SlowGuess/ACL_2020_OCR huggingface dataset:
of-the-art Tree-GRU (Ma et al., 2018), however branch-LSTM outperforms Tree-GRU on the Twitter 16 dataset. On the PHEME dataset performance is comparable and slightly improved over the results in Kochkina et al. (2018). In line with model performance, the effect of rejection using aleatoric and epistemic uncertainties is different for PHEME compared to Twitter 15,16. Figure 4 (a) shows that in PHEME greater improvement in accuracy comes from using aleatoric uncertainty, whereas for Twitter 15 (b) and Twitter 16 (c) there is very little improvement with aleatoric uncertainty compared to epistemic. We believe this is due to the nature of the datasets: folds in PHEME differ widely in size and class balance, resulting in higher/more varied data uncertainty values, in contrast with the very balanced datasets of Twitter 15,16. The effect of rejection using low values of softmax confidence is also positive and often similar to the effect of epistemic uncertainty as it is also estimating model's uncertainty. However softmax is outperformed by other types of uncertainty in most cases (Figure 4).
6.2 Supervised Rejection
Table 2 shows the comparison of two models for supervised rejection versus unsupervised rejection of the same number of instances for all three datasets. Note that performance value in Table 2 differs from that in Figure 4 as this was obtained in a separate set of experiments (as described in section 5).
Having less training data harmed performance on PHEME and Twitter 16. Table 2 shows that using supervised rejection is better than unsupervised in terms of accuracy scores for all datasets and also in terms of macro F-scores for the Twitter 15,16 datasets. We believe that the reason the same effect on macro-F score is not observed in PHEME is the class imbalance in this dataset.
Comparing the two methods, SVM and RF, for supervised rejection we observe that RF leads to a larger amount of instances being removed, achieving higher performance than SVM. However, the difference in performance between the two is very small. As part of future work the meta-classifier can be improved further, made more complex or incorporated in the predictive model, making it closer to active learning, closing the loop from prediction and corresponding uncertainty to classifier improvement. Another benefit of using a supervised model for instance rejection is that it can be further tuned, e.g., by varying the threshold boundary to prioritise high precision over recall. The precision value of this meta-classifier is the same as the accuracy of the predictions obtained after the rejection procedure.
6.3 Timeline analysis
Part of the PHEME dataset was annotated for stance (Derczynski et al., 2017). We used the open-source branch-LSTM model trained on that part to
(a) Epistemic PHEME
(b) Epistemic Twitter 15
(c) Epistemic Twitter 16
Figure 6: Effect of class labels on uncertainty estimates.
True	False	Unverified	Non-Rumour
PHEME	0.569	0.198	0.163	-
Twitter 15	0.679	0.618	0.608	0.503
Twitter 16	0.88	0.729	0.755	0.739
Table 3: Per-class f1-scores of branch-LSTM model on each of the datasets.
obtain predicted stance labels for the rest of the PHEME dataset (Kochkina et al., 2017). There is no stance information for the Twitter 15,16 datasets, so this analysis is only available for the PHEME dataset. Note that we did not provide stance as a feature to train the veracity classifier: we assume that stance is an implicit feature within the tweets. Figure 5 shows examples of timelines of changes in predictions and uncertainty levels over time. Sub-plots (a) - (c) show all types of epistemic uncertainty: variation ratio (blue), entropy (green), variance (orange) as well as softmax confidence (red); on sub-plots (d) - (f) we show aleatoric uncertainty of the conversations corresponding to the above plots separately, as values are on a different scale. Each of the nodes is labeled with its predicted stance label: green - supporting, red - denying, blue - questioning and black - commenting. One could expect to see uncertainty decreasing over time as more information about a rumour becomes available (we can see this effect only very weakly on sub-plot Figure 5(b), showing a correctly predicted False rumour). However, not all responses are equally relevant and also the stance of new posts varies, therefore the uncertainty levels also change. Interestingly, the true rumour on subplot Figure 5(a) (incorrectly predicted as False during the final time steps) had low uncertainty at step 2 and was predicting a correct label. However, the model appears to have been confused by further discussion resulting in an incorrect prediction with higher uncertainty levels. The analysis
of uncertainty as a rumour unfolds can be used not only to analyse the effect of stance but also to study other properties of rumour spread. Only  $5 - 20\%$  of the conversations have a change in predictions as the conversation unfolds suggesting that source tweets are the most important for the model. Furthermore, we can use the timelines of uncertainty measurements in order to only allow predictions at the time steps with lowest uncertainty, which may lead to performance improvements. In experiments with the PHEME dataset accuracy grew from 0.385 to 0.395 using variation ratio and to 0.398 using aleatoric uncertainty estimates.
When analysing the relation between uncertainty and the conversation size, we observed that for the confidence levels represented by the output of the softmax layer, conversations with a larger amount of tweets had higher uncertainty. However, for aleatoric and epistemic estimates we do not observe a strong trend of uncertainty increase with the size of the conversation (see box plots in appendix D), which would indicate that these types of uncertainty are more robust in this respect. Higher levels of uncertainty associated with longer conversations may be due to the fact that responses became less informative and/or conversation changed topic. They may also be stemming from a weakness in model architecture in terms of its ability to process long sequences.
6.4 Uncertainty and Class Labels
Is higher uncertainty associated with a particular class label? Figure 6 shows boxplots of epistemic uncertainty values associated with each of the three classes in the PHEME dataset and each of the four classes in Twitter 15,16. Table 3 shows per-class model performance on the full datasets. In all datasets the True class has significantly lower levels of uncertainty (using Kruskal and Wallis 1952)
No calibration	Histogram Binning
S	A	VR	S	A	VR
PHEME	0.646	0.683	0.492	0.173	0.088	0.111
Twitter 15	0.265	0.333	0.216	0.056	0.039	0.062
Twitter 16	0.191	0.196	0.121	0.164	0.079	0.044
Table 4: Expected Calibration Error before and after applying calibration over uncertainty estimates. S - softmax (LCS), A - aleatoric uncertainty, VR - variation ratio.
test between the groups), while the uncertainties for False and Unverified are higher than True. The difference between False and Unverified is not statistically significant in any cases. Aleatoric uncertainty shows a similar pattern for the class labels. In Twitter 15,16 the Non-Rumour class has the highest uncertainty (and relatively lower f1 score). These outcomes are inline with findings in Kendall (2019) which showed an inverse relationship between uncertainty and class accuracy or class frequency.
6.5 Calibration outcomes
We measure and compare the ECE for all types of uncertainty. We apply Histogram Binning, a simple yet effective approach to improve the calibration for each type of uncertainty. We use the experiment setup with one of the folds reserved as development set to train the calibration method. We convert uncertainty estimates  $u$  into confidence scores as  $1 - u$ , and for aleatoric uncertainty we normalise it to be in [0, 1]. Table 4 shows the ECE before and after calibration, for different uncertainty measures -Softmax (S), Aleatoric (A), Variation Ratio (VR)- where a lower value indicates better calibration (calibration curves can be found in appendix E). Initial ECE for PHEME is higher than for Twitter 15 and 16 datasets. VR has the best initial calibration, however Histogram Binning notably improves calibration across all datasets and uncertainty types.
We have shown that data and model uncertainties can be included as part of the evaluation of any deep learning model without harming its performance. Moreover, even though data uncertainty estimation changes the loss function of a model, it often leads to improvements (Kendall and Gal, 2017). When performing rejection in an unsupervised fashion we need to know when to stop removing instances. Defining a threshold of uncertainty is not straightforward as uncertainty will be on a
different scale for different datasets. Supervised rejection leverages all forms of uncertainty together and dictates the number of instances to remove. Thus to tune both methods availability of a development set is important.
While we are not focusing on user uncertainty here, in rumour verification linguistic markers of user uncertainty (words like "may", "suggest", "possible") are associated with rumours. In the PHEME dataset such expressions often occur in unverified rumours, thus conversations containing them are easier to classify, and hence they are associated with lower predictive uncertainty.
We have presented a method for obtaining model and data uncertainty estimates on the task of rumour verification in Twitter conversations. We have demonstrated two ways in which uncertainty estimates can be leveraged to remove instances that are likely to be incorrectly predicted, so that making a decision concerning those instances can be prioritised by a human. We have also shown how uncertainty estimates can be used to interpret model decisions over time. Our results indicate that the effect of data uncertainty and model uncertainty varies across datasets due to differences in their respective properties. The methods presented here can be selected based on knowledge of the properties of the data at hand, for example prioritising the use of aleatoric uncertainty estimates on imbalanced and heterogeneous datasets such as PHEME. For best results, one should use a combination of aleatoric and epistemic uncertainty estimates and tune the parameters of uncertainty estimation methods using a development set. Using uncertainty estimation methods can help identify which instances are hard for the model to classify, thus highlighting the areas where one should focus during model development.
Future work would include a comparison with other, more complex, methods for uncertainty estimation, incorporating uncertainty to affect model decisions over time, and further investigating links between uncertainty values and linguistic features of the input.
This work was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1.
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A Comparison of unsupervised rejection performance using each type of uncertainty versus random rejection
Tables 5-7 present the results in terms of accuracy of unsupervised rejection of instances with the highest uncertainty and corresponding lowest confidence (softmax) values against random rejection of instances across 3 datasets: PHEME, Twitter 15, Twitter 16.
In all cases random rejection does not lead to consistent performance improvements, and hence, is outperformed by (un)certainty-based rejection.
As discussed in the main text of the paper, removing instances using uncertainty estimates leads to higher performance as higher levels of uncertainty indicate the incorrectly predicted instances. Using epistemic uncertainty is more effective on Twitter 15 and Twitter 16 datasets, while aleatoric is better for the PHEME dataset. Softmax-based rejection also leads to improvements, but is outperformed by either aleatoric or epistemic estimates depending on the dataset.
B Per-fold unsupervised rejection.
As we have explained in the experimental setup section of the main paper, during the cross-validation iterations each fold becomes a testing set once. We first aggregate predictions from each testing fold, and then perform evaluation and unsupervised rejection on the complete dataset. Alternatively, we could first perform the rejection procedure on each fold and then either aggregate the instances together for the evaluation (see tables 9, 10 and 11), or evaluate results on each fold separately (see table 8). The outcomes are shown in tables 9-11 below.
The choice of set up does not affect the main conclusion of the paper regarding the benefits of using uncertainty estimates for this task. We chose to aggregate instances first because of the nonhomogeneous sizes and label distributions of the folds in the PHEME dataset which introduces some artefacts. For example, Ebola-Essien event contains only 14 conversation threads, all of which are False rumours. This does not allow for meaningful conclusions about the model's performance, as it does not have all possible classes present. Furthermore when rejecting highly uncertain instances, the fold becomes even smaller.
In table 8 we see drastic differences between folds in the PHEME dataset, which is not the case
for the Twitter 15 and Twitter 16 datasets both of which contain folds balanced in size and label distribution. This also shows in the difference between the corresponding tables of the two set ups discussed in this section, which is more notable for PHEME (tables 5 and 9) than for the Twitter 15 (tables 6 and 10) and Twitter 16 (tables 7 and 11) datasets.
C Effect of Parameters on Uncertainty Estimates
The methods we use for uncertainty estimates rely on a number of parameters.
For epistemic uncertainty the main parameter is the dropout probability as the method relies on applying dropout at testing time. Aleatoric uncertainty estimates depend on the number of times we perform sampling  $(T)$  and how much weight  $(w)$  the model places on optimising the loss function associated with uncertainty.
We have performed a small parameter sweep comparing the output of models with testing dropout in [0.1, 0.3, 0.5, 0.7], T in [10, 50] and w in [0.2, 0.5]. Plots on Figure 7 show the effect of varying these parameters on unsupervised rejection outcomes in experiments on all datasets. In Figure 7 the Y-axis shows accuracy and the X-axis the proportion of the dataset on which it is measured.
We see that the effect of parameters is dataset-dependent. The method for estimating aleatoric uncertainty affects a model's performance as it is incorporated in its loss function. By contrast estimating epistemic uncertainty using dropout at testing time does not have any effect on model performance.
On the plots for aleatoric uncertainty Figure 7 (a-c) we see that changes in  $T$  and  $w$  strongly affect uncertainty estimates and the way they impact performance after unsupervised rejection. On the balanced Twitter 15,16 datasets aleatoric uncertainty for low  $T$  and  $w$  values does not help disambiguate between correct and incorrect instances very well and needs to be tuned by increasing their values. However, that may lead to deterioration of model performance, introducing a trade-off.
On the highly imbalanced PHEME dataset, aleatoric uncertainty estimates lead to improvements in performance for all parameter values, with the most increase observed when using a higher  $T$  and  $w = 0.2$ . We have not tested values of  $T$  higher than 50, which could lead to further improvements.
However it is likely there will be a maximum value after which we see no further improvements.
Varying the dropout rate during testing leads to changes in epistemic uncertainty estimates and their effect on performance using unsupervised rejection (Figure 7 (d-f)). The performance gains are observed for all three datasets. Increasing the dropout parameter from 0.1 to 0.3 in all datasets, and up to 0.5 in the PHEME and Twitter 16 datasets, leads to further improvements compared to lower values. However further increase of dropout to 0.7 starts to damage performance on the PHEME and Twitter 15 datasets.
D Uncertainty and Conversation Size
We have analysed how the size of the conversations affects uncertainty values. Figure 8 shows boxplots of uncertainty values of the conversations in all three datasets grouped by the number of tweets in each of them for aleatoric and epistemic uncertainty estimates as well as confidence levels (softmax). The conversations were grouped into equal sized bins, with resulting ranges of number of tweets are shown along the x-axis. We observe that for the confidence levels represented by the output of the softmax layer (Figure 8 (g,h,i)), conversations with a larger amount of tweets score lower values i.e., they have higher uncertainty. However for aleatoric and epistemic estimates (Figure 8 (a-f)) we do not observe a strong trend of uncertainty increase with the size of the conversation, so they seem to be more robust in this respect. We have also performed this analysis using the number of branches in the conversation instead of the number of tweets and we have observed a similar pattern.
E Calibration