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            Credal Two Sample Test
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          <h1 class="title is-1 publication-title">Imprecise Learning Framework<br><em>Theory and Applications</em></h1>

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                <a target="_blank" href="https://arxiv.org/pdf/2503.16395"
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                  <span>UAI 25 Oral Paper</span>
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                  <span>ICML 24 Spotlight Paper</span>
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        <span class="dnerf">Imprecise Learning</span> achieves generalisation across multiple user risk levels!
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        <h2 class="title is-3">Abstract</h2>
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            In machine learning and forecasting, practitioners often face epistemic uncertainty arising not only from limited data but also from ambiguous deployment conditions and multiple plausible decision-aggregation strategies. We propose a unified perspective that connects the theory of forecast elicitation with robust generalisation: proper scoring rules, which are foundational in eliciting truthful forecasts, define which loss functions are meaningful for training models to approximate underlying distributions. This economic perspective provides a principled foundation for designing learners that remain imprecise when necessary. In particular, we (i) extend generalisation guarantees to settings where learners optimise over a continuum of risk criteria, deferring commitment to a precise criterion until deployment, and (ii) design mechanisms for eliciting imprecise forecasts (credal sets) that integrate the decision-maker’s aggregation rule and use randomized proper scoring to incentivize truthful reporting. This dual perspective establishes a coherent framework: by treating imprecision as a first-class object, learners and forecasters propagate epistemic uncertainty systematically, and operators receive representations of remaining ambiguity aligned with downstream aggregation and decision logic. Theoretical insights and empirical results illustrate the benefits of this approach for both robust domain generalisation and forecast-elicitation tasks, highlighting a principled pathway toward systems that embrace, rather than ignore, uncertainty.
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          <iframe width="1047" height="589" src="https://www.youtube.com/embed/gGPF9dUug2g" title="SIPTA Seminar by Krikamol Muandet: Imprecise generalisation" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>
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        <h2 class="title is-3">Quantitative Results</h2>
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        <em>Imprecise Learner learns features in context</em>
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        <em>You can now elicit credal sets with our scoring rule. Check out our <a target="_blank" href="https://arxiv.org/pdf/2503.16395">UAI paper</a>!</em>
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       <h2 class="title is-3">Contact Us</h2>
       Please feel free to reach out to <a target="_blank" href="https://anurag14.github.io">Anurag Singh</a> (anurag.singh@cispa.de) for queries and collaborations! 
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<section class="section" id="BibTeX">
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    <h2 class="title">BibTeX</h2>
    <pre><code>
  @inproceedings{singhtruthful,
  title={Truthful Elicitation of Imprecise Forecasts},
  author={Singh, Anurag and Chau, Siu Lun and Muandet, Krikamol},
  booktitle={The 41st Conference on Uncertainty in Artificial Intelligence},
  year={2025}
}
  @inproceedings{singh2024domain,
  title={Domain Generalisation via Imprecise Learning},
  author={Singh, Anurag and Chau, Siu Lun and Bouabid, Shahine and Muandet, Krikamol},
  booktitle={International Conference on Machine Learning},
  pages={45544--45570},
  year={2024},
  organization={PMLR}
}
</code></pre>
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