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    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Explaining Uncertainty: Exploring the Synergies of Explainable Artificial Intelligence and Uncertainty Quantification</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Emily Schiller</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>XITASO GmbH IT &amp; Software Solutions</institution>
          ,
          <addr-line>Austraße 35, 86153 Augsburg</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Despite the transformative potential of machine learning in critical areas such as healthcare, its integration is challenged by a lack of trust, reliability, and transparency. Explainable AI (XAI) aims to make AI predictions interpretable for humans. At the same time, Uncertainty Quantification (UQ) enables the estimation of confidence in predictions - both crucial for responsible AI usage and increasing trust and transparency. The intersection of the two research fields holds significant potential to advance these objectives further; however, research in this area has been limited. This doctoral proposal addresses the need to investigate the intersection of XAI and UQ. My research will emphasize explaining uncertainty estimates in healthcare applications and time series tasks. By developing computationally eficient methods to identify sources of uncertainty in AI predictions, my research seeks to enhance model performance and interpretability. The challenge of scheduling nurses serves as a consistent case study to identify real-world challenges in healthcare applications. By introducing novel techniques to explain uncertainty estimates, this work will explore the synergies of XAI and UQ, contributing to developing more transparent and reliable AI systems and ultimately advancing their integration into high-stakes domains.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Explainable AI</kwd>
        <kwd>Uncertainty Quantification</kwd>
        <kwd>Time Series</kwd>
        <kwd>Healthcare</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Background and Motivation</title>
      <p>
        During the past decade, remarkable progress has been made in the field of deep neural networks,
leading to their adoption across various research disciplines, including earth observation, healthcare,
and autonomous systems. Nevertheless, their practical use in critical real-world scenarios is still
limited, as acceptance and trust among users remain insuficient [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. The intersection of Explainable
AI (XAI) and Uncertainty Quantification ( UQ) presents a promising way to enhance the reliability and
trustworthiness of Artificial Intelligence ( AI) systems, particularly in critical domains such as healthcare.
My doctoral research aims to explore this intersection, focusing on explaining uncertainty estimates as
a key direction.
      </p>
      <sec id="sec-1-1">
        <title>1.1. Bridging Explainability and Uncertainty in AI</title>
        <p>
          The field of XAI is currently experiencing significant research activity, with the goal of making AI
predictions more interpretable for both end users and data scientists [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ]. It covers techniques that
are used to turn a non-interpretable model into an explainable one. By ofering transparency, XAI
not only enhances user trust, but also facilitates the identification and mitigation of biases and errors
within AI models. Furthermore, XAI supports regulatory compliance by aligning with the demands for
accountability and ethical standards in AI deployment [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ].
        </p>
        <p>
          Alongside XAI, UQ is crucial for ensuring trust, safety, and reliability in AI systems [
          <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
          ]. Predictive
uncertainty includes aleatoric uncertainty, arising from data distribution, and epistemic uncertainty,
stemming from model limitations like data sparsity. Both types of uncertainty provide valuable insights
into the confidence of a prediction. Moreover, UQ is a valuable tool for improving robustness to unseen
data, improving decision-making processes, and promoting transparency [
          <xref ref-type="bibr" rid="ref1 ref3">1, 3</xref>
          ].
        </p>
        <p>
          Both XAI and UQ are fields dedicated to enhancing the reliability of AI models, promoting responsible
AI usage, and building user trust. Additionally, XAI and UQ enable data scientists to evaluate the AI
models, uncover their weaknesses and ultimately improve them. The intersection of the two fields of
research holds the potential to further advance these objectives. So far, there has been limited research
on the intersection of XAI and UQ, although interest in this area is growing [
          <xref ref-type="bibr" rid="ref4 ref5">4, 5, 6</xref>
          ], making it a crucial
moment to contribute to this emerging field.
        </p>
        <p>
          More specifically, the intersection of XAI and UQ can be explored in two key directions, also visualized
in Figure 1:
1. Uncertainty in explanations: How certain and reliable are my explanations? Quantifying
uncertainty in explanations is critical for assessing their reliability and efectiveness. Explanations
help to improve models and increase user acceptance. However, the usefulness of these
explanations depends on their quality and reliability. By estimating the uncertainty associated with the
explanations, we can better assess their trustworthiness and prevent misleading information.
2. Explainable uncertainty estimation: Which input patterns lead to the uncertainty in my
prediction? Providing explainable uncertainty estimates can assist both users and data scientists
in comprehending these measures more efectively. For instance, explaining the sources of
uncertainty in predictions can help data scientists enhance their models by identifying areas
where training data is sparse. Additionally, studies have shown that users of AI systems often have
dificulty interpreting numerical information, such as probabilities and standard deviations [
          <xref ref-type="bibr" rid="ref5">5, 7</xref>
          ].
Therefore, I believe that explanations of uncertainty can help users understand these measures
better by providing reasons behind the uncertainty, making it more interpretable and ultimately
ensuring the responsible use of AI.
        </p>
        <p>Both directions ofer significant potential to increase the reliability of Machine Learning ( ML) models,
user trust, and responsible usage of AI. During my PhD, I plan to focus on the emerging research field
of explainable uncertainty estimation. Thus, I will only focus on this direction in the following sections.</p>
      </sec>
      <sec id="sec-1-2">
        <title>1.2. The Role of Explainability and Uncertainty for Healthcare Applications</title>
        <p>
          As a consistent case study, I will examine the challenge of nurse scheduling, which involves assigning
nurses to shifts. Eficient and needs-based scheduling of nurses is crucial given the growing nurse
shortage in many countries which negatively impacts nurse satisfaction, care quality, and patient
satisfaction [8]. ML predictions can support the optimization of nurse scheduling by accurately
forecasting patient demand and stafing needs, ensuring adequate coverage and reducing overstafing or
understafing. Despite the high potential of such AI systems, there remains a low adoption of AI systems
in clinical practice. One reason for low adoption is the lack of trust and understanding of AI systems
among end users in healthcare. Given the high risks associated with healthcare applications and the
often inherent life-or-death consequences, ensuring reliability and trustworthiness of AI systems is
essential and a key factor for their adoption [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ].
        </p>
        <p>
          Explainability and UQ are key tools that can help improve these properties [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ]. While UQ and XAI
methods already allow a deeper understanding of an AI model’s predictions, simply quantifying the
uncertainty does not always give enough information to make a decision based on the prediction. Users
may wonder why the uncertainty arises. Furthermore, AI systems in healthcare have diferent target
user groups, such as patients, nurses, doctors, or administrative staf, requiring diferent communication
of predictive uncertainty. For example, in a cancer diagnostic scenario, a doctor may need quick access
to numeric confidence scores to make time-sensitive decisions. In contrast, a patient might need
comprehensive explanations to understand their diagnosis and the uncertainty behind the prediction [7].
Explanations of uncertainty can be a solution to provide these types of uncertainty representation for
diferent user groups. For data scientists, it is beneficial to know if the uncertainty comes from noisy
samples, a distribution shift, or which features or patterns lead to the model’s uncertainty [9].
        </p>
        <p>
          From a technical perspective, the healthcare domain also presents particular challenges. In healthcare,
data are often multimodal and include (mostly multivariate) time series. Tasks related to time series,
such as classification, forecasting, and regression, remain relatively underexplored in the context of
UQ [
          <xref ref-type="bibr" rid="ref1 ref3">1, 3, 10</xref>
          ]. In addition, XAI methods have to be designed to tackle the challenges of time series
data to capture the prediction’s dependency on temporal patterns and trends and capture correlations
between features. Also, the respective methods must be scalable in order to process large volumes of
multimodal health data and be used in practice.
        </p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>
        Previous work on XAI and UQ has largely explored these fields independently, with each aiming to
improve the reliability and trustworthiness of AI models. However, the intersection of these fields has
only recently begun to attract research interest [
        <xref ref-type="bibr" rid="ref4 ref5">4, 5, 6, 11</xref>
        ]. Although there exist conceptual papers [
        <xref ref-type="bibr" rid="ref5">5, 9</xref>
        ]
that emphasize the importance of closing this gap by researching how to make uncertainty estimates
explainable, very little work has been done in this area. In the following, I describe identified related
work to explain uncertainty estimates.
generative model adds complexity. UA-Backprop [12] uses gradient information to create uncertainty
attribution maps in Bayesian deep learning models, highlighting regions contributing to epistemic
and aleatoric uncertainty. However, since the method relies on Bayesian deep learning models, it
remains rather computationally ineficient. Iversen et al. [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] present a two-step method for explaining
aleatoric uncertainty in neural networks by adding a variance output neuron to pre-trained models
and applying feature attribution methods to the variance output. Compared to the other described
methods, this approach is computationally eficient and simpler to adopt; however, it is not able to
capture epistemic uncertainty. Watson et al. [11] theoretically investigated the application of Shapley
Values to uncertainty measures and evaluated their method in contexts such as covariate shift and
feature selection. While their method is designed to be computationally eficient, calculating Shapley
values can still be computationally intensive, especially for large data sets or complex models, limiting
its applicability in practice. The approach recently introduced by Bley et al. [13] estimates uncertainty
using ensemble-based methods. To explain these estimates, they generate explanations for each
ensemble member and calculate the covariance of these explanations. The computational eficiency of
their approach depends greatly on the chosen ensemble-based method and the explanation method.
Although their approach is applied to time series data, it is not specifically designed for this datatype.
      </p>
      <p>In summary, while these approaches provide promising results in explaining uncertainty estimates,
there are several gaps that remain unaddressed: (a) the lack of methods specifically tailored to time
series related ML tasks, (b) the need for computationally eficient solutions that can handle complex
models without excessive overhead while ensuring high-quality explanations, and (c) the evaluation of
these methods with end users and data scientists.</p>
      <p>My study aims to address these challenges by developing methods that are both interpretable and
computationally eficient, specifically targeting time series data. Additionally, I plan to evaluate my
methods with end users and data scientists. Through my research, I seek to contribute to the development
of more reliable and transparent AI systems by providing insights into the underlying factors that
contribute to uncertainty in ML models.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Research Questions, Hypotheses, and Objectives</title>
      <p>The goal of my research is to design methods for explaining uncertainty in ML models, focusing on
healthcare applications and time series tasks. By developing scalable and computationally eficient
methods that provide insights into the sources of uncertainty in AI predictions, I will contribute to
advancing the integration of XAI and UQ. Ultimately, my work aims to provide actionable insights that
improve the performance of ML models and foster greater trust in AI systems by providing explanations
of uncertainties to diferent stakeholder groups.</p>
      <p>In my PhD research project, I aim to address the following research questions:
• R1: How can existing explainability techniques be efectively combined with UQ in ML models
to explain the source of uncertainty in ML predictions?
• R2: What are the challenges and potential solutions for incorporating UQ and explanations into</p>
      <p>ML models trained on time series data?
• R3: What are the most efective and computationally eficient methods for explaining uncertainty
estimates in ML predictions?
• R4: How should ML models and UQ/XAI methods be designed to provide actionable insights and
explanations for uncertainty in predictions?</p>
      <p>These questions focus on designing methods to explain uncertainty estimates. Once I have developed
approaches to explain the uncertainty in ML model predictions, I plan to explore the impact of these
explanations on users and their benefits for data scientists in training and refining ML models. The
following research questions address these areas:
• R5: How can data scientists use explanations of uncertainty to enhance the performance and
robustness of ML models?
• R6: What impact does the communication of explanations of uncertainties have on users of
healthcare applications? To what extent does it influence user trust and acceptance?</p>
    </sec>
    <sec id="sec-4">
      <title>4. Research Methodology</title>
      <p>My doctoral project adopts a quantitative and exploratory research design to explore the intersection
of XAI and UQ in ML. As can be seen in Figure 2, my research is structured into three phases, each
addressing specific research questions.</p>
      <p>Phase 1: Exploration and Review The initial phase involves a comprehensive review and
experimentation with existing XAI and UQ methods, such as SHAP [15], Layer-wise Relevance Propagation [16],
and Monte Carlo Dropout [17]. This phase aims to evaluate their efectiveness in explaining uncertainty
estimates, particularly in time series data. Scalable techniques for UQ such as Monte Carlo Dropout
will be prioritized, with Bayesian networks serving as potential alternatives and common techniques
such as quantile regression serving as baselines. Furthermore, I will interact with users to identify their
needs through workshops and interviews. The insights gained will inform the development of novel
methods tailored to enhance the interpretability of uncertainty in ML predictions.</p>
      <p>Phase 2: Method Development The second phase focuses on developing novel methods to explain
uncertainty estimates, tailored specifically to time series-related ML tasks. I plan to explore gradient-based
techniques that are architecture-agnostic and do not rely on Bayesian networks, ofering a promising
direction for achieving computational eficiency. The development process will be iterative, adapting
to findings of the initial phase to refine and improve the methods. This approach acknowledges the
inherent uncertainty in research results, allowing flexibility and responsiveness to emerging challenges
and opportunities.</p>
      <p>Phase 3: Application and Validation The final phase explores the practical application of
uncertainty explanations and evaluates their ability to improve user trust and model performance. This
phase involves a comprehensive evaluation and validation process, using both quantitative metrics and
qualitative user studies. User studies will be conducted to gather feedback from healthcare professionals,
ensuring that the explanations are not only technically sound, but also valuable and interpretable for
end users. In addition, I will explore the potential of uncertainty explanations to improve the
underlying model. For example, if an explanation reveals sparsity in a specific data region, additional data
instances can be strategically introduced to enhance model confidence. The efectiveness of this data
augmentation strategy will be evaluated by comparing uncertainty levels before and after augmentation.</p>
      <p>The consistent case study addressing nurse scheduling serves as a real-world example to identify
relevant user needs and requirements for the ML models, explainability and uncertainty estimation
methods. However, I plan to conduct research that can be generalized to diferent domains and use
cases. To perform the case study, data on patients and nurses’ shift plans have been gathered from a
university hospital. To complement this, publicly available data sets such as MIMIC IV [18], ETTh1/h2,
and ETTm1/m2 [19], and other common time series data sets will be utilized to support time series
related ML tasks.</p>
      <p>In summary, my research aims to combine theoretical advancements in XAI and UQ with their
practical applications in healthcare, thus contributing to academic knowledge and real-world impact.</p>
    </sec>
    <sec id="sec-5">
      <title>5. Preliminary Results and Contributions</title>
      <p>In my previous research, I have focused on gaining a comprehensive understanding of the healthcare
domain, particularly in the context of nurse scheduling. This involved an extensive review and
implementation of state-of-the-art models for long-term time series forecasting to predict care capacity
and demand. Such predictions are valuable to support nurse scheduling and ensure eficient healthcare
delivery through AI. Specifically, I conducted a comparative analysis of several advanced forecasting
models, including TSMixer [20] and LightGBM [21] among others. This analysis aimed to evaluate their
performance in forecasting nursing staf capacity over a long time horizon. A key aspect of this study
was the investigation of whether exogenous variables can enhance the accuracy of these long-term
forecasts. We discovered a high increase in performance when including exogenous variables in the
model [22]. This adds complexity when designing methods to explain uncertainty estimates, but at
the same time ofers interesting challenges. The insights gained from this research provide a solid
foundation for further exploration, where the high-performing models identified, such as TSMixer and
LightGBM, will serve as base models for which I aim to develop methods to explain the uncertainties in
their predictions.</p>
      <p>To support the development of novel methods to explain uncertainty estimates, I have pre-processed
two high-quality data sets obtained from the University Hospital. These high-quality and high-resolution
time series data sets will be crucial in training models and evaluating the efectiveness of XAI and UQ
methods. The data sets include data with distribution shifts due to the COVID-19 pandemic, providing
a unique opportunity to analyze and assess the robustness of the proposed methods.</p>
      <p>In addition, I engaged with shift planners, potential end users of AI systems designed to support
nurse scheduling. Through these interactions, I gained valuable insights into their specific needs and
preferences regarding AI systems. A recurring theme in these discussions was the importance of
transparency and understanding the rationale behind AI predictions. This feedback strongly supports
the direction of my future work, which will focus on integrating XAI and UQ to address these user
concerns. Another important aspect for end users is the reliability of these methods. Since wrong
predictions can lead to poor patient care, decreased job satisfaction, and higher absence rates, it is
crucial that the ML models are reliable and trustworthy. This also highlights the need for future work
on uncertainty estimation and its explainability.</p>
      <p>In summary, my preliminary work has laid a strong foundation for advancing the integration of XAI
and UQ in healthcare applications, specifically in the context of nurse scheduling.</p>
    </sec>
    <sec id="sec-6">
      <title>6. Future Research and Expected Contributions</title>
      <p>Given my preliminary work on time series forecasting, my immediate future work will focus on time
series forecasting as underlying ML task. However, it is important to emphasize that my research will
not be limited to time series forecasting alone. As my research is still in its early stages, there are several
key areas that require further investigation to ensure a comprehensive understanding and efective
integration of time series forecasting with UQ and XAI. A primary focus will be on the comparison
of existing XAI and UQ methods with regard to their suitability for time series forecasting, as well as
metrics for their evaluation. This will involve exploring existing methodologies and identifying gaps
where novel approaches can be developed. I will explore and implement various UQ methods tailored
for time series forecasting. These methods include Monte Carlo Dropout, ensemble techniques, and
quantile regression. Furthermore, I plan to implement the few methods that already exist to explain
uncertainty estimates, described in Section 2. The aim is to establish a robust pipeline that not only
incorporates these established methods but also accommodates the development and integration of
innovative approaches. This pipeline will serve as a foundation for future research and allow for
seamless testing and validation of the combination of UQ and XAI methods as well as novel methods as
my research progresses. This approach enables me to quantitatively evaluate and compare existing
methods to those that I plan to develop in the future, ensuring a broad and impactful contribution to
the field.</p>
      <p>Furthermore, I plan to engage with domain experts and end users to ensure that the methods developed
are aligned with real-world needs. After having developed methods that accurately explain uncertainty
estimates, I plan to investigate how these explanations benefit data scientists in model debugging and
performance monitoring, such as detecting distribution shifts. To the best of my knowledge, this has
not been investigated in depth yet.</p>
    </sec>
    <sec id="sec-7">
      <title>7. Conclusion</title>
      <p>In conclusion, the integration of explainability and UQ in ML models holds significant promise for
enhancing trust and acceptance, particularly in high-stakes domains such as healthcare. This research
aims to bridge the gap between two traditionally separate research fields: Explainable AI and Uncertainty
Quantification. My research will explore innovative methods to explain uncertainty estimates, providing
actionable insights that can improve decision-making processes and foster transparency. The expected
contributions include not only theoretical advancements, but also practical frameworks that can be
adopted across various domains, thereby enhancing the overall impact and reach of AI technologies.
Ultimately, my work seeks to contribute to the development of more reliable and transparent AI systems,
thereby advancing the field of ML and its application in critical real-world scenarios.</p>
    </sec>
    <sec id="sec-8">
      <title>Acknowledgments</title>
      <p>I express my sincere gratitude to my scientific supervisor, Jan-Philipp Steghöfer, for his invaluable
guidance and support throughout my research. This research is sponsored by the Bavarian State
Ministry of Economic Afairs, Regional Development and Energy under grant number
41-6618c/570/2LSM-2203-0010.</p>
    </sec>
    <sec id="sec-9">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author used ChatGPT-4 in order to: Grammar and spelling
check, Paraphrase and reword. After using this tool, the author reviewed and edited the content as
needed and takes full responsibility for the publication’s content.
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