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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>A Framework for Identifying Depression on Social Media: MentalRiskES@IberLEF 2023</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Simón Sánchez Viloria</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Daniel Peix del Río</string-name>
          <email>p@10</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Rubén Bermúdez Cabo</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Guillermo Arturo Arrojo Fuentes</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Isabel Segura-Bedmar</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Universidad Carlos III de Madrid (UC3M), Av. Universidad</institution>
          ,
          <addr-line>30 (edificio Sabatini), 28911 Leganés (Madrid)</addr-line>
          ,
          <country country="ES">Spain</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>This paper describes our participation in the MentalRiskES task at IberLEF 2023. The task involved predicting the likelihood of an individual experiencing depression based on their social media activity. The dataset consisted of conversations from 175 Telegram users, each labeled according to their evidence of sufering from the disorder. We used a combination of traditional machine learning and deep learning techniques to solve four predictive subtasks: binary classification, simple regression, multiclass classification, and multi-output regression. We approached this by training a model to solve the multi-output regression case and then transforming the predictions to work for the other three subtasks. We compare the performance of two modeling approaches: fine-tuning a BERT-based model directly for the task or using its embeddings as inputs to a linear regressor, with the latter yielding better results. The code to reproduce our results can be found at: https://github.com/simonsanvil/EarlyDepression-MentalRiskES Mental health is a growing concern in our society. According to the World Health Organization (WHO), 1 in 4 people will be afected by mental disorders at some point in their lives [ 1]. In addition, the COVID-19 pandemic has had a negative impact on the mental health of the general population, with an increase in the number of people sufering from mental disorders [ 2]. Thus, it is becoming increasingly important to evaluate the use of new technologies to assess the risk of mental illness and the healthcare needs of the population [3]. At the same time, social media platforms such as Telegram have become a popular way for people to express their feeling and emotions. Telegram is a free, end-to-end encrypted messaging service that allows users to send and receive messages and media files in private chats or groups that can be focused on particular topics and allow any user to observe or actively participate. These characteristics make Telegram a suitable source for text-mining [4].</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Mental Health</kwd>
        <kwd>Natural Language Processing</kwd>
        <kwd>Depression</kwd>
        <kwd>Social Media</kwd>
        <kwd>Machine Learning</kwd>
        <kwd>Deep Learning</kwd>
        <kwd>Transformers</kwd>
        <kwd>Sentence Embeddings</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        With this context, an interesting approach is to use Natural Language Processing (NLP)
techniques to analyze the language used by people who sufer from mental illness and discover
patterns that can be used to identify them and provide the necessary support. The MentalRiskES
task at IberLEF 2023 [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] aims to promote the development of NLP solutions specifically for
Spanish-speaking social media. They propose three main areas of focus for early-risk detection:
eating disorders (Task 1), depression (Task 2), and non-defined disorders (Task 3).
      </p>
      <p>
        In this work, we present our proposed solution to Task 2 of the 2023 edition of MentalRiskES.
This task involves evaluating the likelihood of a Telegram user experiencing depression based
on their comments within mental-health-focused groups. The task is split into four predictive
subtasks (2a, 2b, 2c, 2d) according to the type of output required. Our main contributions and
ifndings can be then summarized threefold:
1. We conducted experiments using various language models based on BERT [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] to solve
the task. We found that a RoBERTa model [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] that had been previously fine-tuned on a
Spanish corpus to identify suicide behavior [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] tended to yield the most accurate results.
This suggests that fine-tuning for an intermediate task can improve results for related
tasks, which is supported by existing literature [
        <xref ref-type="bibr" rid="ref10 ref9">9, 10</xref>
        ].
2. Our approach to solving the task consisted of training only with the labels of the regression
subtasks (2b, 2d), as we deemed them the most informative. Additionally, we show that
you can use the labels of 2d to recover the labels of the other three subtasks. The models
trained to target task 2d achieved the best results across all subtasks, even outperforming
those that targeted 2b in the simple regression metrics.
3. We attempted two diferent predictive modeling approaches to solve the task using the
language model (LM) mentioned above. The first one involved extracting the sentence
embeddings of the messages of each user and using them as features to train and evaluate
classic linear and non-linear machine-learning regressors. In the second one, we
finetuned the LM directly for the subtask. The first approach proved advantageous in terms
of allowing for quicker, more comprehensive experimentation and resulted in models
that achieved the best overall performance when evaluated on the test set.
      </p>
      <p>The rest of the paper is organized as follows: In the next section, we analyze the dataset used
for the task (Section 2). Then, we describe in detail our methodology for training and evaluating
the models (Section 3). Finally, we discuss the results obtained (Section 4) and present our
conclusions and future lines of work (Section 5).</p>
    </sec>
    <sec id="sec-2">
      <title>2. Dataset Analysis</title>
      <p>The dataset given for the task consisted of a total of 6,248 individual messages from 175 Telegram
users, each with a variable number of messages (see figure 1). The annotation process consisted
of labeling each user based on the evidence from their conversation history of sufering from
depression. Thus, a total of 10 annotators were used for the tasks. Each was asked to assign one
of the following four labels to each user:
• sufer+in favour : Indicates evidence (from text messages) of the user sufering from
depression but is also receptive/willing to help and overcome it.
• sufer+against : Indicates evidence of the user sufering from depression but is against
receiving or providing help to overcome it.
• sufer+other : Indicates evidence of the user sufering from depression, but there’s not
enough information to assign them to any further category (against or in favour)
• control: Indicates no evidence of the user sufering from depression.</p>
      <p>Furthermore, these labels were represented diferently to support each of the four subtasks of
MentalRiskES: simple classification ( task 2a), binary regression (task 2b), multiclass classification
(task 2c), and multi-output regression (task 2d).</p>
      <p>
        In the classification tasks (2a, 2c), the label assigned to each user was the class that obtained
the majority vote from the annotators, with the labels being "1" for the "sufer" classes and "0"
for the control in the case of task 2a. For the regression tasks (2b, 2d), the values of the labels
were presented as numeric probabilities in [
        <xref ref-type="bibr" rid="ref1 ref24">0, 1</xref>
        ] representing the confidence of the respective
class. They were calculated by adding the number of annotators who gave the classification and
dividing by 10 (the total number of annotators). For task 2b, this was presented as one number
representing the probability of sufering from depression, while for task 2d, each subject label
was presented with four numbers representing the probability of each class. Appendix A shows
examples of how this data was given.
      </p>
      <p>The following figure displays the label distribution for each task in the training set. We can
see how over 94 (∼ 54%) of users were classified as having depression. Furthermore, there is an
imbalance in the labels for the classification tasks due to the "sufer" label being divided into
diferent categories (leading to an over-representation of the "control" label). Additionally, the
"sufer+other" category is underrepresented when compared to the other three.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Methodology</title>
      <p>We proceeded to evaluate diferent techniques to solve each of the four subtasks. Two main
predictive-modeling approaches were explored: The first one involved fine-tuning a pre-trained
language model on each subtask and the second was about training a standard ML regressor
using sentence embeddings encoded from the user’s messages as features. The following section
describes the steps taken for each approach, first describing how the data was pre-processed
and later explaining the training and evaluation process done for each subtask.</p>
      <sec id="sec-3-1">
        <title>3.1. Data Processing and Augmentation</title>
        <p>Independent of the approach taken to train the models, the data was pre-processed and
augmented in the same way. The first thing we did was group all the messages by the user they
belonged to and concatenated them into a single string, obtaining a total of 175 messages (one
per user). This was done to obtain a single representation of each user’s conversation history
(from which the labels were assigned) to be able to use it as input for the models.</p>
        <p>
          To prepare for training, the data was split into training and validation sets, leaving a random
26 (15%) users in the latter for stratified cross-validation, where each set receives the same
proportion of samples of each class [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ]. The stratification was done using the labels of task c
to ensure equal representation of the classes in both sets.
        </p>
        <p>To increase the amount of data available for training and, at the same time, attempt to model
early detection (obtaining predictions early on in the lifetime of the message history), we
augmented the training set by adding observations that only contained half of their messages.
This was done by first sorting the messages of each user in the training set by its date and then
only taking the first half, the resulting dataset was then appended to the original training set to
obtain a new one with twice the number of observations to be used for training.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Solving all substaks by solving for regression</title>
        <p>By the discussion in section 2, it should be clear to see that not all labels of the subtasks give the
same amount of information about the condition of the subject and the likelihood of predicting
it based on the available data. Indeed, it’s clear that the probability values of task 2b give more
information about confidence in predicting depression than the simple binary labels of task 2a.
For the same reasons, the labels of task 2d are more informative than those of task 2c as they
give the full probability distribution across the four classes.</p>
        <p>Furthermore, we can show that it’s possible to use the multi-output regression labels (2d) to
recover the labels of the other three subtasks. To illustrate, the multiclass classification labels of
task 2c can be recovered by selecting the class in the distribution that has the highest probability.
Moreover, we can obtain the labels of task 2a by simply converting these classes into binary
(1 for the "sufer" classes and 0 for all others). Lastly, the labels of task 2b can be obtained by
summing the probabilities of the "sufer" classes in the distribution. We have confirmed this by
applying these modifications to the labels of the training set for task 2d and comparing them to
the original labels of the other three tasks.</p>
        <p>
          This observation led us to consider using models that solve for more than one subtask by
only training it with the labels of task 2b or 2d. This allowed us to reduce the number of models
that had to be trained and focus on solving for a single data modality (regression on [
          <xref ref-type="bibr" rid="ref1 ref24">0, 1</xref>
          ]).
        </p>
        <p>
          We approached simple regression in a standard way training models, training models to
minimize the Mean Squared Error between the output values and the real ones. Additionally,
we included the post-processing step of clipping the output predictions of models of this type
to the [
          <xref ref-type="bibr" rid="ref1 ref24">0,1</xref>
          ] range to ensure that they were valid probabilities.
        </p>
        <p>Multi-output regression using standard machine learning regression, on the other hand,
wasn’t as trivial as in the simple regression case. The models we worked on didn’t support
multi-output regression out of the box. The approach we did involve training four regressors for
each model, one for each class, and then combining the predictions. We explored two methods
for this: training independent regressors or training them in a chain as explained by figure 3.
The full details of the process are described in appendix D.</p>
        <p>Finally, similar to the simple regression case, the predictions of the multi-output models
were post-processed by dividing each of the four values by their sum to obtain a vector whose
^
values add up to one. That is, ^ = ∑︀ ^ for each -th class. This was done to ensure that the
predictions were valid probability distributions over the classes.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Modeling Approaches</title>
        <sec id="sec-3-3-1">
          <title>3.3.1. Training a regressor with sentence embeddings</title>
          <p>
            A sentence embedding is a semantically meaningful real-valued vector representation of a
sentence, obtained from the outputs of the hidden layers of a language model. The properties of
this representation are so that sentences that express similar meanings are mapped (encoded)
closer to each other in the vector space [
            <xref ref-type="bibr" rid="ref13">13</xref>
            ].
          </p>
          <p>In this way, the process of encoding text as numeric vectors can be used directly to extract
features for a classifier or regressor, which will try to learn from the semantic information of
these encodings to predict the label of their corresponding messages. Note, however, that this
approach requires the need to have a pre-trained model to perform this encoding. Furthermore,
it assumes that the model will be good enough at capturing the semantic information of the
texts given as input, enough for the classifier/regressor to learn from it.</p>
          <p>Assuming that this is the case, this approach has the advantage that it is much faster to
train these kinds of regressors with regular CPUs, with the most time-consuming part being
obtaining the embeddings of the training/evaluation messages, which only has to be done once.
However, it is necessary to evaluate diferent encoding models and diferent classifiers/regressors
(prediction models) to find the best combination for the task at hand.</p>
          <p>
            As such, we conducted experiments using diferent language models to find the best encoding
model. Particularly, we tested three diferent versions of BERT [
            <xref ref-type="bibr" rid="ref6">6</xref>
            ] trained with diferent corpora
in Spanish. These versions are described in table 1. Additionally, we experimented with over
10 diferent regressors, including Least Squares Linear regression [
            <xref ref-type="bibr" rid="ref14">14</xref>
            ], Random Forest [
            <xref ref-type="bibr" rid="ref15">15</xref>
            ],
and Gradient Boosting [
            <xref ref-type="bibr" rid="ref16">16</xref>
            ], among others. These models were chosen due to their ease of
implementation and the fact that they are commonly used in the literature [
            <xref ref-type="bibr" rid="ref17">17</xref>
            ].
          </p>
          <p>The process of training and evaluating these models proceeded then as follows: First, the
training set was encoded using the language model and the resulting embeddings were used as
features for a regressor. The regressor was then trained using the labels of task 2d (the most
informative ones) and the resulting model was used to predict the labels of the validation set.
The predictions were then evaluated with the root mean squared error (RMSE). This process
was repeated for each combination of language model and regressor.</p>
          <p>Appendix B contains the results of this experiment. Based on that, roberta-suicide-es
was deemed to be the best model for encoding the texts. Additionally, appendix C shows a
detailed report of the evaluation of the best regression model with these embeddings.</p>
          <p>
            Description
RoBERTa-base-bne [
            <xref ref-type="bibr" rid="ref7">7</xref>
            ]
RoBERTa-suicide-es [
            <xref ref-type="bibr" rid="ref8">8</xref>
            ]
          </p>
          <p>
            BETO [
            <xref ref-type="bibr" rid="ref19">19</xref>
            ]
          </p>
          <p>
            RoBERTa model [
            <xref ref-type="bibr" rid="ref18">18</xref>
            ] trained with data from Spain’s National Library.
          </p>
          <p>RoBERTa-base-bne fine-tuned for suicide detection.</p>
          <p>
            Variant of BERT [
            <xref ref-type="bibr" rid="ref6">6</xref>
            ] trained with Spanish corpora.
          </p>
        </sec>
        <sec id="sec-3-3-2">
          <title>3.3.2. Fine-tuning a Language Model for Regression</title>
          <p>
            Apart from the approach mentioned above, we also experimented with the pure Deep Learning
(DL) approach of taking a language model and fine-tuning it with the labels of the corresponding
subtask. The model we fine-tuned was a version of RoBERTa pre-trained for detecting suicidal
behavior from texts in Spanish [
            <xref ref-type="bibr" rid="ref8">8</xref>
            ]. We chose this model due to the fact of having been trained
previously for a task that shares similar characteristics to ours. Intermediate fine-tuning has
been proven to improve the results of downstream tasks by prior literature [
            <xref ref-type="bibr" rid="ref10 ref9">9, 10</xref>
            ].
          </p>
          <p>
            The HuggingFace Transformers [
            <xref ref-type="bibr" rid="ref20">20</xref>
            ] and Pytorch [
            <xref ref-type="bibr" rid="ref21">21</xref>
            ] libraries in Python were utilized for
loading the model weights and implementing the training loop. We changed the head of the
pre-trained model to a linear layer consisting of output dimension 1 for simple regression or
dimension 4 for multi-output regression. The models were trained using an NVIDIA T4 GPU
for a total of 30 epochs, where the weights of the pre-trained model remained fully frozen for
the first half and then were progressively unfrozen each epoch after that as in [
            <xref ref-type="bibr" rid="ref22">22</xref>
            ].
          </p>
          <p>Hyperparameters</p>
          <p>Optimizer
Learning rate
Max Tokens
Num Epochs
Batch Size</p>
          <p>Value
AdamW
1− 5
1024
30
1</p>
          <p>We used an Adam Optimizer with Mean-Squared Error (MSE) for the simple regression
models and a Cross-Entropy loss function for multi-regression (since the labels consisted of
numeric probabilities). Furthermore, since the output for task 2d consisted of a probability
distribution over the four classes, we experimented with a custom loss function that adds a
term to the standard cross-entropy loss to penalize outputs whose sum is diferent from one.
However, this did not improve the results empirically as compared with simply normalizing
the outputs of the predictions after inference. The formula of this loss is shown in equation 1.
Other hyperparameters are shown in table 2.</p>
          <p>
            ℒcustom = ℒ−  +  (1 −
∑︁ ^)2
∈[
            <xref ref-type="bibr" rid="ref1 ref24 ref4">1,4</xref>
            ]
(1)
          </p>
          <p>In the equation above, ^ is the output of the model,  is the target label,  is a hyperparameter
that controls the weight of the penalty term, and  is the -th element of the target label.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Results</title>
      <p>Using the approaches mentioned in the prior section, we came up with diferent models to solve
the four subtasks of Task 2 of MentalRiskES. The results in this section are obtained from
selecting the best-performing models after evaluating the diferent approaches and hyperparameters
on the validation set. The final predictions were obtained from a test set of messages from 149
subjects never observed during the training process and evaluated against the task’s true labels.</p>
      <p>
        In the tables below, we report the relevant metrics obtained for each subtask and compare them
against the ones obtained from baseline models provided by the organizers of the competition.
In particular, we report both absolute metrics, obtained after observing all the messages of each
subject, and early detection metrics, obtained after incrementally observing the messages across
several rounds. Additionally, table 11 displays the inference-time CO2 emissions and energy
consumption of each model, based on computing their absolute predictions on the test set. These
values were estimated using the codecarbon python library [
        <xref ref-type="bibr" rid="ref23">23</xref>
        ].
      </p>
      <p>
        For the absolute metrics, we show the accuracy, precision, recall, and F1 scores for the
classification tasks (2a and 2c) and the root mean squared error (RMSE) and coeficient of
determination (2) for the regression tasks (2b and 2d). The early detection metrics include the
early-risk detection metric (erde) computed after observing diferent rounds of messages as well
as other metrics (more details are provided in the competition guidelines [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]).
      </p>
      <p>The metrics are shown along with the name of the model used to obtain them. The models
are named as follows: [task name]_[model name]_[approach]. For example,
task2b_robertasuicide-es_fine-tuning refers to the model trained with the task 2b (binary classification) labels
by fine-tuning the Roberta model pre-trained for suicide detection. The " approach" can be either
embeddings or fine-tuning for the two approaches described in section 3.</p>
      <p>Furthermore, all ML regressors trained with embeddings as features were Ridge regressors,
and all embeddings were obtained using roberta-suicide-es encodings as this combination
yielded the best results in the evaluation set. The embeddings approaches for task 2d also include
the multi-regression method used (ind indicating that independent regressors were used and
chain for chained regressors).</p>
      <sec id="sec-4-1">
        <title>4.1. Results for task 2a: binary classification</title>
        <sec id="sec-4-1-1">
          <title>2d_roberta_embeddings_ind</title>
          <p>BaseLine - Roberta Large</p>
        </sec>
        <sec id="sec-4-1-2">
          <title>2d_roberta_embeddings_chain</title>
        </sec>
        <sec id="sec-4-1-3">
          <title>2b_roberta_embeddings</title>
        </sec>
        <sec id="sec-4-1-4">
          <title>2d_roberta-suicide-es_fine-tuning</title>
          <p>BaseLine - Deberta</p>
        </sec>
        <sec id="sec-4-1-5">
          <title>2b_roberta-suicide-es_fine-tuning</title>
          <p>BaseLine - Roberta Base</p>
        </sec>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Results for task 2b: Simple Regression</title>
        <p>BaseLine - Roberta Base
BaseLine - Deberta
BaseLine - Roberta Large
2b_roberta-suicide-es_fine-tuning
2b_roberta_embeddings
2d_roberta_embeddings_ind
2d_roberta_embeddings_chain
2d_roberta-suicide-es_fine-tuning
3.000
3.000
2.000
3.000
3.000
2.000
4.000
4.000
RMSE</p>
        <p>r2</p>
      </sec>
      <sec id="sec-4-3">
        <title>4.3. Results for task 2c: Multiclass Classification</title>
      </sec>
      <sec id="sec-4-4">
        <title>4.4. Results for task 2d: Multi-output Regression.</title>
        <p>BaseLine - Deberta</p>
        <sec id="sec-4-4-1">
          <title>2d_roberta_embeddings_ind</title>
          <p>BaseLine - Roberta Large</p>
        </sec>
        <sec id="sec-4-4-2">
          <title>2d_roberta_embeddings_chain</title>
          <p>BaseLine - Roberta Base
2d_roberta-suicide-es_fine-tuning</p>
        </sec>
      </sec>
      <sec id="sec-4-5">
        <title>4.5. Carbon Emissions</title>
        <p>5. Conclusions
duration (secs) emissions (kgCO2eq) cpu_energy
ram_energy
The results show that the approaches considered in this work were successful at modeling each
of the predictive subtasks, with at least one of our models outperforming the baselines in most
cases. We can make the following observations:
• The best-performing approach across all tasks seems to be the one that uses the
embeddings of the messages as input to a multi-output regression model (task 2d). At least one
model trained with this approach reached the top ranking for tasks 2a, 2b, and 2d absolute
ranking metrics and outperformed the baseline absolute metrics across all tasks.
• Most notably, the regression method that uses multi-output chained regressors obtained
the best metrics for task 2d across all models, outperforming the fine-tuning approach by
over 20% in the absolute metrics and reaching the second highest spot in the early-risk
metrics for this task.
• Models trained for multi-output regression perform very well for binary classification
and simple regression tasks, even outperforming the models trained for simple regression
targets in their own subtask. This suggests that using one model to solve for multiple
targets was indeed a good approach to this problem.
• The models obtained with a pure DL approach from fine-tuning a RoBERTa model are
estimated to produce over 3-4x less emissions at inference time than the hybrid approach
from training linear regressors on sentence embeddings. This gap is likely because
the fine-tuning approach requires less computation at inference time than the hybrid
approach, which requires the computation of the sentence embeddings before feeding
them to multiple regressors, while the fine-tuning approach is made in one forward pass.</p>
        <p>Another finding we can conclude from these insights is that while our models achieve great
results in the absolute ranking metrics, they do not perform as well for the metrics that assess
early-risk performance. In our work, we did not model explicitly for an early detection scenario;
we only added information about prior messages through data augmentation. This limitation
means our models may not perform as well in real-world situations where we aim to detect
signs of depression in a conversation early on.</p>
        <p>
          Thus, it may be important to explore diferent training approaches to improve the
performance of early-risk detection. This might include directly employing online learning to predict
and update the model as new messages come in or incorporating an ensemble of models to
make independent decisions about a message’s risk level and combining them for a final
decision (as seen in [
          <xref ref-type="bibr" rid="ref23">23</xref>
          ]). Additionally, we may also look into more eficient implementations
of the hybrid approach to minimize the disparity in emissions compared to pure DL models.
These improvements are crucial when considering the deployment of our models in real-world
situations and will be the focus of future work.
},
{
},
        </p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>A. Dataset Examples</title>
      <p>The data was given in JSON format after requesting the server. The following examples are
meant to show the structure of how the data was given and later parsed.</p>
      <p>"id_message": "1",
"message": "Me parece que es una buena idea, pero no estoy seguro",
"date": "2020-07-27 01:27:31"
"id_message": 2,
"message": "Buen dia a todos",
"date": "2020-07-27 02:03:28"
Example of the raw data describing the messages of one user. The original training set
(later split into training+validation) constituted 175 JSON files like this.</p>
      <p>To complement the files described in the example above, the labels of each subject were given
in CSV format, where each row corresponded to one subject. Four of these files were given, one
for each task. Table 12 below shows some examples of this.</p>
      <p>a_label b_label c_label</p>
      <p>d_sufer_in_favour d_sufer_against d_sufer_other d_control
subject_id
subject101 1
subject104 1
subject106 1
subject108 1
subject109 0</p>
    </sec>
    <sec id="sec-6">
      <title>B. Evaluation of Embedding Models for Regression</title>
    </sec>
    <sec id="sec-7">
      <title>C. Evaluation of Regression models trained with the Sentence</title>
    </sec>
    <sec id="sec-8">
      <title>Embeddings Approach</title>
      <p>
        The estimators mentioned in the table above are implementations of common regressors
from Python’s Scikit-Learn library [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ]. These include: Ordinary ("lr") and Ridge ("ridge")
Least Squares Regression, Ada-Boost regression ("ada"), Light Gradient Boosting Machine
("lgbm"), Support Vector Regression ("svr"), Random Forests ("rf"), and a Multi-Layer Perceptron
("mlp"). References of the implementations of these models can be found in the Scikit-Learn
documentation.
      </p>
    </sec>
    <sec id="sec-9">
      <title>D. Multi-Output Regression with Independent Regressors and</title>
    </sec>
    <sec id="sec-10">
      <title>Regressor Chains</title>
      <p>For task 2d, we were required to obtain four values corresponding to a probability distribution
over the four classes (sufer+in favour, sufer+against, sufer+other, control). In section 3.2, we
explained how this multi-output regression problem can be solved for the sentence embeddings
approach by training four regressors and then combining their predictions using either the
Independent Regressors or Regressor Chain methods.</p>
      <p>Here we explain how these methods work and were implemented. First of all, the two
methods can be summarized as follows, depending on how the regressors are trained to obtain
the probability distributions. Figure 3 shows a graphical representation of the two methods.</p>
      <p>
        To the second method, we can additionally add the option of applying Principal Component
Analysis (PCA) to reduce the dimensionality of the input embeddings before training the models
in the chain. Because the embeddings might have a large dimensionality, this is done to make
these models more likely to use the information of the previous predictions. Both methods
were implemented with the Scikit-Learn library [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] using the MultiOutputRegressor and
RegressorChain classes. The number of components to keep for PCA was chosen using based
on the percent of variance explained. The number of components was fine-tuned and the best
results was obtained with 40 components (85% of variance).
      </p>
    </sec>
  </body>
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