Question: Represent the text to find a very short summary (1-2 sentences max)

Question: Beyond understanding what is being discussed, human communication requires an awareness of what someone is feeling. One challenge for dialogue agents is recognizing feelings in the conversation partner and replying accordingly, a key communicative skill that is trivial for humans. Research in this area is made difficult by the paucity of suitable publicly available datasets both for emotion and dialogues. This work proposes a new task for empathetic dialogue generation and EmpatheticDialogues, a dataset of 25k conversations grounded in emotional situations to facilitate training and evaluating dialogue systems. Our experiments indicate that dialogue models that use our dataset are perceived to be more empathetic by human evaluators, while improving on other metrics as well (e.g. perceived relevance of responses, BLEU scores), compared to models merely trained on large-scale Internet conversation data. We also present empirical comparisons of several ways to improve the performance of a given model by leveraging existing models or datasets without requiring lengthy re-training of the full model. Natural communication is frequently prompted by people sharing their feelings or circumstances. As examples, a recent study found that 80% of Twitter users seem to post mostly about themselves BID28, and ELIZA BID44, one of the earliest chatbots developed, focused on asking its conversational partners why they were feeling a certain way. Interacting in these conversations requires reacting to what people share with an understanding of others' implied feelings. For instance, while the crossed-out response in FIG0 is topically relevant, "Congrats! That's great!" is more natural because it acknowledges the underlying feelings of accomplishment. Responding to people in a way that is empathetic or that acknowledges how the other person feels is a desirable trait for a dialogue agent, but still a nontrivial communicative skill. It is also currently difficult to measure. Although recent work has used large-scale corpora to train reasonably fluent and engaging dialogue agents (e.g. BID24), existing chitchat dialogue benchmarks are not designed to capture whether those agents are responding in an empathetic way to implicit emotional cues. This may indeed be unlikely, given that the sources of Internet conversation data used for training are known to harbor aggressive and callous responses BID0.This works aims to make it easier to evaluate machines' ability to respond in an empathetic way. We introduce a new task for dialogue systems to respond to people discussing everyday situations, based on EMPATHETICDIALOGUES, a novel dataset with 25k personal dialogues. Each dialogue is grounded in a specific situation where a speaker was feeling a given emotion, with a listener responding. The dataset is larger and contains a more extensive set of emotions than many similar emotion prediction datasets from other text domains such as BID34, BID39, BID26, and BID11. Previous dialogue datasets of a similar scale that include emotion labels BID19 BID11 come from crawled Table 1: Two examples from EMPATHETICDIALOGUES training set. The first worker (the speaker) is given an emotion label and writes their own description of a situation when they've felt that way. Then, the speaker tells their story in a conversation with a second worker (the listener).Label: Afraid Situation: Speaker felt this when... "I've been hearing noises around the house at night" Conversation: Speaker: I've been hearing some strange noises around the house at night. Listener: oh no! That's scary! What do you think it is? Speaker: I don't know, that's what's making me anxious. Listener: I'm sorry to hear that. I wish I could help you figure it out Label: Proud Situation: Speaker felt this when... "I finally got that promotion at work! I have tried so hard for so long to get it!" Conversation: Speaker: I finally got promoted today at work! Listener: Congrats! That's great! Speaker: Thank you! I've been trying to get it for a while now! Listener: That is quite an accomplishment and you should be proud! conversations extracted from settings that are quite different from a one-on-one conversation (educational dialogues for English learners for DAILYDIALOG, public social media content for BID11) and cover either a very limited or a very imbalanced set of emotions: only ≈ 5% of the DailyDialog utterances have a label other than'none' or'happy', and BID11 only labels'happy','sad', and'angry'. The open resource we propose consists of crowdsourced one-on-one conversations, and covers a large set of emotions in a balanced way. We then examine how to train a dialogue system that is more adept at responding to emotional cues. While a rule-based system can be built around mapping predicted emotions to responses, end-toend dialogue systems relying on neural networks and trained on conversation corpora BID36 BID42 BID35 BID3 BID24 BID48 offer the promise of better generalization to new contexts. Through an extensive set of experiments, we show that fine-tuning a dialogue agent on our dataset in better performance on a novel empathetic dialogue task. The pretraining of the dialogue agent on Internet conversation data is the most time-consuming step of this pipeline, by an order of magnitude. To make it easier for practitioners to improve performance of a model on the empathetic task with minimal re-training while re-using existing resources, we compare various ways of supplementing a pretrained model with additional representations from external tasks, and show that even simplistic schemes can lead to better performance. The contributions of this work are thus threefold: 1) we release a novel empathetic dialogue dataset as a new benchmark; 2) we show that using this dataset for training can improve the performance of an end-to-end dialogue system on empathetic dialogue; and 3) we compare multiple ways to further improve performance with combined representations while not requiring onerous re-training. Responding well to emotions requires sufficient coverage of human expression. Multiple schemas have attempted to organize the spectrum of emotions, from a handful of basic emotions derived from biological responses BID5 BID32 to larger sets of subtle emotions inferred from contextual situations BID37. We incorporate emotions from multiple annotation schemas, noting that emotions merely inferred from a situation are important in dialogue scenarios. Rich information can be represented by learning multidimensional distributional embeddings from data, as has proven successful for many language applications BID9. These distributional representation approaches are at the core of the current state of the art in emotion classification BID4 BID26 ) that build on deep networks pretrained on large-scale weakly labelled data such as emojis BID6 or hashtags BID27, gathered from public social media content published on Twitter. The SEMEVAL2019 EmoContext challenge also uses conversation data for detection of three basic s e n ti m e n ta l p ro u d c o n fi d e n t fu ri o u s c a ri n g a n g ry te rr ifi e d n o s ta lg ic tr u s ti n g s a d h o p e fu l je a lo u s a s h a m e d g ra te fu l a n x io u s a n ti c ip a ti n g a p p re h e n s iv e lo n e ly d is a p p o in te d e m b a rr a s s e d fa it h fu l Figure 2: Distribution of situation/conversation labels within EMPATHETICDIALOGUES. Percentages per class are also listed in the appendix.emotions over two turns of context from Twitter exchanges BID11. While public social media content has the advantage of being spontaneous (not elicited) data, it suffers from two shortcomings when used to train a model intended for one-on-one conversation (as opposed to, say, a bot designed to post on Twitter). First, the content is extracted from a context of communication in front of large "peripheral audiences" BID8 which include potentially everyone with an Internet connection, where the need for curated self-presentation BID7 and the uncertainty as to how wide that audience may be have been shown to lead to different choices of subject matters compared to private messaging, with people sharing more intense and negative emotions through private channels BID2 BID20. Second, Tweets are generally a short-form format limited to 140 characters, which is not a constraint that applies to general conversation. In this work, we attempt to generate a more balanced coverage of emotions than would appear in public social media content, within a one-on-one framing of unconstrained utterances that is closer to our ultimate goal of training a model for conversation that can respond to any emotion. Several works have attempted to make chit-chat dialogue models more engaging by grounding them in personal contexts BID18 BID48 BID24, but focusing on personal facts ("I am from New York") rather than situations. The DAILYDIALOG dataset BID19, comprising about 13k dialogues obtained by crawling educational websites intended for learners of English, includes many dialogues anchored in everyday situations and has been annotated post-hoc with emotion labels, but only ≈ 5% of the utterances have a label other than "none" or "happy", and dialogues are mostly limited to domains deemed appropriate for use as a language learning tool (ordering from a restaurant, asking for directions, shopping for a specific item, introductions, etc). Our task focuses explicitly on conversations about an emotionally grounded situation, and considers a richer, evenly distributed set of emotions. We also introduce an explicit single listener in the conversation who is reacting to the situation being described in an empathetic way, to make the setting as close as possible to our desired goal of a one-on-one empathetic conversation. Several other works have focused on controlling the emotional content of a text response either through a manually specified target BID50 BID49 BID43 BID12 BID13 or through a general term to encourage higher levels of affect BID1, with evaluations focused on matching a predetermined desired emotion rather than empathetic responding. BID29 generate responses conditioned on a specified politeness setting (polite, rude or neutral), where politeness is viewed as a style of language. BID14 investigate how to respond to emotions detected from an image. By contrast, our work examines how to produce empathetic responses that are appropriate to signals inferred purely from text, and not intended to themselves convey a pre-specified emotion. We consider an open-domain one-on-one conversational setting where two people are discussing a situation that happened to one of them and that led to the experience of a given feeling. Emotional situation grounding Each conversation is grounded in a situation, which one participant writes about in association with a given emotion label. We consider 32 emotion labels, listed in Figure 2. To select this set of labels, we drew inspiration from previous datasets (; BID39 BID37 BID19 BID27, consolidating the labels from each into a merged list. The person who wrote the situation description (Speaker) initiates a conversation to talk about it. The other conversation participant (Listener) becomes aware of the underlying situation through what the Speaker says and responds. Speaker and Listener then exchange up to 6 more turns. We include two example conversations from the training data in Table 1. The models discussed below are tested in the role of Listener responding to the Speaker. The situation description generated by the Speaker is not given to the models (just as it was not given to the Listener during dialogue collection). Our data could also be used to generate conversations for the Speaker conditioned on the situation description; we leave this for later work. The ing dataset comprises 24,850 conversations about a situation description, gathered from 810 different participants, which will be made publicly available online and through ParlAI. The crowdsourced dialogs were obtained using the ParlAI framework to interact with the Amazon Mechanical Turk (MTurk) platform. Details of the crowdsourcing procedure are given in the Supplemental Material. The distribution of emotion label prompts TAB1 ) is close to evenly distributed across categories with a few categories that are selected slightly more/less often. The average situation description is 19.8 words. Each conversation is allowed to be 4-8 utterances long (the average is 4.3 utterances per conversation). The average utterance length is 15.2 words long. We split the conversations into approximately 80% train, 10% validation, and 10% test partitions. To prevent overlap of discussed situations by a same participant between partitions in case a participant chose to discuss the same situation twice, we split the data so that all sets of conversations with the same speaker providing the initial situation description would be in the same partition. The final train/val/test split was 19533 / 2770 / 2547 conversations, respectively. In this section, we examine how our dataset can be used to make generic chitchat models more empathetic, and different ways existing models can be combined to produce more empathetic responses. We use our dialogues to train and evaluate models in the task of generating conversation responses, with the model playing the Listener role. At test time, the dialogue model has access to previous utterances in the dialogue, but not to the emotion word prompt (e.g., "proud"), nor to the situation description generated by the Speaker, as would be the case in a normal conversation. Given a dialogue context x of n previous conversation utterances concatenated and tokenized as x 1, · · ·, x m, followed by a target responseȳ, our models are trained to maximize the likelihood p(ȳ|x) of producing the target response. We investigate both generation and retrieval settings as described in FIG2. We base our models on Transformer networks BID40, which have proven successful in machine translation and dialogue generation tasks BID48 BID24.Retrieval In the retrieval set-up, the model is given a large set Y of candidate responses and picks the "best" one, y *. We use the retrieval Transformer-based architecture from: two Transformer encoders separately embedding the context, x, and candidates, y ∈ Y, as h x and h y, respectively. The model chooses the candidate sentence according to a softmax on the dot product: h x · h y. We minimize the negative log-likelihood of selecting the correct candidate. At train time, we use all of the sentences from the batch as candidates, with a large batch size of 512 to give the model more negative examples. At inference time, we experiment with multiple sets of candidate sentences for the model to choose from. First, we use all of the response utterances in the EMPATHETICDIALOGUES training set (Y ED). We also try including candidate utterances from two other large dialogue datasets: the DailyDialog BID19 training set (Y DD) and up to a million utterances from a dump of 1.7 billion Reddit conversations (Y R). Left: In the retrieval set-up, each candidate y is tokenized into y 1, y 2, · · · and encoded into vector h y by the candidate encoder. The system outputs the candidate y * that maximizes dot product h x · h y. Right: In the generative set-up, the encoded context h x is used as input to the decoder to generate start symbol < /s > and tokens y 1, y 2, · · ·. The model is trained to minimize the negative log-likelihood of target sequenceȳ conditioned on context x. Generation In the generation set-up, we use the full Transformer architecture BID40, consisting of an encoder and a decoder. The Transformer decoder uses the encoder output to predict a sequence of words y, and is trained to minimize the negative log-likelihood of the target sequenceȳ. At inference time, we use diverse beam search from BID41.Training Details We pretrain our models on predicting replies from a dump of 1.7 billion Reddit conversations. We limit the maximum number of word tokens in the context and response to be 100 each. The Transformer networks used in all experiments have the same base architecture (four layers and six transformer heads) from BID24, unless specified. For all models, we train for up to 10 epochs, keeping the version that has the lowest loss on the validation set. We use 300-d word embeddings pretrained on common-crawl data using fastText BID9. Conversations utterances Fine-tuning over the task domain data may improve the model, since our data was explicitly collected with instructions to be empathetic, in a one-on-one setting, which is different from the Reddit conversation data used for pretraining. We fine-tune pretrained models to predict the next utterance over our EMPATHETICDIALOGUES with a context window of four previous utterances, which is the average length of a conversation in our dataset. These models are hereafter referred to as "Base" models. This fine-tuning is conducted for all architectures except those referred to as "Pretrained".Emotion labels If the most appropriate response depends on some information for which supervision is available, e.g., the emotions at play, nudging the model to encode this information could in better performance. We experiment with this by training the base architecture in the one-tomany style of multi-task learning that has been used for NLP seq2seq settings BID23. In this set-up FIG3, MULTITASK, we alter the objective function to also optimize for predicting the emotion label of the conversation to which the utterances being encoded belong. We add to the context encoder a linear layer and softmax that predicts the emotion label from the context sentences. The objective function is altered to be the average of the negative log-likelihood of predicting the next utteranceȳ and the negative log-likelihood of the added linear layer being able to predict the correct emotion. Many existing models have been pretrained on supervised tasks that may be relevant to empathetic responding. For instance, BID6 have released a model trained on more than a billion tweets to predict emoji labels. Combining these models with the representation of our base architecture may reap benefits from previous training time and external training data without having to: Three ways to incorporate additional supervised information, here from an emotion classification task. Left: the context representation h x outputted by the context encoder is used both as input to a classifier, and to generate the next utterance as in the base setting. The encoder is trained with gradients from both output branches. Middle: an input sequence (that can be either a dialogue context or a candidate) is first run through a pretrained classifier, and the top k output labels are prepended to the sequence, which is then run through the corresponding (context or candidate) encoder to output a hidden representation h w (either h x or h y) as in the base setting. Right: an input sequence (that can be either a dialogue context or a candidate) is run through the corresponding encoder as well as a pretrained classifier with the last layer removed. The outputs h w and h c are concatenated and linearly projected into a representation h e.redo the work or requiring access to that data, which may matter to practitioners. Note that this may considerably augment the effective capacity of the ing models, as well as the total amount of training data used overall, so it isn't surprising that this should in better performance. Our goal here is to experiment with a large range of settings, in order to get an empirical sense of how robust performance improvement is to variations in architecture set-up or supervision domain. We experiment with two set-ups for adding explicit supervised information: prepending predicted label words, and ensemble learning over encoders trained on prediction objectives. Prepending Top-K Predicted Labels This set-up FIG3, PREPEND-K, is a very simple way to add supervised information to data, requires no architecture modification, and can be used with black-box classifiers. The top-K predicted labels from the supervised classifier are merely prepended to the beginning of the token sequence as encoder input:I finally got promoted! −→ proud excited joyful I finally got promoted! Similar methods have been used for controlling the style of generated text (e.g. BID29). Here, we use a fastText model BID16 as prediction architecture. Both the context and the candidates are run through the classifier and receive prepended labels. We experiment with two sources of supervision (EMOPREPEND and TOPICPREPEND, respectively). Closest to our task, we train a classifier to predict the emotion label from the description of the situation written by the Speaker before the dialogue for the training set dialogues of our EMPATHETICDIALOGUES. 1 To gauge whether supervision from a more distant task would still be helpful, we also experiment with a classifier trained on the 20-Newsgroup dataset BID15, for topic classification. In this set-up (ENSEM), we augment the encoders to incorporate latent representations from pretrained supervised architectures. We replace each of the encoders in our Transformer networks with the Ensemble encoder in FIG3, similar to a many-to-one style encoder-decoder arhcitecture BID23. This encoder takes the encoding h w from our basic Transformer encoder (either h x or h y), already trained on our data, and concatenates it with the representation h c extracted from the inner layer of a classification network. Here, we use the penultimate layer of a deep classifier. The concatenated encodings are projected linearly to the dimension required by the decoder, whose architecture doesn't change. When training the dialogue model, we freeze both the base Transformer encoder and the pretrained classifier (grayed out in FIG3, and train only the linear layers (and the decoder for generative systems). We used supervision from two sources that are related to emotion: Emojis from Twitter, through the use of the trained Deepmoji system BID6 released by the authors, either as-is (ENSEM-DM) or fine-tuned on the situation descriptions of EMPATHETICDIALOGUES(ENSEM-DM+), and a similarly large-scale dataset of public social media content labelled by their writers with emotion tags such as'annoyed', used to train a second Transformer encoder (ENSEM-TRAN). We evaluate the models on their ability to reproduce the Listener's portion of the conversation (i.e. the ability to react to someone else's story). We use both automated metrics and human evaluation to score each model's retrievals/generations. Human evaluation is useful, as automated metrics don't always correlate with human judgments of dialogue quality BID21 ), but we provide automated metrics to give a sense of how well they align with human judgment on this task. Automated Metrics (Table 2) For both retrieval and generative systems, we compute BLEU scores BID30 for the final response and compare against the gold label (the actual response), following the practice of earlier work in dialogue generation BID45 BID36. For the generative systems, we additionally report perplexity of the actual gold response. For the retrieval systems, we additionally compute p@1,100, the accuracy of the model at choosing the correct response out of a hundred randomly selected examples in the test set. When we compute p@1,100, the actual response is included in the candidates, unlike inference from the retrieval systems for all other metrics, which only uses training utterances as candidates. Human Ratings TAB2 ) We run two sets of crowdsourcing tasks on MTurk for humans to score the model responses. In the first task, participants are given a model's output for a randomly selected test set example and asked to score different aspects of the model. The rating task provides a means of comparing aspects of responses, and we are able to ask raters specifically about whether the response is acknowledging the conversation partner's feelings. We collected at least 100 ratings per model and asked about three aspects of performance, all rated on a likert scale (1: not at all, 3: somewhat, 5: very much):• Empathy/Sympathy: did the responses show understanding of the feelings of the person talking about their experience?• Relevance: did the responses seem appropriate to the conversation? Were they on-topic?• Fluency: could you understand the responses? Did the language seem accurate?Human A/B Rankings TAB4 In the second human evaluation task, participants were given output from two (randomly ordered) models and asked to select the better response, with an additional option of selecting "equal" or "neither". For this task, we only gave workers test set examples where the pair of models had differing responses. We collected at least 50 ratings per pair of models. TAB1 shows that fine-tuning to predict conversation responses on our data improves all automated metrics. Using only in-domain candidates leads to slightly higher BLEU scores. Training in the multitask setting degrades automated metrics compared to fine-tuning without emotion label supervision, except for average BLEU in the retrieval setting. Human evaluations in TAB2 show that fine-tuning a conversational model on the EMPATHETICDIALOGUES data and using the candidates in the dataset substantially improves performance on all metrics, in particular on the Empathy subscore of most interest to us, in both retrieval and generation set-ups. The bulk of the improvement comes from fine-tuning on the dataset, while from the multitask setting suggest slight improvements in the Empathy rating compared to the model fine-tuned with utterances only. Resources and capacity Fine-tuning the pretrained conversation model on dialogue utterances from our data does not change the size of the model, so the performance improvement is not due to increased model capacity. However, the multitask setting slightly increases the capacity of the base architecture (about 10k more parameters out of 84.3M or 85.1M for the retrieval and generative architectures, respectively), which may account for the performance improvement. To give a better sense of how resources and capacities balance out, TAB3 provides figures of resource use and number of parameters. We also include for a larger Transformer model (5 layers instead of 4). A generative model trained on our data performs as well or better than a generative pretrained Transformer model with one extra layer, which has a substantially larger capacity (a million more parameters), but not as well as such a model after it has been fine-tuned on our data. Augmenting conversation models with external pretrained classifiers TAB1 shows automated metrics for retrieval models augmented with external classifiers. Generally, the accuracy of the rankings (p@1,100) worsens, but the average BLEU scores improves. For generative models, the automated metrics are improved only in the Ensemble setting. Human evaluations TAB2 suggest that nearly all models tend to improve over the Base model on the Empathy score, but only a few setups lead to significant improvement. The best performance is achieved by the ensemble trained on emotion tags (Ensem-Tran), but models that prepend topics are overall performing better than similar models trained on emotion supervision, or than the fine-tuned DeepMoji ensemble. Relevance is significantly improved only by models augmented with topic classifiers. Fluency scores are mostly not significantly changed, and remain above 4. The benefit of combining pretrained models is that this requires minimal re-training of parameters and allows for leveraging models that are already trained, or that can be trained in a few hours in the case of fastText classifiers. If re-training is not a concern, pre-training a larger Transformer model and fine-tuning it on our data leads to better performance (see TAB3). We observe that augmenting that model with pre-trained unsupervised sentence representations in an ensemble setting could also be a promising direction, but we leave that for future investigations. 1.56 Table 6: Examples of model responses. In the first example, responses from the models with emotion prediction components focusing on the feelings of the speaker are more generic. In the second example, they focus on the feelings on the speaker while remaining topically specific. Tomorrow is my first university day and I'm very nervousGen-base What are you studying? Gen-multitask Good luck! Gen-emoPrepend-5 I'm sure you will be fine. Gen-ensemb-DM+ Are you nervous? I had to go out of town by myself for three weeks. It was hard not being able to talk to anyone I knew. Do you still talk to the people you went with? Ret-multitask I'm sorry to hear that. Do you think you struggle to communicate with people? Ret-emoPrepend-5 That sounds difficult. Did you try talking to people in your neighborhood? Ret-ensemb-DM+ Did you start to feel a bit lonely?A/B comparisons To try and capture the main takeaways, we show averaged over pairs of models with similar characteristics TAB4. Responses from retrieval systems are frequently chosen over generation systems (generation:retrieval ratio: 0.62). Responses from models with added emotion supervision are often ranked above the raw pretrained model (ratios of 3.67 and 5.73), and less so against the base Transformer model fine-tuned on our data: in the retrieval case, the ratio of picking a line from a model with emotion supervision vs. base model, at 0.97, indicates that raters generally picked from each equally. However, in the generation case, the raters may have favored the models with emotion supervision explicitly represented (average ratio of 1.56). We introduce a new dataset of 25k dialogues grounded in situations prompted by specific emotion labels. Our experiments show that using this dataset to fine-tune conversation models leads to responses that are evaluated by humans as more empathetic, and that simple schemes to augment a fine-tuned model with an external pretrained classifier can lead to better performance without requiring onerous retraining. Future work will investigate how to use this dataset to model the Speaker, and how to integrate empathetic responding into more general dialogue when, for example, the needs for empathy have to be balanced with staying on topic or providing information (see Table 6).Other possible directions would be to see if this data can serve as additional weakly supervised data for more complex emotion-related tasks that look at emotion evolution or causality BID10 BID33. We hope that our and dataset will stimulate more research in the important direction of making dialog systems more empathetic. In TAB5, we include the exact percentage of emotion labels for the situation descriptions in our final dataset. We collected crowdsourced dialogues using the ParlAI platform BID25 to interact with Amazon Mechanical Turk (MTurk). A pair of workers are asked to (i) select an emotion word each and describe a situation when they felt that way, and (ii) have a conversation about each of the situations, as outlined below. Writing a situation description prompted by an emotion label In the first stage of the task, workers are asked to describe in a few sentences a situation based on a feeling label. Each worker is given three labels from our list of 32 emotions. They are asked to select one of the options and write a short description of a personal situation where they felt that way. We ask the workers to try to keep these descriptions between 1-3 sentences. The average response is 19.8 words. Having a conversation In the second stage, two workers are paired and asked to have two short chats with each other. In each chat, one worker (speaker) starts a conversation about the situation they previously described, and the other worker (listener) responds. Neither can see what the other worker was given as emotion label or the situation description they submitted, so they must respond to each others' stories based solely on cues within the conversation. Each conversation is allowed to be 4-8 utterances long (the average is 4.31 utterances per conversation). The average utterance length was 15.2 words long. Ensuring balanced prompt coverage After the first few initial rounds of data collection, we forced workers to select prompts among three emotion labels that had been the least chosen overall so far if it was their first time working on the task. If they had already performed the task, the offered emotion labels were among those that they had not chosen before, or among the three least chosen ones if they had worked on nearly all of them at least once. This process made workers select emotions that they might not spontaneously have preferred, but we observed an initial bias for situations that were easier to describe (e.g, a situation causing surprise). Given that a conversation model trained for empathetic responding needs to be able to handle emotions even if they are less frequent, we opted for this balancing procedure to make training for these categories easier, while still allowing for some measure of choice for workers. Workers 810 US workers were recruited using MTurk. Each worker had to contribute at least one situation description, and one pair of conversations: one as Speaker about the situation they contributed, and one as Listener about the situation contributed by another worker. Workers were allowed to accept additional hits and contribute more sets of situation descriptions, conversations as Speaker, conversations as Listener. The median number of conversation per worker was 8, while We recently got 9 chicks and we've been having to work on making them a coop! I had to do so much research but I think we finally have a place that they'll enjoy living when they aren't able to free range. Listener: OHH! I Love chickens! I have always wanted some. I have a duck! lol-What kind of chickens are they? Speaker: We currently have 2 Australorps, 3 Rhode Island Reds, 3 Barred Plymouth Rocks, and 1 Welsummer, but 4 of the 9 ended up being roosters. Ugh! Listener: Oh man! They fight sometimes. I hope they aren't too bad about waking you up in the morning. Chickens can be very sweet though! Speaker: I love my little hens, especially one I've named Curly. The roosters might get replaced by hens though because the crowing is so frustrating! Label: Surprised Situation: Speaker felt this when... "I got a lottery ticket while I was at work today. I won $100 on the scratch off. I was shocked. I never win." Conversation: Speaker: I won $100 on a scratch off today. I was shocked. I never win. Listener: Wow! How often do you play the lottery? Speaker: I usually go on our Tuesday break to buy one with coworkers. Listener: Neat! Well that is a fantastic feat. Maybe you can win again sometime? the average was 61, and some workers were definitely contributing more hits than others. To ensure quality, we hand-checked random subsets of conversations by our most-frequent workers. They were allowed to participate in as many of these HITs as they wanted for the first 10k conversations, then we added qualifications to limit the more frequently active workers to a maximum of 100 conversations. We include ten randomly selected dialogues from our training set in TAB6. Our dataset can also be used to train or fine-tune an emotion classifier, as we do in our PREPEND-K and ENSEM-DM+ set-ups. To give a sense of where the difficulty falls compared to existing emotion and sentiment classification benchmarks, we reproduce the table from BID6 and add when fine-tuning the Deepmoji model on our dataset, or using a fastText classifier TAB7. A.4.1 CROWDSOURCING DESCRIPTION Human evaluations were collected on MTurk. For the rating task, workers were shown one randomly subsampled example from the test set for a randomly selected model (this was done 100 times per model) and asked to rate that single response. 217 US workers participated in the rating task, and had to perform a minimum of one rating. For the human comparison task, workers were shown a dialogue context, and the two responses from a pair of models presented in a randomized order (this was done 50 times per pair of models). They had to select if they preferred one, the other, both equally, or neither. 337 US workers participated in the model comparison task. In Figure 5, we provide the exact comparisons between model responses for the ranking task. Scores less than 1 indicate that the vertical model is preferred, whereas scores greater than one indicate more of a preference for the horizontal model.

We improve existing dialogue systems for responding to people sharing personal stories, incorporating emotion prediction representations and also release a new benchmark and dataset of empathetic dialogues.

Represent the TLDR for finding the corresponding scientific article.

Humans in the loop revise documents to accord with counterfactual labels, resulting resource helps to reduce reliance on spurious associations.


Question: Represent the article for finding a single-sentence TLDR

Question: Granger causality is a widely-used criterion for analyzing interactions in large-scale networks. As most physical interactions are inherently nonlinear, we consider the problem of inferring the existence of pairwise Granger causality between nonlinearly interacting stochastic processes from their time series measurements. Our proposed approach relies on modeling the embedded nonlinearities in the measurements using a component-wise time series prediction model based on Statistical Recurrent Units (SRUs). We make a case that the network topology of Granger causal relations is directly inferrable from a structured sparse estimate of the internal parameters of the SRU networks trained to predict the processes’ time series measurements. We propose a variant of SRU, called economy-SRU, which, by design has considerably fewer trainable parameters, and therefore less prone to overfitting. The economy-SRU computes a low-dimensional sketch of its high-dimensional hidden state in the form of random projections to generate the feedback for its recurrent processing. Additionally, the internal weight parameters of the economy-SRU are strategically regularized in a group-wise manner to facilitate the proposed network in extracting meaningful predictive features that are highly time-localized to mimic real-world causal events. Extensive experiments are carried out to demonstrate that the proposed economy-SRU based time series prediction model outperforms the MLP, LSTM and attention-gated CNN-based time series models considered previously for inferring Granger causality. The physical mechanisms behind the functioning of any large-scale system can be understood in terms of the networked interactions between the underlying system processes. Granger causality is one widely-accepted criterion used in building network models of interactions between large ensembles of stochastic processes. While Granger causality may not necessarily imply true causality, it has proven effective in qualifying pairwise interactions between stochastic processes in a variety of system identification problems, e.g., gene regulatory network mapping , and the mapping of human brain connectome . This perspective has given rise to the canonical problem of inferring pairwise Granger causal relationships between a set of stochastic processes from their time series measurements. At present, the vast majority of Granger causal inference methods adopt a model-based inference approach whereby the measured time series data is modeled using with a suitable parameterized data generative model whose inferred parameters ultimately reveal the true topology of pairwise Granger causal relationships. Such methods typically rely on using linear regression models for inference. However, as illustrated in the classical bivariate example by , linear model-based Granger causality tests can fail catastrophically in the presence of even mild nonlinearities in the measurements, thus making a strong case for our work which tackles the nonlinearities in the measurements by exploring new generative models of the time series measurements based on recurrent neural networks. Consider a multivariate dynamical system whose evolution from an initial state is fully characterized by n distinct stochastic processes which can potentially interact nonlinearly among themselves. Our goal here is to unravel the unknown nonlinear system dynamics by mapping the entire network of pairwise interactions between the system-defining stochastic processes, using Granger causality as the qualifier of the individual pairwise interactions. In order to detect the pairwise Granger causal relations between the stochastic processes, we assume access to their concurrent, uniformly-sampled measurements presented as an n-variate time series x = {x t : t ∈ N} ⊂ R n. Let x t,i denote the i th component of the n-dimensional vector measurement x t, representing the measured value of process i at time t. Motivated by the framework proposed in , we assume that the measurement samples x t, t ∈ N are generated sequentially according to the following nonlinear, component-wise autoregressive model: x t,i = f i (x t−p:t−1,1, x t−p:t−1,2, . . ., x t−p:t−1,n) + e t,i, i = 1, 2,... n, where x t−p:t−1,j {x t−1,j, x t−2,j, . . ., x t−p,j} represents the most recent p measurements of the j th component of x in the immediate past relative to current time t. The scalar-valued component generative function f i captures all of the linear and nonlinear interactions between the n stochastic processes up to time t − 1 that decide the measured value of the i th stochastic process at time t. The residual e i,t encapsulates the combined effect of all instantaneous and exogenous factors influencing the measurement of process i at time t, as well as any imperfections in the presumed model. Equation 1 may be viewed as a generalization of the linear vector autoregressive (VAR) model in the sense that the components of x can be nonlinearly dependent on one another across time. The value p is loosely interpreted to be the order of the above nonlinear autoregressive model. We now proceed to interpret Granger causality in the context of the above component-wise time series model. Recalling the standard definition by , a time series v is said to Granger cause another time series u if the past of v contains new information above and beyond the past of u that can improve the predictions of current or future values of u. For x with its n components generated according to equation 1, the concept of Granger causality can be extended as suggested by as follows. We say that series j does not Granger cause series i if the componentwise generative function f i does not depend on the past measurements in series j, i.e., for all t ≥ 1 and all distinct pairs x t−p:t−1,j and x t−p:t−1,j, f i (x t−p:t−1,1, . . ., x t−p:t−1,j, . . ., x t−p:t−1,n) = f i x t−p:t−1,1,..., x t−p:t−1,j,..., x t−p:t−1,n. From equation 1, it is immediately evident that under the constraint in equation 2, the past of series j does not assert any causal influence on series i, in alignment with the core principle behind Granger causality. Based on the above implication of equation 2, the detection of Granger noncausality between the components of x translates to identifying those components of x whose past is irrelevant to the functional description of each individual f i featured in equation 1. Note that any reliable inference of pairwise Granger causality between the components of x is feasible only if there are no unobserved confounding factors in the system which could potentially influence x. In this work, we assume that the system of interest is causally sufficient , i.e., none of the n stochastic processes (whose measurements are available) have a common Granger-causing-ancestor that is unobserved. We undertake a model-based inference approach wherein the time series measurements are used as observations to learn an autoregressive model which is anatomically similar to the componentwise generative model described in equation 1 except for the unknown functions f i replaced with their respective parameterized approximations denoted by g i. Let Θ i, 1 ≤ i ≤ n denote the complete set of parameters encoding the functional description of the approximating functions {g i} n i=1. Then, the pairwise Granger causality between series i and the components of x is deduced from Θ i which is estimated by fitting g i's output to the ordered measurements in series i. Specifically, if the estimated Θ i suggests that g i's output is independent of the past measurements in series j, then we declare that series j is Granger noncausal for series i. We aim to design the approximation function g i to be highly expressive and capable of well-approximating any intricate causal coupling between the components of x induced by the component-wise function f i, while simultaneously being easily identifiable from underdetermined measurements. By virtue of their universal approximation property (Schäfer &), recurrent neural networks or RNNs are a particularly ideal choice for g i towards inferring the pairwise Granger causal relationships in x. In this work, we investigate the use of a special type of RNN called the statistical recurrent unit (SRU) for inferring pairwise Granger causality between multiple nonlinearly interacting stochastic processes. Introduced by , an SRU is a highly expressive recurrent neural network designed specifically for modeling multivariate time series data with complex-nonlinear dependencies spanning multiple time lags. Unlike the popular gated RNNs (e.g., long short-term memory (LSTM) and gated recurrent unit (GRU)) , the SRU's design is completely devoid of the highly nonlinear sigmoid gating functions and thus less affected by the vanishing/exploding gradient issue during training. Despite its simpler ungated architecture, an SRU can model both short and long-term temporal dependencies in a multivariate time series. It does so by maintaining multi-time scale summary statistics of the time series data in the past, which are preferentially sensitive to different older portions of the time series x. By taking appropriate linear combinations of the summary statistics at different time scales, an SRU is able to construct predictive causal features which can be both highly component-specific and lag-specific at the same time. From the causal inference perspective, this dual-specificity of the SRU's predictive features is its most desirable feature, as one would argue that causal effects in reality also tend to be highly localized in both space and time. The main contributions of this paper can be summarized as follows: 1. We propose the use of statistical recurrent units (SRUs) for detecting pairwise Granger causality between the nonlinearly interacting stochastic processes. We show that the entire network of pairwise Granger causal relationships can be inferred directly from the regularized block-sparse estimate of the input-layer weight parameters of the SRUs trained to predict the time series measurements of the individual processes. 2. We propose a modified SRU architecture called economy SRU or eSRU in short. The first of the two proposed modifications is aimed at substantially reducing the number of trainable parameters in the standard SRU model without sacrificing its expressiveness. The second modification entails regularizing the SRU's internal weight parameters to enhance the interpretability of its learned predictive features. Compared to the standard SRU, the proposed eSRU model is considerably less likely to overfit the time series measurements. 3. We conduct extensive numerical experiments to demonstrate that eSRU is a compelling model for inferring pairwise Granger causality. The proposed model is found to outperform the multi-layer perceptron (MLP), LSTM and attention-gated convolutional neural network (AG-CNN) based models considered in the earlier works. In the proposed scheme, each of the unknown generative functions f i, 1 ≤ i ≤ n in the presumed component-wise model of x in is individually approximated by a distinct SRU network. The i th SRU network sequentially processes the time series measurements x and outputs a next-step prediction sequencex denotes the predicted value of component series i at time t + 1. The predictionx i,t+1 is computed in a recurrent fashion by combining the current input sample x t at time t with the summary statistics of past samples of x up to and including time t − 1 as illustrated in Figure 1. The following update equations describe the sequential processing of the input time series x within the i th SRU network in order to generate a prediction of x i,t+1. Feedback: Recurrent statistics: Multi-scale summary statistics: Single-scale summary statistics: Output features: Output prediction: The function h in the above updates is the elementwise Rectified Linear Unit (ReLU) operator, h(·):= max(·, 0), which serves as the nonlinear activation in the three dedicated single layer neural networks that generate the recurrent statistics φ i,t, the feedback r i,t and the output features o i,t in the i th SRU network. In order to generate the next-step prediction of series i at time t, the i th SRU network first prepares the feedback r i,t by nonlinearly transforming its last hidden state u i,t−1. As stated in equation 3a, a single layer ReLU network parameterized by weight matrix W Linear C o n c a t e n a t e Concatenate H α1 (z)... For values of scale α ≈ 1, the single-scale summary statistic u α i,t in equation 3d is more sensitive to the recent past measurements in x. On the other hand, α ≈ 0 yields a summary statistic that is more representative of the older portions of the input time series. elaborates on how the SRU is able to generate output features (o i,t, 1 ≤ i ≤ n) that are preferentially sensitive to the measurements from specific past segments of x by taking appropriate linear combinations of the summary statistics corresponding to different values of α in A. in regulates the influence of the individual components of the input time series x on the generation of the recurrent statistics φ i,t, and ultimately the next-step prediction of series i. In real-world dynamical systems, the networked interactions are typically sparse which implies that very few dimensions of the input time series x actually play a role in the generation of its individual components. Bearing this property of the networked interactions in mind, we are interested in learning the parameters Θ We propose to learn the parameters Θ SRU of the i th SRU network by minimizing the penalized mean squared prediction error loss as shown below. In the above, the network outputx i,t depends nonlinearly on W in according to the composite relation described by the updates (3a)-(3f) and W in (:, j) being estimated as the all-zeros vector is that the past measurements in series j do not influence the predicted future value of series i. In this case, we declare that series j does not Granger-cause series i. Moreover, the index set supporting the non-zero columns in the estimated weight matrixŴ in enumerates the components of x which are likely to Granger-cause series i. Likewise, the entire network of pairwise Granger causal relationships in x can be deduced from the non-zero column support of the estimated weight matrices W (i) in, 1 ≤ i ≤ n in the n SRU networks trained to predict the components of x. The component-wise SRU optimization problem in equation 4 is nonconvex and potentially has multiple local minima. To solve forΘ SRU, we use first-order gradient-based methods such as stochastic gradient descent which have been found to be consistently successful in finding good solutions of nonconvex deep neural network optimization problems . Since our approach of detecting Granger noncausality hinges upon correctly identifying the all-zero columns of W (i) in, it is important that the first-order gradient based parameter updates used for minimizing the penalized SRU loss ensure that majority of the coefficients in W in, we follow the same approach as and resort to a first-order proximal gradient descent algorithm to find a regularized solution of the SRU optimization. The gradients needed for executing the gradient descent updates of the SRU network parameters are computed efficiently using the backpropagation through time (BPTT) procedure . By computing the summary statistics of past measurements at sufficiently granular time scales, an SRU can learn predictive causal features which are highly localized in time. While a higher granularity of α in A translates to a more general SRU model that fits better to the time series measurements, it also entails substantial increase in the number of trainable parameters. Since measurement scarcity is typical in causal inference problems, the proposed component-wise SRU based time series prediction model is usually overparameterized and thus susceptible to overfitting. The typical high dimensionality of the recurrent statistic φ t accentuates this issue. To alleviate the overfitting concerns, we propose two modifications to the standard SRU aimed primarily at reducing its likelihood of overfitting the time series measurements. The modifications are relevant regardless of the current Granger causal inference context, and henceforth we refer to the modified SRU as Economy-SRU (eSRU). We propose to reduce the number of trainable parameters in the i th SRU network by substituting the feedback ReLU network parameterized by W Figure 2: Proposed two-stage feedback in economy-SRU. the associated time series measurements, their highdimensional summary statistics learned by the SRU network as u i,t tend to be highly structured, and thus u i,t has significantly fewer degrees of freedom relative to its ambient dimension. Thus, by projecting the md φ -dimensional u i,t onto the d r (md φ) rows of D (i) r, we obtain its low-dimensional embedding v i,t which nonetheless retains most of the contextual information conveyed by the uncompressed u i,t 1;. The second stage of the proposed feedback network is a single/multi-layer ReLU network which maps the sketched summary statistics v i,t to the feedback vector r i,t. The second stage ReLU network is parameterized by weight matrix W,(i) r ∈ R dr×d r and bias b Compared to the standard SRU's feedback whose generation is controlled by md φ d r + d r trainable parameters, the proposed feedback network has only d r d r + d r trainable parameters, which is substantially fewer when d r md φ. Consequently, the modified SRU is less susceptible to overfitting. In the standard SRU proposed by , there are no restrictions on the weight matrix W In this spirit, we propose the following penalized optimization problem to estimate the parameters Θ r } of the eSRU model equipped with the two-stage feedback proposed in Section 4.1: Here λ 1 and λ 2 are positive constants that bias the group sparse penalizations against the eSRU's fit to the measurements in the i th component series. The term o obtained by extracting the weight coefficients indexed by set G j,k. As shown via an example in Fig. 3, the index set G j,k enumerates the m weight coefficients in the row vector W o to the effect that each predictive feature in o i,t depends on only a few components of the recurrent statistic φ i,t via their linearly mixed multi-scale exponentially weighted averages. We opine that the learned linear mixtures, represented by the intermediate products W, are highly sensitive to certain past segments of the input time series x. Consequently, the output features in o i,t are both time-localized and component-specific, a common trait of real-world causal effects. 1 Gaussian random matrices of appropriate dimensions are approximately isometries with overwhelming probability . However, instead of using n independent instantiations of a Gaussian random matrix for initializing D (i) r, 1 ≤ i ≤ n, we recommend initializing them with the same random matrix, as the latter strategy reduces the probability that any one of them is spurious encoder by n-fold. Figure 3: An illustration of the proposed group-wise mixing of the multi-timescale summary statistics u i,t in the i th SRU (with d φ = 5) towards generating the j th predictive feature in o i,t. The weights corresponding to the same colored connections belong to the same group. The above group-sparse regularization of the weight coefficients in W in, is pivotal to enforcing that the occurrence of any future pattern in a time series can be attributed to the past occurrences of a few highly time-localized patterns in the ancestral time series. The of our numerical experiments further confirm that by choosing λ 1 and λ 2 appropriately, the proposed group-wise sparsity inducing regularization of W We evaluate the performance of the proposed SRU-and eSRU-based component-wise time series models in inferring pairwise Granger causal relationships in a multivariate time series. The proposed models are compared to the existing MLP-and LSTM-based models in and the attention-gated CNN-based model (referred hereafter as Temporal Causal Discovery Framework (TCDF)) in. To ensure parity between the competing models, the maximum size of all the input/hidden/output layers in the different NN/RNN time series models is fixed to 10, unless specified otherwise. The complete list of tuned hyperparameters of the considered models used for different datasets is provided in Appendix G. The performance of each method is qualified in terms of its AUROC (Area Under the Receiver Operating Characteristic curve). Here, the ROC curve illustrates the trade off between the true-positive rate (TPR) and the false-positive rate (FPR) achieved by the methods towards the detection of n 2 pairwise Granger causal relationships between the n measured processes in the experiment. The ROC curves of SRU and eSRU models are obtained by sweeping through different values of the regularization parameter λ 1 in equation 4 and equation 5, respectively. Likewise, the ROCs of component-wise MLP and LSTM models are obtained by varying λ 1's counterpart in. For TCDF, the ROC curve is obtained by varying the threshold that is applied to attention scores of the trained AG-CNN model in. In the first set of experiments, the time series measurements x intended for Granger causal inference are generated according to the Lorenz-96 model which has been extensively used in climate science for modeling and prediction purposes . In the Lorenz-96 model of an nvariable system, the individual state trajectories of the n variables are governed by the following set of odinary differential equations: where the first and the second terms on the RHS represent the advection and the diffusion in the system, respectively, and the third term F is the magnitude of the external forcing. The system dynamics becomes increasingly chaotic for higher values of F . We evaluate and compare the accuracy of the proposed methods in inferring pairwise Granger causal relationships between n = 10 variables with Lorenz-96 dynamics. We consider two settings: F = 10 and F = 40 in order to simulate two different strengths of nonlinearity in the causal interactions between the variables. Here, the ground truth is straightforward i.e., for any 1 ≤ i ≤ n, the i th component of time series x is Granger caused by its components with time indices from i − 2 to i + 1. In the case of weak nonlinear interactions (F = 10), from Table 1a, we observe that eSRU achieves the highest AUROC among all competing models. The gap in performance is more pronounced when fewer time series measurements (T = 250) are available. In case of stronger nonlinear interactions (F = 40), we observe that both SRU and eSRU are the only models that are able to perfectly recover the true Granger causal network (Table 1b). Surprisingly, the SRU and eSRU models perform poorer when F is small. This could be attributed to the proposed models not sufficiently regularized when fitted to weakly-interacting time series measurements that are less nonlinear. In the second set of simulations, we consider the time series measurements x to be generated according to a 3 rd order linear VAR model: where the matrices A (i), i = 1, 2, 3 contain the regression coefficients which model the linear interactions between its n = 10 components. The noise term w t is Gaussian distributed with zero mean and covariance 0.01I. We consider a sparse network of Granger causal interactions with only 30% of the regression coefficients in A i selected uniformly being non-zero and the regression matrices A i being collectively joint sparse (same setup as in). All non-zero regression coefficients are set equal to 0.0994 which guarantees the stability of the simulated VAR process. From Table 2, we observe that all time series models generally achieve a higher AUROC as the number of measurements available increases. For T = 500, the component-wise MLP and the proposed eSRU are statistically tied when comparing their average AUROCs. For T = 1000, eSRU significantly outperforms the rest of the time series models and is able to recover the true Granger causal network almost perfectly. In the third set of experiments, we apply the different learning methods to estimate the connections in the human brain from simulated blood oxygenation level dependent (BOLD) imaging data. Here, the individual components of x comprise T = 200 time-ordered samples of the BOLD signals simulated for n = 15 different brain regions of interest (ROIs) in a human subject. To conduct the experiments, we use simulated BOLD time series measurements corresponding to the five different human subjects (labelled as 2 to 6) in the Sim-3.mat file shared at https://www.fmrib.ox.ac.uk/datasets/netsim/index.html. The generation of the Sim3 dataset is described in. The goal here is to detect the directed connectivity between different brain ROIs in the form of pairwise Granger causal relationships between the components of x. From Table 3, it is evident that eSRU is more robust to overfitting compared to the standard SRU and detects the true Granger causal relationships more reliably. Interestingly, a single-layer cMLP model is found to outperform more complex cLSTM and attention gated-CNN (TCDF) models; however we expect the latter models to perform better when more time series measurements are available. In the final set of experiments, we evaluate the performance of the different time series models in inferring gene regulation networks synthesized for the DREAM-3 In Silico Network Challenge . Here, the time series x represents the in silico measurements of the gene expression levels of n = 100 genes, available for estimating the gene regulatory networks of E.coli and yeast. A total of five gene regulation networks are to be inferred (two for E.coli and three for yeast) from the networks' gene expression level trajectories recorded while they recover from 46 different perturbations (each trajectory has 21 time points). All NN/RNN models are implemented with 10 neurons per layer, except for the componentwise MLP model which has 5 neurons per layer. From Table 4, we can observe that the proposed SRU and eSRU models are generally more accurate In this work, we addressed the problem of inferring pairwise Granger causal relationships between stochastic processes that interact nonlinearly. We showed that the such causality between the processes can be robustly inferred from the regularized internal parameters of the proposed eSRU-based recurrent models trained to predict the time series measurements of the individal processes. Future work includes: i Investigating the use of other loss functions besides the mean-square error loss which can capture the exogenous and instantaneous causal effects in a more realistic way. ii Incorporating unobserved confounding variables/processes in recurrent models. iii Inferring Granger causality from multi-rate time series measurements. Initial efforts in testing for nonlinear Granger causality focused mostly on the nonparameteric approach. to the multivariate setting. The biggest common drawback of these nonparameteric tests is the large sample sizes required to robustly estimate the conditional probabilities that constitute the test statistic. Furthermore, the prevalent strategy in these methods of testing each one of the variable-pairs individually to detect pairwise Granger causality is unappealing from a computational standpoint, especially when a very large number of variables are involved. In the model driven approach, the Granger causal relationships are inferred directly from the parameters of a data generative model fitted to the time series measurements. Compared to the nonparameteric approach, the model-based inference approach is considerably more sample efficient, however the scope of inferrable causal dependencies is dictated by the choice of data generative model. Nonlinear kernel based regression models have been found to be reasonably effective in testing of nonlinear Granger causality. Kernel methods rely on linearization of the causal interactions in a kernel-induced high dimensional feature space; the linearized interactions are subsequently modeled using a linear VAR model in the feature space. Based on this idea, proposes a kernel Granger causality index to detect pairwise nonlinear Granger causality in the multivariate case.; , the nonlinear dependencies in the time series measurements are modeled using nonlinear functions expressible as sums of vector valued functions in the induced reproducing kernel Hilbert space (RKHS) of a matrix-valued kernel. , additional smoothness and structured sparsity constraints are imposed on the kernel parameters to promote consistency of the time series fitted nonlinear model. proposes a nonlinear kernel-based structural VAR model to capture instantaneous nonlinear interactions. The existing kernel based regression models are restrictive as they consider only additive linear combinations of the RKHS functions to approximate the nonlinear dependencies in the time series. Furthermore, deciding the optimal order of kernel based regression models is difficult as it requires prior knowledge of the mimimum time delay beyond which the causal influences are negligible. By virtue of their universal approximation ability, RNNs offer a pragmatic way forward in modeling of complex nonlinear dependencies in the time series measurements for the purpose of inferring Granger causal relationships. However, they all adopt the same naïve strategy whereby each pairwise causal relationship is tested individually by estimating its causal connection strength. The strength of the causal connection from series j to series i is determined by the ratio of mean-squared prediction errors incurred by unrestricted and restricted RNN models towards predicting series i using the past measurement sequences of all n component including and excluding the j th component alone, respectively. The pairwise testing strategy however does not scale well computationally as the number of component series becomes very large. This strategy also fails to exploit the typical sparse connectivity of networked interactions between the processes which has unlocked significant performance gains in the existing linear methods . In a recent work by , the pairwise Granger causal relationships are inferred directly from the weight parameters of component-wise MLP or LSTM networks fitted to the time series measurements. By enforcing column-sparsity of the input-layer weight matrices in the fitted MLP/LSTM models, their proposed approach returns a sparsely connected estimate of the underlying Granger causal network. Due to its feedforward architecture, a traditional MLP network is not well-suited for modeling ordered data such as a time series. demonstrated that the MLP network can learn short range temporal dependencies spanning a few time delays by letting the network's input stage process multi-lag time series data over sliding windows. However, modeling long-range temporal dependencies using the same approach requires a larger sliding window size which entails an inconvenient increase in the number of trainable parameters. The simulation in indicate that MLP models are generally outperformed by LSTM models in extracting the true topology of pairwise Granger causality, especially when the processes interact in a highly nonlinear and intricate manner. While purposefully designed for modeling short and long term temporal dependencies in a time series, the LSTM is very general and often too much overparameterized and thus prone to overfitting. While using overparameterized models for inference is preferable when there is abundant training data available to leverage upon, there are several applications where the data available for causal inference is extremely scarce. It is our opinion that using a simpler RNN model combined with meaningful regularization of the model parameters is the best way forward in inferring Granger causal relationships from underdetermined time series measurements. Building on the ideas put forth by Here, 2 is the unregularized SRU loss function, η is the gradientdescent stepsize and S λ1η is the elementwise soft-thresholding operator defined below. The columns of weight matrix W in the i th eSRU model are also updated in exactly the same fashion as above. Likewise, the j th row of the group-norm regularized weight matrix W o in the eSRU optimization in equation 5 is updated as shown below. The gradient of the unregularized loss function l i, 1 ≤ i ≤ n associated with the SRU and eSRU models used in the above updates is evaluated via the backpropagation through time (BPTT) procedure (Table 5, we compare the Granger causality detection performance of this particular eSRU variant and the proposed design wherein D We observe that the performance of these two models is statistically tied, which indicates that the randomly constructed D (i) r is able to distill the necessary information from the high-dimensional summary statistics u i,t−1 required for generating the feedback r i,t. Based on these , we recommend using the proposed eSRU design with its randomly constructed encoding map D (i) r, because of its simpler design and reduced training complexity. In order to highlight the importance of learning time-localized predictive features in detecting Granger causality, we compare the following two time series models: Once again, we use the same experimental settings as mentioned in Section 5. From Table 6, we observe that barring the Lorenz-96(T =250/500,F =40) datasets, for which nearly perfect recovery of the Granger causal network is achieved, the average AUROC improves consistently for the other datasets by switching from unstructured ridge regularization to the proposed group-sparse regularization of the output weight matrix W • Activation function for SRU and eSRU models While the standard SRU proposed by uses ReLU neurons, we found in our numerical experiments that using the Exponential Linear Unit (ELU) activation ed in better performance. The ELU activation function is defined as In our simulations, the constant α is set equal to one. • Number of neural layers in SRU model To approximate the generative functions f i in equation 1, we consider the simplest architecture for the SRU networks, whereby the constituent ReLU networks generating the recurrent features, output features and feedback have a single layer feedforward design with equal number of neurons. • Number of neural layers in Economy-SRU model The ReLU networks used for generating the recurrent and output features in the proposed eSRU model have a single-layer feedforward design. However, the second stage of eSRU's modified feedback can be either single or multi-layered feedforward network. Provided that d r md φ, a multi-layer implementation of the second stage of eSRU's feedback can still have fewer trainable parameters overall compared to the SRU's single layer feedback network. The simulation in Section 5 are obtained using a two-layer ReLU network in the second stage of eSRU's feedback for the DREAM-3 experiments, and while using a three-layer design for the Lorenz-96, VAR and NetSim experiments. • Self-interactions in Dream-3 gene networks The in-silico gene networks synthesized for the DREAM-3 challenge have no selfconnections. Noting that none of the Granger causal inference methods evaluated in our experiments intentionally suppress the self-interactions, the reported AUROC values are computed by ignoring any self-connections in the inferred Granger causal networks. cMLP & cLSTM models Pytorch implementation of the componentwise MLP and LSTM models are taken from https: //github.com/icc2115/Neural-GC. Pytorch implementation of the attention-gated CNN based Temporal Causal Discovery Framework (TCDF) is taken from https://github.com/M-Nauta/TCDF. Proposed SRU and Economy-SRU models Pytorch implementations of the proposed componentwise SRU and eSRU models are shared at https://github.com/sakhanna/SRU_for_GCI. The receiver operating characteristics (ROC) of different Granger causal inference methods are compared in Figures 4-7. Here, an ROC curve represents the trade-off between the true-positive rate (TPR) and the false-positive rate (FPR) achieved by a given method while inferring the underlying pairwise Granger causal relationships. Table 11: Economy-SRU model configuration

A new recurrent neural network architecture for detecting pairwise Granger causality between nonlinearly interacting time series.

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Filter level sparsity emerges implicitly in CNNs trained with adaptive gradient descent approaches due to various phenomena, and the extent of sparsity can be inadvertently affected by different seemingly unrelated hyperparameters.