Optimal harvesting strategy for stochastic hybrid delay Lotka-Volterra systems with Lévy noise in a polluted environment

1.   Introduction

With the continuous advancement of medical artificial intelligence, it is urgent to build a smart clinical decision support system. As an essential component of clinical decision support system, clinical event detection (CED) has attracted constant attention from academia and industry. The CED task aims to identify and classify all clinically relevant events and situations, including symptoms, exams, treatments and other occurrences in Chinese electronic medical records (EMRs). The Chinese EMRs contain a lot of valuable information. It is important that how to extract these relevant information from a large amount of Chinese EMRs quickly and accurately. The correct extraction result can improve the quality of medical text analysis. Moreover, extracting these information quickly and accurately can help doctors make decisions in the process of treatment. In the last decades, numerous methods have been proposed for Chinese CED task, including Hidden Markov Models (HMMs) ^[1], Support Vector Machines (SVMs) ^[2] and Conditional Random Fields (CRFs) ^[3]. Recently, with the development of deep learning, researchers begin to introduce the neural networks ^[4,5,6,7] for Chinese CED task.

Although these methods have achieved significant improvements in Chinese CED task, some issues still have not been well addressed. One significant drawback is that there is no publicly annotated corpus for Chinese CED task. The researchers need to annotate a corpus manually. Owing to the limitation of annotation costs, the scale of manually annotated corpora are usually small. The corpora also contain a great deal of noise. However, the improvements of performance and robustness crucially depend on a large amount of annotated training data. The small-scale corpus will limit the performance and robustness of model. To solve this problem, some researchers integrated external features into Chinese character representations to improve the performance of model ^[8,9]. Nevertheless, the above two approaches rely on external resources. They only work well when external resources are exhaustive. Another weakness is that the above two approaches ignore the importance of contextual information in semantic understanding. Fortunately, the BERT (Bidirectional Encoder Representations from Transformers) ^[10] trained on massive training data and can generate contextual representations dynamically according to contexts. The contextual information coming from the BERT can help model to understand obscure medical terms correctly. Moreover, the introduction of the BERT can improve the performance and robustness of models trained on a small amount of annotated training data. Thus, how to exploit the contextual information coming from the BERT for Chinese CED task is an important problem.

Another issue is that the distribution of categories is unbalanced in corpus. The class imbalance problem degrades overall performance of model and model's decision is biased to majority category samples, which leads to classifying minority category samples incorrectly. If the performance of model varies too much on each category, we can not evaluate overall performance of model objectively. Therefore, how to improve the performance of model on minority category samples is another important problem.

To address the above mentioned issues, we propose a transfer learning method to integrate contextual representations coming from the BERT into Chinese CED task. Moreover, to solve the class imbalance problem, we introduce an adversarial loss to improve the proportion of loss on minority category samples. Finally, we evaluate our model on our manually annotated corpus. Experimental results show that our proposed model achieves better overall performance than state-of-the-art models. In particular, our proposed model outperforms other models on minority category samples.

2.   Related works

2.1.   Chinese CED

Many methods have been proposed for Chinese CED task. All these existing approaches can be roughly divided into four categories: rule-based approaches, knowledge-based approaches, traditional machine learning approaches and deep learning approaches.

Rule-based approaches rely on handcrafted rules to identify clinical events ^[11]. Because of their simplicity, they were used in early Chinese CED systems widely. They work effectively when rules are exhaustive. Rule-based approaches have a shortage of flexibility.

Knowledge-based approaches do not require annotated training data as they rely on lexicon resources and domain-specific knowledge to identify clinical events ^[12]. They also have poor flexibility. Moreover, they may achieve high precision and low recall.

Traditional machine learning approaches aim to make predictions by training on example inputs and their corresponding outputs. Typical methods are HMMs ^[1], SVMs ^[2] and CRFs ^[17]. However, they rely on handcrafted features. They work effectively when handcrafted features are excellent.

In recent years, deep learning approaches have been introduced for Chinese CED task ^[4,5,6,7,13]. Tang et al. ^[6] exploited an attention-based convolution neural network (CNN) to generate the representation of Chinese characters and fed into a bidirectional long short term memory (BiLSTM) to extract features. Finally, they used a conditional random field (CRF) as a decoder and gave a predicted label to each character in the sentences. The BiLSTM-CRF model achieved state-of-the-art performance in Chinese CED task and obtained a competitive result compared with traditional statistical models. Zhou et al. ^[7] treated each clinical narrative as a sequence of short sentences and proposed an end-to-end deep neural network framework for Chinese CED task. Moreover, they also proposed a smoothed viterbi decoder as a sequence labeller without additional parameter training, which can be a good alternative to the conditional random field (CRF) when computing resources are limited. Luo et al. ^[14] integrated attention mechanism into the BiLSTM-CRF model to utilize global information to enforce tag consistency across multiple instances of same token in a document. After that, the BiLSTM-CRF model is usually exploited as a baseline. Recently, transfer learning methods have achieved great success in sequence labeling tasks. For example, Cao et al. ^[15] introduced an adversarial transfer learning framework to jointly train Chinese named entity recognition (NER) task and Chinese word segmentation (WS) task, aiming to extract task-shared word boundary information from Chinese WS task. Johnson et al. ^[16] explored a cross-lingual transfer learning for NER task, focusing on bootstrapping Japanese from English. Different from the above transfer learning methods, we utilize a transfer learning method to integrate contextual representations coming from the BERT into Chinese CED task to enhance Chinese character representations.

2.2.   Pre-trained language model

In recent years, language representation models have been shown to be effective for improving many natural language processing (NLP) tasks ^[19,20]. So we consider integrating the language representation model BERT into Chinese CED task to improve the performance of task. The BERT trained on massive unlabeled texts and merged both left and right contexts in all layers together to represent contextual information. In this work, we integrate contextual information coming from the BERT into Chinese character representations to enhance semantic understanding.

2.3.   Class imbalance problem

The class imbalance problem is prevalent in classification tasks and sequence labeling tasks. All these existing approaches solving this issue can be roughly divided into two categories: Data-based approaches and algorithm-based approaches. The data-based approaches address this issue through two strategies: Over-sampling and under-sampling. However, these two strategies may lead to over-fitting and information loss. The algorithm-based approaches solve this problem by accounting for the disadvantages of algorithms. For instance, Lin et al. ^[18] addressed the class imbalance problem by modifying the standard cross-entropy loss to adjust the loss assigned to well-classified examples. Inspired by Lin et al. ^[18], we introduce the punitive weight to adjust the proportion of loss on each category. The equal proportion of loss on each category can assist the model to obtain an equal opportunity to optimize performance on each category.

3.   Methods

In this paper, we propose an encoder-decoder structure based on transfer learning for Chinese CED task. The architecture of our proposed model is illustrated in Figure 1. The model mainly consists of two components: Semantic encoder and label decoder. In the following section, we will describe each part of our proposed model in detail.

3.1.   Semantic encoder

3.1.1.   BERT

In this work, we encode input sequences as contextual representations by the BERT. Here, we introduce the structure of the BERT briefly ^[10].

The BERT is a multi-layer bidirectional transformer encoder. Each transformer encoder consists of two sub-layers. The first layer is a multi-head self-attention mechanism, and the second is a simple position-wise fully connected feed-forward network. The residual connection network and normalization layer follow each sub-layer. The input of the BERT is constructed by summing character embedding, segment embedding and position embedding.

3.1.2.   Semantic representation

During the semantic encoding stage, we extract the output at the last layer of the BERT as contextual information of Chinese characters. Then, we concatenate each character's contextual representation and initial character embedding as decoder's input. Given an input sequence $s = \{ c_1, c_2, c_3, \ldots, c_n \}$, each character's semantic representation $T_{c_i}$ can be described as follows:

where $R$ represents the output at the last layer of the BERT. The $R_{c_i}, E_{c_i}$ represent contextual information and initialized character embedding of character $c_i$, respectively.

3.2.   Label decoder

In the decoding stage, we adopt two transformer blocks as our label decoder to predict a label for each character. Each transformer block consists of two sub-layers: A multi-head self-attention mechanism and a simple position-wise fully connected feed-forward network. Here, we introduce the structure of transformer block briefly.

3.2.1.   Multi-head self-attention mechanism

The transformer block exploits the multi-head self-attention mechanism to capture the dependencies between any two characters in the sentence and learn inner structure of sentence. The scaled dot-product attention can be defined as follows:

where $Q$, $K$ and $V$ represent the query matrix, key matrix and value matrix, respectively. The $d$ represents the dimension of key matrix. The multi-head self-attention can be expressed as follows:

where $W^Q_j$, $W^K_j$, $W^V_j$ and $W^O$ are trainable projection parameters.

3.2.2.   Position-wise fully connected feed-forward network

Besides the multi-head self-attention mechanism, another essential component of transformer block is the position-wise fully connected feed-forward network, which is applied to each position separately and identically. The position-wise fully connected feed-forward network can be described as follows:

This formula consists of two linear transformations with a $ReLU$ activation function in between.

3.3.   Adversarial loss

We introduce the punitive weight into a standard cross-entropy loss to adjust the contribution of loss on each category. This strategy changes the proportion of loss on each category. The proportion of loss on majority category samples will confront the proportion of loss on minority category samples. More specifically, we utilize a penalty factor to balance the difference of data scale between different categories. We exploit the probability of labels to adjust the contribution of loss on each category. We call this novel loss "adversarial loss". The adversarial loss can be defined as follows:

where $N$ represents the amount of characters, $K$ represents the amount of Chinese clinical event's categories, $y_{i, k}$ represents the true value of the $ith$ character on the $kth$ category, $P_{i, k}$ represents the probability which the $ith$ character is predicted as the $kth$ category, $1-y_{i, k}P_{i, k}$ represents the penalty term and $\alpha$ represents the penalty factor.

4.   Experiments

4.1.   Dataset and evaluation metrics

To evaluate the effectiveness of our proposed model, we conduct a range of experiments on our manually annotated corpus. Specially, we name our manually annotated corpus Chinese CED corpus. The Chinese CED corpus consists of 2000 Chinese EMRs, coming from a third-level grade-A hospital in Gansu province. The Chinese CED corpus is divided as follows during the stage of experiment. Firstly, we divide 2000 annotated clinical narratives into initial train set and test set at a ratio of 3:1. Then, we select 400 clinical narratives from initial train set and test set as the development set randomly. Finally, we choose the rest of initial train set and test set to construct the final train set and test set, respectively. Table 1 shows the distribution of Chinese CED corpus.

In the stage of dataset annotation, we do as follows. More specifically, we work out an annotation specification and develop an annotation tool for Chinese CED corpus. The annotation specification refers to 2012 i2b2 (Informatics for Integrating Biology & the Bedside) clinical temporal relations challenge annotation guidelines. Moreover, we make the following improvements and supplements. We annotate the discharge summaries and progress notes with seven types of clinical events (Problem, Exam, Treatment, Clinical department, Evidence, Occurrence and Aspectual). The "Problem" event type includes patient's complaints, symptoms, diseases and diagnoses. The "Exam" event type is used for clinical tests (laboratory and physical) and test results. The "Treatment" event type includes medications, surgeries and other procedures. The "Clinical department" event type is used to mark the clinical unit. The "Evidence" event type is used to state the source of information. The "Occurrence" event type is used for all the other kinds of clinically relevant events which happened to the patient. The "Aspectual" event type includes the state of current clinical event. Just marking the type of each clinical event is not enough. In order for the annotation to be useful in text analysis, we need to describe each clinical event in more detail. Besides clinical event category, we also annotate another two attributes of clinical events: Polarity and degree. The polarity attribute marks whether a clinical event is positive or negative. Most of the clinical events have "POS" polarity value, that is, the clinical event is not negated. It is to be noted that a clinical event can be POS even if it did not actually occur (If the clinical event is hypothetical or proposed.). If a clinical event is negated by words such as "not", "deny", and so on, its polarity is "NEG". Moreover, we also utilize degree attribute to mark the degree of clinical events. There are three type of clinical event degree attributes: "MOST", "LITTLE" and "NA". Table 2 lists the examples of Chinese clinical events. The bold words represent the clinical events in the sentence.

Twenty copies of same clinical narratives were annotated in pairs before the formal annotation. The annotators record the uncertain textfields in the process of annotation. Two people in the group exchange annotation results and proofread their partner's annotation results after the own data annotation. They also record inconsistent textfields. All crews discuss the uncertain and inconsistent textfields and modify the annotation specification and annotation results together after a round of annotation. Then, we conduct five round of preliminary annotations. The clinical narratives in the five round of preliminary annotations are different. When we conduct the fifth round preliminary annotation, the error rate of all annotators were both less than 5%. So, we think that the annotation specification and annotators have met the requirements of formal annotation. Moreover, the annotators may encounter difficult medical terms during the process of annotation. So our annotation group members consider that twelve laboratory members and two medical students with more than five years of learning experience are involved in annotation specification development and annotation discussion. Besides difficult medical terms, there are other challenges in the process of corpus construction. For example, the corpus may contain a great deal of noise. Noise comes from two stages. Doctors may make writing errors in the EMRs. Moreover, the annotators may make annotation mistakes. In order to reduce the noise, we take the following two steps. Firstly, two medical students in our annotation group modify the writing errors in the EMRs before the formal annotation. Secondly, all annotation members discuss the annotation results and make a double check after the annotation.

In addition, we also record the detailed statistics of the Chinese CED corpus. Table 3 shows the detailed statistics of Chinese CED corpus. We can find that the data scale belonging to "Clinical department" is very small. We view "Clinical department" as a minority category. We adopt the Precision, Recall and F1-score as an evaluation metrics of overall performance in our experiments. Besides, we also use the Recall and F1-score as an evaluation metrics to evaluate the performance of "Clinical department".

4.2.   Experimental settings

For hyper-parameter configurations, we adjust them according to our proposed model's performance on development set of Chinese CED corpus. It's worth noting that we fix all parameters coming from the BERT and only update all parameters coming from label decoder during the model's training stage. In this section, we will introduce the information about semantic encoder and label decoder in detail.

4.2.1.   Pre-trained language model

In this work, we apply the BERT-Base-Chinese Pre-trained Model for obtaining each character's contextual information. The BERT-Base-Chinese Pre-trained Model trained on massive cased Chinese simplified and traditional texts. Table 4 shows the detailed statistics of pre-trained language model.

4.2.2.   Label decoder

In addition, we exploit two transformer blocks as our proposed model's decoder. Each transformer block consists of two sub-layers: A multi-head self-attention mechanism and a simple position-wise fully connected feed-forward network. Table 5 shows the major settings of decoder.

4.3.   Baseline models

In the experimental section, we use multiple baseline models to compare with our proposed method. Here, we introduce baseline models briefly.

● CRF: In this work, we use the CRF++ to implement the CRF model.

● CNN-Softmax: The model utilizes the CNN to extract features and feeds into the multilayer perceptron (MLP) to decode.

● CNN-CRF: The model adopts the CNN to extract features and feeds into the CRF to decode.

● BiGRU-Softmax: The model exploits the bidirectional gated recurrent unit (BiGRU) to extract features and feeds into the MLP to decode.

● BiLSTM-CRF: The model adopts the BiLSTM to extract features and feeds into the CRF to decode.

● Attention-based CNN-BiLSTM-CRF: Tang et al. ^[6] exploited an attention-based CNN to generate the representations of Chinese characters and fed into the BiLSTM to extract features. Finally, they used the CRF as the model's decoder.

● BERT-Softmax: The model utilizes the BERT to obtain semantic representations and feeds into the MLP to decode.

● BERT-BiLSTM-Softmax: The model uses the BERT to obtain semantic representations and feeds into the BiLSTM to decode.

● BERT-Transformer-Softmax: The model adopts the BERT to obtain the semantic representations and feeds into the transformer to decode.

4.4.   Overall experimental results

We compare overall performance of our proposed model with baseline models on test set of Chinese CED corpus. Table 6 shows the detailed experimental results of baseline models and our proposed model. The first column of Table 6 lists baseline models and our proposed model. Our proposed model achieves the highest precision of 83.73%, recall of 86.56% and F1-score of 85.12%. Compared with the BiLSTM-CRF model, our proposed model improves the F1-score from 82.97 to 85.12% and obtains an increase of 2.15%. Compared with the BERT-Softmax model, our proposed model improves the F1-score from 83.34 to 85.12% and obtains an increase of 1.78%. All in all, our proposed model outperforms other state-of-the-art methods significantly and consistently.

Here, we summarize several reasons for the success of our proposed model. Firstly, we adopt the BERT to generate contextual representations and integrate contextual representations into Chinese character embeddings, which enhances the representations of Chinese characters. Secondly, we use the transformer block as our model's decoder, which pays different attention to each position of semantic representations. Thirdly, we utilize an "adversarial loss" to balance the difference of data scale on each category.

4.5.   Experimental results on each category

Besides, we also record the performance of our proposed model on each category. Table 7 shows the detailed experimental results. As shown in Table 7, our proposed model achieves impressive results on majority category samples. For example, the F1-score of "Problem" and "Exam" are 88.77% and 85.85%, respectively.

In our manually annotated corpus, "Clinical department" is viewed as a minority category. The main reason is that the data scale of "Clinical department" is much less than the data scale of other clinical event's categories. As is shown in Table 3, the data scale of "Clinical department" varies from tens to hundreds of times compared with other clinical event's categories. In this work, we introduce an "adversarial loss" to adjust the proportion of loss on each category to improve the performance of model on each category. This strategy compels model to learn more knowledge about "Clinical department". To some extent, it reduces the gap of data scale on each category. Our proposed model achieves the recall of 62.44% and F1-score of 68.03% on "Clinical department".

To prove the effectiveness of "adversarial loss", we conduct a contrasting experiment on Chinese CED corpus. The only difference between contrasting experiment and our proposed model is loss function. Our proposed model exploits the "adversarial loss" as loss function. The contrasting experiment uses a standard cross-entropy loss as loss function. Table 8 shows the experimental results of contrasting experiment.

As shown in Table 8, the F1-score of "Problem" and "Exam" are 86.49 and 84.99%, respectively. We discover that the introduction of "adversarial loss" hardly degrades the performance of model on majority category samples. If model's performance degrades in a particular clinical event, the degradation is minimal. For example, the F1-score of "Treatment" is 85.01% on contrasting experiment. The F1-score of "Treatment" is 84.84% on our proposed model. Specially, our proposed model outperforms contrasting experiment on "Clinical department". The F1-score of "Clinical department" is 67.19% on contrasting experiment. The F1-score of "Clinical department" is 68.03% on our proposed model. Our proposed model obtains an increase of 0.84%.

Besides, we also record the F1-score of existing models and our proposed model on "Clinical department". Figure 2 shows the detailed experimental results.

As shown in Figure 2, our proposed model achieves the highest F1-score of 68.03% on "Clinical department". Compared with the BiLSTM-CRF model, our proposed model improves the F1-score from 63.66 to 68.03% and obtains an increase of 4.37%. Compared with the BERT-Softmax model, our proposed model improves the F1-score from 65.67 to 68.03% and obtains an increase of 2.36%. The above results demonstrate that our proposed strategy can alleviate the class imbalance problem effectively. The main reason is that the introduction of "adversarial loss" can adjust the proportion of loss on each category. More specifically, models usually learn more knowledge from large amount of samples and learn less knowledge from small amount of samples. It will lead to giving correct labels to majority category samples. When model encounters a minority category sample, it will give an incorrect label to sample. In this work, we utilize an "adversarial loss" to adjust the proportion of loss on each category. It will reduce incorrect decisions caused by unbalanced data scale.

5.   Discussions and analysis

5.1.   Effectiveness of contextual information

To validate the effectiveness of contextual information, we conduct the following experiments. The contrasting experiment only uses initial character embeddings from the BERT as the representations of Chinese characters. Table 9 shows the detailed experimental results.

Our proposed model achieves the F1-score of 85.12%. The contrasting experiment gets the F1-score of 83.20%. Our proposed model outperforms contrasting experiment by 1.92%, which indicates contextual information from the BERT is effective for Chinese CED task. The main reason is that our proposed model can utilize contextual information to understand the meaning of sentences under a specific semantic context. This strategy will assist model in harvesting a skill of semantic understanding. This approach is consistent with the process of human thought.

5.2.   Effectiveness of transformer decoder

To evaluate the effectiveness of transformer decoder, we conduct the following experiments. The contrasting experiment utilizes the BiLSTM as its decoder and "adversarial loss" to compute loss. Table 10 shows the experimental results.

Our proposed model achieves the best precision of 83.73%, recall of 86.56% and F1-score of 85.12%. Compared with the BERT-BiLSTM-Softmax (adversarial loss) model, our proposed model improves the F1-score from 84.51 to 85.12% and obtains an increase of 0.61%. It verifies that transformer decoder owns a better decoding capacity than the BiLSTM. The main reason of our proposed model's success is multi-head self-attention mechanism can assist transformer block in paying different attention to each position of sentence. It will help model to capture pivotal information and use these information to assist model in making decisions.

5.3.   Effectiveness of adversarial loss

To confirm the effectiveness of "adversarial loss" on "Clinical department", we conduct the following experiments. We choose the BiLSTM-CRF model and the BERT-Softmax model as basic models. Then, we adopt the standard cross-entropy loss and "adversarial loss" to compute loss, respectively. In addition, we also exploit the standard cross-entropy loss to replace "adversarial loss" to conduct extra experiment. Table 11 shows the detailed experimental results.

The BiLSTM-CRF model using "adversarial loss" outperforms the standard BiLSTM-CRF model and obtains an increase of 1.82% on the F1-score. The BERT-Softmax model using "adversarial loss" outperforms the standard BERT-Softmax model and obtains an increase of 1.35% on the F1-score. Our proposed model outperforms corresponding contrasting experiment and obtains an increase of 0.84% on the F1-score. It proves that "adversarial loss" can alleviate class imbalance problem effectively. Moreover, we also explore the allocation strategy of loss on each category. The contrasting experiment sets a fixed rate of loss allocation on each category. We find that our proposed model outperforms contrasting experiment and obtains an increase of 4.89% on the F1-score. The main reason is that "adversarial loss" can allocate the proportion of loss for each category flexibly.

6.   Case study

The class imbalance problem is prevalent in Chinese CED tasks. The categories containing scarce instances may be significant. We shouldn't ignore the performance of model on minority category samples. In this work, we adopt an "adversarial loss" to solve the class imbalance problem. Here, we take a sentence from test set of Chinese CED corpus as an example for illustrating the effectiveness of our proposed strategy. Table 12 shows the detailed results. In the example, baselines give an "O" label to "神经外科" (neurosurgery department). Our proposed model gives a "Cd" label (Clinical department) to "神经外科" (neurosurgery department). The label predicted by our proposed model is correct. The baselines make incorrect predictions. The reason is that baselines adopt the standard cross-entropy loss to compute loss, which compels model to be biased toward majority category samples and can not obtain crucial information from samples belonging to minority category. Different from baseline models, our proposed model introduces the punitive weight into loss to balance the difference of each category's data scale. It will assist model in learning more crucial information from data belonging to minority category. Moreover, contextual information coming from the BERT can help model understand the meaning of sentence under a specific context.

7.   Conclusions

In this paper, we propose a novel encoder-decoder structure based on transfer learning for Chinese CED task, which integrates contextual representations into Chinese character embeddings to assist model in semantic understanding. Besides, we introduce an "adversarial loss" to solve the class imbalance problem. Experimental results on test set of Chinese CED corpus demonstrate that our proposed model outperforms state-of-the-art methods significantly and consistently. In particular, our model achieves superior performance than other models on minority category samples. In the future, we will explore more allocation strategies of loss and compare experiment result of each strategy.

Acknowledgments

We would like to thank the anonymous reviewers for their valuable comments. The Publication of the article is supported by the National Natural Science Foundation of China (No. 61762081, No. 61662067, No. 61662068) and the Key Research and Development Project of Gansu Province (No. 17YF1GA016).

Conflict of interest

The authors declare that they have no competing interests.