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Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation 36

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Pitfalls of Epistemic Uncertainty Quantification through Los...

36th Conference on Neural Information Processing Systems, NeurIPS 2022

作者： Bengs, Viktor Hüllermeier, Eyke Waegeman, Willem Germany Munich Center for Machine Learning Germany Department of Data Analysis and Mathematical Modeling Ghent University Belgium

ISBN: (纸本)9781713871088

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way. © 2022 Neural information processing systems foundation. All rights reserved.

关键词： Probability distributions

More than Formulas - Integrity, Communication, Computing and Reproducibility in Statistics Education

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arXiv 2024年

作者： Furrer, Eva Cincera, Annina Furrer, Reinhard Epidemiology Biostatistics and Prevention Institute Center for Reproducible Science Switzerland Epidemiology Biostatistics and Prevention Institute Department of Mathematical Modeling and Machine Learning Switzerland Department of Mathematical Modeling and Machine Learning University of Zurich Switzerland

This paper introduces a novel course design in the Master Program in Biostatistics at the University of Zurich that integrates computing skills, effective communication, reproducibility, and scientific integrity within one course. Utilizing a flipped classroom model, the course aims to equip students with the necessary competencies to handle real-world data analysis challenges and effective statistical practice in general. The curriculum includes practical tools such as version control with Git, dynamic reporting, unit testing and containerization to foster reproducibility, and integrity in statistical practice. Feedback gathered from both staff and students post-implementation indicates that the course significantly enhances student readiness for professional and academic environments, demonstrating the effectiveness of this educational approach. © 2024, CC BY-NC-ND.

关键词： Students

COMMUNITY DETECTION ON DIRECTED NETWORKS WITH MISSING EDGES

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arXiv 2024年

作者： Pedreschi, Nicola Lambiotte, Renaud Bovet, Alexandre Mathematical Institute University of Oxford Oxford United Kingdom Department of Mathematical Modeling and Machine Learning University of Zurich Zurich Switzerland

Identifying significant community structures in networks with incomplete data is a challenging task, as the reliability of solutions diminishes with increasing levels of missing information. However, in many empirical contexts, some information about the uncertainty in the network measurements can be estimated. In this work, we extend the recently developed Flow Stability framework, originally designed for detecting communities in time-varying networks, to address the problem of community detection in weighted, directed networks with missing links. Our approach leverages known uncertainty levels in nodes’ out-degrees to enhance the robustness of community detection. Through comparisons on synthetic networks and a real-world network of messaging channels on the Telegram platform, we demonstrate that our method delivers more reliable community structures, even when a significant portion of data is missing. © 2024, CC BY.

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The Perils & Promises of Fact-checking with Large Language Models

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arXiv 2023年

作者： Quelle, Dorian Bovet, Alexandre Department of Mathematical Modeling and Machine Learning Digital Society Initiative University of Zurich Zurich Switzerland

Automated fact-checking, using machine learning to verify claims, has grown vital as misinformation spreads beyond human fact-checking capacity. Large Language Models (LLMs) like GPT-4 are increasingly trusted to write academic papers, lawsuits, and news articles and to verify information, emphasizing their role in discerning truth from falsehood and the importance of being able to verify their outputs. Understanding the capacities and limitations of LLMs in fact-checking tasks is therefore essential for ensuring the health of our information ecosystem. Here, we evaluate the use of LLM agents in fact-checking by having them phrase queries, retrieve contextual data, and make decisions. Importantly, in our framework, agents explain their reasoning and cite the relevant sources from the retrieved context. Our results show the enhanced prowess of LLMs when equipped with contextual information. GPT-4 outperforms GPT-3, but accuracy varies based on query language and claim veracity. While LLMs show promise in fact-checking, caution is essential due to inconsistent accuracy. Our investigation calls for further research, fostering a deeper comprehension of when agents succeed and when they fail. © 2023, CC BY.

关键词： Query languages

ON SECOND-ORDER SCORING RULES FOR EPISTEMIC UNCERTAINTY QUANTIFICATION

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arXiv 2023年

作者： Bengs, Viktor Hüllermeier, Eyke Waegeman, Willem Munich Center for Machine Learning Germany Department of Data Analysis and Mathematical Modeling Ghent University Belgium

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various machine learning methods have recently been developed with the goal to let the learner also represent its epistemic uncertainty, i.e., the uncertainty caused by a lack of knowledge and data. An emerging branch of the literature proposes the use of a second-order learner that provides predictions in terms of distributions on probability distributions. However, recent work has revealed serious theoretical shortcomings for second-order predictors based on loss minimisation. In this paper, we generalise these findings and prove a more fundamental result: There seems to be no loss function that provides an incentive for a second-order learner to faithfully represent its epistemic uncertainty in the same manner as proper scoring rules do for standard (first-order) learners. As a main mathematical tool to prove this result, we introduce the generalised notion of second-order scoring *** Codes 68T37 (Primary) 68T30 (Secondary) Copyright © 2023, The Authors. All rights reserved.

关键词： Probability distributions

GRAPH SPRING NEURAL ODES FOR LINK SIGN PREDICTION

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arXiv 2024年

作者： Rehmann, Andrin Bovet, Alexandre Pasteur Labs New York United States Department of Mathematical Modeling and Machine Learning Digital Society Initiative University of Zurich Switzerland

Signed graphs allow for encoding positive and negative relations between nodes and are used to model various online activities. Node representation learning for signed graphs is a well-studied task with important applications such as sign prediction. While the size of datasets is ever-increasing, recent methods often sacrifice scalability for accuracy. We propose a novel message-passing layer architecture called Graph Spring Network (GSN) modeled after spring forces. We combine it with a Graph Neural Ordinary Differential Equations (ODEs) formalism to optimize the system dynamics in embedding space to solve a downstream prediction task. Once the dynamics is learned, embedding generation for novel datasets is done by solving the ODEs in time using a numerical integration scheme. Our GSN layer leverages the fast-to-compute edge vector directions and learnable scalar functions that only depend on nodes’ distances in latent space to compute the nodes’ positions. Conversely, Graph Convolution and Graph Attention Network layers rely on learnable vector functions that require the full positions of input nodes in latent space. We propose a specific implementation called Spring-Neural-Network (SPR-NN) using a set of small neural networks mimicking attracting and repulsing spring forces that we train for link sign prediction. Experiments show that our method achieves accuracy close to the state-of-the-art methods with node generation time speedup factors of up to 28,000 on large graphs. Copyright © 2024, The Authors. All rights reserved.

关键词： Vector spaces

A CALIBRATION TEST FOR EVALUATING SET-BASED EPISTEMIC UNCERTAINTY REPRESENTATIONS

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arXiv 2025年

作者： Jürgens, Mira Mortier, Thomas Hüllermeier, Eyke Bengs, Viktor Waegeman, Willem Department of Data Analysis and Mathematical Modeling Ghent University Belgium Department of Environment Ghent University Belgium Department of Informatics Munich Center for Machine Learning LMU Munich Germany

The accurate representation of epistemic uncertainty is a challenging yet essential task in machine learning. A widely used representation corresponds to convex sets of probabilistic predictors, also known as credal sets. One popular way of constructing these credal sets is via ensembling or specialized supervised learning methods, where the epistemic uncertainty can be quantified through measures such as the set size or the disagreement among members. In principle, these sets should contain the true data-generating distribution. As a necessary condition for this validity, we adopt the strongest notion of calibration as a proxy. Concretely, we propose a novel statistical test to determine whether there is a convex combination of the set’s predictions that is calibrated in distribution. In contrast to previous methods, our framework allows the convex combination to be instance dependent, recognizing that different ensemble members may be better calibrated in different regions of the input space. Moreover, we learn this combination via proper scoring rules, which inherently optimize for calibration. Building on differentiable, kernel-based estimators of calibration errors, we introduce a nonparametric testing procedure and demonstrate the benefits of capturing instance-level variability on of synthetic and real-world experiments. © 2025, CC BY.

关键词： Self-supervised learning

pasta: Pattern Analysis for Spatial Omics Data

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arXiv 2024年

作者： Emons, Martin Gunz, Samuel Crowell, Helena L. Mallona, Izaskun Furrer, Reinhard Robinson, Mark D. Department of Molecular Life Sciences SIB Swiss Institute of Bioinformatics University of Zurich Zurich Switzerland Barcelona Spain Department of Mathematical Modeling and Machine Learning University of Zurich Zurich Switzerland

Spatial omics assays allow for the molecular characterisation of cells in their spatial context. Notably, the two main technological streams, imaging-based and high-throughput sequencing-based, can give rise to very different data modalities. The characteristics of the two data types are well known in adjacent fields such as spatial statistics as point patterns and lattice data, and there is a wide range of tools available. This paper discusses the application of spatial statistics to spatially-resolved omics data and in particular, discusses various advantages, challenges, and nuances. This work is accompanied by a vignette, pasta, that showcases the usefulness of spatial statistics in biology using several R packages. © 2024, CC BY.

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On the orthogonality of zero-mean Gaussian measures: Sufficiently dense sampling

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arXiv 2022年

作者： Furrer, Reinhard Hediger, Michael Department of Mathematical Modeling and Machine Learning Department of Mathematics Winterthurerstrasse 190 Zurich8057 Switzerland

For a stationary random function ξ, sampled on a subset D of Rd, we examine the equivalence and orthogonality of two zero-mean Gaussian measures P1 and P2 associated with ξ. We give the isotropic analog to the result that the equivalence of P1 and P2 is linked with the existence of a square-integrable extension of the difference between the covariance functions of P1 and P2 from D to Rd. We show that the orthogonality of P1 and P2 can be recovered when the set of distances from points of D to the origin is dense in the set of non-negative real *** Codes 60G10, 60G15, 60G17, 60G30, 60G60 © 2022, CC BY-NC-SA.

关键词： Gaussian distribution