In recent years there has been a surge of interest in leveraging hierarchies (taxonomies) to organize objects (e.g., documents), leading to the development of hierarchical text classification (HTC)—a task that aims to predict for an object multiple appropriate labels in a given label hierarchy, which together constitute a sub-tree. HTC methods have found a wide range of applications such as question answering (Qu et al., 2012), online advertising (Agrawal et al., 2013), and scientific literature organization (Peng et al., 2016). In contrast to “flat” classification, the key challenges of HTC lie in modeling the large-scale, imbalanced, and in particular, structured label space.
Based on how the hierarchy is explored, HTC methods can be summarized into flat, local, and global approaches (Silla and Freitas, 2011). Flat approaches Hayete and Bienkowska (2005); Johnson and Zhang (2014)
assume all the labels in the given hierarchy are independent. Some predict labels at the leaf nodes and heuristically add their ancestor labels, which is problematic as the labels of some objects may not be at the leaf nodes (non-mandatory leaf node prediction, see Fig. 1) and all the non-leaf nodes are completely neglected. Some simply ignore the hierarchy and perform standard multi-label classification, in which label inconsistencies (one label is predicted positive but its ancestors are not) may occur and post-processing is needed to correct such contradictions. Local approaches Koller and Sahami (1997); Cesa-Bianchi et al. (2006) train a set of local classifiers that function independently and predictions are usually made in a top-down order: one node is visited if and only if its ancestors have been predicted positive. One critical issue is that the number of local classifiers depends on the size of the label hierarchy, making local approaches infeasible to scale.
Global approaches use one single classifier and model the label hierarchy more explicitly. Traditional global approaches (Wang et al., 2001; Silla Jr and Freitas, 2009) are largely based on specific flat models and often make unrealistic assumptions Cai and Hofmann (2004) as in flat approaches. Recent neural approaches (Kim, 2014; Yang et al., 2016) mainly focus on flat classification while their performance in HTC is relatively less studied. Even if the classification is supposed to be hierarchical, prior work (Gopal and Yang, 2013; Johnson and Zhang, 2014; Peng et al., 2018) still make flat and independent predictions or utilize simple constraints without considering the holistic quality of label assignment. One recent framework (Wehrmann et al., 2018) attempts to leverage both local and global information but it uses static features as input and its inference process is still flat.
In this paper, we formulate HTC as a Markov decision process to better capture label dependencies and measure the holistic quality of label assignment. We present HiLAP, a global framework that learns a label assignment policy to determine where to place the objects and when to stop the assignment process. HiLAP explores the label hierarchy during both training and inference in a consistent manner, which alleviates the exposure bias often found in prior local and global approaches. By learning when to stop, HiLAP is more flexible than approaches that only support mandatory leaf node prediction or require thresholding. In addition, HiLAP supports multi-path prediction and its predictions of one object on different paths are inter-dependent, which not only guarantees label consistency
but matches the nature of HTC. Furthermore, HiLAP estimates the holistic quality of all the labels assigned to one object via reinforcement learning instead of evaluating each label independently via maximum likelihood as in prior studies. To summarize, HiLAP achieves better effectiveness compared to flat and local approaches as it examines the label hierarchy during both training and inference. HiLAP has more flexibility and generalization capacity than previous global approaches in that it has no constraints on the structure of the hierarchy or the labels of the objects(Cai and Hofmann, 2004), generalizes to neural representation learning models (Gopal and Yang, 2013), and makes inter-dependent predictions while ensuring label consistency (Wehrmann et al., 2018; Peng et al., 2018).
HiLAP can be combined with various neural encoding models and trained in an end-to-end fashion. In our experiments, we select four representative encoding models as the base models to evaluate the effectiveness of HiLAP. Experimental results on five public datasets from different domains show that combining the base models with HiLAP yields an average performance improvement of 33.4% in Macro-F1 over corresponding flat classifiers and outperforms state-of-the-art HTC methods by a large margin. In particular, ablation study shows that HiLAP is especially beneficial to those unpopular labels at the bottom levels.
2 Hierarchical Label Assignment
Problem Formulation. We define a label hierarchy as a tree or DAG (directed acyclic graph)-structured hierarchy with a set of nodes (labels) and a set of edges indicating the parent-child relation between the labels. Taking a set of objects and their labels as input, we aim to learn a label assignment policy to place each object to its labels on the label hierarchy . The label assignment is supposed to be consistent, multi-path, and non-mandatory leaf node prediction (refer to Figs. 1 and 2). We define one base model as a mapping that converts raw object
to a finite dimensional vector,i.e., the object embedding . can be any neural representation learning model and its output is used as the input of for policy learning. The major challenge, compared to standard classification setup, is that we need to model , i.e., the relation between labels.
Our Framework. Prior studies either have a mismatch between training and inference as different routines are followed in the two phases, or compute losses with respect to each individual label and make flat predictions during inference time. In contrast, we learn a policy that (1) makes consistent, inter-dependent predictions by traversing the label hierarchy and maintaining state representation; (2) measures the holistic quality of label assignment via reinforcement learning. Specifically, the policy puts at the root label in the beginning. At each time step, decides which label should be further placed to, among all the children labels of where has been placed, until a special stop action is taken. An illustration of how HiLAP labels one object is shown in Fig. 2 and the overall architecture of HiLAP is shown in Fig. 3.
2.2 Reinforcement Learning for Hierarchical Label Assignment
We describe the details of policy learning including its actions, rewards, states, and the policy network in this section. We formulate HTC as a Markov decision process (MDP): at each time step, the agent observes current state, takes an action, and receives a reward. The end goal is to train a policy network to determine where to place the objects and when to stop.
Actions. Specifically, we regard the process of placing an object to the right positions on the label hierarchy as making a sequence of actions, where an action at time step is to select one label from the action space and place to that label . We denote the children of label as . At the beginning of each episode, is placed at the root label and the action space , i.e., all the labels at level 1. When is placed at another label , its children are then added to the action space while itself is removed. In addition, one stop action with embedding is included in the action space so that the model can automatically learn when to stop placing object to new labels. Intuitively, when the confidence of placing to another label is lower than the stop action, the label assignment process would be terminated.
In short, the action space consists of all the unvisited children labels of where the object has been placed and the stop action. One distinction of HiLAP is that it takes the inter-dependencies of labels across different paths and levels into consideration while previous approaches make independent predictions on different paths. For example, HiLAP can first place
to a label at level 3 if the probability of that label is high and then place it to another label at level 1 on another path.
Rewards. The agent receives scalar rewards as feedback for its actions. Different from existing work where each label of one example222We use “example” and “object” interchangeably. is treated independently, HiLAP measures the quality of all the labels assigned to each example by rewarding the agent with the Example-based F1 (see Sec. 4.1 for details of this metric). Intuitively, the agent would realize how similar the assigned and the ground-truth labels of one example are. Instead of waiting until the end of the label assignment process and comparing the predicted labels with the gold labels, we use reward shaping (Mao et al., 2018), i.e., giving intermediate rewards at each time step, to accelerate the learning process. Specifically, we set the reward of at time step to be the difference of Example-based F1 scores between current and the last time step: .
If current F1 is better than that at the last time step, the reward would be positive, and vice versa. The cumulative reward from current time step to the end of an episode would cancel the intermediate rewards and thus reflect whether the current action improves the holistic label assignment or not. As a result, the learned policy would not focus on the current placement but have a long-term view that takes following actions into account.
States and Policy Network. We parameterize action by a policy network . For each object, its representation is generated by the base model . For each label, a label embedding is randomly initialized and updated during training. The embeddings of the object and currently assigned label are concatenated and projected to a vector via a two-layer feed-forward network. has the same size as the label embedding l and is used as the state representation at time step . By stacking the action embeddings (i.e., the embeddings of candidate labels and stop action), we obtain an action matrix with size . is multiplied with the state embedding
, which outputs the probability distribution of actions. Finally, an actionis sampled based on the probability distribution of the action space.
We use policy gradient (Williams, 1992) as the optimization algorithm. In addition, we adopt a self-critical training approach (Rennie et al., 2017). For each object , two label assignments are generated: is sampled from the probability distribution, and , the baseline label assignment, is greedily obtained by choosing the action with the highest probability at each time step. We use as the actual reward, which ensures that the policy network learns to place the object to positions with higher F1 score than the greedy baseline. Formally, we measure the global loss as follows.
where is the cumulative future reward at time and is the discount factor. At the time of inference, we greedily select labels with the highest probability as .
3 End-to-End Model Learning
3.1 Top-Down Supervised Pre-Training
Instead of learning from scratch, we use supervised learning to pre-train HiLAP. We denote the supervised variant as HiLAP-SL. While most parameters of HiLAP-SL are shared and used to initialize HiLAP (except thatis randomly initialized), its way of exploring the label hierarchy is dissimilar.
The major difference is that HiLAP-SL explores the label hierarchy in a top-down manner independently. At each time step , the object goes down one level on the hierarchy and the labels under the same parent are discriminated locally. Specifically, the local per-parent label probability distribution is estimated as , where
denotes the sigmoid function, anddenotes the candidate embeddings of HiLAP-SL, i.e., an embedding matrix consisting of the children of current label , rather than all the labels where has been placed.
Another difference is that in HiLAP the actions are sampled and thus might place the objects to incorrect labels, while in HiLAP-SL only the ground-truth positions are traversed during training. Specifically, if there are ground-truth labels at the same level, the object embedding would be copied times and losses on the different paths would be measured independently (see Fig. 6 in Appendix for illustration). The local loss of HiLAP-SL is defined as , where is the lowest label’s level of one example and estimates the binary cross entropy over the candidate labels : , where and evaluate label of . Intuitively, HiLAP-SL works as if there were a set of local classifiers, although most of its parameters (except for the label embedding l) are shared by all the labels so that there is no need to train multiple classifiers.
3.2 Combining Flat, Local, and Global Information for Policy Learning
We further add a flat component to HiLAP as a regularization of the base model. Specifically, the flat component is a feed-forward network that projects the object embedding to a label probability distribution of all the labels on the hierarchy: . The combination of the base model and the flat component functions the same as a flat model and ensures that the object representation has the capability of flat classification. We denote the flat loss that measures the binary cross entropy over all the labels by . Combining the flat and local losses, the supervised loss in HiLAP-SL is defined as , where is the mixing ratio. Similar to Celikyilmaz et al. (2018), we also found that mixing a proportion of the supervised loss is beneficial to the learning process of HiLAP. Further combining the global information (i.e., ), the total loss of HiLAP is defined as , where is a scaling factor accounting for the difference in magnitude between and . While we do not use the flat component during inference, it helps the representation learning of the base model and improves the performance of both HiLAP-SL and HiLAP (see Sec. 4.5).
4.1 Experiment Setup
Datasets. We conduct extensive experiments on five public datasets from various domains (summarized in Table 1 and detailed in Appendix A). The first two datasets are related to news categorization, including RCV1 (Lewis et al., 2004) and the NYT annotated corpus (Sandhaus, 2008). The third dataset is the Yelp Dataset Challenge 2018333https://www.yelp.com/dataset/challenge. We hypothesize that one business can be represented by its reviews and use the reviews to predict business categories. The last two datasets are related to protein functional catalogue (FunCat) and gene ontology (GO) prediction Vens et al. (2008), which are used to test the generalization ability of HiLAP to non-textual data. For all the datasets, the lowest labels of one example may not be at the leaf nodes and there could be multiple labels at each level, making them harder and more realistic than mandatory-leaf or single-path datasets such as IPC WIPO (2014) and LSHTC Partalas et al. (2015).
Evaluation Metrics. We use standard metrics (Johnson and Zhang, 2014; Meng et al., 2018; Peng et al., 2018) for HTC, including Micro-F1, Macro-F1, and Example-based F1 (EBF) Partalas et al. (2015); Peng et al. (2016). Let , , denote the true positive, false positive, and false negative for the i-th example in object set , respectively. EBF calculates the F1 scores of all the examples independently and averages them. , , , and . Recall that is used as the reward in HiLAP.
Base Models for Feature Encoding. Different from most of existing global HTC methods that rely on pre-specified features (Gopal and Yang, 2013) as input or build on specific models (Cai and Hofmann, 2004; Vens et al., 2008; Silla Jr and Freitas, 2009), our framework is trained in an end-to-end manner by leveraging a differentiable feature representation learning model as the base model. Specifically, we use TextCNN (Kim, 2014), HAN (Yang et al., 2016), bow-CNN (Johnson and Zhang, 2014) on the three textual datasets, and a feed-forward network on the two non-textual datasets. The details of the base models are provided in Appendix C due to limited space.
To incorporate one base model into our framework, we remove its final feed-forward layer that projects the object representation to a flat probability distribution of all labels (), and use directly as the input of HiLAP. As one will see in the later experiments, HiLAP consistently improves the base model by modeling the label hierarchy in an effective manner.
Local & Global
4.2 Compared Methods
1. Traditional HTC Methods.
A major line of work for HTC is Support Vector Machines (SVM) and its hierarchical variants. Specifically,SVM performs standard multi-label classification using one-vs-the-rest (OvR) strategy. Leaf-SVM treats each leaf node as a label and adds the ancestors of predicted leaf nodes. Variants such as HSVM (Tsochantaridis et al., 2005), Top-Down SVM (TD-SVM) (Liu et al., 2005), and Hierarchically Regularized SVM (HR-SVM) (Gopal and Yang, 2013) are also tested. Other state-of-the-art HTC methods that we compare with include Clus-HMC Vens et al. (2008) and CSSA Bi and Kwok (2011).
2. Neural HTC Methods. There are not many neural methods that specifically target HTC. We mainly compare with two latest neural models: HR-DGCNN (Peng et al., 2018), which extends hierarchical regularization (Gopal and Yang, 2013) to Graph-CNN and compares favorably to flat models like RCNN Lai et al. (2015) and XML-CNN Liu et al. (2017), and HMCN (Wehrmann et al., 2018), which outperforms state-of-the-art HTC methods such as HMC-LMLP Cerri et al. (2016). We also compare with the base models that we use for feature encoding. The main aim is to see how much gain they could obtain by combining each one of them with HiLAP.
4.3 Implementation Details
For datasets without held-out set, we randomly sample 10% from the training set as the validation set following Johnson and Zhang (2014); Peng et al. (2018). We only use the first 256 tokens of each document for representation learning. All the models are trained using an Adam optimizer with initial learning rate 1e-3 and weight decay 1e-6. We use GloVe (Pennington et al., 2014) with size 50 as word embeddings for TextCNN Kim (2014) and HAN Yang et al. (2016). We create a vocabulary of the most frequent 30,000 words in the training data and generate multi-hot vectors as the input of bow-CNN Johnson and Zhang (2014). For our framework, since the parameter updates are performed after steps, we cache the object representation and reuse it at each step for better efficiency. More details are provided in Appendix D for reproducibility.
4.4 Performance Comparison
1. Comparison with State-of-the-art Methods. We compare the performance of HiLAP to state-of-the-art HTC methods and show the results in Tables 2 and 3. On RCV1, HiLAP (HAN) achieves similar performance to HR-DGCNN even though the corresponding base model HAN is originally worse than HR-DGCNN. HiLAP (TextCNN) outperforms most baselines in Macro-F1 and perform similarly to TD-SVM despite that it uses one global classifier while TD-SVM uses a set of classifiers. Among all compared methods, HiLAP (bow-CNN) achieves the best performance on all the three metrics.444The results are not comparable with Johnson and Zhang (2014) due to implementation details and the fact that they tune the threshold for each label using k-fold cross-validation. See Appendix B for more discussions. On NYT, similar results are observed: TextCNN and HAN are both improved when combining with HiLAP and HiLAP (bow-CNN) again achieves the best performance. On Yelp, HiLAP (HAN) achieves the best Micro-F1 and EBF, while HiLAP (bow-CNN) obtains the highest Macro-F1.
2. Comparison using Same Base Models. We compare the performance of different frameworks that support the use of exactly the same base models and summarize the results in Fig. 4.555For HMCN, we replace its static features with the same base model for fair comparison. Due to the extreme imbalance of the data, directly applying a flat model may suffer from low Macro-F1, i.e., the predictions of flat models are inevitably biased to the most popular labels. HMCN also has the same issue, resulting in Macro-F1 lower than 10 when combining with some base models. In contrast, HiLAP outperforms the baselines significantly in Macro-F1, which implies that our method is better at tackling labels with relatively few examples. It is also observed that HiLAP-SL sometimes may have a negative effect in terms of Micro-F1, although it is usually marginal compared with the gains in Macro-F1. However, such negative effects are eliminated by HiLAP through better exploration of the label hierarchy. Overall, HiLAP achieves the highest performance on 24 of 27 results among the combinations of three datasets, three base models, and three evaluation metrics. In particular, HiLAP yields an average improvement of 33.4% in Macro-F1 compared to corresponding base models.
3. Results on Functional Genomics Prediction. We compare HiLAP with CSSA Bi and Kwok (2011), CLUS-HMC (Vens et al., 2008), and HMCN (Wehrmann et al., 2018) on the FunCat and GO datasets, as they represent the state-of-the-art on these datasets. An SVM classifier is also evaluated to better understand the difficulties of the task. We use the same raw features as the input of all the methods for apples-to-apples comparison and list the results in Table 4. Note that the metric area under the average precision-recall curve (AUPRC) Wehrmann et al. (2018) is not applicable because HiLAP does not use a flat probability distribution of all the labels. As one can see, HiLAP outperforms all the baselines on both datasets by a large margin. In particular, we observe significant improvement on Macro-F1 over the best baseline (47.9% and 53.9%, respectively), which shows that our method is especially better at classifying sparse labels than previous approaches.
4.5 Performance Analysis
1. Ablation Study on Different Framework Components. We show the ablation analysis of HiLAP in Table 5. Using Flat-Only degenerates HiLAP to the flat baseline. By comparing the results of Flat-Only and HiLAP-SL-NoFlat (a variant of HiLAP-SL without flat loss), we further confirm that flat approaches are likely to neglect sparse labels, which results in low Macro-F1. Local approaches (HiLAP-SL-NoFlat), on the other hand, are slightly worse in terms of Micro-F1 and EBF but significantly better on Macro-F1. By combining flat and local information, HiLAP-SL achieves performance close to Flat-Only on Micro-F1 and EBF, and even higher Macro-F1 than HiLAP-SL-NoFlat. HiLAP-NoSL is initialized by the pre-trained HiLAP-SL model without mixing the supervised loss during its training. We can see that using the reinforced loss alone still improves the performance on all the three metrics. After removing the flat loss during the training of HiLAP, HiLAP-NoFlat shows slightly lower performance than the full HiLAP model, indicating that the flat component serves as a regularization of the base model and is beneficial to the overall performance.
2. Performance Study on Label Granularity and Popularity. We analyze the sources of performance gains by dividing the labels based on their levels and number of supporting examples. Fig. 5 shows the absolute Macro-F1 differences between several methods and the base model. We observe similar results for other setups and omit them for a clearer view. As depicted in Fig. 5, HiLAP and HiLAP-SL are especially beneficial to unpopular labels (P3) at the bottom levels (L3).
3. Analysis of Label Inconsistency. Label inconsistencies often happen in approaches that perform flat inference, but they are not measured by standard evaluation metrics like F1 scores. To provide a picture of how severe the issue is, we further conduct experiments to check the percentage of objects that are predicted with inconsistent labels (Table 6). We found, for example, 29,186/781,265 (3.74%) predictions of TextCNN have inconsistent on RCV1. In contrast, HiLAP ensures 0% label inconsistency without the need of post-processing, because its predictions are always valid sub-trees of the label hierarchy (refer to Fig. 2).
5 Related Work
Hierarchical classification approaches have been developed for many applications. For text classification, both traditional methods (Lewis et al., 2004; Gopal and Yang, 2013) and neural methods (Johnson and Zhang, 2014; Peng et al., 2018) have been proposed to classify, e.g., the topics of newswire and web content (Sun and Lim, 2001) or categories of laws and patents (Bi and Kwok, 2015; Cai and Hofmann, 2004; Rousu et al., 2005). Many previous studies (Liu et al., 2005; Sun and Lim, 2001) train a set of local classifiers and make predictions in a top-down manner. In particular, Bi and Kwok (2015) develop Bayes-optimal predictions that minimize the global risks but their model is still locally trained. Such local approaches are not popularly used among recent neural-based HTC models (Johnson and Zhang, 2014; Peng et al., 2018) since it is usually infeasible to train many neural classifiers locally.
Global methods, on the other hand, train only one classifier. Although global methods are desirable, they are relatively less studied due to the complexity of the problem. Existing global models are generally modified based on specific flat models. Hierarchical-SVM (Cai and Hofmann, 2004; Qiu et al., 2009)
generalizes Support Vector Machine (SVM) learning based on discriminant functions that are structured in a way that mirrors the label hierarchy. One limitation is that Hierarchical-SVM only supports balanced tree (all possible labels are presumed to be at the same level in their experiments). Hierarchical naive Bayes(Silla Jr and Freitas, 2009) modifies naive Bayes by updating weights of one’s ancestors as well whenever one label’s weights are updated. There are other global methods that are based on association rules (Wang et al., 2001), C4.5 (Clare and King, 2003), kernel machines (Rousu et al., 2005)
, and decision tree(Vens et al., 2008). Constraints such as the regularization that enforces the parameters of one node and its parent to be similar (Gopal and Yang, 2013) are also proposed to leverage the label hierarchy while maintaining scalability. However, their use of the label hierarchies is somewhat limited compared with HiLAP.
We proposed an end-to-end reinforcement learning approach to hierarchical text classification (HTC) where objects are labeled by placing them at the proper positions in the label hierarchy. The proposed framework makes consistent and inter-dependent predictions, in which any neural-based representation learning model can be used as a base model and a label assignment policy is learned to determine where to place the objects and when to stop the assignment process. Experiments on five public datasets and four base models showed that our approach outperforms state-of-the-art HTC methods significantly. For future work, we will explore the effectiveness of the proposed framework on other base models and forms of data (e.g., images). We will introduce more losses covering other aspects in the objective function to further improve the performance of our framework.
Research was sponsored in part by U.S. Army Research Lab under Cooperative Agreement No. W911NF-09-2-0053 (NSCTA), DARPA under Agreement No. W911NF-17-C-0099, National Science Foundation IIS 16-18481, IIS 17-04532, and IIS-17-41317, grant 1U54GM-114838 awarded by NIGMS, National Science Foundation SMA 18-29268, DARPA MCS and GAILA, IARPA BETTER, Schmidt Family Foundation, Amazon Faculty Award, Google Research Award, Snapchat Gift, and JP Morgan AI Research Award. We thank Chao Zhang, Xiao-Yang Liu, Qingrong Chen, Jun Yan, collaborators in the INK research lab, and anonymous reviewers for their help and valuable feedback.
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Appendix A Reproducibility Details of Datasets
In this section, we describe the details of the datasets used in our experiments.
The RCV1 dataset (Lewis et al., 2004) is a manually labeled newswire collection of Reuters News from 1996 to 1997. Its news documents are categorized with three aspects: industries, topics, and regions. We follow the original training/test split for RCV1 and use its topic-based label hierarchy for classification as it has been well used in prior work (Gopal and Yang, 2013; Johnson and Zhang, 2014; Peng et al., 2018; Wehrmann et al., 2018). There are 103 categories and four levels in total including all labels except for the root label in the hierarchy.
The NYT annotated corpus (Sandhaus, 2008) is a collection of New York Times news from 1987 to 2007. Due to its large size, we randomly sampled 36,107 documents from all the news documents, and further split them into training and test set of 25,279 and 10,828 examples, respectively. We use the first three levels in the hierarchy and keep the labels with at least 40 supporting examples.
For the Yelp dataset, the label hierarchy is taken from the Yelp Business Categories666https://www.yelp.com/developers/documentation/v3/all_category_list, which Fig. 2 is a subset of. For preprocessing, we first removed categories that have fewer than 100 businesses and then businesses that have fewer than 5 reviews. We concatenated (at most) the first 10 reviews of each business as its representation. We set the training/test ratio to 70%/30%, which results in a training set of 87,375 examples and a test set of 37,517 examples. This is an even more challenging task because the reviews are usually written in an informal way and it is more imbalanced than the RCV1 or NYT datasets. For example, label Restaurants has 32,357 businesses in the training set while Retirement Homes has 23.
For the FunCat and GO datasets, we take the cellcycle data from Vens et al. (2008)777https://dtai.cs.kuleuven.be/clus/hmcdatasets/. Compared with the text datasets above, raw features are provided as input for all compared methods. Furthermore, their training data is rather limited while the label space is much larger (4,125 vs. 539). Since there are many labels that do not have any example in either training set or test set, we exclude such labels when calculating Macro-F1. Note that it does not have any effect on the ratio of results from two different methods as the F1 scores of those labels without supporting examples are always zero. The features provided by the datasets are taken as input as they are except that the missing values are replaced with the mean value of corresponding features. All the compared methods take the same raw features for fair comparison.
Appendix B Performance Analysis of Baselines
There are several things to note in terms of the performance of the baselines. First, our results are not comparable to Lewis et al. (2004); Johnson and Zhang (2014) due to implementation details (e.g., we only take the first 256 tokens) and the fact that they tune the threshold for each label using scutfbr Lewis et al. (2004). According to the implementation in LibSVM888https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/multilabel/, the scutfbr threshold tuning algorithm uses two nested 3-fold cross validation for each of the 103 labels and the classifier is trained times, which is infeasible in our case.
Secondly, we found that the original performance of HMCN (Wehrmann et al., 2018) is sometimes much lower than expected. After tuning their model, we observed that if we first conduct a weighted sum of the local and global outputs and then apply the sigmoid function, the performance of HMCN becomes much better (see Table 7) than doing them in the opposite order as in Wehrmann et al. (2018). In addition, we found that HMCN + HAN (Yang et al., 2016)
would result in extremely low performance. We had to remove HMCN’s batch normalization to make it compatible with HAN. Combining HMCN with other base models did not encounter similar issues.
Thirdly, our implementation of TextCNN (Kim, 2014) and HAN (Yang et al., 2016) shows better performance than those reported in Peng et al. (2018) due to implementation details. A comparison can be found in Table 8.
Appendix C Details of Base Models
1. Base Models for Encoding Text Objects. For the text classification datasets, three representative text encoding models with different characteristics are selected as the base models to prove the robustness and versatility of HiLAP. We briefly describe the base models and the reasons we choose them as follows.
TextCNN (Kim, 2014)
is a classic convolutional neural network for text classification. In our implementation, TextCNN is composed of one convolutional layer with three kernels of different sizes (3, 4, 5), followed by max pooling, dropout, and fully-connected layers. We choose TextCNN because it is one of the first successful and well used neural-based models for text classification.
HAN (Yang et al., 2016) first learns the representation of sentences by feeding words in each sentence to a GRU-based sequence encoder (Bahdanau et al., 2014) and then feeds the representation of the encoded sentences into another GRU-based sequence encoder, which generates the representation of the whole document. Attention mechanism such as word attention and sentence attention is also used. We choose HAN because it uses RNNs instead of CNNs and is shown to be effective on the flat Yelp Review datasets.
bow-CNN (Johnson and Zhang, 2014) employs bag of words (multi-hot zero-one vectors) as input to represent text objects and directly applies CNNs to the high-dimensional multi-hot vectors encoding. It learns the representation of small text regions (rather than single words) for use in classification. We choose bow-CNN since it does not use any word embeddings as in TextCNN and HAN. In addition, bow-CNN achieved state-of-the-art performance RCV1 (Lewis et al., 2004).
2. Base Model for Encoding Raw Features.
For functional genomics prediction, one feed-forward neural network is used for simplicity as raw features are already provided in the datasets.
Appendix D Reproducibility Details of Implementation
We implement the base models and HMCN Wehrmann et al. (2018) according to the original papers and existing implementations. We use the official implementation of Clus-HMC Vens et al. (2008)999https://dtai.cs.kuleuven.be/clus/ and one open-source implementation of CSSA Bi and Kwok (2011)101010https://github.com/sushobhannayak/cssag. We use scikit-learn for SVM-based methods. TF-IDF features are used for text classification when raw features are needed as input.
For our framework, we specify the number of steps in HiLAP-SL to be the number of levels in the label hierarchy. We set the maximum number of steps in HiLAP to be reasonably large (depending on the average number of labels of one object) so that it could explore the hierarchy and learn when to stop by itself. For the purpose of batch training, we convert the original indefinite-horizon MDPs to finite-horizon by adding an absorbing state, i.e., after visiting the most fine-grained label in HiLAP-SL or entering the stop state in HiLAP, it would loop in the current state until the maximum number of steps, waiting for other objects in the same batch to finish.
We set the size of to 500 and the sizes of and label embedding to 50 in all the text classification datasets and set them to 1,000 in the other datasets. We did not observe clear performance changes when varying the probability of dropout in base models like TextCNN. We set batch size to 32 as it performs well on the validation set and a batch size as large as 128 may cause performance losses.