Year: 2021

Abstract:
The COVID-19 pandemic has spread rapidly worldwide, overwhelming manual contact tracing in many countries and resulting in widespread lockdowns for emergency containment. Large-scale digital contact tracing (DCT)1 has emerged as a potential solution to resume economic and social activity while minimizing spread of the virus. Various DCT methods have been proposed, each making trade-offs between privacy, mobility restrictions, and public health. The most common approach, binary contact tracing (BCT), models infection as a binary event, informed only by an individual’s test results, with corresponding binary recommendations that either all or none of the individual’s contacts quarantine. BCT ignores the inherent uncertainty in contacts and the infection process, which could be used to tailor messaging to high-risk individuals, and prompt proactive testing or earlier warnings. It also does not make use of observations such as symptoms or pre-existing medical conditions, which could be used to make more accurate infectiousness predictions. In this paper, we use a recently-proposed COVID-19 epidemiological simulator to develop and test methods that can be deployed to a smartphone to locally and proactively predict an individual’s infectiousness (risk of infecting others) based on their contact history and other information, while respecting strong privacy constraints. Predictions are used to provide personalized recommendations to the individual via an app, as well as to send anonymized messages to the individual’s contacts, who use this information to better predict their own infectiousness, an approach we call proactive contact tracing (PCT). Similarly to other works, we find that compared to no tracing, all DCT methods tested are able to reduce spread of the disease and thus save lives, even at low adoption rates, strongly supporting a role for DCT methods in managing the pandemic. Further, we find a deep-learning based PCT method which improves over BCT for equivalent average mobility, suggesting PCT could help in safe re-opening and second-wave prevention.

heading: 1 INTRODUCTION
text: Until pharmaceutical interventions such as a vaccine become available, control of the COVID-19 pandemic relies on nonpharmaceutical interventions such as lockdown and social distancing. While these have often been successful in limiting spread of the disease in the short term, these restrictive measures have important negative social, mental health, and economic impacts. Digital contact tracing (DCT), a technique to track the spread of the virus among individuals in a population using smartphones, is an attractive potential solution to help reduce growth in the number of cases and thereby allow more economic and social activities to resume while keeping the number of cases low.
Most currently deployed DCT solutions use binary contact tracing (BCT), which sends a quarantine recommendation to all recent contacts of a person after a positive test result. While BCT is simple
1All bolded terms are defined in the Glossary; Appendix 1. *,†,‡ Equal contributions, alphabetically sorted; aMila, Québec; bUniversity of Oxford; cMax-Planck Institute for Intelligent Systems Tübingen; dUniversity of Ottawa; e McGill University; fUniversité de Montreal; gÉcole Polytechnique de Montreal; hThe Alan Turing Institute; iHEC Montréal
and fast to deploy, and most importantly can help curb spread of the disease (Abueg et al., 2020), epidemiological simulations by Hinch et al. (2020) suggest that using only one bit of information about the infection status can lead to quarantining many healthy individuals while failing to quarantine infectious individuals. Relying only on positive test results as a trigger is also inefficient for a number of reasons: (i) Tests have high false negative rates (Li et al., 2020); (ii) Tests are administered late, only after symptoms appear, leaving the asymptomatic population, estimated 20%-30% of cases (Gandhi et al., 2020), likely untested; (iii) It is estimated that infectiousness is highest before symptoms appear, well before someone would get a test (Heneghan et al., 2020), thus allowing them to infect others before being traced, (iv) Results typically take at least 1-2 days, and (v) In many places, tests are in limited supply.
Recognizing the issues with test-based tracing, Gupta et al. (2020) propose a rule-based system leveraging other input clues potentially available on a smartphone (e.g. symptoms, pre-existing medical conditions), an approach they call feature-based contact tracing (FCT). Probabilistic (nonbinary) approaches, using variants of belief propagation in graphical models, e.g. (Baker et al., 2020; Satorras & Welling, 2020; Briers et al., 2020), could also make use of features other than test results to improve over BCT, although these approaches rely on knowing the social graph, either centrally or via distributed exchanges between nodes. The latter solution may require many bits exchanged between nodes (for precise probability distributions), which is challenging both in terms of privacy and bandwidth. Building on these works, we propose a novel FCT methodology we call proactive contact tracing (PCT), in which we use the type of features proposed by Gupta et al. (2020) as inputs to a predictor trained to output proactive (before current-day) estimates of expected infectiousness (i.e. risk of having infected others in the past and of infecting them in the future). The challenges of privacy and bandwidth motivated our particular form of distributed inference where we pretrain the predictor offline and do not assume that the messages exchanged are probability distributions, but instead just informative inputs to the node-level predictor of infectiousness.
We use a recently proposed COVID-19 agent-based simulation testbed (Gupta et al., 2020) called COVI-AgentSim to compare PCT to other contact tracing methods under a wide variety of conditions. We develop deep learning predictors for PCT in concert with a professional app-development company, ensuring inference models are appropriate for legacy smartphones. By leveraging the rich individual-level data produced by COVI-AgentSim to train predictors offline, we are able to perform individual-level infectiousness predictions locally to the smartphone, with sensitive personal data never required to leave the device. We find deep learning based methods to be consistently able to reduce the spread of the disease more effectively, at lower cost to mobility, and at lower adoption rates than other predictors. These results suggest that deep learning enabled PCT could be deployed in a smartphone app to help produce a better trade-off between the spread of the virus and the economic cost of mobility constraints than other DCT methods, while enforcing strong privacy constraints.

heading: 1.1 SUMMARY OF TECHNICAL CONTRIBUTIONS
text: 1. We examine the consequential problem of COVID-19 infectiousness prediction and propose a new method for contact tracing, called proactive contact tracing (see Sec. 2).
2. In order to perform distributed inference with deep learning models, we develop an architectural scaffold whose core is any set-based neural network. We embed two recently proposed networks, namely Deep Sets (Zaheer et al., 2017) and Set Transformers (Lee et al., 2018) and evaluate the resulting models via the COVI-AgentSim testbed (Gupta et al., 2020) (see Sec. 3.1).
3. To our knowledge the combination of techniques in this pipeline is entirely novel, and of potential interest in other settings where privacy, safety, and domain shift are of concern. Our training pipeline consists of training an ML infectiousness predictor on the domain-randomized output of an agent-based epidemiological model, in several loops of retraining to mitigate issues with (i) non-stationarity and (ii) distributional shift due to predictions made by one phone influencing the input for the predictions of other phones. (see Sec. 3.2)
4. To our knowledge this is the first work to apply and benchmark a deep learning approach for probabilistic contact tracing and infectiousness risk assessment. We find such models are able to leverage weak signals and patterns in noisy, heterogeneous data to better estimate infectiousness compared to binary contact tracing and rule-based methods (see Sec. 4)

heading: 2 PROACTIVE CONTACT TRACING
text: Proactive contact tracing (PCT) is an approach to digital contact tracing which leverages the rich suite of features potentially available on a smartphone (including information about symptoms, preexisting conditions, age and lifestyle habits if willingly reported) to compute proactive estimates of an individual’s expected infectiousness. These estimates are used to (a) provide an individualized recommendation and (b) propagate a graded risk message to other people who have been in contact with that individual (see Fig. 1). This stands in contrast with existing approaches for contact tracing, which are either binary (recommending all-or-nothing quarantine to contacts), or require centralized storage of the contact graph or other transfers of information which are incompatible with privacy constraints in many societies. Further, the estimator runs locally on the individual’s device, such that any sensitive information volunteered does not need to leave the device.
In Section 2.1, we formally define the general problem PCT solves. In Section 2.2, we describe how privacy considerations inform and shape the design of the proposed framework and implementation. Finally, in Section 3.1, we introduce deep-learning based estimators of expected infectiousness, which we show in Section 4 to outperform DCT baselines by a large margin.

heading: 2.1 PROBLEM SETUP
text: We wish to estimate infectiousness yd ′ i of an agent i on day d ′, given access to locally observable information Odi now on day d ≥ d′ and over the past dmax days (d′ ≥ d − dmax) Some of the information available on day d is static, including reported age, sex, pre-existing conditions, and lifestyle habits (e.g. smoking), denoted gi, the health profile. Other information is measured each day: the health status hdi of reported symptoms and known test results. Finally, O d i also includes information about encounters in the last dmax days, grouped in edi for day d. Thus:
Odi = (gi, h d i , e d i , h d−1 i , e d−1 i , . . . h d−dmax i , e d−dmax i ) (1)
The information ed ′ i about the encounters from day d ′ is subject to privacy constraints detailed in Section 2.2 but provides indications about the estimated infectiousness of the persons encountered at d′, given the last available information by these contacts as of day d, hence these contacts try to estimate their past infectiousness a posteriori. Our goal is thus to model the history of the agent’s infectiousness (in the last dmax days), which is what enables the recommendations of PCT to be proactive and makes it possible for an infected asymptomatic person to receive a warning from their contact even before they develop symptoms, because their contact obtained sufficient evidence that they were contagious on the day of their encounter. Formally, we wish to model Pθ(y d i |O d i ), where y d i = (y d i , y d−1 i , . . . , y d−dmax i ) is the vector of present and past infectiousness of agent i and θ specifies the parameters of the predictive model. In our experiments we only estimate conditional expectations with a predictor fθ, with ŷdi = (ŷ d i , ..., ŷ d−dmax i ) = fθ(O d i ) an estimate of the conditional expected per-day present and past infectiousness EPθ [ydi |O d i ].
The predicted expected values are used in two ways. First, they are used to generate messages transmitted on day d to contacts involved in encounters on day d′ ∈ (d− dmax, d). These messages
contain the estimates ŷd ′ i of the expected infectiousness of i at day d ′, quantized to 4 bits for privacy reasons discussed in section 2.2. Second, the prediction for today ŷdi is also used to form a discrete recommendation level ζdi ∈ {0, 1, ..., n} regarding the behavior of agent i at day d via a recommendation mapping ψ, i.e. ζdi = ψ(ŷ d i ).
2 At ζdi = 0 agent i is not subjected to any restrictions, ζdi = 1 is baseline restrictions of a post-lockdown scenario (as in summer 2020 in many countries), ζdi = n is full quarantine (also the behaviour recommended for contacts of positively diagnosed agents under BCT), and intermediate levels interpolate between levels 1 and n.
Here we make two important observations about contact tracing: (1) There is a trade-off between decelerating spread of disease, measured by the reproduction number R, or as number of cases,3 and minimizing the degree of restriction on agents, e.g., measured by the average number of contacts between agents. Managing this tradeoff is a social choice which involves not just epidemiology but also economics, politics, and the particular weight different people and nations may put on individual freedoms, economic productivity and public health. The purpose of PCT is to improve the corresponding Pareto frontier. A solution which performs well on this problem will encode a policy that contains the infection while applying minimal restrictions on healthy individuals, but it may be that different methods are more appropriate depending on where society stands on that tradeoff. (2) A significant challenge comes from the feedback loop between agents: observables Odi of agent i depend on the predicted infectiousness histories and the pattern of contacts generated by the behavior ζj of other agents j. This is compounded by privacy restrictions that prevent us from knowing which agent sent which message; we discuss our proposed solution in the following section.

heading: 2.2 PRIVACY-PRESERVING PCT
text: One of the primary concerns with the transmission and centralization of contact information is that someone with malicious intent could identify and track people. Even small amounts of personal data could allow someone to infer the identities of individuals by cross-referencing with other sources, a process called re-identification (El Emam et al., 2011). Minimizing the number of bits being transmitted and avoiding information that makes it easy to triangulate people is a protection against big brother attacks, where a central authority with access to the data can abuse its power, as well as against little brother attacks, where malicious individuals (e.g. someone you encounter) could use your information against you. Little brother attacks include vigilante attacks: harassment, violence, hate crimes, or stigmatization against individuals which could occur if infection status was revealed to others. Sadly, there have been a number of such attacks related to COVID-19 (Russell, 2020). To address this, PCT operates with (1) no central storage of the contact graph; (2) de-identification (Sweeney, 2002) and encryption of all data leaving the phones; (3) informed and optional consent to share information (only for the purpose of improving the predictor); and (4) distributed inference which can achieve accurate predictions without the need for a central authority. Current solutions (Woodhams, 2020) share many of these goals, but are restricted to only binary CT. Our solution achieves these goals while providing individual-level graded recommendations.
Each app records contacts which are defined by Health Canada (2020) as being an encounter which lasts at least 15 minutes with a proximity under 2 meters. Once every 6 hours, each application processes contacts, predicts infectiousness for days d to dmax, and may update its current recommended behavior. If the newly predicted infectiousness history differs from the previous prediction on some day (e.g. typically because the agent enters new symptoms, receives a negative or positive test result, or receives a significantly updated infectiousness estimate), then the app creates and sends small update messages to all relevant contacts. These heavily quantized messages reduce the network bandwidth required for message passing as well as provide additional privacy to the individual. We follow the communication and security protocol for these messages introduced by Alsdurf et al. (2020). We note that a naive method would tend to over-estimate infectiousness in these conditions, because repeated encounters with the same person (a very common situation, for example people living in the same household) should carry a lower predicted infectiousness than the same number of encounters with different people. To mitigate this over-estimation while not identifying anyone, messages are clustered based on time of receipt and risk level as in Gupta et al. (2020).
2The recommendations for each level are those proposed by Gupta et al. (2020), hand-tuned by behavioural experts to lead to a reduction in the number of contacts; details in Appendix 5. Full compliance with recommendations is not assumed.
3Note that the the number of cases is highly non-stationary; it grows exponentially over time, even where R, which is in the exponent, is constant.

heading: 3 METHODOLOGY FOR INFECTIOUSNESS ESTIMATION

heading: 3.1 DISTRIBUTED INFERENCE
text: Distributed inference networks seek to estimate marginals by passing messages between nodes of the graph to make predictions which are consistent with each other (and with the local evidence available at each node). Because messages in our framework are highly constrained by privacy concerns in that we are prevented from passing distributions or continuous values between identifiable nodes, typical distributed inference approaches (e.g. loopy belief propagation (Murphy et al., 1999), variational message passing (Winn & Bishop, 2005), or expectation propagation (Minka, 2001)) are not readily applicable. We instead propose an approach to distributed inference which uses a trained ML predictor for estimating these marginals (or the corresponding expectations). The predictor f is trained offline on simulated data to predict expected infectiousness from the locally available information Odi for agent i on day d. The choice of ML predictor is informed by several factors. First and foremost, we expect the input edi (a component of O d i ) to be variable-sized, because we do not know a priori how many contacts an individual will have on any day. Further, privacy constraints dictate that the contacts within the day cannot be temporally ordered, implying that the quantity edi is set-valued. Second, given that we are training the predictor on a large amount of domain-randomized data from many epidemiological scenarios (see Section 3.2), we require the architecture to be sufficiently expressive. Finally, we require the predictor to be easily deployable on edge devices like legacy smartphones.
To these ends, we construct a general architectural scaffold in which any neural network that maps between sets may be used. In this work, we experiment with Set Transformers (Lee et al., 2018) and a variant of Deep Sets (Zaheer et al., 2017). The former is a variant of Transformers (Vaswani et al., 2017), which model pairwise interactions between all set elements via multi-head dot-product attention and can therefore be quite expressive, but scales quadratically with elements. The latter relies on iterative max-pooling of features along the elements of the set followed by a broadcasting of the aggregated features, and scales linearly with the number of set elements (see Figure 2).
In both cases, we first compute two categories of embeddings: per-day and per-encounter. Per-day, we have embedding MLP modules φh of health status, φg for the health profile, and a linear map φδd for the day-offset δd = d− d′. Per-encounter, the cluster matrix edi can be expressed as the set {(rdj→i, ndj→i)}j∈Kdi where j is in the set K d i of putative anonymous persons encountered by i at d, rj→i is the risk level sent from j to i and nj→i is the number of repeated encounters between i and j at d. Accordingly, we define the risk level embedding function φ(r)e and φ (n) e for the number of repeated encounters. φ(r)e is parameterized by an embedding matrix, while φ (n) e by the vector
(φ(n)e (n))2i = sin (n/10000 i) and (φ(n)e (n))2i+1 = cos (n/10000i) (2)
which resembles the positional encoding in (Vaswani et al., 2017) and counteracts the spectral bias of downstream MLPs (Rahaman et al., 2019; Mildenhall et al., 2020). We tried alternative encoding schemes like thermometer encodings (Buckman et al., 2018), but they did not perform better in our experiments. Next, we join the per-day and per-encounter embeddings to obtain Ddi and Edi respectively. Where ⊗ is the concatenation operation, we have:
Ddi = {φh(hd ′ i )⊗ φg(gi)⊗ φδd(d′ − d) | d′ ∈ {d, ..., d− dmax}} (3) Edi = {φ(r)e (rd ′ j→i)⊗ φ(n)e (nd ′ j→i)⊗ φh(hd ′ i )⊗ φδd(d′ − d) | j ∈ Kd ′ i , ∀ d′ ∈ {d, ..., d− dmax}}
The union of Ddi and Edi forms the input to a set neural network fS , that predicts infectiousness:
ŷdi = fS(Odi ) where Odi = Ddi ∪ Edi and ŷ d i ∈ R dmax + (4)
The trunk of both models – deep-set (DS-PCT) and set-transformer (ST-PCT) – is a sequence of 5 set processing blocks (see Figure 2). A subset of outputs from these blocks (corresponding to Ddi ) is processed by a final MLP to yield ŷdi . As a training objective for agent i, we minimize the Mean Squared Error (MSE) between ydi (which is generated by the simulator) and the prediction ŷdi . We treat each agent i as a sample in batch to obtain the sample loss Li = MSE(y d i , ŷ d i ) =
1 dmax ∑d d′=d−dmax(y d′ i − ŷd ′ i ) 2. The net loss is the sum of Li over all agents i.
pre-existing conditions , day offsets , risk message clusters , and symptoms information to be fed into a stack of 5 either Deep-Set (DS) or Set Transformer (ST) blocks . Right-top: (ST) self-attention block featuring Multi-Head Dot Product Attention (MHDPA), Fully-Connected layers with ReLU (FC + R) and residual connections. Right-bottom: (DS) set processing block. Here, the ⊗ denotes concatenation and the ⊕ addition operation.

heading: 3.2 TRAINING PROCEDURE
text: Unlike existing contact tracing methods like BCT and the NHSx contact tracing app (Briers et al., 2020) that rely on simple and hand-designed heuristics to estimate the risk of infection, our core hypothesis is that methods using a machine-learning based predictor can learn from patterns in rich but noisy signals that might be available locally on a smartphone. In order to test this hypothesis prior to deployment in the real world, we require a simulator built with the objective to serve as a testbed for app-based contact tracing methods. We opt to use COVI-AgentSim (Gupta et al., 2020), which features an agent specific virology model together with realistic agent behaviour, mobility, contact and app-usage patterns. With the simulator, we generate large datasets of O(107) samples comprising the input and target variables defined in sections 2.1 and 3.1. Most importantly for our prediction task, this includes a continuous-valued infectiousness parameter as target for each agent.
We use 240 runs of the simulator to generate this dataset, where each simulation is configured with parameters randomly sampled from selected intervals (See Appendix 5.2). These parameters include the adoption rate of the contact tracing app, initial fraction of exposed agents in the population, the likelihood of agents ignoring the recommendations, and strength of social distancing and mobility restriction measures. There are two reasons for sampling over parameter ranges: First, the intervals these parameters are sampled from reflect both the intrinsic uncertainty in the parameters, as well as the practical setting and limitations of an app-based contact tracing method (e.g. we only care about realistic levels of app usage). Second, randomly sampling these key parameters significantly improves the diversity of the dataset, which in turn yields predictors that can be more robust when deployed in the real world. The overall technique resembles that of domain-randomization (Tobin et al., 2017; Sadeghi & Levine, 2016) in the Sim2Real literature, where its efficacy is well studied for transfer from RGB images to robotic control, e.g. (Chebotar et al., 2018; OpenAI et al., 2018).
We use 200 runs for training and the remaining 40 for validation (full training and other reproducibility details are in Appendix 5). The model with the best validation score is selected for online evaluation, wherein we embed it in the simulator to measure the reduction in the R as a function of the average number of contacts per agent per day. While the evaluation protocol is described in section 4, we now discuss how we mitigate a fundamental challenge that we share with offline reinforcement learning methods, that of auto-induced distribution shift when the model is used in the simulation loop (Levine et al., 2020; Krueger et al., 2020).
To understand the problem, consider the case where the model is trained on simulation runs where PCT is driven by ground-truth infectiousness values, i.e. an oracle predictor. The predictions made by an oracle will in general differ from ones made by a trained model, as will resulting dynamics of spread of disease. This leads to a distribution over contacts and epidemiological scenarios that
the model has not encountered during training. For example, oracle-driven PCT might even be successful in eliminating the disease in its early phases – a scenario unlikely to occur in model-driven simulations. For similar reasons, oracle-driven simulations will also be less diverse than model-driven ones. To mitigate these issues, we adopt the following strategy: First, we generate an initial dataset with simulations driven by a noisy-oracle, i.e. we add multiplicative and additive noise to the groundtruth infectiousness to partially emulate the output distribution resulting from trained models. The corresponding noise levels are subject to domain-randomization (as described above), resulting in a dataset with some diversity in epidemiological scenarios and contact patterns. Having trained the predictor on this dataset (until early-stopped), we generate another dataset from simulations driven by the thus-far trained predictor, in place of the noisy-oracle. We then fine-tune the predictor on the new dataset (until early stopped) to obtain the final predictor. This process can be repeated multiple times, in what we call iterative retraining. We find three steps yields a good trade-off between performance and compute requirement.

heading: 4 EXPERIMENTS
text: We evaluate the proposed PCT methods, ST-PCT and DS-PCT, and benchmark them against: testbased BCT; a rule-based FCT Heuristic method proposed by Gupta et al. (2020)4; and a baseline No Tracing (NT) scenario which corresponds to recommendation level 1 (some social distancing).
EXP1: In Figure 3, we plot the Pareto frontier between spread of disease (R) and the amount of restriction imposed. To traverse the frontier at 60% adoption rate, we sweep through multiple values of the simulator’s global mobility scaling factor, a parameter which controls the strength of social distancing and mobility restriction measures. Each method uses 3000 agents for 50 days with 12 random seeds, and we plot the resulting number of contacts per day per human. We fit a Gaussian Process Regressor to the simulation outcomes and highlight the average reduction in R obtained in the vicinity of R ≈ 1, finding DS-PCT and ST-PCT reduce R to below 1 at a much lower cost to mobility on average. For subsequent plots, we select the number of contacts per day per human such that the no-tracing baseline yields a realistic post-lockdown R of around 1.2 (Brisson & et al., 2020)5.
EXP2: Figure 4 compares various DCT methods in terms of their cumulative cases and their fraction of false quarantine: the number of healthy agents the method wrongly recommends to quarantine.
4While we did experiment with additional methods like linear regression and MLPs, they did not improve the performance over the rule-based FCT heuristic proposed by Gupta et al. (2020).
5To estimate this number, we use the GP regression fit in figure 3 and consider the x value for which the mean of the NT process is at 1.2. We find an estimate at 5.61, and select only the runs yielding effective number of contacts that lie within the interval (5.61− 0.5, 5.61 + 0.5).
Again, all DCT methods have a clear advantage over the no-tracing baseline, while the number of agents wrongly recommended quarantine is much lower for ML-enabled PCT. 6
EXP3: In Figure 5 Left we plot the bootstrapped distribution of mean R for different DCT methods. Recall R is an estimate of how many other agents an infectious agent will infects, i.e. even a numerically small improvement in R could yield an exponential improvement in the number of cases. We find that both PCT methods yield a clear improvement over BCT and the rule-based heuristic, all of which significantly improve over the no-tracing baseline. We hypothesize this is because deep neural networks are better able to capture the non-linear relationship between features available on the phone, interaction patterns between agents, and individual infectiousness.
EXP4: In Figure 5 Right we investigate the effect of iterative retraining on the machine-learning based methods, DS-PCT and ST-PCT. We evaluate all 3 iterations of each method in the same experimental setup as in Figure 5 and find that DS-PCT benefits from the 3 iterations, while ST-PCT saturates at the second iteration. We hypothesize that this is a form of overfitting, given that the set transformer (ST) models all-to-all interactions and is therefore more expressive than deep-sets (DS).
6Note that the baseline no tracing method also has false quarantines, because household members of an infected individual are also recommended quarantine, irrespective of whether they are infected.
EXP5: In Figure 6, we analyze the sensitivity of the various methods to adoption rate, which measures what percent of the population actively uses the CT app. Adoption rate is an important parameter for DCT methods, as it directly determines the effectiveness of an app. We visualize the effect of varying the adoption rate on the reproduction number R. Similarly to prior work (Abueg et al., 2020), we find that all DCT methods improve over the no-tracing baseline even at low adoptions and PCT methods dominate at all levels of adoption.

heading: 5 CONCLUSION
text: Our results demonstrate the potential benefit of digital contact tracing approaches for saving lives while reducing mobility restrictions and preserving privacy, independently confirming previous reports (Ferretti et al., 2020; Abueg et al., 2020). Of all methods in our study, we find that deep learning based PCT provides the best trade-off between restrictions on mobility and reducing the spread of disease under a range of settings, making it a potentially powerful tool for saving lives in a safe deconfinement. This area of research holds many interesting avenues of future work in machine learning, including: (1) The comparison of methods for fitting parameters of the epidemiological simulator data using spatial information (not done here to avoid the need for GPS), (2) Using reinforcement learning to learn (rather than expert hand-tune) the mapping from estimated infectiousness and individual-level features (number of contacts, age, etc.), and thereby target desirable outcomes for heterogeneous populations.
Accurate and practical models for contact tracing are only a small part of the non-pharmaceutical efforts against the pandemic, a response to which is a complex venture necessitating cooperation between public health, government, individual citizens, and scientists of many kinds - epidemiologists, sociologists, behavioural psychologists, virologists, and machine learning researchers, among many others. We hope this work can play a role in fostering this necessary collaboration.

heading: ACKNOWLEDGEMENTS
text: We thank all members of the broader COVI project https://covicanada.org for their dedication and teamwork; it was a pleasure and honour to work with such a great team. We also thank the Mila and Empirical Inference communities, in particular Xavier Bouthillier, Vincent Mai, Gabriele Prato, and Georgios Arvanitidis, for detailed and helpful feedback on early drafts. The authors gratefully acknowledge the following funding sources: NSERC, IVADO, CIFAR. This project could not have been completed without the resources of MPI-IS cluster, Compute Canada & Calcul Quebec, in particular the Beluga cluster. In gratitude we have donated to a project to help understand and protect the St. Lawrence beluga whales for whom the cluster is named https://baleinesendirect.org/

heading: 5.1 ML ARCHITECTURES AND BASELINE DETAILS:
text: Binary contact tracing quarantines app-users who had high-risk encounters with an app-user who receives a positive PCR test. Under BCT1, if Alice gets a positive test result, then every user who encountered Alice within 14 days of her receiving the positive test result is sent a message which places them in app-recommendation level 3 (quarantine) for 14 days. Formally, ζdi = ψ(ŷ d i ) = 3.
Set Transformer Recall that in Section 3 we proposed two parameterizations of the model (DS and ST in Figure 2). In the first proposal, we use a set transformer (ST) to model interactions between the elements in the set Ddi ∪ Edi . We now describe the precise architecture of the model used. The model comprises 5 embedding modules, namely: the health status embedding φhs, health profile embedding φhp, day offset embedding φdo, risk message embedding φ (r) e and an embedding φ (n) e of the number of repeated encounters.
The model was trained for 160 epochs on a domain randomized dataset (see below) comprising∼ 107 samples. We used a batch-size of 1024, resulting in ∼ 80k training steps. The learning rate schedule is such that the first 2.5k steps are used for linear learning-rate warmup, wherein the learning rate is linearly increased from 0 to 2 × 10−4, followed by a cosine annealing schedule that decays the learning rate from 2× 10−4 to 8× 10−6 in 50k steps.

heading: 5.2 DOMAIN RANDOMIZATION
text: Inspired by research in hyper-parameter search (Bergstra & Bengio, 2012) and recent advances in deep reinforcement learning (Tobin et al., 2017) we created the transformer’s training data by sampling uniformly in the following ranges:
1. Adoption rate ∈ [30− 60] 2. Carefulness ∈ [0.5− 0.8] 3. Initial proportion of exposed people ∈ [0.002, 0.006] 4. Oracle additive noise ∈ [0.05− 0.15] 5. Oracle multiplicative noise ∈ [0.2− 0.8] 6. Global mobility scaling factor ∈ [0.3− 0.9] 7. Symptoms dropout: Likelihood of not reporting some symptoms ∈ [0.1, 0.6] 8. Symptoms drop-in: Likelihood of falsely reporting symptoms ∈ [0.0001, 0.001] 9. Quarantine dropout (test) ∈ [0.01, 0.03]: likelihood of not quarantining when recommended
to quarantine due to a positive test 10. Quarantine dropout (household) ∈ [0.02, 0.05]: likelihood of not quarantining when recom-
mended to quarantine because a household member got a positive test 11. All-levels dropout ∈ [0.01, 0.05]: likelihood of not following app-recommended behavior
and instead exhibit pre-pandemic behavior

heading: 5.3 TRAINING TIME
text: Our ML experiments use approximately 250 days training time on GPUs while simulations required approximately 41 days of CPU time. All CPU time was run on compute using renewable resources.
APPENDIX 5: RELEVANT BACKGROUND ON COVI-AGENTSIM
Details on the simulator can be found in Gupta et al. (2020), and the code is open-source at https:// github.com/mila-iqia/COVI-AgentSim. Here we summarize some of the most relevant details about the simulator for ease of reference.

heading: 5.4 APP ADOPTION
text: COVI-AgentSim models app adoption proportional to smartphone usage statistics, shown in Table 1.

heading: 1 1.50

heading: 30 42.15

heading: 40 56.18

heading: 60 84.15

heading: 70 98.31

heading: 5.5 RECOMMENDATION LEVELS AND CONTAINMENT PROTOCOL
text: In Gupta et al. (2020), the implementation of binary contact tracing uses a simple, binary containment protocol: quarantine at home for 14 days if in contact with someone who has had a positive test result, otherwise do nothing. In contrast, the graded recommendation levels used by feature-based contact tracing methods including Heuristic and Proactive Contact Tracing are not binary, and do not model an explicit containment protocol. Instead, Gupta et al. (2020) models the effects of behavioural recommendations through reducing the number of daily effective contacts with respect to pre-confinement contact rates defined by Prem et al. (2017).
We denote by Cl the number of contacts that occurred at a location l during pre-confinement. While operating under recommendation level 0, an agent visiting location l will on average contact Cl other agents. Post-confinement contact patterns surveyed in Quebec during summer 2020 (Brisson & et al., 2020) are used to scale down the number of pre-confinement interactions across different locations, the percentage reduction per location are denoted αl. Table 2 show the number of contacts and percentage reduction as a result of confinement.
There are 5 recommendation levels described by Table 3 with their corresponding expected number of contacts. When these recommendations are followed, they modulate the number of effective contacts that agents have while at locations. Recommendation level 3 scales down the contacts at a location by αl. Levels 1 and 2 are successively obtained by reducing the location dependent contacts by half from level 3, while level 4 is used to impose full quarantine i.e. no contacts. Level 0 is not used except to represent the behavior when an agent does not adhere to the recommendations modeled by a daily dropout parameter.

heading: 5.6 INFECTIVITY (TRANSMISSION) MODEL
text: Effective viral load (EVL) varies [0., 1.], and represents the ’severity’ of viral load the agent is currently experiencing (which takes into account both the viral load and the interaction of the virus with the host’s immune system), as shown in Figure 8. Each agent’s disease progresses according to this curve, and the probability of transmission is also proportional to EVL.

heading: 5.7 TAILORING THE SIMULATOR TO REGIONAL DEMOGRAPHICS AND OTHER DISEASES
text: Many aspects of the simulator are customizable to a particular region’s statistics, including individual agent features (pre-existing medical conditions, biological sex, etc.), contact patterns, and prevalence of other diseases (which affect the predictions of COVID-19 by introducing other reasons for an agent to experience symptoms. The simulator provides details of fit to real data for the region of Montreal, Canada, with the confounding symptom-producing conditions of flu, allergies, and colds. The process for tailoring the simulator to other regions is detailed in their work, but briefly, configuration files with the appropriate statistics need to be provided in https://github.com/mila-iqia/ COVI-AgentSim/blob/master/src/covid19sim/configs/.

Review summaries:
In this paper the authors propose a novel method of contact tracing which they dub Proactive Contact Tracing (PCT). PCT is aimed at detecting an individual's infectivity given locally observed information (and history), as can be carried on say a mobile device. As the name suggests, being able to estimate infectivity given this local information is useful in large part due to the fact that individuals can be asymptomatic, or they can have significant infectivity before demonstrating symptoms if they are to be symptomatic. Proactively estimating infectivity levels thus provides another tool in combatting viral spread through proper containment protocols. 

This paper introduces a deep learning based digital contact tracing method to minimize the spread of COVID19. The proposed method is based on locally processed information collected on the mobile app. Unlike the most commonly used digital tracing approach that sends quarantine recommendations to all recent contacts of a newly diagnosed person, the developed method in this paper considers all the information related to the users and the ones who have been in contacts with them in order to make user specific recommendations. This is not an easy problem because of different conflicting factors involving in making recommendation decisions, i.e. user privacy, mobility restrictions, and public health. The proposed method, called proactive content tracing, is a set-based architecture (that uses attention) and perform distributed inference to preserve privacy.