prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. What data was presented to the subjects to elicit event-related responses?
Context 1: Introduction
Decoding intended speech or motor activity from brain signals is one of the major research areas in Brain Computer Interface (BCI) systems BIBREF0 , BIBREF1   In particular, speech-related BCI technologies attempt to provide effective vocal communication strategies for controlling external devices through speech commands interpreted from brain signals BIBREF2   Not only do they provide neuro-prosthetic help for people with speaking disabilities and neuro-muscular disorders like locked-in-syndrome, nasopharyngeal cancer, and amytotropic lateral sclerosis (ALS), but also equip people with a better medium to communicate and express thoughts, thereby improving the quality of rehabilitation and clinical neurology BIBREF3 , BIBREF4   Such devices also have applications in entertainment, preventive treatments, personal communication, games, etc  Furthermore, BCI technologies can be utilized in silent communication, as in noisy environments, or situations where any sort of audio-visual communication is infeasible 
Among the various brain activity-monitoring modalities in BCI, electroencephalography (EEG) BIBREF5 , BIBREF6 has demonstrated promising potential to differentiate between various brain activities through measurement of related electric fields  EEG is non-invasive, portable, low cost, and provides satisfactory temporal resolution  This makes EEG suitable to realize BCI systems  EEG data, however, is challenging: these data are high dimensional, have poor SNR, and suffer from low spatial resolution and a multitude of artifacts  For these reasons, it is not particularly obvious how to decode the desired information from raw EEG signals  Although the area of BCI based speech intent recognition has received increasing attention among the research community in the past few years, most research has focused on classification of individual speech categories in terms of discrete vowels, phonemes and words BIBREF7 , BIBREF8 , BIBREF9 , BIBREF10 , BIBREF11 , BIBREF12 , BIBREF13 , BIBREF14 , BIBREF15   This includes categorization of imagined EEG signal into binary vowel categories like /a/, /u/ and rest BIBREF7 , BIBREF8 , BIBREF9 ; binary syllable classes like /ba/ and /ku/ BIBREF1 , BIBREF10 , BIBREF11 , BIBREF12 ; a handful of control words like 'up', 'down', 'left', 'right' and 'select' BIBREF15 or others like 'water', 'help', 'thanks', 'food', 'stop' BIBREF13 , Chinese characters BIBREF14 , etc  Such works mostly involve traditional signal processing or manual feature handcrafting along with linear classifiers (e g , SVMs)  In our recent work BIBREF16 , we introduced deep learning models for classification of vowels and words that achieved 23 45% improvement of accuracy over the baseline 
Production of articulatory speech is an extremely complicated process, thereby rendering understanding of the discriminative EEG manifold corresponding to imagined speech highly challenging  As a result, most of the existing approaches failed to achieve satisfactory accuracy on decoding speech tokens from the speech imagery EEG data  Perhaps, for these reasons, very little work has been devoted to relating the brain signals to the underlying articulation  The few exceptions include BIBREF17 , BIBREF18   In BIBREF17 , Zhao et al  used manually handcrafted features from EEG data, combined with speech audio and facial features to achieve classification of the phonological categories varying based on the articulatory steps  However, the imagined speech classification accuracy based on EEG data alone, as reported in BIBREF17 , BIBREF18 , are not satisfactory in terms of accuracy and reliability  We now turn to describing our proposed models 
Proposed Framework
Cognitive learning process underlying articulatory speech production involves incorporation of intermediate feedback loops and utilization of past information stored in the form of memory as well as hierarchical combination of several feature extractors  To this end, we develop our mixed neural network architecture composed of three supervised and a single unsupervised learning step, discussed in the next subsections and shown in Fig  FIGREF1   We formulate the problem of categorizing EEG data based on speech imagery as a non-linear mapping INLINEFORM0 of a multivariate time-series input sequence INLINEFORM1 to fixed output INLINEFORM2 , i e, mathematically INLINEFORM3 : INLINEFORM4 , where c and t denote the EEG channels and time instants respectively 
Preprocessing step
We follow similar pre-processing steps on raw EEG data as reported in BIBREF17 (ocular artifact removal using blind source separation, bandpass filtering and subtracting mean value from each channel) except that we do not perform Laplacian filtering step since such high-pass filtering may decrease information content from the signals in the selected bandwidth 
Joint variability of electrodes
Multichannel EEG data is high dimensional multivariate time series data whose dimensionality depends on the number of electrodes  It is a major hurdle to optimally encode information from these EEG data into lower dimensional space  In fact, our investigation based on a development set (as we explain later) showed that well-known deep neural networks (e g , fully connected networks such as convolutional neural networks, recurrent neural networks and autoencoders) fail to individually learn such complex feature representations from single-trial EEG data  Besides, we found that instead of using the raw multi-channel high-dimensional EEG requiring large training times and resource requirements, it is advantageous to first reduce its dimensionality by capturing the information transfer among the electrodes  Instead of the conventional approach of selecting a handful of channels as BIBREF17 , BIBREF18 , we address this by computing the channel cross-covariance, resulting in positive, semi-definite matrices encoding the connectivity of the electrodes  We define channel cross-covariance (CCV) between any two electrodes INLINEFORM0 and INLINEFORM1 as: INLINEFORM2   Next, we reject the channels which have significantly lower cross-covariance than auto-covariance values (where auto-covariance implies CCV on same electrode)  We found this measure to be essential as the higher cognitive processes underlying speech planning and synthesis involve frequent information exchange between different parts of the brain  Hence, such matrices often contain more discriminative features and hidden information than mere raw signals  This is essentially different than our previous work BIBREF16 where we extract per-channel 1-D covariance information and feed it to the networks  We present our sample 2-D EEG cross-covariance matrices (of two individuals) in Fig  FIGREF2  
CNN & LSTM
In order to decode spatial connections between the electrodes from the channel covariance matrix, we use a CNN BIBREF19 , in particular a four-layered 2D CNN stacking two convolutional and two fully connected hidden layers  The INLINEFORM0 feature map at a given CNN layer with input INLINEFORM1 , weight matrix INLINEFORM2 and bias INLINEFORM3 is obtained as: INLINEFORM4   At this first level of hierarchy, the network is trained with the corresponding labels as target outputs, optimizing a cross-entropy cost function  In parallel, we apply a four-layered recurrent neural network on the channel covariance matrices to explore the hidden temporal features of the electrodes  Namely, we exploit an LSTM BIBREF20 consisting of two fully connected hidden layers, stacked with two LSTM layers and trained in a similar manner as CNN 
Deep autoencoder for spatio-temporal information
As we found the individually-trained parallel networks (CNN and LSTM) to be useful (see Table TABREF12 ), we suspected the combination of these two networks could provide a more powerful discriminative spatial and temporal representation of the data than each independent network  As such, we concatenate the last fully-connected layer from the CNN with its counterpart in the LSTM to compose a single feature vector based on these two penultimate layers  Ultimately, this forms a joint spatio-temporal encoding of the cross-covariance matrix 
In order to further reduce the dimensionality of the spatio-temporal encodings and cancel background noise effects BIBREF21 , we train an unsupervised deep autoenoder (DAE) on the fused heterogeneous features produced by the combined CNN and LSTM information  The DAE forms our second level of hierarchy, with 3 encoding and 3 decoding layers, and mean squared error (MSE) as the cost function 
Classification with Extreme Gradient Boost
At the third level of hierarchy, the discrete latent vector representation of the deep autoencoder is fed into an Extreme Gradient Boost based classification layer BIBREF22 , BIBREF23 motivated by BIBREF21   It is a regularized gradient boosted decision tree that performs well on structured problems  Since our EEG-phonological pairwise classification has an internal structure involving individual phonemes and words, it seems to be a reasonable choice of classifier  The classifier receives its input from the latent vectors of the deep autoencoder and is trained in a supervised manner to output the final predicted classes corresponding to the speech imagery 
Dataset
We evaluate our model on a publicly available dataset, KARA ONE BIBREF17 , composed of multimodal data for stimulus-based, imagined and articulated speech state corresponding to 7 phonemic/syllabic ( /iy/, /piy/, /tiy/, /diy/, /uw/, /m/, /n/ ) as well as 4 words(pat, pot, knew and gnaw)  The dataset consists of 14 participants, with each prompt presented 11 times to each individual  Since our intention is to classify the phonological categories from human thoughts, we discard the facial and audio information and only consider the EEG data corresponding to imagined speech  It is noteworthy that given the mixed nature of EEG signals, it is reportedly challenging to attain a pairwise EEG-phoneme mapping BIBREF18   In order to explore the problem space, we thus specifically target five binary classification problems addressed in BIBREF17 , BIBREF18 , i e presence/absence of consonants, phonemic nasal, bilabial, high-front vowels and high-back vowels 
Training and hyperparameter selection
We performed two sets of experiments with the single-trial EEG data  In PHASE-ONE, our goals was to identify the best architectures and hyperparameters for our networks with a reasonable number of runs  For PHASE-ONE, we randomly shuffled and divided the data (1913 signals from 14 individuals) into train (80%), development (10%) and test sets (10%)  In PHASE-TWO, in order to perform a fair comparison with the previous methods reported on the same dataset, we perform a leave-one-subject out cross-validation experiment using the best settings we learn from PHASE-ONE 
The architectural parameters and hyperparameters listed in Table TABREF6 were selected through an exhaustive grid-search based on the validation set of PHASE-ONE  We conducted a series of empirical studies starting from single hidden-layered networks for each of the blocks and, based on the validation accuracy, we increased the depth of each given network and selected the optimal parametric set from all possible combinations of parameters  For the gradient boosting classification, we fixed the maximum depth at 10, number of estimators at 5000, learning rate at 0 1, regularization coefficient at 0 3, subsample ratio at 0 8, and column-sample/iteration at 0 4  We did not find any notable change of accuracy while varying other hyperparameters while training gradient boost classifier 
Performance analysis and discussion
To demonstrate the significance of the hierarchical CNN-LSTM-DAE method, we conducted separate experiments with the individual networks in PHASE-ONE of experiments and summarized the results in Table TABREF12 From the average accuracy scores, we observe that the mixed network performs much better than individual blocks which is in agreement with the findings in BIBREF21   A detailed analysis on repeated runs further shows that in most of the cases, LSTM alone does not perform better than chance  CNN, on the other hand, is heavily biased towards the class label which sees more training data corresponding to it  Though the situation improves with combined CNN-LSTM, our analysis clearly shows the necessity of a better encoding scheme to utilize the combined features rather than mere concatenation of the penultimate features of both networks 
The very fact that our combined network improves the classification accuracy by a mean margin of 14 45% than the CNN-LSTM network indeed reveals that the autoencoder contributes towards filtering out the unrelated and noisy features from the concatenated penultimate feature set  It also proves that the combined supervised and unsupervised neural networks, trained hierarchically, can learn the discriminative manifold better than the individual networks and it is crucial for improving the classification accuracy  In addition to accuracy, we also provide the kappa coefficients BIBREF24 of our method in Fig  FIGREF14   Here, a higher mean kappa value corresponding to a task implies that the network is able to find better discriminative information from the EEG data beyond random decisions  The maximum above-chance accuracy (75 92%) is recorded for presence/absence of the vowel task and the minimum (49 14%) is recorded for the INLINEFORM0  
To further investigate the feature representation achieved by our model, we plot T-distributed Stochastic Neighbor Embedding (tSNE) corresponding to INLINEFORM0 and V/C classification tasks in Fig  FIGREF8   We particularly select these two tasks as our model exhibits respectively minimum and maximum performance for these two  The tSNE visualization reveals that the second set of features are more easily separable than the first one, thereby giving a rationale for our performance 
Next, we provide performance comparison of the proposed approach with the baseline methods for PHASE-TWO of our study (cross-validation experiment) in Table TABREF15   Since the model encounters the unseen data of a new subject for testing, and given the high inter-subject variability of the EEG data, a reduction in the accuracy was expected  However, our network still managed to achieve an improvement of 18 91, 9 95, 67 15, 2 83 and 13 70 % over BIBREF17   Besides, our best model shows more reliability compared to previous works: The standard deviation of our model's classification accuracy across all the tasks is reduced from 22 59% BIBREF17 and 17 52% BIBREF18 to a mere 5 41% 
Conclusion and future direction
In an attempt to move a step towards understanding the speech information encoded in brain signals, we developed a novel mixed deep neural network scheme for a number of binary classification tasks from speech imagery EEG data  Unlike previous approaches which mostly deal with subject-dependent classification of EEG into discrete vowel or word labels, this work investigates a subject-invariant mapping of EEG data with different phonological categories, varying widely in terms of underlying articulator motions (eg: involvement or non-involvement of lips and velum, variation of tongue movements etc)  Our model takes an advantage of feature extraction capability of CNN, LSTM as well as the deep learning benefit of deep autoencoders  We took BIBREF17 , BIBREF18 as the baseline works investigating the same problem and compared our performance with theirs  Our proposed method highly outperforms the existing methods across all the five binary classification tasks by a large average margin of 22 51% 
Acknowledgments
This work was funded by the Natural Sciences and Engineering Research Council (NSERC) of Canada and Canadian Institutes for Health Research (CIHR) 

ground_truth: 7 phonemic/syllabic ( /iy/, /piy/, /tiy/, /diy/, /uw/, /m/, /n/ ) as well as 4 words(pat, pot, knew and gnaw)

KARA ONE BIBREF17 , composed of multimodal data for stimulus-based, imagined and articulated speech state corresponding to 7 phonemic/syllabic ( /iy/, /piy/, /tiy/, /diy/, /uw/, /m/, /n/ ) as well as 4 words(pat, pot, knew and gnaw)

prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. How much data is needed to train the task-specific encoder?
Context 2: Introduction
Assembling training corpora of annotated natural language examples in specialized domains such as biomedicine poses considerable challenges  Experts with the requisite domain knowledge to perform high-quality annotation tend to be expensive, while lay annotators may not have the necessary knowledge to provide high-quality annotations  A practical approach for collecting a sufficiently large corpus would be to use crowdsourcing platforms like Amazon Mechanical Turk (MTurk)  However, crowd workers in general are likely to provide noisy annotations BIBREF0 , BIBREF1 , BIBREF2 , an issue exacerbated by the technical nature of specialized content  Some of this noise may reflect worker quality and can be modeled BIBREF0 , BIBREF1 , BIBREF3 , BIBREF4 , but for some instances lay people may simply lack the domain knowledge to provide useful annotation 
In this paper we report experiments on the EBM-NLP corpus comprising crowdsourced annotations of medical literature BIBREF5   We operationalize the concept of annotation difficulty and show how it can be exploited during training to improve information extraction models  We then obtain expert annotations for the abstracts predicted to be most difficult, as well as for a similar number of randomly selected abstracts  The annotation of highly specialized data and the use of lay and expert annotators allow us to examine the following key questions related to lay and expert annotations in specialized domains:
Can we predict item difficulty? We define a training instance as difficult if a lay annotator or an automated model disagree on its labeling  We show that difficulty can be predicted, and that it is distinct from inter-annotator agreement  Further, such predictions can be used during training to improve information extraction models 
Are there systematic differences between expert and lay annotations? We observe decidedly lower agreement between lay workers as compared to domain experts  Lay annotations have high precision but low recall with respect to expert annotations in the new data that we collected  More generally, we expect lay annotations to be lower quality, which may translate to lower precision, recall, or both, compared to expert annotations  Can one rely solely on lay annotations? Reasonable models can be trained using lay annotations alone, but similar performance can be achieved using markedly less expert data  This suggests that the optimal ratio of expert to crowd annotations for specialized tasks will depend on the cost and availability of domain experts  Expert annotations are preferable whenever its collection is practical  But in real-world settings, a combination of expert and lay annotations is better than using lay data alone 
Does it matter what data is annotated by experts? We demonstrate that a system trained on combined data achieves better predictive performance when experts annotate difficult examples rather than instances selected at i i d  random 
Our contributions in this work are summarized as follows  We define a task difficulty prediction task and show how this is related to, but distinct from, inter-worker agreement  We introduce a new model for difficulty prediction combining learned representations induced via a pre-trained `universal' sentence encoder BIBREF6 , and a sentence encoder learned from scratch for this task  We show that predicting annotation difficulty can be used to improve the task routing and model performance for a biomedical information extraction task  Our results open up a new direction for ensuring corpus quality  We believe that item difficulty prediction will likely be useful in other, non-specialized tasks as well, and that the most effective data collection in specialized domains requires research addressing the fundamental questions we examine here 
Related Work
Crowdsourcing annotation is now a well-studied problem BIBREF7 , BIBREF0 , BIBREF1 , BIBREF2   Due to the noise inherent in such annotations, there have also been considerable efforts to develop aggregation models that minimize noise BIBREF0 , BIBREF1 , BIBREF3 , BIBREF4  
There are also several surveys of crowdsourcing in biomedicine specifically BIBREF8 , BIBREF9 , BIBREF10   Some work in this space has contrasted model performance achieved using expert vs  crowd annotated training data BIBREF11 , BIBREF12 , BIBREF13   Dumitrache et al  Dumitrache:2018:CGT:3232718 3152889 concluded that performance is similar under these supervision types, finding no clear advantage from using expert annotators  This differs from our findings, perhaps owing to differences in design  The experts we used already hold advanced medical degrees, for instance, while those in prior work were medical students  Furthermore, the task considered here would appear to be of greater difficulty: even a system trained on $\sim $ 5k instances performs reasonably, but far from perfect  By contrast, in some of the prior work where experts and crowd annotations were deemed equivalent, a classifier trained on 300 examples can achieve very high accuracy BIBREF12  
More relevant to this paper, prior work has investigated methods for `task routing' in active learning scenarios in which supervision is provided by heterogeneous labelers with varying levels of expertise BIBREF14 , BIBREF15 , BIBREF16 , BIBREF17 , BIBREF14   The related question of whether effort is better spent collecting additional annotations for already labeled (but potentially noisily so) examples or novel instances has also been addressed BIBREF18   What distinguishes the work here is our focus on providing an operational definition of instance difficulty, showing that this can be predicted, and then using this to inform task routing 
Application Domain
Our specific application concerns annotating abstracts of articles that describe the conduct and results of randomized controlled trials (RCTs)  Experimentation in this domain has become easy with the recent release of the EBM-NLP BIBREF5 corpus, which includes a reasonably large training dataset annotated via crowdsourcing, and a modest test set labeled by individuals with advanced medical training  More specifically, the training set comprises 4,741 medical article abstracts with crowdsourced annotations indicating snippets (sequences) that describe the Participants (p), Interventions (i), and Outcome (o) elements of the respective RCT, and the test set is composed of 191 abstracts with p, i, o sequence annotations from three medical experts 
Table 1 shows an example of difficult and easy examples according to our definition of difficulty  The underlined text demarcates the (consensus) reference label provided by domain experts  In the difficult examples, crowd workers marked text distinct from these reference annotations; whereas in the easy cases they reproduced them with reasonable fidelity  The difficult sentences usually exhibit complicated structure and feature jargon 
An abstract may contain some `easy' and some `difficult' sentences  We thus perform our analysis at the sentence level  We split abstracts into sentences using spaCy  We excluded sentences that comprise fewer than two tokens, as these are likely an artifact of errors in sentence splitting  In total, this resulted in 57,505 and 2,428 sentences in the train and test set abstracts, respectively 
Quantifying Task Difficulty
The test set includes annotations from both crowd workers and domain experts  We treat the latter as ground truth and then define the difficulty of sentences in terms of the observed agreement between expert and lay annotators  Formally, for annotation task $t$ and instance $i$ :
$$\text{Difficulty}_{ti} = \frac{\sum _{j=1}^n{f(\text{label}_{ij}, y_i})}{n}$$   (Eq  3)
where $f$ is a scoring function that measures the quality of the label from worker $j$ for sentence $i$ , as compared to a ground truth annotation, $y_i$   The difficulty score of sentence $i$ is taken as an average over the scores for all $n$ layworkers  We use Spearmans' correlation coefficient as a scoring function  Specifically, for each sentence we create two vectors comprising counts of how many times each token was annotated by crowd and expert workers, respectively, and calculate the correlation between these  Sentences with no labels are treated as maximally easy; those with only either crowd worker or expert label(s) are assumed maximally difficult 
The training set contains only crowdsourced annotations  To label the training data, we use a 10-fold validation like setting  We iteratively retrain the LSTM-CRF-Pattern sequence tagger of Patel et al  patel2018syntactic on 9 folds of the training data and use that trained model to predict labels for the 10th  In this way we obtain predictions on the full training set  We then use predicted spans as proxy `ground truth' annotations to calculate the difficulty score of sentences as described above; we normalize these to the [ $0, 1$ ] interval  We validate this approximation by comparing the proxy scores against reference scores over the test set, the Pearson's correlation coefficients are 0 57 for Population, 0 71 for Intervention and 0 68 for Outcome 
There exist many sentences that contain neither manual nor predicted annotations  We treat these as maximally easy sentences (with difficulty scores of 0)  Such sentences comprise 51%, 42% and 36% for Population, Interventions and Outcomes data respectively, indicating that it is easier to identify sentences that have no Population spans, but harder to identify sentences that have no Interventions or Outcomes spans  This is intuitive as descriptions of the latter two tend to be more technical and dense with medical jargon 
We show the distribution of the automatically labeled scores for sentences that do contain spans in Figure 1   The mean of the Population (p) sentence scores is significantly lower than that for other types of sentences (i and o), again indicating that they are easier on average to annotate  This aligns with a previous finding that annotating Interventions and Outcomes is more difficult than annotating Participants BIBREF5  
Many sentences contain spans tagged by the LSTM-CRF-Pattern model, but missed by all crowd workers, resulting in a maximally difficult score (1)  Inspection of such sentences revealed that some are truly difficult examples, but others are tagging model errors  In either case, such sentences have confused workers and/or the model, and so we retain them all as `difficult' sentences 
Content describing the p, i and o, respectively, is quite different  As such, one sentence usually contains (at most) only one of these three content types  We thus treat difficulty prediction for the respective label types as separate tasks 
Difficulty is not Worker Agreement
Our definition of difficulty is derived from agreement between expert and crowd annotations for the test data, and agreement between a predictive model and crowd annotations in the training data  It is reasonable to ask if these measures are related to inter-annotator agreement, a metric often used in language technology research to identify ambiguous or difficult items  Here we explicitly verify that our definition of difficulty only weakly correlates with inter-annotator agreement 
We calculate inter-worker agreement between crowd and expert annotators using Spearman's correlation coefficient  As shown in Table 2 , average agreement between domain experts are considerably higher than agreements between crowd workers for all three label types  This is a clear indication that the crowd annotations are noisier 
Furthermore, we compare the correlation between inter-annotator agreement and difficulty scores in the training data  Given that the majority of sentences do not contain a PICO span, we only include in these calculations those that contain a reference label  Pearson's r are 0 34, 0 30 and 0 31 for p, i and o, respectively, confirming that inter-worker agreement and our proposed difficulty score are quite distinct 
Predicting Annotation Difficulty
We treat difficulty prediction as a regression problem, and propose and evaluate neural model variants for the task  We first train RNN BIBREF19 and CNN BIBREF20 models 
We also use the universal sentence encoder (USE) BIBREF6 to induce sentence representations, and train a model using these as features  Following BIBREF6 , we then experiment with an ensemble model that combines the `universal' and task-specific representations to predict annotation difficulty  We expect these universal embeddings to capture general, high-level semantics, and the task specific representations to capture more granular information  Figure 2 depicts the model architecture  Sentences are fed into both the universal sentence encoder and, separately, a task specific neural encoder, yielding two representations  We concatenate these and pass the combined vector to the regression layer 
Experimental Setup and Results
We trained models for each label type separately  Word embeddings were initialized to 300d GloVe vectors BIBREF21 trained on common crawl data; these are fine-tuned during training  We used the Adam optimizer BIBREF22 with learning rate and decay set to 0 001 and 0 99, respectively  We used batch sizes of 16 
We used the large version of the universal sentence encoder with a transformer BIBREF23   We did not update the pretrained sentence encoder parameters during training  All hyperparamaters for all models (including hidden layers, hidden sizes, and dropout) were tuned using Vizier BIBREF24 via 10-fold cross validation on the training set maximizing for F1 
As a baseline, we also trained a linear Support-Vector Regression BIBREF25 model on $n$ -gram features ( $n$ ranges from 1 to 3) 
Table 3 reports Pearson correlation coefficients between the predictions with each of the neural models and the ground truth difficulty scores  Rows 1-4 correspond to individual models, and row 5 reports the ensemble performance  Columns correspond to label type  Results from all models outperform the baseline SVR model: Pearson's correlation coefficients range from 0 550 to 0 622  The regression correlations are the lowest 
The RNN model realizes the strongest performance among the stand-alone (non-ensemble) models, outperforming variants that exploit CNN and USE representations  Combining the RNN and USE further improves results  We hypothesize that this is due to complementary sentence information encoded in universal representations 
For all models, correlations for Intervention and Outcomes are higher than for Population, which is expected given the difficulty distributions in Figure 1   In these, the sentences are more uniformly distributed, with a fair number of difficult and easier sentences  By contrast, in Population there are a greater number of easy sentences and considerably fewer difficult sentences, which makes the difficulty ranking task particularly challenging 
Better IE with Difficulty Prediction
We next present experiments in which we attempt to use the predicted difficulty during training to improve models for information extraction of descriptions of Population, Interventions and Outcomes from medical article abstracts  We investigate two uses: (1) simply removing the most difficult sentences from the training set, and, (2) re-weighting the most difficult sentences 
We again use LSTM-CRF-Pattern as the base model and experimenting on the EBM-NLP corpus BIBREF5   This is trained on either (1) the training set with difficult sentences removed, or (2) the full training set but with instances re-weighted in proportion to their predicted difficulty score  Following BIBREF5 , we use the Adam optimizer with learning rate of 0 001, decay 0 9, batch size 20 and dropout 0 5  We use pretrained 200d GloVe vectors BIBREF21 to initialize word embeddings, and use 100d hidden char representations  Each word is thus represented with 300 dimensions in total  The hidden size is 100 for the LSTM in the character representation component, and 200 for the LSTM in the information extraction component  We train for 15 epochs, saving parameters that achieve the best F1 score on a nested development set 
Removing Difficult Examples
We first evaluate changes in performance induced by training the sequence labeling model using less data by removing difficult sentences prior to training  The hypothesis here is that these difficult instances are likely to introduce more noise than signal  We used a cross-fold approach to predict sentence difficulties, training on 9/10ths of the data and scoring the remaining 1/10th at a time  We then sorted sentences by predicted difficulty scores, and experimented with removing increasing numbers of these (in order of difficulty) prior to training the LSTM-CRF-Pattern model 
Figure 3 shows the results achieved by the LSTM-CRF-Pattern model after discarding increasing amounts of the training data: the $x$ and $y$ axes correspond to the the percentage of data removed and F1 scores, respectively  We contrast removing sentences predicted to be difficult with removing them (a) randomly (i i d ), and, (b) in inverse order of predicted inter-annotator agreement  The agreement prediction model is trained exactly the same like difficult prediction model, with simply changing the difficult score to annotation agreement  F1 scores actually improve (marginally) when we remove the most difficult sentences, up until we drop 4% of the data for Population and Interventions, and 6% for Outcomes  Removing training points at i i d  random degrades performance, as expected  Removing sentences in order of disagreement seems to have similar effect as removing them by difficulty score when removing small amount of the data, but the F1 scores drop much faster when removing more data  These findings indicate that sentences predicted to be difficult are indeed noisy, to the extent that they do not seem to provide the model useful signal 
Re-weighting by Difficulty
We showed above that removing a small number of the most difficult sentences does not harm, and in fact modestly improves, medical IE model performance  However, using the available data we are unable to test if this will be useful in practice, as we would need additional data to determine how many difficult sentences should be dropped 
We instead explore an alternative, practical means of exploiting difficulty predictions: we re-weight sentences during training inversely to their predicted difficulty  Formally, we weight sentence $i$ with difficulty scores above $\tau $ according to: $1-a\cdot (d_i-\tau )/(1-\tau )$ , where $d_i$ is the difficulty score for sentence $i$ , and $a$ is a parameter codifying the minimum weight value  We set $\tau $ to 0 8 so as to only re-weight sentences with difficulty in the top 20th percentile, and we set $a$ to 0 5  The re-weighting is equivalent to down-sampling the difficult sentences  LSTM-CRF-Pattern is our base model 
Table 4 reports the precision, recall and F1 achieved both with and without sentence re-weighting  Re-weighting improves all metrics modestly but consistently  All F1 differences are statistically significant under a sign test ( $p<0 01$ )  The model with best precision is different for Patient, Intervention and Outcome labels  However re-weighting by difficulty does consistently yield the best recall for all three extraction types, with the most notable improvement for i and o, where recall improved by 10 percentage points  This performance increase translated to improvements in F1 across all types, as compared to the base model and to re-weighting by agreement 
Involving Expert Annotators
The preceding experiments demonstrate that re-weighting difficult sentences annotated by the crowd generally improves the extraction models  Presumably the performance is influenced by the annotation quality 
We now examine the possibility that the higher quality and more consistent annotations of domain experts on the difficult instances will benefit the extraction model  This simulates an annotation strategy in which we route difficult instances to domain experts and easier ones to crowd annotators  We also contrast the value of difficult data to that of an i i d  random sample of the same size, both annotated by experts 
Expert annotations of Random and Difficult Instances
We re-annotate by experts a subset of most difficult instances and the same number of random instances  As collecting annotations from experts is slow and expensive, we only re-annotate the difficult instances for the interventions extraction task  We re-annotate the abstracts which cover the sentences with predicted difficulty scores in the top 5 percentile  We rank the abstracts from the training set by the count of difficult sentences, and re-annotate the abstracts that contain the most difficult sentences  Constrained by time and budget, we select only 2000 abstracts for re-annotation; 1000 of these are top-ranked, and 1000 are randomly sampled  This re-annotation cost $3,000  We have released the new annotation data at: https://github com/bepnye/EBM-NLP 
Following BIBREF5 , we recruited five medical experts via Up-work with advanced medical training and strong technical reading/writing skills  The expert annotator were asked to read the entire abstract and highlight, using the BRAT toolkit BIBREF26 , all spans describing medical Interventions  Each abstract is only annotated by one expert  We examined 30 re-annotated abstracts to ensure the annotation quality before hiring the annotator 
Table 5 presents the results of LSTM-CRF-Pattern model trained on the reannotated difficult subset and the random subset  The first two rows show the results for models trained with expert annotations  The model trained on random data has a slightly better F1 than that trained on the same amount of difficult data  The model trained on random data has higher precision but lower recall 
Rows 3 and 4 list the results for models trained on the same data but with crowd annotation  Models trained with expert-annotated data are clearly superior to those trained with crowd labels with respect to F1, indicating that the experts produced higher quality annotations  For crowdsourced annotations, training the model with data sampled at i i d  random achieves 2% higher F1 than when difficult instances are used  When expert annotations are used, this difference is less than 1%  This trend in performance may be explained by differences in annotation quality: the randomly sampled set was more consistently annotated by both experts and crowd because the difficult set is harder  However, in both cases expert annotations are better, with a bigger difference between the expert and crowd models on the difficult set 
The last row is the model trained on all 5k abstracts with crowd annotations  Its F1 score is lower than either expert model trained on only 20% of data, suggesting that expert annotations should be collected whenever possible  Again the crowd model on complete data has higher precision than expert models but its recall is much lower 
Routing To Experts or Crowd
So far a system was trained on one type of data, either labeled by crowd or experts  We now examine the performance of a system trained on data that was routed to either experts or crowd annotators depending on their predicted difficult  Given the results presented so far mixing annotators may be beneficial given their respective trade-offs of precision and recall  We use the annotations from experts for an abstract if it exists otherwise use crowd annotations  The results are presented in Table 6  
Rows 1 and 2 repeat the performance of the models trained on difficult subset and random subset with expert annotations only respectively  The third row is the model trained by combining difficult and random subsets with expert annotations  There are around 250 abstracts in the overlap of these two sets, so there are total 1 75k abstracts used for training the D+R model  Rows 4 to 6 are the models trained on all 5k abstracts with mixed annotations, where Other means the rest of the abstracts with crowd annotation only 
The results show adding more training data with crowd annotation still improves at least 1 point F1 score in all three extraction tasks  The improvement when the difficult subset with expert annotations is mixed with the remaining crowd annotation is 3 5 F1 score, much larger than when a random set of expert annotations are added  The model trained with re-annotating the difficult subset (D+Other) also outperforms the model with re-annotating the random subset (R+Other) by 2 points in F1  The model trained with re-annotating both of difficult and random subsets (D+R+Other), however, achieves only marginally higher F1 than the model trained with the re-annotated difficult subset (D+Other)  In sum, the results clearly indicate that mixing expert and crowd annotations leads to better models than using solely crowd data, and better than using expert data alone  More importantly, there is greater gain in performance when instances are routed according to difficulty, as compared to randomly selecting the data for expert annotators  These findings align with our motivating hypothesis that annotation quality for difficult instances is important for final model performance  They also indicate that mixing annotations from expert and crowd could be an effective way to achieve acceptable model performance given a limited budget 
How Many Expert Annotations?
We established that crowd annotation are still useful in supplementing expert annotations for medical IE  Obtaining expert annotations for the one thousand most difficult instances greatly improved the model performance  However the choice of how many difficult instances to annotate was an uninformed choice  Here we check if less expert data would have yielded similar gains  Future work will need to address how best to choose this parameter for a routing system 
We simulate a routing scenario in which we send consecutive batches of the most difficult examples to the experts for annotation  We track changes in performance as we increase the number of most-difficult-articles sent to domain experts  As shown in Figure 4 , adding expert annotations for difficult articles consistently increases F1 scores  The performance gain is mostly from increased recall; the precision changes only a bit with higher quality annotation  This observation implies that crowd workers often fail to mark target tokens, but do not tend to produce large numbers of false positives  We suspect such failures to identify relevant spans/tokens are due to insufficient domain knowledge possessed by crowd workers 
The F1 score achieved after re-annotating the 600 most-difficult articles reaches 68 1%, which is close to the performance when re-annotating 1000 random articles  This demonstrates the effectiveness of recognizing difficult instances  The trend when we use up all expert data is still upward, so adding even more expert data is likely to further improve performance  Unfortunately we exhausted our budget and were not able to obtain additional expert annotations  It is likely that as the size of the expert annotations increases, the value of crowd annotations will diminish  This investigation is left for future work 
Conclusions
We have introduced the task of predicting annotation difficulty for biomedical information extraction (IE)  We trained neural models using different learned representations to score texts in terms of their difficulty  Results from all models were strong with Pearson’s correlation coefficients higher than 0 45 in almost all evaluations, indicating the feasibility of this task  An ensemble model combining universal and task specific feature sentence vectors yielded the best results 
Experiments on biomedical IE tasks show that removing up to $\sim $ 10% of the sentences predicted to be most difficult did not decrease model performance, and that re-weighting sentences inversely to their difficulty score during training improves predictive performance  Simulations in which difficult examples are routed to experts and other instances to crowd annotators yields the best results, outperforming the strategy of randomly selecting data for expert annotation, and substantially improving upon the approach of relying exclusively on crowd annotations  In future work, routing strategies based on instance difficulty could be further investigated for budget-quality trade-off 
Acknowledgements
This work has been partially supported by NSF1748771 grant  Wallace was support in part by NIH/NLM R01LM012086 

ground_truth: 57,505 sentences

57,505 sentences

prompt_front: You are given a scientific article and a question. Answer the question as concisely as you can, using a single phrase or sentence if possible. If the question cannot be answered based on the information in the article, write "unanswerable". If the question is a yes/no question, answer "yes", "no", or "unanswerable". Do not provide any explanation.

Please answer the questions based on the text provided below. What can word subspace represent?
Context 3: Introduction
Text classification has become an indispensable task due to the rapid growth in the number of texts in digital form available online  It aims to classify different texts, also called documents, into a fixed number of predefined categories, helping to organize data, and making easier for users to find the desired information  Over the past three decades, many methods based on machine learning and statistical models have been applied to perform this task, such as latent semantic analysis (LSA), support vector machines (SVM), and multinomial naive Bayes (MNB) 
The first step in utilizing such methods to categorize textual data is to convert the texts into a vector representation  One of the most popular text representation models is the bag-of-words model BIBREF0 , which represents each document in a collection as a vector in a vector space  Each dimension of the vectors represents a term (e g , a word, a sequence of words), and its value encodes a weight, which can be how many times the term occurs in the document 
Despite showing positive results in tasks such as language modeling and classification BIBREF1 , BIBREF2 , BIBREF3 , the BOW representation has limitations: first, feature vectors are commonly very high-dimensional, resulting in sparse document representations, which are hard to model due to space and time complexity  Second, BOW does not consider the proximity of words and their position in the text and consequently cannot encode the words semantic meanings 
To solve these problems, neural networks have been employed to learn vector representations of words BIBREF4 , BIBREF5 , BIBREF6 , BIBREF7   In particular, the word2vec representation BIBREF8 has gained attention  Given a training corpus, word2vec can generate a vector for each word in the corpus that encodes its semantic information  These word vectors are distributed in such a way that words from similar contexts are represented by word vectors with high correlation, while words from different contexts are represented by word vectors with low correlation 
One crucial aspect of the word2vec representation is that arithmetic and distance calculation between two word vectors can be performed, giving information about their semantic relationship  However, rather than looking at pairs of word vectors, we are interested in studying the relationship between sets of vectors as a whole and, therefore, it is desirable to have a text representation based on a set of these word vectors 
To tackle this problem, we introduce the novel concept of word subspace  It is mathematically defined as a low dimensional linear subspace in a word vector space with high dimensionality  Given that words from texts of the same class belong to the same context, it is possible to model word vectors of each class as word subspaces and efficiently compare them in terms of similarity by using canonical angles between the word subspaces  Through this representation, most of the variability of the class is retained  Consequently, a word subspace can effectively and compactly represent the context of the corresponding text  We achieve this framework through the mutual subspace method (MSM) BIBREF9  
The word subspace of each text class is modeled by applying PCA without data centering to the set of word vectors of the class  When modeling the word subspaces, we assume only one occurrence of each word inside the class 
However, as seen in the BOW approach, the frequency of words inside a text is an informative feature that should be considered  In order to introduce this feature in the word subspace modeling and enhance its performance, we further extend the concept of word subspace to the term-frequency (TF) weighted word subspace 
In this extension, we consider a set of weights, which encodes the words frequencies, when performing the PCA  Text classification with TF weighted word subspace can also be performed under the framework of MSM  We show the validity of our modeling through experiments on the Reuters database, an established database for natural language processing tasks  We demonstrate the effectiveness of the word subspace formulation and its extension, comparing our methods' performance to various state-of-art methods 
The main contributions of our work are:
The remainder of this paper is organized as follows  In Section "Related Work" , we describe the main works related to text classification  In Section "Word subspace" , we present the formulation of our proposed word subspace  In Section "Conventional text classification methods" , we explain how text classification with word subspaces is performed under the MSM framework  Then, we present the TF weighted word subspace extension in Section "TF weighted word subspace"   Evaluation experiments and their results are described in Section "Experimental Evaluation"   Further discussion is then presented in Section "Discussion" , and our conclusions are described in Section "Conclusions and Future Work"  
Related Work
In this section, we outline relevant work towards text classification  We start by describing how text data is conventionally represented using the bag-of-words model and then follow to describe the conventional methods utilized in text classification 
Text Representation with bag-of-words
The bag-of-words representation comes from the hypothesis that frequencies of words in a document can indicate the relevance of the document to a query BIBREF0 , that is, if documents and a query have similar frequencies for the same words, they might have a similar meaning  This representation is based on the vector space model (VSM), that was developed for the SMART information retrieval system BIBREF10   In the VSM, the main idea is that documents in a collection can be represented as a vector in a vector space, where vectors close to each other represent semantically similar documents 
More formally, a document $d$ can be represented by a vector in $\mathbb {R}^{n}$ , where each dimension represents a different term  A term can be a single word, constituting the conventional bag-of-words, or combinations of $N$ words, constituting the bag-of-N-grams  If a term occurs in the document, its position in the vector will have a non-zero value, also known as term weight  Two documents in the VSM can be compared to each other by taking the cosine distance between them BIBREF1  
There are several ways to compute the term weights  Among them, we can highlight some: Binary weights, term-frequency (TF) weights, and term-frequency inverse document-frequency (TF-IDF) weights 
Consider a corpus with documents $D = \lbrace d_i\rbrace _{i=1}^{|D|}$ and a vocabulary with all terms in the corpus $V = \lbrace w_i\rbrace _{i=1}^{|V|}$   The term weights can be defined as:
Binary weight: If a term occurs in the document, its weight is 1  Otherwise, it is zero 
Term-frequency weight (TF): The weight of a term $w$ is defined by the number of times it occurs in the document $d$  
$$TF(w,d) = n_d^w$$   (Eq  8)
Inverse document-frequency: The weight of a term $w$ , given the corpus $D$ , is defined as the total number of documents $|D|$ divided by the number of documents that have the term $w$ , $|D^w|$  
$$IDF(w | D) = \frac{|D|}{|D^w|}$$   (Eq  10)
Term-frequency inverse document-frequency (TF-IDF): The weight of a term $w$ is defined by the multiplication of its term-frequency and its inverse document-frequency  When considering only the TF weights, all terms have the same importance among the corpus  By using the IDF weight, words that are more common across all documents in $D$ receive a smaller weight, giving more importance to rare terms in the corpus 
$$TFIDF(w,d | D)=TF \times IDF$$   (Eq  12)
In very large corpus, it is common to consider the logarithm of the IDF in order to dampen its effect 
$$TFIDF(w,d | D)=TF \times log_{10}(IDF)$$   (Eq  13)
Conventional text classification methods
Multi-variate Bernoulli (MVB) and multinomial naive Bayes (MNB) are two generative models based on the naive Bayes assumption  In other words, they assume that all attributes (e g , the frequency of each word, the presence or absence of a word) of each text are independent of each other given the context of the class BIBREF11  
In the MVB model, a document is represented by a vector generated by a bag-of-words with binary weights  In this case, a document can be considered an event, and the presence or the absence of the words to be the attributes of the event  On the other hand, the MNB model represents each document as a vector generated by a bag-of-words with TF weights  Here, the individual word occurrences are considered as events and the document is a collection of word events 
Both these models use the Bayes rule to classify a document  Consider that each document should be classified into one of the classes in $C=\lbrace c_j\rbrace _{j=1}^{|C|}$   The probability of each class given the document is defined as:
$$P(c_j|d_i) = \frac{P(d_i|c_j)P(c_j)}{P(d_i)} $$   (Eq  16)
The prior $P(d_i)$ is the same for all classes, so to determine the class to which $d_i$ belongs to, the following equation can be used:
$$prediction(d_i) = argmax_{c_j}P(d_i|c_j)P(c_j)$$   (Eq  17)
The prior $P(c_j)$ can be obtained by the following equation:
$$P(c_j) = \frac{1+|D_j|}{|C|+|D|},$$   (Eq  18)
where $|D_j|$ is the number of documents in class $c_j$  
As for the posterior $P(d_i|c_j)$ , different calculations are performed for each model  For MVB, it is defined as:
$$P(d_i|c_j) = \prod _{k=1}^{|V|}P(w_k|c_j)^{t_i^k}(1-P(w_k|c_j))^{1-t_i^k},$$   (Eq  19)
where $w_k$ is the k-th word in the vocabulary $V$ , and $t_i^k$ is the value (0 or 1) of the k-th element of the vector of document $d_i$  
For the MNB, it is defined as:
$$P(d_i|c_j) = P(|d_i|)|d_i|!\prod _{k=1}^{|V|}\frac{P(w_k|c_j)^{n_i^k}}{n_i^k!},$$   (Eq  20)
where $|d_i|$ is the number of words in document $d_i$ and $n_i^k$ is the k-th element of the vector of document $d_i$ and it represents how many times word $w_k$ occurs in $d_i$  
Finally, the posterior $P(w_k|c_j)$ can be obtained by the following equation:
$$P(w_k|c_j) = \frac{1+|D_j^k|}{|C|+|D|},$$   (Eq  21)
where $|D_j^k|$ is the number of documents in class $c_j$ that contain the word $w_k$  
In general, MVB tends to perform better than MNB at small vocabulary sizes whereas MNB is more efficient on large vocabularies 
Despite being robust tools for text classification, both these models depend directly on the bag-of-words features and do not naturally work with representations such as word2vec 
Latent semantic analysis (LSA), or latent semantic indexing (LSI), was proposed in BIBREF12 , and it extends the vector space model by using singular value decomposition (SVD) to find a set of underlying latent variables which spans the meaning of texts 
It is built from a term-document matrix, in which each row represents a term, and each column represents a document  This matrix can be built by concatenating the vectors of all documents in a corpus, obtained using the bag-of-words model, that is, $ {X} = [ {v}_1, {v}_2,    , {v}_{|D|}]$ , where ${v}_i$ is the vector representation obtained using the bag-of-words model 
In this method, the term-document matrix is decomposed using the singular value decomposition,
$${X} = {U\Sigma V}^\top ,$$   (Eq  23)
where $U$ and $V$ are orthogonal matrices and correspond to the left singular vectors and right singular vectors of $X$ , respectively  $\Sigma $ is a diagonal matrix, and it contains the square roots of the eigenvalues of $X^TX$ and $XX^T$   LSA finds a low-rank approximation of $X$ by selecting only the $k$ largest singular values and its respective singular vectors,
$${X}_k = {U}_k{\Sigma }_k {V}_k^{\top } $$   (Eq  24)
To compare two documents, we project both of them into this lower dimension space and calculate the cosine distance between them  The projection ${\hat{d}}$ of document ${d}$ is obtained by the following equation:
$${\hat{d}} = {\Sigma }_k^{-1} {U}_k^\top {d} $$   (Eq  25)
Despite its extensive application on text classification BIBREF13 , BIBREF14 , BIBREF15 , this method was initially proposed for document indexing and, therefore, does not encode any class information when modeling the low-rank approximation  To perform classification, 1-nearest neighbor is usually performed, placing a query document into the class of the nearest training document 
The support vector machine (SVM) was first presented in BIBREF16 and performs the separation between samples of two different classes by projecting them onto a higher dimensionality space  It was first applied in text classification by BIBREF17 and have since been successfully applied in many tasks related to natural language processing BIBREF18 , BIBREF19  
Consider a training data set $D$ , with $n$ samples
$$D = \lbrace ({x}_i,c_i)|{x}_i\in \mathbb {R}^p, c_i \in \lbrace -1,1\rbrace  \rbrace _{i=1}^{n},$$   (Eq  27)
where $c_i$ represents the class to which ${x}_i$ belongs to  Each ${x}_i$ is a $p$ -dimensional vector  The goal is to find the hyperplane that divides the points from $c_i = 1$ from the points from $c_i = -1$   This hyperplane can be written as a set of points $x$ satisfying:
$${w} \cdot {x} - b = 0,$$   (Eq  28)
where $\cdot $ denotes the dot product  The vector ${w}$ is perpendicular to the hyperplane  The parameter $\frac{b}{\Vert {w}\Vert }$ determines the offset of the hyperplane from the origin along the normal vector ${w}$  
We wish to choose ${w}$ and $b$ , so they maximize the distance between the parallel hyperplanes that are as far apart as possible, while still separating the data 
If the training data is linearly separable, we can select two hyperplanes in a way that there are no points between them and then try to maximize the distance  In other words, minimize $\Vert {w}\Vert $ subject to $c_i({w}\cdot {x}_u-b) \ge 1, i=\lbrace 1,2,   ,n\rbrace $   If the training data is not linearly separable, the kernel trick can be applied, where every dot product is replaced by a non-linear kernel function 
Word subspace
All methods mentioned above utilize the BOW features to represent a document  Although this representation is simple and powerful, its main problem lies on disregarding the word semantics within a document, where the context and meaning could offer many benefits to the model such as identification of synonyms 
In our formulation, words are represented as vectors in a real-valued feature vector space $\mathbb {R}^{p}$ , by using word2vec BIBREF8   Through this representation, it is possible to calculate the distance between two words, where words from similar contexts are represented by vectors close to each other, while words from different contexts are represented as far apart vectors  Also, this representation brings the new concept of arithmetic operations between words, where operations such as addition and subtraction carry meaning (eg , “king”-“man”+“woman”=“queen”) BIBREF20  
Consider a set of documents which belong to the same context $D_c = \lbrace d_i\rbrace _{i=1}^{|D_c|}$   Each document $d_i$ is represented by a set of $N_i$ words, $d_i = \lbrace w_k\rbrace _{k=1}^{N_i}$   By considering that all words from documents of the same context belong to the same distribution, a set of words $W_c = \lbrace w_k\rbrace _{k=1}^{N_c}$ with the words in the context $c$ is obtained 
We then translate these words into word vectors using word2vec, resulting in a set of word vectors $X_c = \lbrace {x}^k_c\rbrace _{k=1}^{N_c} \in \mathbb {R}^p$   This set of word vectors is modeled into a word subspace, which is a compact, scalable and meaningful representation of the whole set  Such a word subspace is generated by applying PCA to the set of word vectors 
First, we compute an autocorrelation matrix, ${R}_c$ :
$${R}_c = \frac{1}{N_c}\sum _{i=1}^{N_c}{x}^{i}_c{x}_c^{i^{\top }} $$   (Eq  29)
The orthonormal basis vectors of $m_c$ -dimensional subspace ${Y}_c$ are obtained as the eigenvectors with the $m_c$ largest eigenvalues of the matrix ${R}_c$   We represent a subspace ${Y}_c$ by the matrix ${Y}_c \in \mathbb {R}^{p \times m_c}$ , which has the corresponding orthonormal basis vectors as its column vectors 
Text classification based on word subspace
We formulate our problem as a single label classification problem  Given a set of training documents, which we will refer as corpus, $D = \lbrace d_i\rbrace _{i=1}^{|D|}$ , with known classes $C = \lbrace c_j\rbrace _{j=1}^{|C|}$ , we wish to classify a query document $d_q$ into one of the classes in $C$  
Text classification based on word subspace can be performed under the framework of mutual subspace method (MSM)  This task involves two different stages: A learning stage, where the word subspace for each class is modeled, and a classification stage, where the word subspace for a query is modeled and compared to the word subspaces of the classes 
In the learning stage, it is assumed that all documents of the same class belong to the same context, resulting in a set of words $W_c = \lbrace w_c^k\rbrace _{k=1}^{N_c}$   This set assumes that each word appears only once in each class  Each set $\lbrace W_c\rbrace _{c=1}^{|C|}$ is then modeled into a word subspace ${Y}_c$ , as explained in Section "Word subspace"   As the number of words in each class may vary largely, the dimension $m_c$ of each class word subspace is not set to the same value 
In the classification stage, for a query document $d_q$ , it is also assumed that each word occurs only once, generating a subspace ${Y}_q$  
To measure the similarity between a class word subspace ${Y}_c$ and a query word subspace ${Y}_q$ , the canonical angles between the two word subspaces are used BIBREF21   There are several methods for calculating canonical angles BIBREF22 , BIBREF23 , and BIBREF24 , among which the simplest and most practical is the singular value decomposition (SVD)  Consider, for example, two subspaces, one from the training data and another from the query, represented as matrices of bases, ${Y}_{c} = [{\Phi }_{1} \ldots {\Phi }_{m_c}] \in \mathbb {R}^{p \times m_c}$ and ${Y}_{q} = [{\Psi }_{1} \ldots {\Psi }_{m_q}] \in \mathbb {R}^{p \times m_q}$ , where ${\Phi }_{i}$ are the bases for ${Y}_c$ and ${\Psi }_{i}$ are the bases for ${Y}_q$   Let the SVD of ${Y}_c^{\top }{Y}_q \in \mathbb {R}^{m_c \times m_q}$ be ${Y}_c^{\top }{Y}_q = {U \Sigma V}^{\top }$ , where ${Y}_q$0 , ${Y}_q$1 represents the set of singular values  The canonical angles ${Y}_q$2 can be obtained as ${Y}_q$3 ${Y}_q$4   The similarity between the two subspaces is measured by ${Y}_q$5 angles as follows:
$$S_{({Y}_c,{Y}_q)}[t] = \frac{1}{t}\sum _{i = 1}^{t} \cos ^{2} \theta _{i},\; 1 \le t \le m_q, \; m_q \le m_c $$   (Eq  30)
Fig  1 shows the modeling and comparison of sets of words by MSM  This method can compare sets of different sizes, and naturally encodes proximity between sets with related words 
Finally, the class with the highest similarity with $d_q$ is assigned as the class of $d_q$ :
$$prediction(d_q) = argmax_c(S_{({Y}_c,{Y}_q)}) $$   (Eq  32)
TF weighted word subspace
The word subspace formulation presented in Section "Word subspace" is a practical and compact way to represent sets of word vectors, retaining most of the variability of features  However, as seen in the BOW features, the frequency of words is relevant information that can improve the characterization of a text  To incorporate this information into the word subspace modeling, we propose an extension of the word subspace, called the term-frequency (TF) weighted word subspace 
Like the word subspace, the TF weighted word subspace is mathematically defined as a low-dimensional linear subspace in a word vector space with high dimensionality  However, a weighted version of the PCA BIBREF25 , BIBREF26 is utilized to incorporate the information given by the frequencies of words (term-frequencies)  This TF weighted word subspace is equivalent to the word subspace if we consider all occurrences of the words 
Consider the set of word vectors $\lbrace {x}_c^k\rbrace _{k=1}^{N_c} \in \mathbb {R}^{p}$ , which represents each word in the context $c$ , and the set of weights $\lbrace \omega _i\rbrace _{i=1}^{N_c}$ , which represent the frequencies of the words in the context $c$  
We incorporate these frequencies into the subspace calculation by weighting the data matrix ${X}$ as follows:
$${\widetilde{X}}={X}{\Omega }^{1/2},$$   (Eq  33)
where ${X} \in \mathbb {R}^{p \times N_c}$ is a matrix containing the word vectors $\lbrace {x}_c^k\rbrace _{k=1}^{N_c}$ and ${\Omega }$ is a diagonal matrix containing the weights $\lbrace \omega _i\rbrace _{i=1}^{N_c}$  
We then perform PCA by solving the SVD of the matrix ${\widetilde{X}}$ :
$${\widetilde{X}}={AMB}^{\top },$$   (Eq  34)
where the columns of the orthogonal matrices ${A}$ and ${B}$ are, respectively, the left-singular vectors and right-singular vectors of the matrix ${\widetilde{X}}$ , and the diagonal matrix ${M}$ contains singular values of ${\widetilde{X}}$  
Finally, the orthonormal basis vectors of the $m_c$ -dimensional TF weighted subspace ${W}$ are the column vectors in ${A}$ corresponding to the $m_c$ largest singular values in ${M}$  
Text classification with TF weighted word subspace can also be performed under the framework of MSM  In this paper, we will refer to MSM with TF weighted word subspace as TF-MSM 
Experimental Evaluation
In this section we describe the experiments performed to demonstrate the validity of our proposed method and its extension  We used the Reuters-8 dataset without stop words from BIBREF27 aiming at single-label classification, which is a preprocessed format of the Reuters-21578  Words in the texts were considered as they appeared, without performing stemming or typo correction  This database has eight different classes with the number of samples varying from 51 to over 3000 documents, as can be seen in Table 1  
To obtain the vector representation of words, we used a freely available word2vec model, trained by BIBREF8 , on approximately 100 billion words, which encodes the vector representation in $\mathbb {R}^{300}$ of over 3 million words from several different languages  Since we decided to focus on English words only, we filtered these vectors to about 800 thousand words, excluding all words with non-roman characters 
To show the validity of our word subspace representation for text classification and the proposed extension, we divided our experiment section into two parts: The first one aims to verify if sets of word vectors are suitable for subspace representation, and the second one puts our methods in practice in a text classification test, comparing our results with the conventional methods described in Section "Related Work"  
Evaluation of the word subspace representation
In this experiment, we modeled the word vectors from each class in the Reuters-8 database into a word subspace  The primary goal is to visualize how much of the text data can be represented by a lower dimensional subspace 
Subspace representations are very efficient in compactly represent data that is close to a normal distribution  This characteristic is due to the application of the PCA, that is optimal to find the direction with the highest variation within the data 
In PCA, the principal components give the directions of maximum variance, while their corresponding eigenvalues give the variance of the data in each of them  Therefore, by observing the distribution of the eigenvalues computed when performing PCA in the modeling of the subspaces, we can suggest if the data is suitable or not for subspace representation 
For each class, we normalized the eigenvalues by the largest one of the class  Fig  2 shows the mean of the eigenvalues and the standard deviation among classes  It is possible to see that the first largest eigenvalues retain larger variance than the smallest ones  In fact, looking at the first 150 largest eigenvalues, we can see that they retain, on average, 86 37% of the data variance  Also, by observing the standard deviation, we can understand that the eigenvalues distribution among classes follows the same pattern, that is, most of the variance is in the first dimensions  This plot indicates that text data represented by vectors generated with word2vec is suitable for subspace representation 
Text classification experiment
In this experiment, we performed text classification among the classes in the Reuters-8 database  We compared the classification using the word subspace, and its weighted extension, based on MSM (to which we will refer as MSM and TF-MSM, respectively) with the baselines presented in Section "Related Work" : MVB, MNB, LSA, and SVM  Since none of the baseline methods work with vector set classification, we also compared to a simple baseline for comparing sets of vectors, defined as the average of similarities between all vector pair combinations of two given sets  For two matrices ${A}$ and ${B}$ , containing the sets of vectors $\lbrace  {x}^{i}_a \rbrace _{i = 1}^{N_A}$ and $\lbrace  {x}^{i}_b \rbrace _{i = 1}^{N_B}$ , respectively, where $N_A$ and $N_B$ are the number of main words in each set, the similarity is defined as:
$$Sim_{(A,B)} = \frac{1}{N_A N_B}\sum _{i}^{N_A}\sum _{j}^{N_B}{{x}_a^i}^{\top }{x}_b^j $$   (Eq  41)
We refer to this baseline as similarity average (SA)  For this method, we only considered one occurrence of each word in each set 
Different features were used, depending on the method  Classification with SA, MSM, and TF-MSM was performed using word2vec features, to which we refer as w2v  For MVB, due to its nature, only bag-of-words features with binary weights were used (binBOW)  For the same reason, we only used bag-of-words features with term-frequency weights (tfBOW) with MNB  Classification with LSA and SVM is usually performed using bag-of-words features and, therefore, we tested with binBOW, tfBOW, and with the term-frequency inverse document-frequency weight, tfidfBOW  We also tested them using word2vec vectors  In this case, we considered each word vector from all documents in each class to be a single sample 
To determine the dimensions of the class subspaces and query subspace of MSM and TF-MSM, and the dimension of the approximation performed by LSA, we performed a 10-fold cross validation, wherein each fold, the data were randomly divided into train (60%), validation (20%) and test set (20%) 
The results can be seen in Table 2   The simplest baseline, SA with w2v, achieved an accuracy rate of 78 73%  This result is important because it shows the validity of the word2vec representation, performing better than more elaborate methods based on BOW, such as MVB with binBOW 
LSA with BOW features was almost 10% more accurate than SA, where the best results with binary weights were achieved with an approximation with 130 dimensions, with TF weights were achieved with 50 dimensions, and with TF-IDF weights were achieved with 30 dimensions  SVM with BOW features was about 3% more accurate than LSA, with binary weights leading to a higher accuracy rate 
It is interesting to note that despite the reasonably high accuracy rates achieved using LSA and SVM with BOW features, they poorly performed when using w2v features 
Among the baselines, the best method was MNB with tfBOW features, with an accuracy of 91 47%, being the only conventional method to outperform MSM  MSM with w2v had an accuracy rate of 90 62%, with the best results achieved with word subspace dimensions for the training classes ranging from 150 to 181, and for the query ranging from 3 to 217  Incorporating the frequency information in the subspace modeling resulted in higher accuracy, with TF-MSM achieving 92 01%, with dimensions of word subspaces for training classes ranging from 150 to 172, and for the query, ranging from 2 to 109  To confirm that TF-MSM is significantly more accurate than MNB, we performed a t-test to compare their results  It resulted in a p-value of 0 031, which shows that at a 95% significance level, TF-MSM has produced better results 
Discussion
Given the observation of the eigenvalues distribution of word vectors, we could see that word vectors that belong to the same context, i e , same class, are suitable for subspace representation  Our analysis showed that half of the word vector space dimensions suffice to represent most of the variability of the data in each class of the Reuters-8 database 
The results from the text classification experiment showed that subspace-based methods performed better than the text classification methods discussed in this work  Ultimately, our proposed TF weighted word subspace with MSM surpassed all the other methods  word2vec features are reliable tools to represent the semantic meaning of the words and when treated as sets of word vectors, they are capable of representing the content of texts  However, despite the fact that word vectors can be treated separately, conventional methods such as SVM and LSA may not be suitable for text classification using word vectors 
Among the conventional methods, LSA and SVM achieved about 86% and 89%, respectively, when using bag-of-words features  Interestingly, both methods had better performance when using binary weights  For LSA, we can see that despite the slight differences in the performance, tfidfBOW required approximations with smaller dimensions  SVM had the lowest accuracy rate when using the tfidfBOW features  One possible explanation for this is that TF-IDF weights are useful when rare words and very frequent words exist in the corpus, giving higher weights for rare words and lower weights for common words  Since we removed the stop words, the most frequent words among the training documents were not considered and, therefore, using TF-IDF weights did not improve the results 
Only MNB with tfBOW performed better than MSM  This result may be because tfBOW features encode the word frequencies, while MSM only considers a single occurrence of words  When incorporating the word frequencies with our TF weighted word subspace, we achieved a higher accuracy of 92 01%, performing better than MNB at a significance level of 95% 
Conclusions and Future Work
In this paper, we proposed a new method for text classification, based on the novel concept of word subspace under the MSM framework  We also proposed the term-frequency weighted word subspace which can incorporate the frequency of words directly in the modeling of the subspace by using a weighted version of PCA 
Most of the conventional text classification methods are based on the bag-of-words features, which are very simple to compute and had been proved to produce positive results  However, bag-of-words are commonly high dimensional models, with a sparse representation, which is computationally heavy to model  Also, bag-of-words fail to convey the semantic meaning of words inside a text  Due to these problems, neural networks started to be applied to generate a vector representation of words  Despite the fact that these representations can encode the semantic meaning of words, conventional methods do not work well when considering word vectors separately 
In our work, we focused on the word2vec representation, which can embed the semantic structure of words, rendering vector angles as a useful metric to show meaningful similarities between words  Our experiments showed that our word subspace modeling along with the MSM outperforms most of the conventional methods  Ultimately, our TF weighted subspace formulation resulted in significantly higher accuracy when compared to all conventional text classification methods discussed in this work  It is important to note that our method does not consider the order of the words in a text, resulting in a loss of context information  As a future work, we wish to extend our word subspace concept further in mainly two directions  First, we seek to encode word order, which may enrich the representation of context information  Second, we wish to model dynamic context change, enabling analysis of large documents, by having a long-short memory to interpret information using cues from different parts of a text 
Acknowledgment
This work is supported by JSPS KAKENHI Grant Number JP16H02842 and the Japanese Ministry of Education, Culture, Sports, Science, and Technology (MEXT) scholarship 

ground_truth: Word vectors, usually in the context of others within the same class