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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Torino, Italy
* Corresponding author.
$ matthias@stat.uni-muenchen.de (M. Aßenmacher)</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Towards Enhancing Deep Active Learning with Weak Supervision and Constrained Clustering</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Matthias Aßenmacher</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Lukas Rauch</string-name>
          <xref ref-type="aff" rid="aff5">5</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jann Goschenhofer</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Andreas Stephan</string-name>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Bernd Bischl</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Benjamin Roth</string-name>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Bernhard Sick</string-name>
          <xref ref-type="aff" rid="aff5">5</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Statistics, LMU Munich</institution>
          ,
          <addr-line>Ludwigstr. 33, D-80539 Munich</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Fraunhofer IIS</institution>
          ,
          <addr-line>Erlangen</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Munich Center for Machine Learning (MCML), LMU Munich</institution>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>Research Group Data Mining and Machine Learning, University of Vienna</institution>
          ,
          <addr-line>Kolingasse 14-16, A-1090 Vienna</addr-line>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>UniVie Doctoral School Computer Science</institution>
          ,
          <addr-line>Vienna</addr-line>
          ,
          <country country="AT">Austria</country>
        </aff>
        <aff id="aff5">
          <label>5</label>
          <institution>University of Kassel</institution>
          ,
          <addr-line>Wilhelmshöher Allee 73, D-34121 Kassel</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2023</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0003</lpage>
      <abstract>
        <p>Three fields revolving around the question of how to cope with limited amounts of labeled data are Deep Active Learning (DAL), deep Constrained Clustering (CC), and Weakly Supervised Learning (WSL). DAL tackles the problem by adaptively posing the question of which data samples to annotate next in order to achieve the best incremental learning improvement, although it sufers from several limitations that hinder its deployment in practical settings. We point out how CC algorithms and WSL could be employed to overcome these limitations and increase the practical applicability of DAL research. Specifically, we discuss the opportunities to use the class discovery capabilities of CC and the possibility of further reducing human annotation eforts by utilizing WSL. We argue that the practical applicability of DAL algorithms will benefit from employing CC and WSL methods for the learning and labeling process. We inspect the overlaps between the three research areas and identify relevant and exciting research questions at the intersection of these areas.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;deep active learning</kwd>
        <kwd>constrained clustering</kwd>
        <kwd>weak labels</kwd>
        <kwd>weak supervision</kwd>
        <kwd>labels</kwd>
        <kwd>deep learning</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        In the age of large (partially) unlabeled data, we observe a natural rise in research eforts
exploring approaches that address situations of missing, low-informative, or incomplete labels;
heavily skewed label distributions; or availability of only a few labeled instances. One of the
most prominent examples is Deep Active Learning (DAL), which selects unlabeled observations
for labeling that are deemed most beneficial for the current model. However, a notable number
of benchmark scenarios in this area are partially constructed or artificial and rely on unrealistic
assumptions – e.g., perfect knowledge about the true number of classes, or the presence of
omniscient human annotators [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. This leads to unreliable results, casting doubt on the broader
applicability of DAL in practice [
        <xref ref-type="bibr" rid="ref2 ref3">2, 3</xref>
        ]. Further, incorporating concepts from (a) Constrained
Clustering (CC [
        <xref ref-type="bibr" rid="ref4 ref5">4, 5</xref>
        ]), which uses binary constraints as labels, and (b) Weakly Supervised
Learning (WSL), which employs diferent label-generating mechanisms, may alleviate this
limitation and enhance the practical relevance of research in this field. When combining these
approaches, we argue that they might complement each other, correct some of the shortcomings
of DAL, and mutually extend their capabilities. In the following, we will elaborate on some of
the weaknesses of current DAL research, show how CC and WSL potentially alleviate these
shortcomings by allowing for dynamic changes of the label set and more eficient learning, and
deduce efective research questions. These research questions mainly focus on how pool-based
DAL can accommodate a time-varying number of classes via CC and how WSL can support
generating the constraints in a meaningful manner.
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Current Practice of DAL Research</title>
      <p>
        Assuming that a large pool of unlabeled data is available and the goal is to strategically select a
subset that is expected to yield the highest performance gains, pool-based DAL can be seen as a
scenario of limited labeled data. However, the presumption that the allegedly omniscient oracle
is queried for instance-wise labels implies that the number of classes constituting the label set is
static and known. We challenge both of these assumptions, since they impose a high barrier to
the practical applicability of DAL and severely limit the transferability of research findings into
practical settings. As opposed to benchmark data sets with a known, fixed label set and data
from the same domain, in real-world settings, it will be much more common to face an unknown
and/or dynamic set of classes and samples potentially subject to domain shift [
        <xref ref-type="bibr" rid="ref6 ref7">6, 7</xref>
        ]. Further
critical issues in evaluating DAL include the arbitrary selection of hyperparameters in empirical
studies, due to the nature of DAL as a one-time learning problem [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. Resorting to default
hyperparameter values – which are expected to work out-of-the-box without a validation set –
limits the comparability across studies as well as the practical implications of these findings [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
While we do not address this issue, it must be considered an important future challenge.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Leveraging Constrained Clustering and Weak Supervision</title>
      <p>
        Instead of using conventionally labeled samples (, ) where  ∈ ,  = {1, . . . , }, in
CC, we consider constraint pairs of the form (,  ,  ) where ,  are two feature vectors
and  ∈ {0, 1} is the associated binary constraint describing whether the samples are in the
same cluster ( = 1, Must-Link) or diferent clusters (  = 0, Cannot-Link) [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. Dedicated loss
functions allow the training of neural-network-based models that are usable for the inductive
prediction of instance-wise class labels [
        <xref ref-type="bibr" rid="ref4 ref5">4, 5</xref>
        ]. As a rather young research field, characteristics
of deep CC are not yet fully explored. For instance, it sufers from constraint imbalancedness
in scenarios where an increasing number of underlying distinct clusters (the cardinality ||)
naturally leads to more Cannot-Link than Must-Link constraints, with a Must-Link proportion
of roughly 1 . Further, deep CC shows inferior performance compared to standard Supervised
||
Learning approaches when given a subset of all potential constraint annotations [
        <xref ref-type="bibr" rid="ref10 ref11">10, 11</xref>
        ] and
requires the Hungarian Matching algorithm for model evaluation [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ], which is typical for deep
clustering. Nevertheless, DAL might benefit from CC’s adaptive capabilities by overcoming
the assumption of a static label set and simultaneously helping alleviate the problem of
imbalancedness in CC. WSL is a promising approach that leverages noisy, incomplete, or imprecise
labels based on weak supervision signals, often formalized by so-called labeling functions
 :  →  ∪ {∅}, where ∅ means that the labeling function abstains from labeling. Examples
include dictionary lookups, heuristics, or pre-trained models [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ]. However, there are also
several shortcomings and challenges in current WSL research. While WSL allows for cheap and
fast label generation, it sometimes struggles to generalize to unseen or out-of-distribution data,
since the weak supervision signals do not fully cover the variations present in the data [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ].
Similarly to common DAL research, weak labels are typically provided at the instance level.
However, in many real-world scenarios, they may be available at diferent granularities [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ].
Finally, while the focus typically lies on classification tasks with a fixed set of predefined classes,
this is often unrealistic as the set of classes may evolve over time. While a weak supervision
signal typically refers to a single class, it has the potential to be dynamically adjusted over time.
      </p>
    </sec>
    <sec id="sec-4">
      <title>4. Resulting Research Questions</title>
      <p>We identify four promising research questions in the intersection between the three research
areas to improve the practical applicability of DAL, highlighting commonalities and challenges.</p>
      <sec id="sec-4-1">
        <title>Is it possible to extend DAL beyond known classes via CC? Given the adaptive capa</title>
        <p>
          bilities of CC models [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ], they might be well-suited to extend the practical applicability of
DAL research. The authors [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ] show how to use CC to detect the true number of classes and
to dynamically adapt to a changing number of classes over time. In the world of pool-based
DAL, this means that instead of querying the oracle for the label of one instance, the desired
annotations would be pairwise constraints. This procedure would (a) require less domain
knowledge from an annotator’s point of view [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ] and (b) allow starting the DAL cycle without prior
knowledge of the true number of classes, hence resulting in a more realistic setting. However, a
problem is the increased computational complexity of the selection: instead of performing the
inference step for all  samples, the complexity now scales quadratically with the number of
samples. Given that even the computational overhead of performing the inference steps on all
 samples sometimes may be prohibitively large, this issue poses a severe threat to feasibility.
As a result, dedicated research is needed for active sample selection to address this limitation.
Further, existing DAL query strategies would have to be adapted to be capable of executing
these pairwise queries (for which they currently do not work out-of-the-box). This can be seen
as a chance to develop query strategies that are able to “grasp” the entire space of the data.
In order to answer this research question, it might be beneficial to also closely inspect the
methods introduced for the related, but not identical task of (active) domain adaptation.1 In the
realm of DAL for computer vision there has been prior work on (active) domain adaptation [
          <xref ref-type="bibr" rid="ref17 ref18 ref19">17,
18, 19</xref>
          ] while, to the best of our knowledge, no comparable research exists for natural language
1Note, that we do not assume a complete shift of the domain, but rather address the scenario of only partial knowledge
about, e.g., the true number of classes or the possibility of newly emerging ones for a given domain.
processing. Further work on class distribution mismatch [
          <xref ref-type="bibr" rid="ref20">20</xref>
          ] and open-set classification [
          <xref ref-type="bibr" rid="ref21">21</xref>
          ] in
the computer vision domain could serve as a blueprint to disseminate and adapt these strategies
to other domains.
        </p>
        <p>
          Can we generate constraints in an informed manner? Since WSL methods enable the
automatic generation of weak or noisy labels, they represent a promising technique to further
reduce human labor in the DAL cycle [
          <xref ref-type="bibr" rid="ref22 ref23">22, 23</xref>
          ]. While there are established and efective
frameworks for WSL on an instance level [
          <xref ref-type="bibr" rid="ref13 ref24">13, 24</xref>
          ], the generation of weak pairwise constraints
is yet to be explored. We argue – especially for a large set of classes – that it might be easier to
write appropriate labeling functions  for generating constraints than for generating
instancewise labels. Very simplistic ideas in the natural language processing domain could be to consider
word overlap between documents or cosine similarities of the embeddings, which does not
require any domain knowledge (as opposed to writing labeling functions for single instances).
This is based on the same intuition, reasoning that it is also an easier task for humans to annotate
this way. Yet, such automatic labeling of pairs entails typical WSL problems, such as noisy
labels or limited coverage. Therefore, specialized treatment and research are needed. Another
approach for, e.g., noisy annotation of texts is the use of the impressive generative capabilities
of large language models (e.g. ChatGPT [
          <xref ref-type="bibr" rid="ref25">25</xref>
          ]) to generate a suitable second sample  , given
a pivotal sample  and the desired type of constraint  . An example of how this approach
would look is shown in Figures 1, 2, and 3 in Appendix A. Work in that direction might also be
able to solve the problem of increased computational complexity when combining DAL with CC,
since only the pivotal sample  would have to be selected. Again, sample selection and prompt
generation need a dedicated research efort. Moreover, using such a generative approach, it is
possible to specifically target classes that are dificult for the model to distinguish.
Does DAL work with mixed supervision? Human-in-the-loop approaches for weak labels
beyond instance-wise class labels allow for the combination of labels of diferent strengths, an
area that is referred to as mixed supervision and is connected to multi-task learning [
          <xref ref-type="bibr" rid="ref26 ref27">26, 27</xref>
          ]. In
mixed supervision, annotations for the same data set with diferent degrees of informativeness
are combined for model training, e.g. the mixing of some segmentation masks and some class
labels in medical imaging [
          <xref ref-type="bibr" rid="ref28">28</xref>
          ]. A first step in that direction would be the design of a DAL query
strategy that intelligently queries weak constraint annotations, instance-wise class labels, or
both.2 This could enable a model-driven balancing of the tradeof between ease of annotation
(i.e., quantity, as pairs in some cases3 might be more efortless to annotate than single instances)
and the annotation informativeness (i.e., quality, as instance-wise class labels contain more
information than binary constraints). This tradeof would also allow accounting for the diferent
annotation costs of instance- vs. pairwise labels, where the latter is often assumed to be cheaper.4
        </p>
      </sec>
      <sec id="sec-4-2">
        <title>Can DAL help to break the constraint imbalancedness? A major problem of CC is the</title>
        <p>
          increasing imbalancedness of constraint labels with increasing class cardinality: the more classes
2A related approach is ALICE [
          <xref ref-type="bibr" rid="ref29">29</xref>
          ], with queries aiming at diferentiating between classes instead of labeling instances.
3This might, e.g., hold for the annotation of pairs short texts or pairs of images for easy object detection tasks.
4However, empirically determining the cost ratio of instance- vs. pairwise labels is still an open research question.
exist, the more likely CC is to face a Cannot-Link pair during the data annotation process. In turn,
this leads to a notably higher number of Cannot-Link constraints than Must-Link constraints in
the training data, consequently hampering the learning process of the model. When enabled to
actively select which data samples (or pairs of data samples) to annotate next, this selection
process could be steered in a direction where the DAL strategy is used to actively query a higher
portion of similar pairs, resulting in a higher likelihood to obtain Must-Link constraints.
        </p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion and Outlook</title>
      <p>With this contribution, we hope to provide some inspiration for how to potentially combine
multiple promising research fields for learning from limited labeled data. When used in
conjunction, these methods might be able to alleviate the shortcomings that emerge when each method
is used in isolation. This approach may also overcome problems regarding computational
overhead as well as limitations caused by insuficient amounts of humanly labeled data sets.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>We would like to thank the three anonymous referees for their constructive comments and
suggestions, which helped improve this paper considerably. This work has been partially
funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) as part
of BERD@NFDI - grant number 460037581.</p>
    </sec>
    <sec id="sec-7">
      <title>A. Generating constraints with ChatGPT</title>
    </sec>
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