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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>IIR</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Beyond the Parameters: Measuring Actual Privacy in Obfuscated Texts</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Francesco Luigi</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>De Faveri</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Guglielmo</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Faggioli</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nicola</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ferro</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Information Engineering, University of Padova</institution>
          ,
          <addr-line>Padova</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2024</year>
      </pub-date>
      <volume>14</volume>
      <fpage>5</fpage>
      <lpage>6</lpage>
      <abstract>
        <p>Evaluating privacy provided by obfuscation mechanisms remains an open problem in the research community. Especially for textual data, in Natural Language Processing (NLP) and Information Retrieval (IR) tasks, privacy guarantees are measured by analyzing the hyper-parameters of a mechanism, e.g., the privacy budget  in Diferential Privacy ( DP), and the impact of these on the performances. However, considering only the privacy parameters is not enough to understand the actual level of privacy achieved by a mechanism from a real user perspective. We analyse the requirements and the features needed to actually evaluate the privacy of obfuscated texts beyond the formal privacy provided by the analysis of the mechanisms' parameters, and suggest some research directions to devise new evaluation measures for this purpose.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Privacy-Preserving Information Retrieval</kwd>
        <kwd>Evaluation Measures</kwd>
        <kwd>Diferential Privacy</kwd>
        <kwd>Information Security</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Natural Language Processing (NLP) and Information Retrieval (IR) systems are developed using
extensive textual datasets, including queries, documents, reviews, and online posts, which
frequently contain sensitive and personal user information. The presence in such texts of
personal information, e.g., the user profile and personal opinions, poses a serious matter for
users interacting with the systems. Such privacy concerns, if not properly mitigated, can
endanger the users’ safety after text analysis has been pursued. For instance, imagine a scenario,
where a user expresses on a social network his disagreement with a specific political view in an
illiberal country [
        <xref ref-type="bibr" rid="ref1 ref2">1, 2</xref>
        ]. Moreover, from the browser search history, it is possible to infer and
disclose sensitive information, such as his salary or medical conditions, by analyzing the search
queries and documents retrieved [
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ]. To address such privacy concerns in a formal manner,
-Diferential Privacy ( DP) [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], -anonymity [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], ℓ-diversity [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ], -closeness [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] represent the
Gold Standard definitions of providing privacy. Formally, the privacy parameters, e.g.,  and ,
regulate the amount of obfuscation provided to the original data. Thus, these values serve as
indicators of the amount of formal privacy provided by the obfuscation mechanisms.
      </p>
      <p>
        However, the actual amount of real privacy achieved is often overlooked. Indeed, just
analyzing these values is not suficient for assessing the real level of privacy of the obfuscated
texts produced. For instance, a -DP mechanism might replace the original text “melanoma
breast cancer” with “disease breast tumour”. Although the formal privacy level is ensured by
the  value, the actual privacy is efectively zero because an external human auditor can quickly
infer the user information need. As confirmed by previous studies [
        <xref ref-type="bibr" rid="ref10 ref9">9, 10</xref>
        ], taking into account
only the value of privacy parameters is not enough to measure the privacy and new measures of
evaluation are needed to inspect the similarities of the original and obfuscated text [11, 12, 13].
      </p>
      <p>In this paper, we discuss several key aspects to be considered when measuring privacy
in textual obfuscation. We present the theoretical background on the mechanisms used for
textual obfuscation in IR tasks. Once an obfuscation mechanism has produced the private texts,
we stress the need for a privacy analysis beyond the only study of the mechanisms’ privacy
parameters. Furthermore, we discuss the challenges of evaluating privacy, highlighting the
distinctions between the formal and practical value of privacy in the obfuscated texts.</p>
      <p>The paper is organized as follows: Section 2 explains how privacy is achieved in text
obfuscation; Section 3 addresses the challenges in measuring privacy and proposes new directions on
how to assess a concrete level of privacy beyond the obfuscation parameters.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Preserving Privacy in texts</title>
      <sec id="sec-2-1">
        <title>2.1. Parameter-Based Obfuscation</title>
        <p>
          -anonymity and ℓ-diversity [
          <xref ref-type="bibr" rid="ref6 ref7">6, 7</xref>
          ] are privacy metrics based on the pre-image cardinality of an
obfuscation mechanism. By generalizing and suppressing the original data, -anonymity and
ℓ-diversity ofer the needed amount of obfuscation determined by the parameters  and ℓ.
        </p>
        <p>
          On the other hand, -closeness [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] is a metric based on the conditional distribution between
original and obfuscated data. -closeness estimates the divergence between the obfuscated data
released which is controlled by the threshold . Akin to -anonymity and ℓ-diversity the data
are generalized and suppressed until the required level  is verified. However, privacy is only
measured by the privacy budget set, without considering the efective obfuscation of the data.
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Diferential Privacy Obfuscation</title>
        <p>
          The principal framework to formally define privacy is -DP, introduced by Dwork et al. [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ].
Essentially, DP introduces carefully calibrated noise levels during output computation using a
privacy budget denoted as , which controls the equilibrium between data privacy and utility.
The definition of DP is based on the notion of neighbouring datasets, i.e., datasets that diverge
by at most one record. The formal definition of DP states that a randomized mechanism ℳ, i.e.,
a mechanism that takes as input the original data and produces a noisy output, is -DP if for
any pair of neighbouring datasets  and ′ and a privacy budget  ∈ R+, Equation 1 holds.
        </p>
        <p>Pr [ℳ() ∈ ] ≤  · Pr [︀ ℳ(′) ∈ ]︀
∀ ⊂ Im(ℳ)
(1)</p>
        <p>When a randomized mechanism respects -DP, it ensures that the likelihood of observing any
output remains nearly equal for any neighbouring datasets. Consequently, the mechanism keeps
user privacy by introducing uncertainty regarding the original data. As per the definition, the
lower values of  correspond to elevated privacy levels. Specifically, if  = 0, the output of the
mechanism becomes independent of the input, as indicated by the equation Pr [ℳ() ∈ ] =
Pr [ℳ(′) ∈ ] ∀ ⊂ Im(ℳ). Thus, the important information-theoretic property that DP
provides the user is the “Plausible Deniability”, i.e., the statistical indistinguishability: thus, an
adversary cannot definitively link the original data to the obfuscated output.</p>
        <p>Diferent obfuscation methods have been proposed to protect sensitive information in texts for
the NLP domain. Once the word embedding vector () has been computed, a DP mechanism
takes as input () randomizes its original value. Specifically, to achieve DP, two strategies can
be employed: after adding statistical noise to the original word embedding, the nearest value is
selected as the candidate obfuscated word. On the other hand, the mechanism accounts for the
distances from all words in a vocabulary to create a ranked list of potential candidates, then,
the new term is chosen from the list based on a probability distribution, parametrized by .</p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Heuristic-Based Obfuscation</title>
        <p>Obfuscating texts using DP is not the only strategy to achieve the privacy desired. Previously
proposed methods relied on non-formal privacy methods. A study by Arampatzis et al. [14]
explored an obfuscation technique leveraging WordNet [15]. This method involves extracting
synonyms, hypernyms, and holonyms from WordNet for each term in a sentence. Therefore, the
approach considers sets of terms two steps away on the WordNet hierarchy and computes the
obfuscation candidates as the Cartesian product between the sets. To avoid exposure of the initial
terms, a similarity function is employed to filter out words too similar to the original. Fröbe et al.
[16] develop an extension of the Arampatzis et al. [17, 18] method based on word statistics. This
approach involves using a local corpus to select and filter candidate obfuscations. To enhance
privacy, all candidates chosen from the possible combinations among the top- documents are
discarded if they are synonyms, hypernyms, or hyponyms. On one hand, these approaches
efectively mask the actual user information needs by altering words through a lexical approach,
thereby providing tangible privacy that limits the inference of the true meaning of the texts.
On the other hand, no formal privacy guarantees are provided, as the mechanisms operate
independently of  or any other formal parameter.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. General Challenges of Measuring Privacy</title>
      <sec id="sec-3-1">
        <title>3.1. Contextual Privacy Evaluation</title>
        <p>While individual terms lack inherent sensitivity, their impact is contingent on the context in
which they are used. The sensitivity of a term is generated by the interactions between words
used in the sentence where the term is placed. Thus, the context of a sentence provides the
original meaning that the user needs to communicate by using the initial word. Introducing a metric
to assess the context’s sensitivity before text obfuscation can help moderate the diference
between formal and actual privacy. By evaluating the context prior to the obfuscation, privacy can
be measured in a broader scenario. Such a context is independent of the obfuscation parameters
and needs to be assessed during an initial privacy analysis of texts, as also motivated by prior
studies [19, 20, 21]. The absence of context in the obfuscation may result in the mechanisms
failing to capture the intended meaning, tone, or sentiment of the text, consequently generating
irrelevant or inaccurate obfuscations. Therefore, utilizing a NLP model to comprehend context
is essential for efectively managing the variability and richness of natural language, taking
into account both the lexical and semantic structures of sentences [22, 23].</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Limits of Traditional Privacy Measures</title>
        <p>Traditional privacy measures are based on the information-theoretic concept of entropy [24].
Specifically, the metrics used to evaluate the failure rates of DP an obfuscation mechanism ℳ
are derived from an extension of classical entropy, namely the entropy introduced by Rényi
[25]. This entropy is employed to assess the probability of a failure during the obfuscation,
denoted as  = Pr[ℳ() = ], and the cardinality of the smallest output set defined
as  = min|{ ⊆  : Pr[ℳ() ∈/ ] ≤  }|. These measures are typically calculated by
simulating the obfuscation of a randomly sampled word  over a specified number of iterations
 , e.g., in [26, 27, 28] the authors agree to use  = 100. The frequency with which the
mechanism returns  represents the approximation of , and the ratio of unique words
generated over the  simulations provides the estimate of . Intuitively, a proper setting of 
in a DP mechanism should ensure that  is small and  is (almost) all words  ∈ .</p>
        <p>However, these uncertainty statistics retain certain limitations. Consider a scenario where a
mechanism appends a special symbol to the last character of the obfuscated word regardless of
the original term, or it changes a word with a synonym like [14, 16]. As a result, the probability
that the mechanism obfuscates a word by mapping it to itself would always be equal to zero.
Consequently,  = 0 for all possible values of the obfuscation parameter. On the other hand,
if we let the mechanism change the special symbol appended to the obfuscated word, the set of
possible obfuscated candidates will never be zero. Therefore, conducting such an assessment on
its own is not enough to truly comprehend the concrete privacy provided by the mechanisms.
Furthermore, widely used metrics for evaluating the quality of machine-generated texts, such
as BLEU [29], ROUGE [30], and METEOR [31], are not traditionally used to evaluate the lexical
and semantic obfuscation levels provided by the DP mechanisms.</p>
        <p>These metrics can be helpful for estimating the proportions of n-grams, longest common
subsequences, stemming, and synonyms in the obfuscated texts; thus ensuring a deeper analysis
of the privacy provided. However, such measures sufer from a lack of semantic understanding,
not catching the true semantic relationships between terms in the text, thus obfuscating the
original terms with synonyms and hyponyms. To address this limitation, Transformer-based
metrics, e.g., BERT-Scores [32], can efectively encode the entire sentence and capture the true
similarities between original and obfuscated phrases. Nonetheless, BERT-Scores deeply depend
on the pre-trained models used (RoBERTa, ALBERT, etc.) and yield diferent results, introducing
biases in the privacy evaluation from models trained on specific domains. As a preliminary study,
Faggioli and Ferro [33] proposed to adopt also the Jaccard Index and the sentence embedding
computed by a Language Model to explore the lexical and semantic similarity between original
and obfuscated texts. However, the former does not consider synonyms and hyponyms of terms,
and the Transformer method can yield diferent results depending on the model used. We recap
the benefits and the disadvantages of adopting the aforementioned measures in Table 1.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Adversarial Capacity of Breaking Privacy</title>
        <p>Privacy is a security objective that guarantees that the information is used without revealing
personal information to external entities. Attackers seek to decode obfuscated sentences and
uncover the original content with the purpose of gaining insights into user data for malicious
activities. Diferent strategies are used to evaluate the probability of a successful attack [ 12].
The attack scenarios chosen are based on the attacker’s characteristics, i.e., available resources
and prior knowledge. Additionally, the principal classes used to evaluate the success probability
of an attack include Membership and Attribute Inference Attacks [34, 35], whose probability of
success is strictly evaluated depending on the privacy budget parameter. The former estimates
the likelihood that a sampled text belongs to a specific dataset; the latter quantifies the probability
that an adversary can infer sensitive attributes about individuals from the obfuscated texts.</p>
        <p>However, no longitudinal analysis of textual obfuscation has been conducted to investigate
the adversarial risks associated with disclosing personal information in the output generated
by the obfuscation mechanisms. To address this gap, a parameter-independent metric for
assessing adversarial privacy risks over time could be the key to mitigating this issue efectively.
Such metrics should take into account the evolving distributions of text obfuscation and the
advancing capabilities of the adversaries. This approach facilitates the identification of potential
vulnerabilities that may emerge as attackers adapt and refine their strategies. Moreover, it
enables the continuous improvement of obfuscation mechanisms to neutralise these evolving
threats, thereby improving the overall robustness of the privacy-preserving methods.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Conclusion and Future Work</title>
      <p>In this study, we framed the problem of assessing privacy for obfuscated texts beyond the privacy
parameters, e.g., , . Furthermore, we described the theoretical context of text obfuscation and
the open challenges of measuring privacy, proposing diferent aspects to take into account when
assessing the privacy provided to the original texts. In future directions, we plan to evaluate
Privacy-Preserving Information Retrieval pipelines to empirically address such measures for
estimating the concrete level of privacy achieved by the obfuscation mechanisms.
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