Scientific Inference With Interpretable Machine Learning - Analyzing Models to Learn About Real-World Phenomena

Aug 4, 2026

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Scientific inference often relies on models with elementwise interpretability, yet modern machine learning models provide strong predictive power without direct interpretability of internal parameters such as neural network weights. Interpretable machine learning addresses opacity by analyzing models holistically, but existing work frequently targets model auditing rather than scientific inference. This paper introduces a framework based on property descriptors grounded in statistical learning theory, enabling extraction of relevant properties of the observational data’s joint probability distribution and guiding new descriptor design with quantified epistemic uncertainty.

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arXiv :2206 .05487v3 [ stat .ML] 15 Jul 2024 Scientific Inference With Interpretable Machine Learning Analyzing Models to Learn About Real-World Phenomena Timo Freiesleben 1*, Gunnar Knig 1 , Christoph Molnar2 , Alvaro Tejero-Cantero 1 1* Cluster of Excellence Machine Learning for Science, University of T¨ubingen, Maria-von-Linden-Straße 6, T¨ubingen, 72076, Germany. 2Independent Researcher, Munich, Germany. *Corresponding author(s). E-mail(s): [timo.freiesleben@uni-tuebingen.de](timo.freiesleben@uni-tuebingen.de) ; Abstract To learn about real world phenomena, scientists have traditionally used models with clearly interpretable elements. However, modern machine learning (ML) models, while powerful predictors, lack this direct elementwise interpretability (e.g. neural network weights) . Interpretable machine learning (IML) offers a solution by analyzing models holistically to derive interpretations. Yet, current IML research is focused on auditing ML models rather than leveraging them for scientific inference. Our work bridges this gap, presenting a framework for designing IML methods—termed ’property descriptors’—that illuminate not just the model, but also the phenomenon it represents. We demonstrate that property descriptors, grounded in statistical learning theory, can effectively reveal relevant properties of the joint probability distribution of the observational data. We identify existing IML methods suited for scientific inference and provide a guide for developing new descriptors with quantified epistemic uncertainty. Our framework empowers scientists to harness ML models for inference, and provides directions for future IML research to support scientific understanding. Keywords: Scientific Modeling, Interpretable Machine Learning, Scientific Representation, Inference, XAI, IML 1 Introduction Scientists increasingly use machine learning (ML) in their daily work. This development isnot limited to natural sciences like material science (Schmidt et al. 2019) or the geosciences (Reichstein et al. 2019), but extends to social sciences such as educational science (Luan and Tsai 2021) and archaeology (Bickler 2021) . 1 When building predictive models for problems with complex data structures, ML outcompetes classical statistical models in both performance and convenience. Impressive recent examples of successful prediction models in science include the automated particle tracking at CERN (Farrell et al. 2018), or DeepMind’s AlphaFold, which has made substantial progress in predicting protein structures from amino acid sequences (Senior et al. 2020) . In such examples, some see a paradigm shift towards theory-free science that “lets the data speak”(Anderson 2008, Mayer-Schnberger and Cukier 2013, Kitchin 2014, Spinney 2022) . However, purely prediction driven research has its limits: In a survey with more than 1,600 scientists, almost 70% expressed the fear that the use of ML in science could lead to a reliance on pattern recognition without understanding (Van Noorden and Perkel 2023) . This is in line with the philosophy of science literature, which does recognize the importance of predictions (Douglas 2009, Luk 2017), but also emphasizes other goals such as explaining and understanding phenomena (Salmon 1979, Shmueli 2010, Longino 2018, Toulmin 1961) . The reason why understanding phenomena with ML is difficult is that, unlike traditional scientific models, ML models do not provide a cognitively accessible representation of the underlying causal mechanism (Hooker and Hooker 2017, Boge 2022, Molnar and Freiesleben 2024) . The link between the ML model and phenomenon is unclear, leading to the so-called opacity problem (Sullivan 2022) . Interpretable machine learning (IML, also called XAI, for eXplainable artificial intelligence) aims to tackle the opacity problem by analyzing individual model elements or inspecting specific model properties (Molnar 2020) . However, it often remains unclear how

FAQs

What problem does interpretable machine learning aim to solve in scientific settings?

It tackles the opacity problem by providing interpretations from model analyses, so researchers can better connect machine learning outputs to scientific understanding.

What does the paper propose as a way to use IML for scientific inference?

It presents a framework using property descriptors that illuminate both the model and the phenomenon it represents, grounded in statistical learning theory.

How are uncertainties handled in the proposed approach?

The framework guides the development of new descriptors with quantified epistemic uncertainty, improving the reliability of interpretations used for inference.

Aug 4, 2026

Upload by Liam