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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Case-based Explanation for Black-Box Time Series and Image Models with Applications in Smart Agriculture</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Eoin D</string-name>
          <email>eoin.delaney@insight-centre.org</email>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Insight Centre for Data Analytics</institution>
          ,
          <addr-line>Dublin</addr-line>
          ,
          <country country="IE">Ireland</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>School of Computer Science, University College Dublin</institution>
          ,
          <addr-line>Belfield, Dublin 4</addr-line>
          ,
          <country country="IE">Ireland</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>VistaMilk SFI Research Centre</institution>
          ,
          <addr-line>Dublin</addr-line>
          ,
          <country country="IE">Ireland</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <abstract>
        <p>Black-box models are frequently deployed for high stakes prediction tasks in a variety of domains (e.g., disease diagnosis and agricultural prediction). The predictions of these opaque systems are often plagued by a lack of transparency, motivating novel research in eXplainable AI (XAI) aiming to understand why a certain prediction was made. One increasingly promising form of explanation is counterfactual explanation where the aim is to elucidate how a prediction could change, given some change in the input space. While the majority of existing work has focused on producing counterfactual explanations for tabular data, significantly less focus has been placed on generating and evaluating counterfactual explanations for time series and image data. Explaining predictions for these data types, arguably, presents a whole new set of issues for XAI, due to the complex and multi-dimensional nature of the data. In this research, we examine how leveraging case-based reasoning (CBR) techniques such as NearestUnlike-Neighbors (NUNs) can aid the generation and evaluation of explanations in these domains. We also demonstrate the inadequacies of many traditional techniques that are used to evaluate explanations and highlight the promise of CBR and user studies in the evaluation of explanations.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        In recent years, the predictive prowess of machine learning systems has been undermined
by a worrying lack of interpretability, fairness, accountability and transparency [
        <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
        ]. These
challenges have resulted in major research eforts in Explainable AI (XAI) where the core
objective is to ofer insights into the predictions of black-box models that are commonly deployed
in high stakes scenarios. One such scenario that is of particular interest to our research is in
smart agriculture. Previous CBR research has already shown immense promise in both grass
growth and grasshopper infestation prediction [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ]. While the majority of XAI research focus
has been on tabular data, less attention has been attributed to time series data, introducing a new
set of complex issues for XAI due to high data dimensionality and strong feature dependencies
[
        <xref ref-type="bibr" rid="ref5">5</xref>
        ].
nEvelop-O
LGOBE
∗Corresponding author.
CEUR
      </p>
      <p>
        A variety of eXplainable CBR (XCBR) methods have shown immense promise for XAI (see
[
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] for a review). These XCBR techniques provide factual, example-based explanations (e.g.,
[
        <xref ref-type="bibr" rid="ref7 ref8">7, 8</xref>
        ]), feature-weighting explanations (CBR-LIME; [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]), and counterfactual explanations [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]
with a focus typically on tabular and sometimes image data.
      </p>
      <p>
        Counterfactual explanations aim to elucidate how a prediction could change if some input
was diferent. There is growing evidence from psychology, philosophy and sociology indicating
that they provide more human friendly and GDPR compliant explanations in comparison to
other popular forms of explanations [
        <xref ref-type="bibr" rid="ref10 ref11 ref12">11, 12, 10</xref>
        ]. While there are over 100 techniques proposed
to generate counterfactual explanations [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ], very few of these methods focus on image data,
and even fewer on time series data (see e.g., [
        <xref ref-type="bibr" rid="ref14 ref15">14, 15</xref>
        ] for closest works). In a similar fashion,
it is unclear if the proposed properties of good counterfactual explanations for tabular data
such as proximity, sparsity, and plausibility [
        <xref ref-type="bibr" rid="ref10 ref12">12, 10</xref>
        ] will extend to other data types. Moreover,
evaluating these properties is non trivial and there is growing evidence to suggest that user
studies are desperately needed in order to reliably evaluate explanations [
        <xref ref-type="bibr" rid="ref10 ref16">16, 10</xref>
        ].
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Research Plan and Objectives</title>
      <p>
        The overall goal of this research is to develop techniques that can be used to generate and
evaluate explanations for time series and image data through leveraging case-based reasoning.
Building on evidence from psychology, philosophy and social science [
        <xref ref-type="bibr" rid="ref11 ref12 ref13">11, 12, 13</xref>
        ], a core focus
of this research is in the generation and evaluation of counterfactual explanations.
      </p>
      <p>I have identified several research questions that underpin the goal of generating and evaluating
counterfactual explanations for time series and image data;
• Can case-based reasoning be leveraged to generate good explanations for applied time
series prediction tasks both in terms of (i) counterfactual explanations for classification
and (ii) explanations for applied agricultural forecasting problems?
• What are the properties of good counterfactual explanations for time series and image
data, and do they mirror the properties of good counterfactual explanations for tabular
data (e.g., proximity, sparsity and plausibility)?
• Do explanations that are automatically generated by computational techniques align with
explanations that are informative for human users?</p>
      <p>
        In previous work, Keane and Smyth [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] designed a novel case based technique to generate
counterfactual explanations for tabular data through leveraging existing counterfactual instances
in the training data (i.e., nearest unlike neighbors (NUNs) [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ]). So, exploring the role of NUNs
in the generation of counterfactual explanations is a promising line of research in the context
of time series and image data. The combination of CBR with Deep Learning feature weighting
techniques (e.g., class activation mapping [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ]) in a Twin-Systems framework [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ] is another
promising area of research for the development of counterfactual explanations for time series
and image data. Feature weighting techniques are perhaps the most common XAI method in
time series classification [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], and the availability of open source data on the UCR archive [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ]
readily facilitates the development and experimental comparison of XAI techniques.
      </p>
      <p>
        In terms of time series forecasting, one untapped line of work from our review of the
psychological literature is in prefactual explanation. Prefactual explanations describe conditional
(if-then) propositions about, as yet not undertaken, actions and the corresponding outcomes
that may (or may not) take place in the future [
        <xref ref-type="bibr" rid="ref21 ref22">21, 22</xref>
        ]. While counterfactuals focus on the past,
prefactuals look to the future, capturing the idea of something that is not yet a fact, but could
become a fact [
        <xref ref-type="bibr" rid="ref21">21</xref>
        ]. Such explanations could also be leveraged in other challenging domains
such as reinforcement learning [
        <xref ref-type="bibr" rid="ref23">23</xref>
        ].
      </p>
      <p>
        One applied area that is of particular interest to our research is in smart and sustainable
agriculture. We have a data set from an industry partner containing information about milk
yield from over 2000 commercial dairy herds. One of our goals is to accurately provide long term
milk supply forecasts to farmers, supplementing the predictions with explanations that indicate
diferent actions they could take to boost milk yield in future years. Related CBR work in
goalbased recommendation has shown how diferent training plans can be recommended to runners
to produce new personal best times [
        <xref ref-type="bibr" rid="ref24">24</xref>
        ], so relating this CBR research to producing prefactual
explanations for farmers to improve their output is a promising line for novel research.
      </p>
      <p>
        Finally, it is unclear if the properties of good explanations for tabular data will extend to time
series and image data. For example, when generating explanations one popular technique is
to minimize the distance between the query and the counterfactual [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ]. However, this runs
the risk of generating adversarial explanations that may not be noticeably diferent for users in
relation to the query instance. In time series and image data, discriminative and semantically
meaningful information is often contained in localized regions of the time series or image. So, it
is clear that user evaluation and rigorous testing of explanation evaluation metrics are needed
in this research.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Progress Summary</title>
      <p>
        We developed a novel CBR technique, Native-Guide, to generate counterfactual explanations
for time series classification tasks [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. The technique leverages both in-sample counterfactual
explanations (e.g., Nearest Unlike Neighbors [
        <xref ref-type="bibr" rid="ref10 ref17">17, 10</xref>
        ]) and feature weight vectors from techniques
such as class-activation mapping [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] to create explanations. This work was presented at
ICCBR’21 where it received a best-student paper award. More recently, we developed a novel
forecasting technique and a method to provide prefactual explanations with applications in
milk supply prediction [
        <xref ref-type="bibr" rid="ref25">25</xref>
        ]. Specifically, we highlighted how producing explanations through
comparatively contrasting high performing exemplar herds and low performing herds (retrieved
using class prototypes) could boost future on-farm performance - ”Your projected milk supply
for next year is 250’000 litres. However, if you reduced the calving period (In a similar fashion to
farmer Y), your projected supply would be 300’000 litres and your milk would likely have a higher
protein content”. This work will appear in the main proceedings of ICCBR’22.
      </p>
      <p>
        In terms of counterfactual evaluation, we conducted a literature review of over 100 papers
and discussed five key deficits to rectify in the evaluation of counterfactual XAI techniques.
This review paper was presented at IJCAI’21 [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. We noted the over-reliance on computational
proxy measures for proximity, sparsity and plausibility without any conclusive evidence from
user studies. In work presented at the ICML Workshop on Algorithmic Recourse we identified
the utility of case-based evaluation methods in determining how well a counterfactual fit the
data distribution, and highlighted that optimizing for proximity often generated adversarial
explanations that would not be noticeably diferent than the query for a human user [
        <xref ref-type="bibr" rid="ref26">26</xref>
        ].
Results in our work in time series classification also demonstrated similar results [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. So, a
natural avenue for current and future work is to focus on evaluating counterfactual explanations
through conducting user studies.
      </p>
      <p>
        Currently we are focusing on addressing some of the central issues presented in our IJCAI
review paper and we are conducting large scale user studies to evaluate explanations and
critically assess the suitability of computational evaluation techniques. In our latest
experiments human users (N=42) created counterfactuals through correcting misclassifications of a
convolutional neural network on the MNIST and Google Quickdraw data sets using a drawing
tool. This data represents the first ground truth explanation data set for counterfactual visual
explanations. By comparing explanations generated by humans with those that are generated
automatically by computational techniques, we aim to provide novel insights into (i) the
properties of good explanations according to humans and (ii) the unreliability of many popular
evaluation metrics (e.g.,  1 and  2 distances for proximity). Contrary to popular belief, our
initial results indicate that people do not minimally edit instances when creating counterfactual
visual explanations. Instead they modify a larger, and often semantically meaningful region
when creating an explanation, often pushing the explanation towards a class prototype. So,
leveraging psychologically grounded models of similarity such as Tversky’s contrast model
of similarity [
        <xref ref-type="bibr" rid="ref27">27</xref>
        ] in counterfactual generation and evaluation may result in more informative
explanations and is an interesting avenue for future work.
      </p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>D.</given-names>
            <surname>Gunning</surname>
          </string-name>
          , D. Aha,
          <article-title>Darpa's explainable artificial intelligence (xai) program</article-title>
          ,
          <source>AI</source>
          Magazine
          <volume>40</volume>
          (
          <year>2019</year>
          )
          <fpage>44</fpage>
          -
          <lpage>58</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <given-names>A.</given-names>
            <surname>Adadi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Berrada</surname>
          </string-name>
          ,
          <article-title>Peeking inside the black-box: A survey on Explainable Artificial Intelligence (XAI)</article-title>
          ,
          <source>IEEE Access 6</source>
          (
          <year>2018</year>
          )
          <fpage>52138</fpage>
          -
          <lpage>52160</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>E. M.</given-names>
            <surname>Kenny</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Ruelle</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Geoghegan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Shalloo</surname>
          </string-name>
          ,
          <string-name>
            <surname>M. O'Leary</surname>
          </string-name>
          ,
          <string-name>
            <surname>M. O'Donovan</surname>
            ,
            <given-names>M. T.</given-names>
          </string-name>
          <string-name>
            <surname>Keane</surname>
          </string-name>
          ,
          <article-title>Predicting grass growth for sustainable dairy farming: A cbr system using bayesian caseexclusion and post-hoc, personalized explanation-by-example (xai)</article-title>
          ,
          <source>in: International Conference on Case-Based Reasoning</source>
          , Springer,
          <year>2019</year>
          , pp.
          <fpage>172</fpage>
          -
          <lpage>187</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>J.</given-names>
            <surname>Hastings</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Branting</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Lockwood</surname>
          </string-name>
          ,
          <article-title>Carma: A case-based rangeland management adviser</article-title>
          ,
          <source>AI</source>
          Magazine
          <volume>23</volume>
          (
          <year>2002</year>
          )
          <fpage>49</fpage>
          -
          <lpage>49</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>E.</given-names>
            <surname>Delaney</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Greene</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. T.</given-names>
            <surname>Keane</surname>
          </string-name>
          ,
          <article-title>Instance-based counterfactual explanations for time series classification</article-title>
          ,
          <source>in: International Conference on Case-Based Reasoning</source>
          , Springer,
          <year>2021</year>
          , pp.
          <fpage>32</fpage>
          -
          <lpage>47</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>J. M.</given-names>
            <surname>Schoenborn</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R. O.</given-names>
            <surname>Weber</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D. W.</given-names>
            <surname>Aha</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Cassens</surname>
          </string-name>
          ,
          <string-name>
            <surname>K.-D. Althof</surname>
          </string-name>
          ,
          <article-title>Explainable case-based reasoning: A survey</article-title>
          ,
          <source>in: AAAI-21 Workshop Proceedings</source>
          ,
          <year>2021</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>M. T.</given-names>
            <surname>Keane</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E. M.</given-names>
            <surname>Kenny</surname>
          </string-name>
          ,
          <article-title>How case-based reasoning explains neural networks: A theoretical analysis of xai using post-hoc explanation-by-example from a survey of anncbr twin-systems</article-title>
          ,
          <source>in: Proc. ICCBR'19</source>
          , Springer,
          <year>2019</year>
          , pp.
          <fpage>155</fpage>
          -
          <lpage>171</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <given-names>F.</given-names>
            <surname>Sørmo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Cassens</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Aamodt</surname>
          </string-name>
          ,
          <article-title>Explanation in case-based reasoning-perspectives and goals</article-title>
          ,
          <source>Artificial Intelligence Review</source>
          <volume>24</volume>
          (
          <year>2005</year>
          )
          <fpage>109</fpage>
          -
          <lpage>143</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>J. A.</given-names>
            <surname>Recio-García</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Díaz-Agudo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V.</given-names>
            <surname>Pino-Castilla</surname>
          </string-name>
          ,
          <article-title>CBR-LIME: A Case-Based Reasoning Approach to Provide Specific Local Interpretable Model-Agnostic Explanations</article-title>
          , in: ICCBR, Springer,
          <year>2020</year>
          , pp.
          <fpage>179</fpage>
          -
          <lpage>194</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>M. T.</given-names>
            <surname>Keane</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Smyth</surname>
          </string-name>
          ,
          <article-title>Good counterfactuals and where to find them: A case-based technique for generating counterfactuals for explainable ai (xai)</article-title>
          ,
          <source>in: Proc. ICCBR'20</source>
          , Springer,
          <year>2020</year>
          , pp.
          <fpage>163</fpage>
          -
          <lpage>178</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>T.</given-names>
            <surname>Miller</surname>
          </string-name>
          ,
          <article-title>Explanation in artificial intelligence: Insights from the social sciences</article-title>
          ,
          <source>Artificial Intelligence</source>
          <volume>267</volume>
          (
          <year>2019</year>
          )
          <fpage>1</fpage>
          -
          <lpage>38</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>S.</given-names>
            <surname>Wachter</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Mittelstadt</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Russell</surname>
          </string-name>
          ,
          <article-title>Counterfactual explanations without opening the black box: automated decisions and the gdpr</article-title>
          ,
          <source>Harv.J.Law Tech</source>
          .
          <volume>31</volume>
          (
          <year>2017</year>
          )
          <fpage>841</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <given-names>M. T.</given-names>
            <surname>Keane</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E. M.</given-names>
            <surname>Kenny</surname>
          </string-name>
          ,
          <string-name>
            <given-names>E.</given-names>
            <surname>Delaney</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Smyth</surname>
          </string-name>
          ,
          <article-title>If only we had better counterfactual explanations: Five key deficits to rectify in the evaluation of counterfactual xai techniques</article-title>
          ,
          <source>in: IJCAI-21</source>
          ,
          <year>2021</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <given-names>E.</given-names>
            <surname>Ates</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Aksar</surname>
          </string-name>
          ,
          <string-name>
            <given-names>V. J.</given-names>
            <surname>Leung</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. K.</given-names>
            <surname>Coskun</surname>
          </string-name>
          ,
          <article-title>Counterfactual explanations for machine learning on multivariate time series data</article-title>
          , arXiv preprint arXiv:
          <year>2008</year>
          .
          <volume>10781</volume>
          (
          <year>2020</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <given-names>Y.</given-names>
            <surname>Goyal</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Z.</given-names>
            <surname>Wu</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Ernst</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Batra</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Parikh</surname>
          </string-name>
          ,
          <string-name>
            <given-names>S.</given-names>
            <surname>Lee</surname>
          </string-name>
          ,
          <article-title>Counterfactual visual explanations</article-title>
          , in: ICML, PMLR,
          <year>2019</year>
          , pp.
          <fpage>2376</fpage>
          -
          <lpage>2384</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <given-names>F.</given-names>
            <surname>Doshi-Velez</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Kim</surname>
          </string-name>
          ,
          <article-title>Towards a rigorous science of interpretable machine learning</article-title>
          ,
          <source>arXiv preprint arXiv:1702.08608</source>
          (
          <year>2017</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <string-name>
            <given-names>C.</given-names>
            <surname>Nugent</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Doyle</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Cunningham</surname>
          </string-name>
          ,
          <article-title>Gaining insight through case-based explanation</article-title>
          ,
          <source>Journal of Intelligent Information Systems</source>
          <volume>32</volume>
          (
          <year>2009</year>
          )
          <fpage>267</fpage>
          -
          <lpage>295</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          [18]
          <string-name>
            <given-names>B.</given-names>
            <surname>Zhou</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Khosla</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Lapedriza</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Oliva</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Torralba</surname>
          </string-name>
          ,
          <article-title>Learning deep features for discriminative localization</article-title>
          ,
          <source>in: IEEE CVPR</source>
          ,
          <year>2016</year>
          , pp.
          <fpage>2921</fpage>
          -
          <lpage>2929</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          [19]
          <string-name>
            <given-names>E. M.</given-names>
            <surname>Kenny</surname>
          </string-name>
          , M. T. Keane,
          <article-title>Twin-systems to explain artificial neural networks using casebased reasoning: comparative tests of feature-weighting methods in ann-cbr twins for xai</article-title>
          ,
          <source>in: IJCAI-19</source>
          ,
          <year>2019</year>
          , pp.
          <fpage>2708</fpage>
          -
          <lpage>2715</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          [20]
          <string-name>
            <given-names>H. A.</given-names>
            <surname>Dau</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Bagnall</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Kamgar</surname>
          </string-name>
          ,
          <string-name>
            <surname>C.-C. M. Yeh</surname>
            ,
            <given-names>Y.</given-names>
          </string-name>
          <string-name>
            <surname>Zhu</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          <string-name>
            <surname>Gharghabi</surname>
            ,
            <given-names>C. A.</given-names>
          </string-name>
          <string-name>
            <surname>Ratanamahatana</surname>
            ,
            <given-names>E. Keogh,</given-names>
          </string-name>
          <article-title>The UCR time series archive</article-title>
          ,
          <source>IEEE/CAA Journal of Automatica Sinica</source>
          <volume>6</volume>
          (
          <year>2019</year>
          )
          <fpage>1293</fpage>
          -
          <lpage>1305</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          [21]
          <string-name>
            <given-names>K.</given-names>
            <surname>Epstude</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Scholl</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N. J.</given-names>
            <surname>Roese</surname>
          </string-name>
          ,
          <article-title>Prefactual thoughts: Mental simulations about what might happen</article-title>
          ,
          <source>Review of General Psychology</source>
          <volume>20</volume>
          (
          <year>2016</year>
          )
          <fpage>48</fpage>
          -
          <lpage>56</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref22">
        <mixed-citation>
          [22]
          <string-name>
            <surname>R. M. Byrne</surname>
            ,
            <given-names>S. M.</given-names>
          </string-name>
          <string-name>
            <surname>Egan</surname>
          </string-name>
          ,
          <article-title>Counterfactual and prefactual conditionals</article-title>
          .,
          <source>Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale 58</source>
          (
          <year>2004</year>
          )
          <fpage>113</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref23">
        <mixed-citation>
          [23]
          <string-name>
            <given-names>C.</given-names>
            <surname>Rudin</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Chen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>Z.</given-names>
            <surname>Chen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Huang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Semenova</surname>
          </string-name>
          ,
          <string-name>
            <surname>C. Zhong,</surname>
          </string-name>
          <article-title>Interpretable machine learning: Fundamental principles and 10 grand challenges</article-title>
          ,
          <source>Statistics Surveys</source>
          <volume>16</volume>
          (
          <year>2022</year>
          )
          <fpage>1</fpage>
          -
          <lpage>85</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref24">
        <mixed-citation>
          [24]
          <string-name>
            <given-names>B.</given-names>
            <surname>Smyth</surname>
          </string-name>
          ,
          <string-name>
            <given-names>P.</given-names>
            <surname>Cunningham</surname>
          </string-name>
          ,
          <article-title>A novel recommender system for helping marathoners to achieve a new personal-best</article-title>
          ,
          <source>in: Proceedings of the eleventh ACM conference on recommender systems</source>
          ,
          <year>2017</year>
          , pp.
          <fpage>116</fpage>
          -
          <lpage>120</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref25">
        <mixed-citation>
          [25]
          <string-name>
            <given-names>E.</given-names>
            <surname>Delaney</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Greene</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Shalloo</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Lynch</surname>
          </string-name>
          , M. T. Keane,
          <article-title>Forecasting for sustainable dairy produce: Enhanced long-term, milk-supply forecasting using k-nn for data augmentation, with prefactual explanations for xai</article-title>
          ., in: To appear
          <source>in ICCBR'22</source>
          ,
          <year>2022</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref26">
        <mixed-citation>
          [26]
          <string-name>
            <given-names>E.</given-names>
            <surname>Delaney</surname>
          </string-name>
          ,
          <string-name>
            <given-names>D.</given-names>
            <surname>Greene</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M. T.</given-names>
            <surname>Keane</surname>
          </string-name>
          ,
          <article-title>Uncertainty estimation and out-of-distribution detection for counterfactual explanations: Pitfalls and solutions</article-title>
          ,
          <source>arXiv preprint arXiv:2107.09734</source>
          (
          <year>2021</year>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref27">
        <mixed-citation>
          [27]
          <string-name>
            <given-names>A.</given-names>
            <surname>Tversky</surname>
          </string-name>
          , Features of similarity.,
          <source>Psychological review 84</source>
          (
          <year>1977</year>
          )
          <fpage>327</fpage>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>