generalization: Abstract and Intro

Starting Simple: The Strategic Advantage of Baseline Models in Machine Learning

Hey hackers! Did you know that HackerNoon runs a to gauge reader sentiment on topics of interest? That’s right, every Monday readers are greeted with a new poll curated by a HackerNoon editor on some of the most trending news on the web (plus some general, wacky ones too just for fun!). weekly poll Now all that’s great, but what if we told you that there’s a way to go a step further with these polls and truly analyze readers’ sentiment? Let’s look at the : current poll running on HackerNoon Poll #1 Lesson: How to vote? This week's poll focuses on the debate over the potential ban of ByteDance’s TikTok in the US over national security concerns. Is it an overreach by the US government or a step in the right direction? To vote, pick the option that best aligns with your thoughts and compare it with the broader reader population 😎 Poll #2 Lesson: How to check past polls? Click on the “ ” to access a list of all the polls HackerNoon has run in the past. Poll of the Week Now, select a poll that has already closed and analyze the results 🥳 Poll #3 Lesson: How do I access polls' templates? Let’s look at the “ ” poll: if you click on the poll, it should show you a prompt that you can use to start analyzing the results right away! Take a look: What is your web browser of choice Got it?! AWESOME 👏 Here are some of our favorite polls that are definitely worthy of your analysis: How Much Faith Do You Have in Your Government to Effectively Regulate AI? Will AI stocks suffer the same fate as the dot-com bubble? Where do YOU think bitcoin's price is heading by the end of the year? Do You Think the "Metaverse" Will Ever Truly Take Off? Other News Around The Web Nvidia GTC Ah, Nvidia. What can be said about the company that hasn’t been said already after it became the arms dealer of choice for the generative artificial intelligence boom. Well, apparently a lot! The company its annual GPU Technology Conference, or GTC, heralding the launch of the Blackwell class of AI chips that are supposed to be better than their Hopper predecessors. But what could these new processors mean for the development of more powerful AI and what does Nvidia’s change in business direction mean for consumers at large? recently held Let us know ! here TikTok’s Future in the US Should TikTok face a ban in the US? That’s the question we’re readers this week as we highlight this important issue. The US House recently passed a bill requiring ByteDance, the parent company of TikTok, to divest from the app within 180 days or face prohibition (a ban) in the U.S. However, Senate supporters argue that this is not a ban but rather a transition of ownership to ensure national security. Is this overreaction, and perhaps, an overreach by the US government? asking and share your thoughts . Vote in the Poll here Sam Bankman-(never getting)Freed Looks like Sam Bankman-Fried’s days as a billionaire and crypto entrepreneur are over (not that there was ever a chance he would be able to dazzle in crypto ever again anyway). The once wildly successful owner of crypto exchange FTX learned this past week what financial mismanagement gets you; a quarter of a century in prison. SBF’s sentencing, which he’s going to appeal, apparently also saw a wild increase in the prices of memecoins (we’re talking thousands of %age up). In light of what’s happened, what do you of the sentencing and how do you in 2024? think feel about cryptocurrencies Optout Writing Contest HackerNoon’s partnership with Aut Labs is still going strong and we’ve seen some great entries these past few weeks! If you’d like to take a stab at thousands of dollars in USDT, simply head on down to and start writing on the Contest and tell us how YOU are opting out of a system that does not represent you. winning our template here #Optout Happy writing!

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NFTs on the Solana blockchain have been gaining significant traction recently, leading to a surge in popularity and adoption. This growth can be attributed to several key factors that have contributed to the rise of NFTs on Solana, making them increasingly convenient and appealing to users. Let's delve into the reasons behind the current boom of NFTs on Solana, explore some main use cases, highlight their convenience, and discuss the volumes involved in this burgeoning market. If you’re running an NFT/Web3 project (including the ones that on SOL), and you need advice on marketing and community building, you can directly. message me NFTs on Solana: A Rising Trend The emergence of Solana (SOL) NFTs and the innovative platform Blast have been making significant waves in the crypto space. Solana NFTs have seen explosive growth, with sales surpassing $5 billion in just a few months. This surge in activity highlights the increasing popularity and value of NFTs on the Solana blockchain. Additionally, Blast, a layer-2 solution, has attracted developers due to its deep liquidity and successful founder background. Protocols built on Blast have quickly amassed a total value locked (TVL) of nearly $1 billion within two weeks of its mainnet launch. The success of Solana NFTs and Blast can be attributed to various factors, including the pragmatic approach of building user-friendly products that drive adoption. The founder of Blast, Roquerre, who previously co-founded Blur, a prominent NFT marketplace, has demonstrated a keen understanding of the market dynamics and user preferences. The strategic use of incentives like points systems to encourage user engagement and participation has been instrumental in driving growth on platforms like Blur and Blast.Moreover, the involvement of reputable entities like Paradigm, a well-known crypto venture capital firm, has further bolstered confidence in Blast. Paradigm's participation in Blast's seed round and subsequent collaboration to enhance the project's upgrade system underscore the industry's recognition of Blast's potential despite initial criticisms Main Use Cases of NFTs on Solana Art and Collectibles NFTs on Solana have become a popular medium for artists and creators to tokenize their work, providing a secure and transparent way to buy, sell, and collect digital art pieces. This has led to the emergence of various NFT marketplaces on Solana, such as Solanart and DigitalEyes, which offer a diverse range of digital artworks and collectibles. 2.Gaming The gaming industry has embraced NFTs on Solana, integrating them into games to offer unique in-game assets, characters, and experiences that players can own and trade. This has opened up new possibilities for gamers and developers alike, creating new revenue streams and enhancing the gaming experience. 3. Digital Real Estate NFTs on Solana are also being used to represent ownership of virtual real estate, enabling users to buy, sell, and trade virtual land and properties in decentralized virtual worlds. This has led to the creation of new digital economies and communities, such as Portals and Solana Monkey Business. 4. Music and Entertainment Musicians and entertainers are leveraging NFTs on Solana to release exclusive content, concert tickets, and merchandise, creating new revenue streams and engaging directly with their fans. This has the potential to revolutionize the music and entertainment industries, providing artists with more control over their content and creating new opportunities for fan engagement. Volumes and Market Dynamics The Solana blockchain has witnessed a significant increase in NFT trading volumes, with various collections and projects gaining traction in the market. Platforms like Solanart and SolSea have emerged as prominent marketplaces for buying, selling, and trading NFTs on Solana, offering a diverse range of collections and artworks to users. The total market capitalization of NFTs on Solana has surpassed $1 billion, reflecting the growing interest and investment in digital assets on the Solana blockchain. All these metrics indicate a strong growing interest and investment in this space, reflecting the increasing popularity and demand for digital assets on the Solana blockchain. Convenience and Benefits of NFTs on Solana 1. Solana's low transaction fees make it cost-effective for users to buy, sell, and trade NFTs, reducing barriers to entry and enabling broader participation in the market. Low Transaction Costs: 2. Solana's high throughput and low latency ensure that NFT transactions are processed quickly, providing users with a seamless and efficient trading experience. Fast Transactions: 3. NFTs on Solana can be easily integrated with other blockchain platforms, allowing for cross-chain compatibility and expanding the reach and utility of these digital assets. Interoperability: 4. : Solana NFT platforms like SolSea offer embedded copyright licenses, providing creators with legal protection and ensuring the authenticity and ownership of their digital creations. Embedded Licenses How To Create Your Own NFT On Solana? To create your own NFT on Solana, you can follow these steps based on the information from the provided sources: 1. Setting Up Tools: - You will need tools like NodeJS, Git, "yarn" (a package manager), and TS-node for creating NFTs on Solana. - NodeJS serves as a JavaScript runtime, Git for cloning repositories, and "yarn" to install dependencies. 2. Using Metaplex's NFT Candy Machine: - Metaplex is a popular NFT ecosystem that offers an easy way to create NFTs on Solana. - Metaplex provides tools like NFT Candy Machine, which simplifies the NFT creation process on the Solana blockchain. 3. Initial Setup: - Start by setting up Candy Machine v2 by installing the necessary tools and dependencies. - Clone the repository, install required dependencies, and set up the execution environment using TS-node. 4. Uploading NFT Files and Metadata: - Utilize the 'upload' command to upload NFT images and JSON files to decentralized storage of your choice. - Follow the command lines in the Metaplex documentation, making relevant modifications to paths. 5. Creating NFT Collection: - Use specific command lines from the Metaplex docs to create your NFT collection. - Deploy an instance of Candy Machine on the Solana devnet and upload all assets to prepare your NFT collection. 6. Minting the NFTs: - Copy the required command from Metaplex docs and adjust it according to your file paths for minting NFTs. - Choose between individual minting or batch minting for creating multiple NFTs in a single transaction. 7. Exploring Compressed NFTs: - Solana offers the unique feature of creating compressed NFTs using Merkle trees and state compression to reduce storage costs. - Compressed NFTs store metadata on the ledger instead of in a Solana account, enhancing efficiency and cost-effectiveness. To wrap up, the current boom of NFTs on Solana can be attributed to the platform's technical capabilities, user-friendly features, and the diverse range of use cases that appeal to creators and collectors alike. With low transaction costs, fastz processing speeds, and innovative applications across various industries, NFTs on Solana have established themselves as a vibrant and dynamic market with significant growth potential in the digital economy. P.S. Check out some of my previous articles at HackerNoon: NFT Marketing Guide - The Most Complete and Detailed Playbook Bitcoin NFTs: Trends and How to Create It Autoglyphs: The $14.6 mln NFT Phenomenon Explained Cracking the NFT Code: The Psychology Behind Buying Digital Assets Breaking Down the Next Big Thing in NFTs: ERC-404 Spotlight Nobody Buys an NFT Just for Art DeFi Community Building: A Step-by-Step Guide for Crypto Startups

NFTs on Solana: A Rapidly Expanding Market with Unique Advantages


In the presentation below, Weißer Hase, Technical Lead at , presented on the advantages and challenges of designing a cross-chain oracle solution using Uniswap V3. DeFi Wonderland https://youtu.be/Ezd6h-AQFac?si=fmOTzvrLcvhCJPyn&embedable=true Below is a glossary of key concepts mentioned during Weißer’s talk, intended as a supplement to his video presentation. What Is Defi Wonderland? is a community of developers, researchers, investors, and other DeFi enthusiasts with the collective mission of fostering a decentralized and open financial landscape. The team works with prominent DeFi protocols such as , , and to push the boundaries of innovation in the DeFi space. DeFi Wonderland Optimism Reflexer Connext The Keep3r Network is a decentralized multi-chain job-matching protocol that connects projects that require external development services to individuals or teams, referred to as keepers, that can perform those services. It allows projects to outsource operations or computations like price feed monitoring, smart contract upgrades, liquidation assistance, etc., to external parties securely and efficiently. The Keep3r network Keepers must hold a minimum amount of KEEP tokens which are held as collateral and may be slashed if the individual acts maliciously. Each time keepers perform a job, they are rewarded in either ETH, tokens or the native token, $KP3R. Cross-Chain Oracles Cross-chain oracles are a type of oracle system that facilitates communication and data exchange between different blockchain networks. They serve as trusted intermediaries that foster interoperability by moving both data and assets between chains and monitoring the activities of various blockchains to report their conditions to other chains. Implementing secure cross-chain oracles can be a challenging task but projects like and , among others, are working on such solutions to meet the growing demand for interoperability as the DeFi ecosystem expands. Chainlink Band Protocol Liquidity Fragmentation Liquidity fragmentation refers to the phenomenon where the liquidity of a particular asset or trading pair is spread out across multiple decentralized exchanges (DEXs) or liquidity pools instead of being concentrated in a single platform. Liquidity fragmentation can reduce trading efficiency as it becomes more difficult to find a single liquidity pool with enough assets for substantial orders. Furthermore, it can lead to price discrepancies, interoperability challenges, and may expose DEXs to frontrunning, flash loan attacks, and price feed manipulation. Ticks A tick is a price level at which liquidity is provided, and each tick represents a specific price ratio between two assets in the trading pair. For example, if the trading pair is ETH/USDC, a tick might represent the price of 1 ETH in terms of USDC. By providing liquidity at specific tick levels, liquidity providers facilitate trades between the two assets within the defined price boundaries. Time Weighed Average Price (TWAP) TWAP is a price-averaging method that reduces price volatility by calculating the average price of an asset over a set period. This is preferable to the spot price which represents the immediate value of an asset in the market and is vulnerable to flash loan attacks or price feed manipulation techniques. TWAP is obtained by choosing a price point interval, e.g., 15s, summing the price points at those intervals, e.g., $20 at 0s, $22 at 15s, $18 at 30s, and then dividing that sum by the number of time points. For instance, the TWAP calculated from the examples would be $20. Learn more about DeFi Wonderland: Wonderland Website Wonderland GitHub Wonderland Twitter Weißer Hase Twitter The Blockchain Oracle Summit is the world’s only technical summit that dives deep into the use cases, limitations, and impacts of oracles on the wider blockchain ecosystem. Leading speakers worldwide gathered in Paris to share their work and experience building and using Oracle solutions. Article by . Michael Abiodun

The Advantages and Challenges of Building a Decentralized Cross-Chain Oracle Solution Using Uniswap

Uniswap ব্যবহার করে একটি বিকেন্দ্রীভূত ক্রস-চেইন ওরাকল সলিউশন তৈরির সুবিধা এবং চ্যালেঞ্জ

Die Vorteile und Herausforderungen beim Aufbau einer dezentralen kettenübergreifenden Oracle-Lösung mit Uniswap

Las ventajas y desafíos de crear una solución Oracle descentralizada entre cadenas utilizando Uniswap

Les avantages et les défis de la création d'une solution Oracle inter-chaînes décentralisée à l'aide d'Uniswap

Uniswap का उपयोग करके एक विकेन्द्रीकृत क्रॉस-चेन Oracle समाधान बनाने के लाभ और चुनौतियाँ

Uniswap を使用して分散型クロスチェーン Oracle ソリューションを構築する利点と課題

Uniswap을 사용하여 분산형 교차 체인 Oracle 솔루션 구축의 장점과 과제

As vantagens e desafios de construir uma solução Oracle descentralizada entre cadeias usando Uniswap

Преимущества и проблемы построения децентрализованного межсетевого решения Oracle с использованием Uniswap

Uniswap Kullanarak Merkezi Olmayan Zincirler Arası Oracle Çözümü Oluşturmanın Avantajları ve Zorlukları

Những thuận lợi và thách thức của việc xây dựng giải pháp Oracle chuỗi chéo phi tập trung bằng Uniswap

使用 Uniswap 构建去中心化跨链预言机解决方案的优势和挑战

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments E Proof of Corollary 4.1 Let m0 = |H0|. We establish the following more general result. Now, let us prove Lemma E.1.

Transductive Conformal Inference With Adaptive Scores: Proof of Corollary 4.1

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments C Proofs C.1 Proof of Proposition 2.1 which finishes the proof. C.2 Proof of Proposition 2.2 If there are no tied scores, which by assumption (NoTies) happens with probability 1, the ranks Ri of the ordered scores are well-defined and the vector (p1, . . . , pm) is only a function of the rank vector (R1, . . . , Rn+m). Namely, Ri ≤ Rj if and only if Si ≤ Sj , and the conformal p-values (1) can be written as C.3 Proof of Theorem A.1 By (Exch),(NoTies) the permutation that orders the scores (S1, . . . , Sn+m) that is σ such that Proof of (ii) This event can be formally described as follows: By using (27) of (ii), we have Proof of (i) Now, we have where we have used (ii) and the multinomial coefficient C.4 Proof of Theorem 2. First observe that the LHS of (9) is 0 if λ ≥ 1 so that we can assume λ < 1 Let us prove (9) with the more complex bounce Below, we establish This leads to

Transductive Conformal Inference With Adaptive Scores: Proof

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments H Additional experiments In this section, we provide experiments to illustrate the FDP confidence bounds for AdaDetect, as mentioned in Remark 4.2 and Section G. The two procedures used are of the AdaDetect type (48) but with two different score functions: the Random Forest classifier from Marandon et al. (2022) (adaptive score), and the one class classifier Isolation Forest as in Bates et al., 2023 (non adaptive score). The hyperparameters of these two machine learning algorithms are those given by Marandon (2022). The FDP and the corresponding bounds are computed for the two procedures. The true discovery proportion is defined by Following the numerical experiments of Marandon et al. (2022) and Bates et al. (2023), we consider the three different real data from OpenML dataset (Vanschoren et al., 2013) given in Table 1. The results are displayed in Figure 6 for comparison of adaptive versus non-adaptive scores for the different FDP confidence bounds and the TDP. On Figure 7, we focus on the adaptive scores and corresponding FDP bounds only; we compare the effect (on the bounds) of demanding a more conservative error guarantee (δ = 0.05 versus δ = 0.2), as well as the effect of estimating m0 via (25) instead of just using the inequality (24) with ˆm0 = m. The high-level conclusions are the following: Table 1: Summary of datasets. • using adaptive scores rather that non-adaptive ones results in a performance improvement (better true discovery proportion for the same target FDR level) • estimating the estimator ˆm0 from (25) yields sharper bounds on the FDP and is therefore advantageous.

Transductive Conformal Inference With Adaptive Scores: Additional Experiments

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments G Uniform FDP bound for AdaDetect It is proved there to control the false discovery rate (FDR), defined as the mean of the FDP: Applying Corollary 24, we obtain on the top of the in-expectation guarantee (49) the following uniform FDP bound for ADα: with probability at least 1 − δ, we have

Transductive Conformal Inference With Adaptive Scores: Uniform FDP Bound for AdaDetect

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments F The Simes inequality As proved in Marandon et al. (2022), and since the joint distribution of the conformal p-values does not change from one context to another (Proposition 2.2), the conformal p-values are positively regressively dependent on each one of a subset (PRDS) under (Exch) and (NoTies), see Benjamini and Yekutieli (2001) for a formal definition of the latter. Hence, by Benjamini and Yekutieli (2001), the Simes inequality (Simes, 1986) is valid, that is, for all λ > 0, we have This envelope can be applied in the two applications of the paper as follows: (PI) Under the condition of Corollary 3.1, the bound is valid for (17). (ND) Under the condition of Corollary 4.1 the following control is valid for for any estimator

Transductive Conformal Inference With Adaptive Scores: the Simes Inequality

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments B Numerical bounds and templates The bound proposed in Theorem 2.3 are explicit and elegant, but can be conservative in some cases and we develop here the numerical approach mentioned in Remark 2.5. Hence, let us consider

Transductive Conformal Inference With Adaptive Scores: Numerical Bounds and Templates

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments A Exact formulas for Pn,m Theorem A.1 (ii) provides the exact dependency structure between the p-values: for instance, M(j)! = 1 when the coordinates of j = (j1, . . . , jm) are all distinct, while M(j)! = m! when the coordinates of j = (j1, . . . , jm) are the same. This means that the distribution slightly favors the j with repeated entries. This shows that the conformal p-values are not i.i.d. but have a positive structure of dependency. This is in accordance with the specific positive dependence property (called PRDS) already shown by Bates et al. (2023); Marandon et al. (2022).

Transductive Conformal Inference With Adaptive Scores: Exact Formulas for Pn,m

This paper is available on arxiv under CC 4.0 license. Authors: (1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation, (2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay, (3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation. Table of Links Abstract & Introduction Main results Application to prediction intervals Application to novelty detection Conclusion, Acknowledgements and References Appendix A: Exact formulas for Pn,m Appendix B: Numerical bounds and templates Appendix C: Proof Appendix D: Explicit control of (16) for α=0 Appendix E: Proof of Corollary 4.1 Appendix F: The Simes inequality Appendix G: Uniform FDP bound for AdaDetect Appendix H:  Additional experiments 5 Conclusion The main takeaway from this work is the characterization of a “universal” joint distribution Pn,m for conformal p-values based on n calibration points and m test points. We derived as a consequence a non-asymptotic concentration inequality for the p-value empirical distribution function; numerical procedures can also be of use for calibration in practice. This entails uniform error bounds on the false coverage/false discovery proportion that hold with high probability, while standard results are only marginal or in expectation and not uniform in the decision. Since the results hold under the score exchangeability assumption only, they are applicable to adaptive score procedures using the calibration and test sets for training. Acknowledgements We would like to thank Anna Ben-Hamou and Claire Boyer for constructive discussions and Ariane Marandon for her support with the code. The authors acknowledge the grants ANR-21-CE23-0035 (ASCAI) and ANR-19-CHIA-0021-01 (BISCOTTE) of the French National Research Agency ANR and the Emergence project MARS. References Balasubramanian, V., Ho, S.-S., and Vovk, V. (2014). Conformal prediction for reliable machine learning: theory, adaptations and applications. Morgan Kaufmann books. Bashari, M., Epstein, A., Romano, Y., and Sesia, M. (2023). 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