SlowGuess/ACL_2020_OCR huggingface dataset:
sume the user quit creating a dictionary with  $10\%$  probability at every iteration, has a higher  $WCpI$  than the left one with  $\alpha = 0.0$
We conduct an experiment following the automatic evaluation framework by using public datasets and oracle dictionaries created through crowdsourcing. In the experiment, we compare several methods in addition to our proposed method. As emulation parameters, we set number of seed terms  $\left( \left| U_0 \right| \right)$ , the number of terms in one suggestion  $\left( \left| C \right| \right)$ , and number of total iterations  $(I)$  to 3, 10, and 30, respectively. Note that we tried different numbers of seeds (1 and 5), but the overall tendencies were the same.
We used crowdsourcing to create oracle dictionaries on the Amazon review corpus (Blitzer et al., 2007), which is publicly available.2 First, we explain the corpus processing and the procedure to construct the oracle dictionaries. We then describe the evaluation items. Our evaluation items will be publicly available for the system evaluation in future research.
Corpus. The corpus originally consists of sub corpora from 25 domains. Given that size and domain vary, we pick five domains; apparel (APP), baby (BAB), camera & photo (CAM), health & personal care (HEL), and sports & outdoors (SPO). We process the raw texts with spaCy  $^{3}$  and its dis
$^{2}$ https://www.cs.jhu.edu/ mdredze/datasets/sentiment/
tributed English model  $^{4}$ . We then construct the vocabulary with words and noun chunks that appeared more than five times except for standard stopwords. Note that all terms in the vocabulary are identified after lemmatization by spaCy.
Oracle Dictionaries. For each selected corpus, we create oracle dictionaries through crowdsourcing.<sup>5</sup> In the task for workers, we provide predefined dictionaries and ask the worker to choose one or more dictionaries to which a given term belongs. For example, we prepared three independent dictionaries nursery items dictionaries for sleeping, movement, and safety in the BAB corpus, and asked a worker to judge which dictionary includes the term "car seat". With respect to each corpus, we define multiple dictionaries and request three workers to make judgments for every term in the vocabulary. We determine that a term is included in a dictionary when at least one of three workers choose the dictionary for the term. Note that we filter noisy users and their answers beforehand according to the reliability score estimated by the crowdsourcing service.<sup>6</sup>. Finally, we also manually clean each dictionary. Excluding dictionaries consisting of less than 15 terms or too much noise, we eventually obtain 22 dictionaries. We list the dictionaries and example terms in Table 1.
Evaluation Item. We generate ten evaluation items per dictionary, for 220 items in total. An evaluation item consists of a unique set of seed terms  $(U_0)$  and the remaining terms in the corresponding dictionary as the oracle  $(U^{*} := U \setminus U_{0})$ . We suggest that fewer seed terms are adequate for evaluating an interactive dictionary construction method; because the purpose is to gather terms with a minimum human effort as mentioned in §2.
We compare four methods: Word2Vec, SetExpan, logistic regression, and our proposed method with several configurations. All methods possess the same vocabulary  $W$ , and all methods excluding Word2Vec use the same feature spaces: tf-ids of Bag of Words, unigrams, bigrams, and word embeddings. Any feature space is applicable, though.
Word2Vec: Word2Vec is a popular and promising method for representing word meanings in a continuous vector space, and the vector similarity is naturally applicable to interactive dictionary construction (Alba et al., 2018). We use two computation methods of candidate selection based on Word2Vec. The first is w2v (avg) and involves simply taking cosine similarity with an averaged vector of terms among  $\widetilde{U}$ . The second is w2v (rank) and calculates the mean reciprocal rank from terms in  $\widetilde{U}$ . Both select the candidates in order of their estimated scores. The embeddings are learned for each corpus with the gensim implementation using the default parameters.
SetExpan: We implement SetExpan (SE; Shen et al. 2017), which is a feature-selection method for conventional set expansion. The original version does not involve the user in the iteration and updates  $\widetilde{U}_i$  according to its own criteria to filter incorrect terms. In our scenario, we provide the correct terms in the update phase of  $\widetilde{U}_i$ . We use the same input features with other methods and set the hyperparameters to those Shen et al. (2017) reported as best.
Logistic Regression: We include logistic regression in our comparison because the feature weighting is one of the conventional types of linear discriminant analysis. The logistic regression version, LR, takes a word representation and then predicts the probability of the word appearing in a current dictionary. For word representation, we concatenate vectors in each feature space (explained in §5.2) and then use the vector compressed into 300 dimensions with singular value decomposition. In every iteration, we train LR from scratch with positive and negative terms. For the negative terms at the first iteration (i.e.,  $N_0$ ), however, we randomly select  $|U_0|$  of negative words from the entire vocabulary except for dictionary terms. We select candidates following the order of estimated probabilities. While we tried other regression models (SVM and Random Forest) and dimensions of the input vector (non-compression, 50, 100, 200, 500, and 1000), the above condition was the best configuration.
Feature Weighting with Predefined Similarity: We test six versions of our proposed methods:
- FWPS: Our base model without optimization
<sup>7</sup>https://radimrehurek.com/gensim/models/word2vec.html
4https://spacy.io/models/en#en_core_web_sm
<sup>5</sup>https://www_figure-eight.com/
Although we also tried other thresholds such as correspondence between three workers, this criterion provided the best balance of data cleanliness and size.
Corpus	Dictionary name	Size	Examples
APP	Accessory	63	flower, watch, glove, ring, case, scarf, garter, holder
Wearables for upper body	92	visor, tuxedo, sweatshirt, tank, pajama, blanket, glass, outer gown, robe, harness, sandal jersey, boot, loafer, nightgown
Wearables for lower body	83	sweatshirt, glove, trunk, bike, backpack, coat, hat
Items for outdoor	39
BAB	Nursery items for transport	37	carrier, stroller, leash, walker, backpack, strap, seat cover, sunshade cover, sterilizer, infant car seat, seat belt, beeping, monitor, sunshade cover, hammock, bedding, mattress, sleep sack, bumper, cushion, lamp
Nursery items for safety	74
Nursery items for sleeping	62
Enjoyments for baby	134	car, playmat, crayon, ring, dad, bell, bird, toy box
Wearables for baby	52	shoe, bouncer, towel, cloth, comforter, fleece, diaper, head support
CAM	Scene of photograph	84	summer, space, excursion, cruise, pool, face, wildlife, land
Subject of photograph	71	space, performer, ocean, magic, young, garden, action, snow
Functions of camera	108	remote switch, waterproof, trigger, telephoto, interface, portrait
External accessories	93	station, remote switch, polarizer, trigger, case, battery, microphone
HEL	Health equipment or product	54	bathtub, air bed, vitamin, heater, read glass, flosser, supplement, pillow
Appearance description	58	clear, oily, tint, sharp, handy, masculine, cheap, small
Functional description	86	naturally, refill, powerful, rapid, oily, sharp, smooth shave, handy
Beauty equipment or product	88	mirror, nivea, eyebrow, vanity, straightner, dryer, vitamin, fragrance
SPO	Body	57	blood, knuckle, eye, nose, chin, nail, knee, face, bone, palm
Wearables	70	pedometer, roll, strap, vest, rattle, cloth, boat, tent, slip, altimeter
Items for exercise	148	fanny pack, dumbbell, pod, rower, bottle, pedometer, knee pad, rack, towel
Items for outdoors	132	bicycle, opener, bottle, rack, towel, strap, guitar, fanny pack
Movements in exercise	86	sit, twist, pull, stand, situp, running, roll, rowing, swing setter, punch
Table 1: Examples of dictionaries.
where  $\pmb{w}$  is uniform distribution  $\rightarrow \S 3$
- +PickOne: Selecting only one feature space with the highest similarity scores among positive terms  $\rightarrow$  §3.3
-  $+\mathrm{Op}(\mathfrak{p})$ : With optimization using positive feedback  $\rightarrow$  Eq.(7)
-  $+Op(p/n)$ : With optimization using both positive and negative feedback  $\rightarrow$  Eq.(8)
$\bullet +\mathsf{F}\mathsf{d}(\mathsf{p})$  : With  $+\mathrm{Op}(p)$  and feedback denoising  $\rightarrow \S 3.4$
$\bullet +\mathrm{Fd}(\mathfrak{p} / \mathfrak{n})$  :With  $+0\mathrm{p}(\mathrm{p} / \mathrm{n})$  and feedback denoising  $\rightarrow \S 3.4$
We use the K-means algorithm for  $+0\mathrm{p}(\mathfrak{p})$  and  $+0\mathrm{p}(\mathfrak{p} / \mathfrak{n})$  with  $K = 3$ , though the overall trend was almost the same with  $K = 2$  and 5.
Hybrid: We also introduce a joint method HB that combines LR and an FWPS version. The strategy is simple; HB firstly uses FWPS's mechanism to broadly cover candidate terms, and then switches to LR when the amount of feedback increases. This mechanism naturally solves LR's problems that require negative feedback from the beginning and demand a moderate number of labels for training. Any of the FWPS versions can be combined with LR; therefore, we chose the best one for our experiment. The switch timing is empirically set to the 5-th iteration.
Table 2 lists the  $WCpI$  scores for each method across five corpora with  $\alpha = 0.0$ . In all domain texts, HB outperforms the others. The scores of LR are second highest, which implies that a combination with a FWPS model boosts performance. Among the versions of FWPS, +PickOne largely drops in score, which indicates the importance of the min-maximizing optimization strategy for this task (see §3.3). However, at least when  $\alpha = 0.0$  that assumes the user never quit the process in the midway through, the performances of FWPS and other versions with optimized  $w$  are not different much. In particular, the negative feedback tends to degrade the performance. Subsequently, SE, w2v(avg), and w2v (rank) perform poorly. SE may not be suitable for gathering arbitrary terms from a nonlarge corpus because it was originally designed and tested for collecting ontological terms from large-scaled data (Shen et al., 2017). Also, we find that leveraging embeddings in a straightforward manner is not sufficient, especially for interactive dictionary construction.
Let us now discuss changes when adjusting the  $WCpI$ 's  $\alpha$  listed in Table 3. Ignoring corpus differences, we take the average scores among all evaluation items. The most crucial change can be found in LR which significantly drops in score along with an increase in  $\alpha$ . When  $\alpha = 0.1$ , the score of LR already becomes inferior to most
Methods	APP	BAB	CAM	HEL	SPO
SE	21.20	18.83	11.34	17.01	16.79
w2v (avg)	18.51	12.77	10.36	14.60	14.28
w2v (rank)	24.39	12.71	10.29	18.63	17.04
LR	51.99	36.76	31.18	38.17	37.59
FWPS	46.90	34.32	27.61	38.17	35.56
+PickOne	18.51	12.79	10.36	14.40	14.28
+Op (p)	45.60	33.73	26.13	36.43	35.29
+Op (p/n)	43.42	30.88	23.13	33.19	31.91
+Fd (p)	46.17	34.92	26.76	37.60	36.03
+Fd (p/n)	46.33	32.01	25.36	37.04	34.63
HB (+Fd (p))	53.07	37.38	32.31	42.22	39.74
Table 2:  ${WCpI}$  scores across corpora  $\left( {\alpha  = {0.0}}\right)$
Methods	α
0.0	0.1	0.3	0.5
SE	17.05	14.36	14.26	15.46
w2v(avg)	14.10	10.83	9.39	9.63
w2v(rank)	16.61	12.42	9.95	9.68
LR	39.14	30.06	23.39	22.45
FWPS	36.51	32.02	30.49	31.51
+PickOne	14.07	10.93	9.64	9.95
+Op(p)	35.44	31.79	30.72	31.58
+Op(p/n)	32.50	29.17	28.89	30.32
+Fd(p)	36.30	32.42	31.10	31.95
+Fd(p/n)	35.07	30.92	29.56	30.53
HB(+Fd(p))	40.95	34.14	30.97	31.62
Table 3: Change in  $WCpI$  scores when increasing  $\alpha$ . The scores are averaged among all evaluation items.
of the FWPS versions. Also, the scores of FWPS tend to be higher with a larger value of  $\alpha$ . When  $\alpha \geq 0.3$ ,  $+\mathrm{Fd}(\mathfrak{p})$  performs the best among all methods. In short, LR suggests correct terms in latter iterations; while FWPS, in particular with trainable ones  $(+Op(p), +Fd(p))$ , suggests correct terms in earlier iterations.
Figure 7 directly describes the score differences with different alphas by showing the hit ratios defined as  $|U_i| / |C|$  in terms of each iteration number for LR,  $+\mathrm{Fd}(\mathfrak{p})$ , and HB. Regardless of the number of seed terms, LR suggests fewer correct terms in earlier iterations, but its hit ratio stably goes beyond  $+\mathrm{Fd}(\mathfrak{p})$  after obtaining a moderate number of training labels (around five iterations, i.e., fifty labels). On the other hand,  $+\mathrm{Fd}(\mathfrak{p})$  performs better by a large margin in earlier iterations than LR. In short, our method using predefined term similarities overcomes the smaller sample issue which a conventional linear classifier suffers from and contributes to quick dictionary construction. This result is practically important because the analyst will go through repeated trial and error - observing documents from various points of views - by creating many small dictionaries. In addition, such contrasts are much stronger when
Figure 7: Hit ratio  $(|U_i| / |C|)$  in terms of each iteration number by LR,  $+\mathrm{Fd}(\mathfrak{p})$ , and HB. The upper and lower graphs start with one and three seeds, respectively.
we give only one seed term (the upper graph), which is also meaningful because the user often starts dictionary construction with only one seed term in a real situation.
HB enjoys both benefits of coverage by LR and quickness by  $+\mathrm{Fd}(\mathfrak{p})$ . In other words, a conventional classifier and our method are complementary; LR becomes favorable when the user prioritizes coverage than quickness, and  $+\mathrm{Fd}(\mathfrak{p})$  becomes favorable when vice versa. As a possible use case of HB, the analyst may quickly find interesting perspectives by creating various dictionaries with one of the FWPS methods, and once finding those, he/she switches to a linear classifier to expand the promising dictionaries more.
To the best of our knowledge, this paper proposes the first formulation of interactive dictionary construction for text analytics, which clarifies the critical issues to resolve. In response to those issues, we provide the method, the evaluation framework, and the experimental dataset. Also, our experimental results show the promising performances of our method in concern with real situations of text analytics. Our systematic study will pave the way to future research about the effective construction of dictionaries for text analytics.
We appreciate anonymous reviewers and their insightful comments. Also, we are grateful to Tadayuki Yoshida and Ryuki Tachibana for helpful discussions based on practical use-cases.
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We prove that our formulation of the optimization problem is a natural extension of that of SetExpan, assuming a reasonable normalization constraint for entity vectors and their weights. Notations follow from the main paper. Recall that the formulation of SetExpan is
$$
F ^ {*} = \underset {| F | = Q} {\arg \max } \sum_ {1 \leq i <   j \leq n} S i m \left(e _ {i}, e _ {j} \mid F\right), \quad (1)
$$
where  $Q$  is the number of features in  $F$  and is a fixed integer value.
Building on this, our formulation is
$$
\boldsymbol {w} ^ {*} = \arg \max  _ {\boldsymbol {w}} \sum_ {i = 1} ^ {n} \operatorname {S i m} \left(e _ {i}, \widetilde {U} | \boldsymbol {w}\right). \tag {4}
$$
Substitute (2) and (3) in the main paper into the above formulation to obtain
$$
\begin{array}{l} \boldsymbol {w} ^ {*} = \arg \max _ {\boldsymbol {w}} \sum_ {i = 1} ^ {n} \left\{\frac {1}{n} \sum_ {j = 1} ^ {n} S i m (e _ {i}, e _ {j} | \boldsymbol {w}) \right\} \\ = \arg \max  _ {\boldsymbol {w}} \frac {1}{n} \left\{2 \times \sum_ {1 \leq i <   j \leq n} S i m \left(e _ {i}, e _ {j} \mid \boldsymbol {w}\right) \right. \\ + \sum_ {i = 1} ^ {n} S i m (e _ {i}, e _ {i} | \boldsymbol {w}) \} \\ = \arg \max  _ {\boldsymbol {w}} \left\{\frac {2}{n} \sum_ {1 \leq i <   j \leq n} S i m \left(e _ {i}, e _ {j} \mid \boldsymbol {w}\right) \right. \\ \left. + \frac {1}{n ^ {2}} \sum_ {k = 1} ^ {L} w _ {k} \Big (\sum_ {i = 1} ^ {n} \| \pmb {v} _ {f _ {k}} (e _ {i}) \| \Big). \right\} \\ \end{array}
$$
In the right-hand side of the last equation, the second term is a constant when all of the vectors  $\{\pmb{v}_{f_k}(e_i)\}_{i = 1,\dots,n}$  have the same norm and  $\sum_{k = 1}^{L}w_{k} = 1$ . Then our optimization problem is equivalent to
$$
\boldsymbol{w}^{*} = \operatorname *{arg  max}_{\boldsymbol{w}}\sum_{1\leq i <   j\leq n}Sim(e_{i},e_{j}|\boldsymbol {w}),
$$
which is a continuous version of (1).
Next, let us prove that in the modified version of our optimization problem ((7) in the main paper),
$$
\min  _ {1 \leq i \leq n} S i m \left(e _ {i}, \widetilde {U} | \boldsymbol {w}\right) \tag {10}
$$
is a concave function of  $\pmb{w}$ . Hence we can apply standard techniques of convex optimization to solve (7). First let us rewrite (10) as follows:
$$
\begin{array}{l} \min  _ {1 \leq i \leq n} S i m \left(e _ {i}, \widetilde {U} | \boldsymbol {w}\right) \\ = \min  _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} w _ {k} \cdot \left(\boldsymbol {v} _ {f _ {k}} \left(e _ {i}\right) \cdot \boldsymbol {v} _ {f _ {k}} (\widetilde {U})\right) \\ = \min _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} w _ {k} \cdot x _ {i k}, \\ \end{array}
$$
where  $x_{ik} = \pmb{v}_{f_k}(e_i)\cdot \pmb{v}_{f_k}(\widetilde{U})$ . Then it is sufficient to prove the following lemma.
Lemma 1. The following function is concave for  $\pmb{w}$  when  $\pmb{w}$  is defined on a convex set.
$$
g (\boldsymbol {w}) := \min  _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} w _ {k} \cdot x _ {i k} \tag {11}
$$
Proof. It is a straightforward calculation by the definition of concavity. for any  $\pmb{w_1} = \{w_{11},\dots ,w_{1L}\}$ ,  $\pmb{w_2} = \{w_{21},\dots ,w_{2L}\}$ , and  $\lambda \in (0,1)$ , we need to prove that
$$
g ((1 - \lambda) \boldsymbol {w} _ {1} + \lambda \boldsymbol {w} _ {2}) \geq (1 - \lambda) g (\boldsymbol {w} _ {1}) + \lambda g (\boldsymbol {w} _ {2}).
$$
We can compute the left-hand side of this equation by using (11):
$$
\begin{array}{l} g ((1 - \lambda) \boldsymbol {w} _ {1} + \lambda \boldsymbol {w} _ {2}) \\ = \min _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} ((1 - \lambda) w _ {1 k} + \lambda w _ {2 k}) \cdot x _ {i k} \\ = \min  _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} \left\{\left(1 - \lambda\right) w _ {1 k} x _ {i k} + \lambda w _ {2 k} x _ {i k} \right\} \\ \geq \min _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} (1 - \lambda) w _ {1 k} x _ {i k} \\ + \min  _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} \lambda w _ {2 k} x _ {i k} \\ = (1 - \lambda) \min _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} w _ {1 k} x _ {i k} \\ + \lambda \min  _ {1 \leq i \leq n} \sum_ {k = 1} ^ {L} w _ {2 k} x _ {i k} \\ = (1 - \lambda) g (\boldsymbol {w} _ {\mathbf {1}}) + \lambda g (\boldsymbol {w} _ {\mathbf {2}}). \\ \end{array}
$$
Here we use the inequality  $\min_{1\leq i\leq n}(A_i + B_i)$ $\geq \min_{1\leq i\leq n}A_{i} + \min_{1\leq i\leq n}B_{i}$  that holds for any sequences of real numbers  $\{A_i\}_{i = 1,\dots,n}$  and  $\{B_i\}_{i = 1,\dots,n}$ .