Wat zei je? Detecting Out-of-Distribution Translations with Variational Transformers

1 INTRODUCTION . Statistical Machine Translation ( SMT , ( Brown et al. , 1993 ; Och , 2003 ) ) , built on top of probabilistic modelling foundations such as the IBM alignment models ( Vogel et al. , 1996 ; Brown et al. , 1993 ; Gal & Blunsom , 2013 ) , has largely been replaced in recent years following the emergence of Neural Machine Translation approaches ( NMT , ( Kalchbrenner & Blunsom , 2013 ; Bahdanau et al. , 2015 ; Luong et al. , 2015 ; Vaswani et al. , 2017 ) ) . This change has brought with it huge performance gains to the field ( Sennrich et al. , 2016 ) , but at the same time we have lost many desirable properties of these models . Statistical probabilistic models can inform us when they are guessing at random on inputs they never saw before ( Ghahramani , 2015 ) . This information can be used , for example , to detect out-of-training-distribution examples for selective classification by referring uncertain inputs to an expert for annotation ( Leibig et al. , 2017 ) , or for a human-in-the-loop approach to reduce data labelling costs ( Gal et al. , 2017 ; Walmsley et al. , 2019 ; Kirsch et al. , 2019 ) . With new tools in machine learning we can now incorporate such probabilistic foundations into deep learning NLP models without sacrificing performance . This field , known as Bayesian Deep Learning ( BDL , ( Neal , 2012 ; Gal , 2016 ) ) , is concerned with the development of scalable tools which capture epistemic uncertainty—the model ’ s notion of “ I don ’ t know ” , a measure of a model ’ s lack of knowledge e.g . due to lack of training data , or when an input is given to the model which is very dissimilar to what the model has seen before . Such BDL tools have been used extensively in the Computer Vision literature ( Kendall & Gal , 2017 ; Litjens et al. , 2017 ) , and have been demonstrated to be of practical use for applications including medical imaging ( Litjens et al. , 2017 ; Nair et al. , 2020 ) , robotics ( Gal et al. , 2016 ; Chua et al. , 2018 ) , and astronomy ( Hon et al. , 2018 ; Soboczenski et al. , 2018 ; Hezaveh et al. , 2017 ) . In this paper we extend these tools , often used for vision tasks , to the language domain . We demonstrate how these tools can be used effectively on the task of selective classification in NMT by identifying source sentences the translation model has never seen before , and referring such source sentences to an expert for translation . We demonstrate this with state-of-the-art Transformer models , and show how model performance increases when rejecting sentences the model is uncertain about—i.e . the model ’ s measure of epistemic uncertainty correlates with mistranslations . For this we develop several measures of epistemic uncertainty for applications in natural language processing , concentrating on the task of machine translation ( §3 ) . We compare these measures both with standard deterministic Transformer models , as well as with Variational Transformers , a new approach we introduce to capture epistemic uncertainty in sequence models using dropout approximate inference ( Gal , 2016 ) . We give an extensive analysis of the methodology , and compare the different approaches quantitatively in the out-of-training-distribution settings ( §4 ) , which shows our proposed uncertainty estimate BLEUVar works well for measuring the epistemic uncertainty for machine translation . We also analyse the performance of BLEUVar qualitatively from both the influence of sentence length and from the linguistic perspective . We finish with a discussion in potential use cases for the new methodogy proposed . The closest NLP task to the above problem definition is the quality estimation ( QE ) task in Machine Translation ( Specia et al. , 2010 ; Blatz et al. , 2004 ) , which tries to solve a similar problem by predicting the quality of a translation with a score called Human Translation Error Rate ( HTER , ( Snover et al. , 2006 ) ) . This is done by training a surrogate QE model on source sentences and their corresponding machine-generated translations in a specific domain , with the target of the surrogate to predict the the percentage of edits needed to be fixed . While many methods have been shown to successfully solve the task of estimating the quality of translations ( Kim et al. , 2017 ; Martins et al. , 2016 ; 2017 ; Kreutzer et al. , 2015 ) , by definition QE crucially relies on examples of mistranslations to train the surrogate . The assumption that such training data is available is often violated in practice though ( e.g . in active learning ) , thus existing approaches in QE research can not generally be used to detect out-of-training-distribution examples ( see Appendix C for detail discussion about the differences between QE and our task , as well as other related work that is similar to ours but not solving the same problem ) . 2 BACKGROUND : UNCERTAINTY IN DEEP LEARNING . For most machine learning models , the optimisation objectives give us a point estimate of the model parameters , which maximise the likelihood of the model generating the training data ( i.e . p ( Y |X , ω = ω∗ ) , ω∗ ∈ Ω s.t . Ω is the set of all possible model parameters , Y , X are the training data ) . Such point estimate ω∗ gives us a very good prediction when the test data follow the same distribution as the training data distribution . Given a new input x∗ at test time , the model prediction for the corresponding y∗ is ŷ∗ = arg max y∗ p ( y∗|x∗ , ω∗ ) . ( 1 ) However , we can not expect the model to perform well on out-of-distribution ( OOD ) data which it never saw before . Instead , we would wish for the model to indicate its uncertainty towards such inputs . We could use p ( ŷ∗|x∗ , ω∗ ) as an estimate for model uncertainty , but as we show below , it would not be a well calibrated one . It might be the case that many ω might give equally good predictions on the train set , but might widely disagree with their predictions on OOD data . In fact , ω∗ might give arbitrary predictions on OOD training data which is very dissimilar to previously observed inputs . Thus , a high score does not distinguish whether x∗ is OOD or not , and whether we should trust the model ’ s prediction . 2.1 BAYESIAN INFERENCE . Bayesian probabilistic models capture the notion of uncertainty explicitly . Rather than considering a single point estimate ω∗ , Bayesian models aim to capture the entire distribution of ω from the training data . The resulting distribution is called posterior distribution p ( ω|X , Y ) = p ( Y |X , ω ) p ( ω ) p ( Y |X ) . ( 2 ) At test time , we can make prediction about the corresponding y∗ by integrating out all possible ω p ( y∗|x∗ , X , Y ) = ∫ p ( y∗|x∗ , ω ) p ( ω|X , Y ) dω . ( 3 ) Using the variance of the predictive distribution p ( y∗|x∗ , X , Y ) as the uncertainty measure would have taken into account the variance of ω . Hence , an uncertainty measure based on this quantity could be a strong indicator for x∗ being OOD . 2.2 APPROXIMATE INFERENCE . The difficulty in doing Bayesian inference comes from the intractability of calculating the evidence p ( Y |X ) = ∫ p ( Y |X , ω ) p ( ω ) dω . ( 4 ) There might be a closed form solution for a simple model . But for most interesting problems , it is too difficult to compute an exact solution . Therefore , approximations are often used for such inference problems . Variational inference ( VI ) is a pragmatic popular method for doing approximate inference ( Jordan et al. , 1999 ) . The method involves defining an approximating distribution qθ ( ω ) , and trying to find the parameter θ for that minimises the Kullback-Leibler ( KL ) divergence ( Kullback & Leibler , 1951 ) between qθ ( ω ) and the posterior KL ( qθ ( ω ) ‖p ( ω|X , Y ) ) = ∫ qθ ( ω ) log qθ ( ω ) p ( ω|X , Y ) dω . ( 5 ) The resulting θ∗ gives us the closest approximation for the posterior in the family of distribution qθ ( ω ) . However , calculating the KL divergence here is also intractable as we still have to do the integration for the evidence in posterior . Fortunately , a tractable and equivalent objective for minimising the KL divergence is to maximise the evidence lower bound ( ELBO , ( Blei et al. , 2017 ) ) of qθ ( ω ) ELBO ( qθ ) = ∫ qθ ( ω ) log p ( Y |X , ω ) dω −KL ( qθ ( ω ) ‖p ( ω ) ) . ( 6 ) This is tractable as we know all the distributions ( both qθ ( ω ) , p ( Y |X , ω ) and p ( ω ) are defined by the model or by our assumptions ) . 2.3 BAYESIAN INFERENCE IN DEEP LEARNING . Almost all deep models treat the units in a deep neural network as deterministic functions . To adapt Bayesian methods in deep learning , we need to first turn our model into a probabilistic model . It can be done by modelling the weights in each unit of the network as samples from probability distributions . Such networks are called Bayesian neural networks ( Neal , 2012 ) . One major challenge with Bayesian neural networks is that the integration in ELBO becomes intractable when we have more than one hidden layer ( Gal , 2016 ) . Many works have tried tackling this problem . One practical method proposed by Gal ( 2016 ) is MC Dropout . Gal ( 2016 ) showed that optimising any neural networks with dropout can be viewed as an approximate inference in a probabilistic model ( when dropout p is tuned correctly ) , which implies that a trained neural network with dropout can be interpreted as a Bayesian neural network Gal ( 2016 ) . Stochastic forward passes with dropout ‘ turned-on ’ at test time then correspond to draws from the predictive distribution . Here we extend on these ideas and propose the Variational Transformer , which is based on MC Dropout applied to the original Transformer model . We perform extensive empirical evaluation with this model on the task of NMT . Representing uncertainty in a translation model is the first step towards detecting OOD data . We next discuss how to use this uncertainty effectively , and provide the main contribution of this work . 3 MEASURES OF UNCERTAINTY FOR NMT . Principally , we care about measuring the variance of a model ’ s outputs around some given input point . In the context of a simple classifier model , the solution is often found by measuring the mutual information between the predicted discrete distribution and model parameters , evaluating the output ’ s entropy , or simply computing the variance of model outputs ( Gal , 2016 ) . In the domain of language , however , there are many semantically equivalent alternatives to the same prediction , and it is a difficult matter to measure the disagreement between the predicted discrete sequences , which in turn complicates the estimation of variance in the output space . Much worse , when attempting to naively use MI or entropy with long sequences or large sets of discrete random variables , we quickly discover that even approximate integration over the product space becomes prohibitive ( Kirsch et al. , 2019 ) . In order to capture epistemic uncertainty in the task of NMT , we propose several measures of uncertainty appropriate for long sequences of discrete variables ( Beam Score and Sequence Probability are measures similar to ( Wang et al. , 2019 ; Fomicheva et al. , 2020 ) ) : 1 . Beam Score : we assign a confidence to output y generated ( using beam search ) from input x using the score assigned to y ’ s beam ( Wu et al. , 2016 ) , where length_penalty ( y ; α ) = ( 5+|y| 5+1 ) α . BS = log ( pω∗ ( y|x ) ) length_penalty ( y ; 0.6 ) ( 7 ) 2 . Sequence Probability : we assign a confidence to the deterministic model output y generated from input x by taking the log predictive probability under the weight distribution . SP = log ( Eω∼qθ∗ ( ω ) pω ( y|x ) ) length_penalty ( y ; 0.6 ) ( 8 ) 3 . BLEU Variance : ideally , we would like to measure the variance of outputs y as the uncertainty at an input x , i.e . : Var = Eω∼qθ∗ ( ω ) Ey∼pω ( y|x ) ( y − µ ) 2 = Eω∼qθ∗ ( ω ) Ey , y′∼pω ( y|x ) 1 2 ( y − y′ ) 2 , ( 9 ) where µ = Ey∼pω ( y|x ) [ y ] . If we treat sentences as points in some high dimensional space , ||y−y′|| corresponds to a distance between these two points , which is a numerical value representing the difference between two sentences . Thus , any metric for measuring the difference between sentences will allow us to calculate the variance of output y . In our experiments we choose BLEU ( Papineni et al. , 2002 ) . The BLEU score of a candidate text to the reference text is a number between 0 and 1 , with the value closer to 1 indicating the two texts are more similar1 . Now , we can estimate the variance at an input x by producing pairs of outputs from the model and measuring the squared complement of the BLEU between them , i.e . ||y − y′||2 : = ( 1− BLEU ( y , y′ ) ) 2 , and we have : BLEUVar = Eω∼qθ∗ ( ω ) Ey , y′∼pω ( y|x ) ( 1− BLEU ( y , y ′ ) ) 2 ( 10 ) For the beam score we use the deterministic model found by gradient descent and simply take the probabilities from under its output probabilities . This will be our baseline . For sequence probability and BLEU variance we use MC Dropout ( Gal , 2016 ) and take a number of samples ( N ) to estimate the expectations2 : SP ≈ log ( ∑N i=1 pωi ( y|x ) ) length_penalty ( y ; 0.6 ) ( 11 ) For the BLEUVar approximation , we opt for decoding outputs using beam search applied to different model samples ( realised by randomising the dropout masks ) and measuring the complement BLEU between pairs of these examples . BLEUVar ≈ N∑ i=1 N∑ j 6=i ( 1− BLEU ( decωi ( x ) , decωj ( x ) ) ) 2 . ( 12 ) Additionally , out of the N sample sequences generated by BLEUVar , we need to choose one or generate a new sequence as the result for a specific input . In regression , the mean of the samples is normally chosen as the result , which is an approximation for the predictive mean . In our case , the ‘ mean ’ of N sentences is hard to derive or even not properly defined . Therefore , we use the sampled sequence that is the closest to the ideal ‘ mean ’ as an approximation . Since we can measure the disagreement between any two sentences using BLEU , the sequence that is the closest to the ‘ mean ’ of the N samples must have the smallest disagreement with rest of the N − 1 samples . Hence , the final output sequence of the method BLEU Variance is : µ̃ = arg min yi ( N∑ ∀j 6=i ( 1− BLEU ( yi , y′j ) ) + N∑ ∀j 6=i ( 1− BLEU ( y′j , yi ) ) ) . ( 13 ) One remark for the above three methods is that the two methods BS and SP have the same resulting translation y given x , but with different values as its uncertainty estimates . For the method BLEUVar , it uses µ̃ for the resulting translation , and a value in a different range as the uncertainty estimate . This is reflected in the plots from the experiments section . For example , in Figure 6 ( b ) , BS and SP converged into the same value , while BLEUVar converged to a different value .

Summary: The paper proposes a technique for assessing the uncertainty of a Transformer-based NMT model on a given input $x$. The technique relies on computing a variance-like estimate over a collection of translation candidates for $x$, where these candidates are obtained by perturbing the decoding mechanism through the use of dropout at test time. Experiments compare this technique with other ways of measuring the "epistemic uncertainty" of the NMT model. In limited training data conditions, the proposed measure is better aligned with the actual performance of the model than competing measures, and in particular is better able to detect Out-of-Domain translation requests.