Venue: NAACL 2021

# Diversity-Aware Batch Active Learning for Dependency Parsing

Tianze Shi

Cornell University

tianze@cs.cornell.edu &Adrian Benton

Bloomberg L.P.

abenton10@bloomberg.net

Igor Malioutov

Bloomberg L.P.

imalioutov@bloomberg.net &Ozan Irsoy

Bloomberg L.P.

oirsoy@bloomberg.net

Work done during an internship at Bloomberg L.P.

###### Abstract

While the predictive performance of modern statistical dependency parsers relies heavily on the availability of expensive expert-annotated treebank data, not all annotations contribute equally to the training of the parsers. In this paper, we attempt to reduce the number of labeled examples needed to train a strong dependency parser using batch active learning (AL). In particular, we investigate whether enforcing diversity in the sampled batches, using determinantal point processes (DPPs), can improve over their diversity-agnostic counterparts. Simulation experiments on an English newswire corpus show that selecting diverse batches with DPPs is superior to strong selection strategies that do not enforce batch diversity, especially during the initial stages of the learning process. Additionally, our diversity-aware strategy is robust under a corpus duplication setting, where diversity-agnostic sampling strategies exhibit significant degradation.

## 1 Introduction

Though critical to parser training, data annotations for dependency parsing are both expensive and time-consuming to obtain. Syntactic analysis requires linguistic expertise and even after extensive training, data annotation can still be burdensome. The Penn Treebank project Marcus et al. (1993) reports that after two months of training, the annotators average \(750\) tokens per hour on the bracketing task; the Prague Dependency Treebank Bohmova et al. (2003) cost over $600,000 and required \(5\) years to annotate roughly \(90{,}000\) sentences (over $5 per sentence). These high annotation costs present a significant challenge to developing accurate dependency parsers for under-resourced languages and domains.

Active learning AL settles (2009) is a promising technique to reduce the annotation effort required to train a strong dependency parser by intelligently selecting samples to annotate such that the return of each annotator hour is as high as possible. Popular selection strategies, such as uncertainty sampling, associate each instance with a _quality_ measure based on the uncertainty or confidence level of the current parser, and higher-quality instances are selected for annotation.

We focus on _batch mode_ AL, since it is generally more efficient for annotators to label in bulk. While early work in AL for parsing Tang et al. (2002); Hwa (2000, 2004) cautions against using individually-computed quality measures in the batch setting, more recent work demonstrates empirical success e.g., Li et al. (2016) without explicitly handling intra-batch _diversity_. In this paper, we explore whether a diversity-aware approach can improve the state of the art in AL for dependency parsing. Specifically, we consider samples drawn from determinantal point processes (DPPs) as a query strategy to select batches of high-quality, yet dissimilar instances Kulesza and Taskar (2012).

In this paper, we (1) propose a diversity-aware batch AL query strategy for dependency parsing compatible with existing selection strategies, (2) empirically study three AL strategies with and without diversity factors, and (3) find that diversity-aware selection strategies are superior to their diversity-agnostic counterparts, especially during the early stages of the learning process, in simulation experiments on an English newswire corpus. This is critical in low-budget AL settings, which we further confirm in a corpus duplication setting.1

Footnote 1: Our code is publicly available at [https://github.com/tzshi/dpp-al-parsing-naacl21](https://github.com/tzshi/dpp-al-parsing-naacl21).

## 2 Active Learning for Dependency Parsing

### Dependency Parsing

Dependency parsing Kubler et al. (2008) aims to find the syntactic dependency structure, \(y\), given a length-\(n\) input sentence \(x=x_{1},x_{2},\ldots,x_{n}\), where

\(y\) is a set of \(n\) arcs over the tokens and the dummy root symbol \(x_{0}\), and each arc \((h,m)\in y\) specifies the head, \(h\), and modifier word, \(m\).2 In this work, we adopt the conceptually-simple edge-factored deep biaffine dependency parser Dozat and Manning (2017), which is competitive with the state of the art in terms of accuracy, The parser assigns a locally-normalized attachment probability \(P_{\text{att}}(\text{head}(m)=h~{}|~{}x)\) to each attachment candidate pair \((h,m)\) based on a biaffine scoring function. Refer to Appendix A for architecture details.

Footnote 2: For clarity, here we describe unlabeled parsing. In our experiments, we train labeled dependency parsers, which additionally predict a dependency relation label \(l\) for each arc.

We define the score of the candidate parse tree \(s(y~{}|~{}x)\) as \(\sum_{(h,m)\in y}\log P_{\text{att}}(\text{head}(m)=h~{}|~{}x)\). The decoder finds the best scoring \(\hat{y}\) among all valid trees \(\mathcal{Y}(x)\): \(\hat{y}=\operatorname*{arg\,max}_{y\in\mathcal{Y}(x)}s(y~{}|~{}x)\).

### Active Learning (AL)

We consider the pool-based batch AL scenario where we assume a large collection of unlabeled instances \(\mathcal{U}\) from which we sample a small subset at a time to annotate after each round to form an expanding labeled training set \(\mathcal{L}\)Lewis and Gale (1994). We use the superscript \(i\) to denote the pool of instances \(\mathcal{U}^{i}\) and \(\mathcal{L}^{i}\) after the \(i\)-th round. \(\mathcal{L}^{0}\) is a small set of seed labeled instances to initiate the process. Each iteration starts with training a model \(\mathcal{M}^{i}\) based on \(\mathcal{L}^{i}\). Next, all unlabeled data instances in \(\mathcal{U}^{i}\) are parsed by \(\mathcal{M}^{i}\) and we select a batch \(\mathcal{U}^{\prime}\) to annotate based on some criterion \(\mathcal{U}^{\prime}=\mathcal{C}(\mathcal{M}^{i},\mathcal{U}^{i})\). The resulting labeled subset \(\mathcal{L}^{\prime}\) is added to \(\mathcal{L}^{i+1}=\mathcal{L}^{i}\bigcup\mathcal{L}^{\prime}\) and \(\mathcal{U}^{i+1}=\mathcal{U}^{i}-\mathcal{U}^{\prime}\).

The definition of the selection criterion \(\mathcal{C}\) is critical. A typical strategy associates each unlabeled instance \(\mathcal{U}_{i}\) with a quality measure \(q_{i}\) based on, for example, the model uncertainty level when parsing \(\mathcal{U}_{i}\). A _diversity-agnostic_ criterion sorts all unlabeled instances by their quality measures and takes the top-\(k\) as \(\mathcal{U}^{\prime}\) for a budget \(k\).

### Quality Measures

We consider three commonly-used quality measures adapted to the task of dependency parsing, including uncertainty sampling, Bayesian active learning, and a representativeness-based strategy.

**Average Marginal Probability (AMP)** measures parser uncertainty Li et al. (2016):

\[\mathsf{AMP}=1-\tfrac{1}{n}\sum_{(\hat{h},m)\in\hat{y}}P_{\text{mar}}(\text{ head}(m)=\hat{h}~{}|~{}x),\]

where \(P_{\text{mar}}\) is the marginal attachment probability \(P_{\text{mar}}(\text{head}(m)=h~{}|~{}x)=\sum_{(h,m)\in y}P(y~{}|~{}x),\) and \(P(y~{}|~{}x)=\frac{\exp(s(y|x))}{\sum_{y^{\prime}\in\mathcal{Y}(x)}\exp(s(y^{ \prime}|x))}\). The marginal probabilities can be derived efficiently using Kirchhoff's theorem Tutte (1984); Koo et al. (2007).

Bayesian Active Learning by Disagreement (BALD)measures the mutual information between the model parameters and the predictions. We adopt the Monte Carlo dropout-based variant Gal et al. (2017); Siddhant and Lipton (2018) and measure the disagreement among predictions from a neural model with \(K\) different dropout masks, which has been applied to active learning in NLP. We adapt BALD to dependency parsing by aggregating disagreement at a token level:

\[\mathtt{Bald}=1-\tfrac{1}{n}\sum_{m}\frac{\text{count}(\text{mode}(h^{1}_{m},.. .,h^{K}_{m}))}{K},\]

where \(h^{k}_{m}\) denotes that \((h^{k}_{m},m)\) appears in the prediction given by the \(k\)-th model.

Information Density (ID) mitigates the tendency of uncertainty sampling to favor outliers by weighing examples by how _representative_ they are of the entire dataset Settles and Craven (2008):

\[\texttt{ID}=\mathsf{AMP}\times\left(\tfrac{1}{|\mathcal{U}|}\sum_{x^{\prime} \in\mathcal{U}}\text{sim}(x,x^{\prime})\right),\]

where cosine similarity is computed from the averaged contextualized features (SS3.2).

### Learning from Partial Annotations

We follow Li et al. (2016) and select tokens to annotate their heads instead of annotating full sentences. We first pick the most informative sentences and then choose \(p\%\) tokens from them based on the token-level versions of the quality measures (e.g., marginal probability instead of AMP).

## 3 Selecting Diverse Samples

Near-duplicate examples are common in real-world data Broder et al. (1997); Manku et al. (2007), but they provide overlapping utility to model training. In the extreme case, with a diversity-agnostic strategy for active learning, identical examples will be selected/excluded at the same time Hwa (2004). To address this issue and to best utilize the annotation budget, it is important to consider diversity. We adapt Bivik et al. (2019) to explicitly model diversity using determinantal point processes (DPPs).

### Determinantal Point Processes

A DPP defines a probability distribution over subsets of some ground set of elements Kulesza (2012). In AL, the ground set is the unlabeled 

pool \({\cal U}\) and a subset corresponds to a batch of instances \({\cal U^{\prime}}\) drawn from \({\cal U}\). DPPs provide an explicit mechanism to ensure high-quality yet diverse sample selection by modeling both the quality measures and the similarities among examples. We adopt the \(L\)-ensemble representation of DPPs using the quality-diversity decomposition Kulesza and Taskar (2012) and parameterize the matrix \(L\) as \(L_{ij}=q_{i}\phi_{i}\phi_{j}^{T}q_{j}\), where each \(q_{i}\in\mathbb{R}\) is the quality measure for \({\cal U}_{i}\) and each \(\phi_{i}\in\mathbb{R}^{1\times d}\) is a \(d\)-dimensional vector representation of \({\cal U}_{i}\), which we refer to as \({\cal U}_{i}\)'s _diversity features_.3 The probability of selecting a batch \(B\) is given by \(P(B\subseteq{\cal U})\propto\det(L_{B})\), where \(\det(\cdot)\) calculates the determinant and \(L_{B}\) is the submatrix of \(L\) indexed by elements in \(B\).

Footnote 3: Although certain applications of DPPs may learn \(q\) and \(\phi\) representations from supervision, we define \(q\) and \(\phi\)_a priori_, since acquiring supervision in AL is, by definition, expensive.

DPPs place high probability on diverse subsets of high-quality items. Intuitively, the determinant of \(L_{B}\) corresponds to the volume spanned by the set of vectors \(\{q_{i}\phi_{i}~{}|~{}i\in B\}\), and subsets with larger \(q\) values and orthogonal \(\phi\) vectors span larger volumes than those with smaller \(q\) values or similar \(\phi\) vectors. We follow Kulesza (2012) and adapt their greedy algorithm for finding the approximate mode \(\arg\max_{B}P(B\subseteq{\cal U})\). This algorithm is reproduced in Algorithm E1 in the appendix.

### Diversity Features

We consider two possibilities for the diversity features \(\phi\). Each feature vector is unit-normalized.

Averaged Contextualized Featuresare defined as \(\frac{1}{n}\sum_{i}{\bf x}_{i}\), where \({\bf x}_{i}\) is a contextualized vector of \(x_{i}\) from the feature extractor used by the parser. By this definition, we consider the instances to be similar to each other when the neural feature extractor returns similar features such that the parser is likely to predict similar structures for these instances.

Predicted Subgraph Countsexplicitly represent the predicted tree structure. To balance richness and sparsity, we count the labeled but unlexicalized subgraph formed by the grandparent, the parent and the token itself. Specifically, for each token \(m\), we can extract a subgraph denoted by \((r_{1},r_{2})\), assuming the predicted dependency relation between its grandparent \(g\) and its parent \(h\) is \(r_{1}\), and the relation between \(h\) and \(m\) is \(r_{2}\). The parse tree for a length-\(n\) sentence contains \(n\) such subgraphs. We apply tf-idf weighting to discount the influence from frequent subgraphs.

## 4 Experiments and Results

DatasetWe use the Revised English News Text Treebank4Bies et al. (2015) converted to Universal Dependencies 2.0 using the conversion tool included in Stanford Parser Manning et al. (2014) version 4.0.0. We use sections 02-21 for training, 22 for development and 23 for test.

SettingWe perform experiments by simulating the annotation process using treebank data. We sample \(128\) sentences uniformly for the initial labeled pool and each following round selects \(500\) tokens for partial annotation. We run each setting five times using different random initializations and report the means and standard deviations of the labeled attachment scores (LAS). Appendix B has unlabeled attachment score (UAS) results.

BaselinesWhile we construct our own baselines for self-contained comparisons, the diversity-agnostic AMP (w/o DPP) largely replicates the state-of-the-art selection strategy of Li et al. (2016).

ImplementationWe finetune a pretrained multilingual XLM-RoBERTa base model Conneau et al. (2020) as our feature extractor.5 See Appendix E for implementation details.

Footnote 5: [https://catalog.ldc.upenn.edu/LDC2015T13](https://catalog.ldc.upenn.edu/LDC2015T13)

Main ResultsTable 1 compares LAS after \(5\) and \(10\) rounds of annotation. Our dependency parser reaches \(95.64\) UAS and \(94.06\) LAS, when trained with the full dataset (more than one million tokens). Training data collected from \(30\) annotation rounds (\(\approx 17{,}500\) tokens) correspond to roughly \(2\%\) of the full dataset, but already support an LAS of up to \(92\) through AL. We find that diversity-aware strategies generally improve over their diversity-agnostic counterparts. Even for a random selection strategy, ensuring diversity with a DPP is superior

\begin{table}
\begin{tabular}{l|c c|c c} \hline \hline Batch & \multicolumn{2}{c|}{\(5\)} & \multicolumn{2}{c}{\(10\)} \\ \hline Strategy & w/o DPP & w/DPP & w/o DPP & w/ DPP \\ \hline Random & \(85.68_{\pm.26}\) & \(\mathbf{86.61}_{\pm.28}\) & \(87.84_{\pm.26}\) & \(\mathbf{88.55}_{\pm.23}\) \\ AMP & \(85.98_{\pm.22}\) & \(\mathbf{86.77}_{\pm.43}\) & \(88.80_{\pm.18}\) & \(\mathbf{89.23}_{\pm.29}\) \\ BALD & \(86.24_{\pm.40}\) & \(\mathbf{86.86}_{\pm.31}\) & \(88.66_{\pm.36}\) & \(\mathbf{89.03}_{\pm.10}\) \\ ID & \(\mathbf{86.68}_{\pm.26}\) & \(86.56_{\pm.24}\) & \(88.96_{\pm.20}\) & \(\mathbf{89.06}_{\pm.16}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: LAS after \(5\) and \(10\) rounds of annotation for strategies with and without modeling diversity through DPP.

 

to simple random selection. With AMP and BALD, our diversity-aware strategy sees a larger improvement earlier in the learning process. ID models representativeness of instances, and our diversity-aware strategy adds less utility compared with other quality measures, although we do notice a large improvement after the first annotation round for ID: \(82.40_{\pm.48}\) vs. \(83.36_{\pm.54}\) (w/ DPP) - a similar trend to AMP and BALD, but at an earlier stage of AL.

**Experiments with Different Diversity Features** Figure 1 compares our two definitions of diversity features, and we find that predicted subgraph counts provide stronger performance than that of averaged contextualized features. We hypothesize this is due to the fact that the subgraph counts represent structures more explicitly, thus they are more useful in maintaining structural diversity in AL.

Intra-Batch DiversityTo quantify intra-batch diversity among the set of sentences \(B\) picked by the selection strategies, we adapt the measures used by Chen et al. (2018) and define intra-batch average distance (IBAD) and intra-batch minimal distance (IBMD) as follows:

Iband \[=\mathop{\mathrm{mean}}\limits_{i,j\in B,i\neq j}(1-\text{sim}_{ \text{cos}}(i,j)),\] IBMD \[=\mathop{\mathrm{mean}}\limits_{i\in B}\min_{j\in B,i\neq j}(1- \text{sim}_{\text{cos}}(i,j)).\]

A higher value on these measures indicates better intra-batch diversity. Figure 2 compares diversity-agnostic and diversity-aware sampling strategies using the two different diversity features. We confirm that DPPs indeed promote diverse samples in the selected batches, while intra-batch diversity naturally increases even for the diversity-agnostic strategies. Additionally, we observe that the benefits of DPPs are more prominent when using predicted subgraph counts compared with averaged contextualized features. This can help explain the relative success of the former diversity features.

Corpus Duplication SettingIn our qualitative analysis (Appendix C), we find that diversity-agnostic selection strategies tend to select near-duplicate sentences. To examine this phenomenon in isolation, we repeat the training corpus twice and observe the effect of diversity-aware strategies. The corpus duplication technique has been previously used to probe semantic models (Schofield et al., 2017). Figure 3 shows learning curves for strategies under the original and corpus duplication settings. As expected, diversity-aware strategies consistently outperform their diversity-agnostic counterparts across both settings, while some diversity-agnostic strategies (e.g., AMP) even underperform uniform random selection in the duplicated setting.

Interpreting the Effectiveness of Diversity-Agnostic ModelsFigure 4 visualizes the density distributions of the top \(200\) data instances by AMP over the diversity feature space reduced to two dimensions through t-SNE (van der Maaten and Hinton, 2008). During the initial stage of active learning, data with the highest quality measures are con

Figure 1: Learning curves for our DPP-based diversity-aware selection strategies, comparing predicted subgraph counts versus averaged contextualized features as diversity features. Both use AMP as their quality measures.

Figure 2: Intra-batch average distance (IBAD) and intra-batch minimal distance (IBMD) measures comparing diversity-agnostic and diversity-aware AMP-based sample selection strategies. The distances are derived from averaged contextualized features (top) and predicted subgraph counts (bottom). A higher value indicates better intra-batch diversity.

 

centrated within a small neighborhood. A diversity-agnostic strategy will sample similar examples for annotation. After a few rounds of annotation and model training, the distribution of high quality examples spreads out, and an AMP selection strategy is likely to sample a diverse set of examples without explicitly modeling diversity. Our analysis corroborates previous findings Thompson et al. (1999) that small annotation batches are effective early in uncertainty sampling, avoiding selecting many near-duplicate examples when intra-batch diversity is low, but a larger batch size is more efficient later in training once intra-batch diversity increases.

## 5 Related Work

Modeling diversity in batch-mode AL Brinker (2003) has recently attracted attention in the machine learning community. Kirsch et al. (2019) introduce a Bayesian batch-mode selection strategy by estimating the mutual information between a set of samples and the model parameters. Ash et al. (2020) present a diversity-inducing sampling method using gradient embeddings. Most related to our work, Biyik et al. (2019) first apply DPPs to batch-mode AL. Building on their approach, we flesh out a DPP treatment for AL for a structured prediction task, dependency parsing. Previously, Shen et al. (2018) consider named entity recognition but they report negative results for a diversity-inducing variant of their sampling method.

Due to the high annotation cost, AL is a popular technique for parsing and parse selection Osborne and Baldridge (2004). Recent advances focus on reducing full-sentence annotations to a subset of tokens within a sentence Sassano and Kurohashi (2010); Mirroshandel and Nasr (2011); Majidi and Crane (2013); Flannery Mori (2015); Li et al. (2016). We show that AL for parsing can further benefit from diversity-aware sampling strategies.

DPPs have previously been successfully applied to the tasks of extractive text summarization Cho et al. (2019, 2019) and modeling phoneme inventories Cotterell and Eisner (2017). In this work, we show that DPPs also provide a useful framework for understanding and modeling quality and diversity in active learning for NLP tasks.

## 6 Conclusion

We show that compared with their diversity-agnostic counterparts, diversity-aware sampling strategies not only lead to higher data efficiency, but are also more robust under corpus duplication settings. Our work invites future research into methods, utility and success conditions for modeling diversity in active learning for NLP tasks.

## Acknowledgements

We thank the anonymous reviewers for their insightful reviews, and Prabhanjan Kambadur, ChenTse Tsai, and Minjie Xu for discussion and comments. Tianze Shi acknowledges support from Bloomberg's Data Science Ph.D. Fellowship.

Figure 4: tSNE visualization of the distributions of the \(200\) highest-quality unlabeled sentences over the diversity feature space after the \(1^{st}\) (left) and the \(10^{th}\) (right) annotation rounds using AMP without DPPs. Darker region indicates more data points residing in that diversity feature neighborhood. The left figure contains a dense region, while the data in the right figure are spread out in the feature space.

Figure 3: Learning curves of different sampling strategies based on AMP (left), BALD (middle) and ID (right), comparing diversity-aware (w/DPP) and diversity-agnostic variants using the original and duplicated corpus (dup). The \(x\)-axis shows the number of rounds for annotation. Random (dup) curves overlap with those of Random and are omitted for readability.

 



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## Appendix A Dependency Parser

We adopt the deep biaffine dependency parser proposed by Dozat and Manning (2017). The parser is conceptually simple and yet competitive with state-of-the-art dependency parsers. The parser has three components: feature extraction, unlabeled parsing and relation labeler.

Feature ExtractionFor a length-\(n\) sentence \(x=x_{0},x_{1},x_{2},\dots,x_{n}\), where \(x_{0}\) is the dummy root symbol, we extract contextualized features at each word position. In our experiments, we use a pre-trained multilingual XLM-RoBERTa base model Conneau et al. (2020), and fine-tune the feature extractor along with the rest of our parser:

\[[\mathbf{x}_{0},\mathbf{x}_{1},\dots,\mathbf{x}_{n}]=\text{XLM-R}(x_{0},x_{1}, \dots,x_{n}).\]

Each word input to the XLM-RoBERTa model is processed with the SentencePiece tokenizer Kudo and Richardson (2018), and we follow Kitaev et al. (2019) and retain the vectors corresponding to the last sub-word units as their representations. For \(\mathbf{x}_{0}\), we use the vector of the [CLS] token, which is appended by XLM-RoBERTa to the beginning of each sentence.

Unlabeled ParserThe parser uses a deep bi-affine attention mechanism to derive locally-normalized attachment probabilities for all potential head-dependent pairs:

\[\mathbf{h}^{\text{arc-head}}_{i} =\text{MLP}^{\text{arc-head}}(\mathbf{x}_{i})\] \[\mathbf{h}^{\text{arc-dep}}_{j} =\text{MLP}^{\text{arc-dep}}(\mathbf{x}_{j})\] \[s_{i,j} =[\mathbf{h}^{\text{arc-head}}_{i};1]^{\top}U^{\text{arc}}[ \mathbf{h}^{\text{arc-dep}}_{j};1]\] \[P_{\text{att}}(\text{head(j)}=i\mid x) =\text{softmax}_{i}(s_{:,j}),\]

where MLPare-head and MLPare-dep are two multi-layer perceptrons (MLPs) projecting \(\mathbf{x}\) vectors into \(d^{\text{arc}}\)-dimensional \(\mathbf{h}\) vectors, \([;1]\) appends an element of \(1\) at the end of the vectors, and \(U^{\text{arc}}\in\mathbb{R}^{(d^{\text{arc}}+1)\times(d^{\text{arc}}+1)}\) is a bilinear scoring matrix. This component is trained with cross-entropy loss of the gold-standard attachments. During inference, we use the Chu-Liu-Edmonds algorithm Chu and Liu (1965); Edmonds (1967) to find the spanning tree with the highest product of locally-normalized attachment probabilities.

Relation LabelerThe relation labeling component employs a similar deep biaffine scoring function as the unlabeled parsing component:

\[\mathbf{h}^{\text{rel-head}}_{i} =\text{MLP}^{\text{rel-head}}(\mathbf{x}_{i})\] \[\mathbf{h}^{\text{rel-dep}}_{j} =\text{MLP}^{\text{rel-dep}}(\mathbf{x}_{j})\] \[t_{i,j,r} =[\mathbf{h}^{\text{rel-head}}_{i};1]^{\top}U^{\text{rel}}_{r}[ \mathbf{h}^{\text{rel-dep}}_{j};1]\] \[P(\text{rel}(i,j)=r) =\text{softmax}_{r}(t_{i,j,:}),\]

where each \(U^{\text{rel}}_{r}\in\mathbb{R}^{(d^{\text{rel}}+1)\times(d^{\text{rel}}+1)}\), and there are as many such matrices as the size of the dependency relation label set \(|R|\). The relation labeler is trained using cross entropy loss on the gold-standard head-dependent pairs. During inference, the labeling decision for each arc is made independently given the predicted unlabeled parse tree.

## Appendix B Results with UAS Evaluation

We also evaluate different learning strategies based on unlabeled attachment scores (UAS), and the results are shown in Table B1. In line with LAS-based experiments, we find that modeling diversity is more helpful during initial stages of learning. For ID, we observe this effect even earlier than the fifth round of annotation: \(86.57_{\pm.44}\) vs. \(87.40_{\pm.51}\) after the first annotation round.

## Appendix C Sentence Selection Examples

In Table C2 we compare batches sampled by a diversity-aware selection strategy with a diversity-agnostic one. We observe that by modeling diversity in the sample selection process, DPPs avoid selecting duplicate or near-duplicate sentences and thus the annotation budget can be maximally utilized.

## Appendix D BALD under High Duplication Setting

Figure D1 shows the learning curves for BALD-based selection strategies under a high corpus duplication setting where the corpus is repeated



**Sentences selected by AMP (highest-quality ones first):**

Downgraded to Moody's were Home Lightness j offset - mortgege bonded and secured pollution - control bench to single - A -? from single - A -? incorrect pollution -control bench to pass -10 from single - A -? preferred not possible j offset. -A ?from single - A -? from single - A -? from a preliminary rating of single - A -? back full registration for collateralized debt activities to a preliminary rating of single - A -? from a preliminary rating of single - A -?, and the unit was firing for commercial power pump - Hine -? from single - ?

With a while in the 1970s we demand M. More such on a spending over time, with purchas or the former Vice Week Head and is adjacent Manhattan Center; a fading / processing compartment but includes it Alaska, Massachusetts, Virginia and Lithuanians -- a former Christian Brothers mannistry manager (both springwavenly situated on the Hudson River); shares it thanks from Washington to Uruguay -- a motion future production company -- newspapers , ash as the Washington Times. New York City Urban (cequisite); the News World J., and the successful Spanish -- Japanese locations and Islands.

LONDON LATE EIRODOLOLLES*3.8116 (\(\sim\) 50% on total); and (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on month); & (\(\sim\) 85% on total); & (\(\sim\) 85% on total); & (\(\sim\) 85% on month); & (

five times. In this extreme setting, the diversity-agnostic strategy significantly underperforms the diversity-aware one. We posit that the relative success of BALD compared to AMP in the twice-duplicated setting is due to the fact that BALD randomly draws dropout masks to estimate model uncertainty, so that identical examples could still have different quality measures.

## Appendix E Implementation Details and Hyperparameters

We do not tune our hyperparameters since in practice, active learning systems only have a single shot at success, without tuning. Instead, we follow recommendations from relevant prior work in setting our learning details and hyperparameters.

Active LearningFollowing Li et al. (2016), our active learning set-up proceeds in two stages for each annotation round. In the first stage, we select sentences filling in a budget of \(2500\) tokens; in the second stage, we pick \(500\) tokens out of the subset of sentences. For a diversity-agnostic strategy, we choose the top-\(k\) highest-quality candidates within the token budget, while our diversity-aware selection strategy uses a separate DPP for each stage. The active learning process is bootstraped with a seed set of \(128\) labeled sentences. For the BALD quality measure, we set \(K=5\).

Greedy MAP Inference for DPPsAlgorithm E1 illustrates the procedure for selecting items from DPPs under a budget constraint. This greedy MAP inference algorithm is adapted from Kulesza (2012). During sentence selection, the size of a sentence is its number of tokens, and each token has a size of \(1\) in the token selection stage.

Dependency ParserWe set the hyperparameters according to Dozat and Manning (2017). All the MLPs in the deep biaffine attention architecture have single hidden layers with ReLU activation functions and a dropout probability of \(0.33\), and we set \(d^{\text{arc}}\) and \(d^{\text{rel}}\) to be \(500\) and \(100\) respectively.

Training and OptimizationEach training batch contains \(16\) sentences and gradient norms are clipped to \(5.0\). We use the Adam optimizer Kingma and Ba (2015) with a learning rate of \(10^{-5}\) with \(640\) warmup steps with a linearly-increasing learning rate starting from \(0\).

ImplementationOur implementation is in PyTorch Paszke et al. (2019), and we use the transformers package6 to interface with the pre-trained XLM-RoBERTa model.