Original: Contactless Oxygen Monitoring with Gated Transformer
Revised: Contactless Oxygen Monitoring with Gated Transformer

Original: Abstract
Revised: Abstract

Original: With the increasing popularity of telehealth, it becomes critical to ensure thatbasic physiological signals can be monitored accurately at home, with minimalpatient overhead.
Revised: With the increasing popularity of telehealth, it becomes critical to ensure that basic physiological signals can be monitored accurately at home, with minimal patient overhead.

Original: In this paper, we propose a contactless approach for monitoringpatients’ blood oxygen at home, simply by analyzing the radio signals in the room,without any wearable devices.
Revised: In this paper, we propose a contactless approach for monitoring patients’ blood oxygen at home, simply by analyzing the radio signals in the room, without any wearable devices.

Original: We extract the patients’ respiration from the radiosignals that bounce off their bodies and devise a novel neural network that infers apatient’s oxygen estimates from their breathing signal.
Revised: We extract the patients’ respiration from the radio signals that bounce off their bodies and devise a novel neural network that infers a patient’s oxygen estimates from their breathing signal.

Original: Our model, called Gated
Revised: Our model, called Gated

Original: BERT-UNet , is designed to adapt to the patient’s medical indices (e.g., gender,sleep stages).
Revised: BERT-UNet , is designed to adapt to the patient’s medical indices (e.g., gender, sleep stages).

Original: It has multiple predictive heads and selects the most suitable head viaa gate controlled by the person’s physiological indices.
Revised: It has multiple predictive heads and selects the most suitable head via a gate controlled by the person’s physiological indices.

Original: Extensive empirical resultsshow that our model achieves high accuracy on both medical and radio datasets.
Revised: Extensive empirical results show that our model achieves high accuracy on both medical and radio datasets.

Original:  Introduction
Revised:  Introduction

Original: Remote health monitoring and telehealth are increasingly popular because they reduce costs andfacilitate access to healthcare, particularly for people in remote locations [2].
Revised: Remote health monitoring and telehealth are increasingly popular because they reduce costs and facilitate access to healthcare, particularly for people in remote locations [2].

Original: Further, remote healthmonitoring can track the long-term physiological state of a patient or an older person who lives aloneat home and enable family and professional caregivers to provide timely help [6, 40, 13].
Revised: Further, remote health monitoring can track the long-term physiological state of a patient or an older person who lives alone at home and enable family and professional caregivers to provide timely help [6, 42, 13, 47].

Original: Deliveringsuch services, however, depends on the availability of solutions that continuously measure people’sphysiological signals at home with minimal overhead to patients.
Revised: Delivering such services, however, depends on the availability of solutions that continuously measure people’s physiological signals at home, with minimal overhead to patients.

Original: Oxygen saturation is an important physiological signal whose at-home monitoring would benefitvery old adults and individuals at high risk for low blood oxygen [27].
Revised: Oxygen saturation is an important physiological signal whose at-home monitoring would benefit very old adults and individuals at high risk for low blood oxygen [29].

Original: Oxygen saturation refers tothe amount of oxygen in the blood – that is the fraction of oxygen-saturated hemoglobin relative tothe total blood hemoglobin.
Revised: Oxygen saturation refers to the amount of oxygen in the blood – that is the fraction of oxygen-saturated hemoglobin relative to the total blood hemoglobin.

Original: Normal oxygen levels range from 94% to 100%.
Revised: Normal oxygen levels range from 94% to 100%.

Original: Lower oxygen can bedangerous and if severe, lead to brain and lung failure [10, 21].
Revised: Lower oxygen can be dangerous, and if severe, lead to brain and lung failure [10, 21].

Original: Today, measuring oxygen saturation requires the person to wear a pulse oximeter on their finger andactively measure themselves.
Revised: Today, measuring oxygen saturation requires the person to wear a pulse oximeter on their finger, and actively measure themselves.

Original: While pulse oximeters are very helpful, they can be impractical insome at-home monitoring scenarios.
Revised: While pulse oximeters are very helpful, they can be impractical in some at-home monitoring scenarios.

Original: In particular, old people in their late 80’s and 90’s are at highrisk for low blood oxygen [30], and should regularly monitor their oxygen.
Revised: In particular, old people in their late 80’s and 90’s are at high risk for low blood oxygen [32], and should regularly monitor their oxygen.

Original: Many of them howevermay suffer from dementia or cognitive impairment that prevent them from measuring themselves.
Revised: Many of them however may suffer from dementia or cognitive impairment that prevent them from measuring themselves.

Original: COVID and pneumonia patients recovering at home can suffer from delirium [17], which can affecttheir reasoning and ability to measure their oxygen levels.
Revised: COVID and pneumonia patients recovering at home can suffer from delirium [17], which can affect their reasoning and ability to measure their oxygen levels.

Original: Additionally, blood oxygen tends to dropduring sleep, making it particularly important to track oxygen overnight [31, 15].
Revised: Additionally, blood oxygen tends to drop during sleep, making it particularly important to track oxygen overnight [33, 15].

Original: Yet people cannot actively measure themselves while asleep.
Revised: Yet people cannot actively measure themselves while asleep.

Original: The above use cases motivate us to try to complement pulse oximetry with a new approach that canwork passively and continuously, assessing blood oxygen throughout the night without requiring theperson to wear a sensor or actively measure themselves. Prior attempts at estimating blood oxygen passively without a wearable sensor rely on cameras [25, 41, 42, 37, 3, 16]. For example, [25]
Revised: The above use cases motivate us to try to complement pulse oximetry with a new approach that can work passively and continuously, assessing blood oxygen throughout the night without requiring the

Original: [Figure]
Revised: [Figure]

Original:  𝐹 !
Revised: OxygenSaturation 𝐹 !

Original: (b)GatedBERT-UNet … 𝑦" ! …
Revised: (b)GatedBERT-UNet … 𝑦" ! …

Original: 𝑦" 𝐺 … 𝐹 " 𝐹 # 𝑢$ 𝑣 𝑦" " 𝑥
Revised: 𝑦" 𝐺 … 𝐹 " 𝐹 # 𝑢$ 𝑣 𝑦" " 𝑥

Original: BERT 𝐹 𝐸 𝑦" (a) BERT-UNet 𝑥
Revised: BERT 𝐹 𝐸 𝑦" (a) BERT-UNet 𝑥

Revised: BERT 𝐸 person to wear a sensor or actively measure themselves.

Revised: Prior attempts at estimating blood oxygen passively, without a wearable sensor, rely on cameras [27, 43, 44, 39, 3, 16].

Original: BERT 𝐸 proposes a convolution neural network that analyzes a video of the person’s palm to estimate his/herblood oxygen.
Revised: For example, [27] proposes a convolution neural network that analyzes a video of the person’s palm to estimate his/her blood oxygen.

Original: While not requiring wearable sensors, it cannot work continuously since the usercannot keep their hand in front of the camera for a long time.
Revised: While not requiring wearable sensors, it cannot work continuously since the user cannot keep their hand in front of the camera for a long time.

Original: It also cannot operate in dark settingsand thus cannot monitor one’s oxygen during sleep.
Revised: It also cannot operate in dark settings and thus cannot monitor one’s oxygen during sleep.

Original: To bypass the limitations imposed by cameras,we propose a different sensing modality, radio-frequency (RF) signals .
Revised: To bypass the limitations imposed by cameras, we propose a different sensing modality, radio-frequency (RF) signals .

Original: We propose to monitor oxygen saturation by analyzing the radio signals that bounce off a person’sbody.
Revised: We propose to monitor oxygen saturation by analyzing the radio signals that bounce off a person’s body.

Original: Recent research has demonstrated the feasibility of monitoring breathing, heart rate, and evensleep stages by transmitting a very low power RF signal and analyzing its reflections off a person’sbody [1, 43].
Revised: Recent research has demonstrated the feasibility of monitoring breathing, heart rate, and even sleep stages by transmitting a very low power RF signal and analyzing its reflections off a person’s body [1, 50].

Original: The medical literature shows an inherent dependence and dynamic interaction betweenthe breathing signal and oxygen saturation [18, 4, 32].
Revised: The medical literature shows an inherent dependence and dynamic interaction between the breathing signal and oxygen saturation [18, 4, 34].

Original: Building on these advances, we use RF signalsto track a person’s breathing signal and train a neural network to infer oxygen from respiration.
Revised: Building on these advances, we use RF signals to track a person’s breathing signal and train a neural network to infer oxygen from respiration.

Original: Such a design can measure a person’s oxygen without any physical contact or wearable devices.
Revised: Such a design can measure a person’s oxygen without any physical contact or wearable devices.

Original: Thus, it does not burden the patient or interfere with their sleep.
Revised: Thus, it does not burden the patient or interfere with their sleep.

Original: Using breathing as a mediator hasan additional side benefit.
Revised: Using breathing as a mediator has an additional side benefit.

Original: It would be very hard to collect a large dataset of radio signals and thecorresponding oxygen levels.
Revised: It would be very hard to collect a large dataset of radio signals and the corresponding oxygen levels.

Original: Luckily however there are multiple large medical datasets that containcontinuous breathing signals paired with oxygen measurements.
Revised: Luckily however there are multiple large medical datasets that contain continuous breathing signals paired with oxygen measurements.

Original: This allows us to train a model toinfer oxygen from breathing and test it directly on breathing extracted from radio signals.
Revised: This allows us to train a model to infer oxygen from breathing and test it directly on breathing extracted from radio signals.

Original: While designing our model, motivated by personalized medicine, we aim for a model that can adaptto the patient’s medical indices (e.g., gender, disease diagnoses).
Revised: While designing our model, motivated by personalized medicine, we aim for a model that can adapt to the patient’s medical indices (e.g., gender, disease diagnoses).

Original: We observe that many medicalindices are binary or categorical.
Revised: We observe that many medical indices are binary or categorical.

Original: To leverage such variables, we propose Gated BERT-UNet , a newtransformer model that has multiple predictive heads.
Revised: To leverage such variables, we propose Gated BERT-UNet , a new transformer model that has multiple predictive heads.

Original: It selects the most suitable head for each personvia a gate controlled by the person’s categorical indices.
Revised: It selects the most suitable head for each person via a gate controlled by the person’s categorical indices.

Original: We evaluate our model on medical and RFdatasets.
Revised: We evaluate our model on medical and RF datasets.

Original: Experiments show that our model’s average absolute error in predicting oxygen saturation is1.3%, which is significantly lower than the state-of-the-art (SOTA) camera-based models [25].
Revised: Experiments show that our model’s average absolute error in predicting oxygen saturation is 1.3%, which is significantly lower than the state-of-the-art (SOTA) camera-based models [27].

Original:  Our System and Model (Gated BERT-UNet)
Revised:  Our System and Model (Gated BERT-UNet)

Original: The proposed oxygen estimation solution operates in two steps: (1) Extracting breathing signalsfrom RF signals and (2) Estimating SpO2 from breathing signals.
Revised: The proposed oxygen estimation solution operates in two steps: (1) Extracting breathing signals from RF signals and (2) Estimating SpO2 from breathing signals.

Original: Please refer to Appendix B for thedetails of step one.
Revised: Please refer to Appendix B for the details of step one.

Original: We focus on step two in this section.
Revised: We focus on step two in this section.

Original: We formulate the oxygen saturation prediction from respiration signals as a sequence-to-sequenceregression task.
Revised: We formulate the oxygen saturation prediction from respiration signals as a sequence-to-sequence regression task.

Original: Figure 1 left shows an example of respiration signals and corresponding bloodoxygen saturation.
Revised: Figure 1 left shows an example of respiration signals and corresponding blood oxygen saturation.

Original: The model takes the breathing signal x ∈ R 1 × f b T over a T -second interval andpredicts the oxygen time series y ∈ R 1 × f o T over the same period, where f b and f o are the samplingfrequencies of respiration and oxygen, respectively.
Revised: The model takes the breathing signal x ∈ R 1 × f b T over a T -second interval and predicts the oxygen time series y ∈ R 1 × f o T over the same period, where f b and f o are the sampling frequencies of respiration and oxygen, respectively.

Original: In this study, the default sampling rates forrespiration and oxygen are f b = 10 Hz and f o = 1 Hz .
Revised: In this study, the default sampling rates for respiration and oxygen are f b = 10 Hz and f o = 1 Hz .

Original:  As shown in Figure 1(a), our backbone model is a combination of a BERT module [9] and UNet [36].
Revised: [Table] As shown in Figure 1(a) [Table] our backbone model is a combination of a BERT module [9] and UNet [38]

Revised: [Table]

Original: The BERT-UNet backbone consists of an encoder E and an oxygen predictor F .
Revised: The BERT-UNet backbone consists of an encoder E and an oxygen predictor F .

Original: The encoder hasconvolutional layers and bidirectional attention modules while the decoder is fully convolutional[Table] and has skip-links from the encoder.
Revised: The encoder has convolutional layers and bidirectional attention modules while the decoder is fully convolutional and has skip-links from the encoder.

Original: The backbone is simply trained by L 1 loss and correlation loss.
Revised: The backbone is simply trained by L 1 loss and correlation loss.

Original: Please refer to Appendix C for the details of model architecture and loss functions.
Revised: Please refer to Appendix C for the details of model architecture and loss functions.

Original: Our full model, Gated BERT-UNet augments BERT-UNet with multiple predictive heads to adapt themodel’s prediction to different medical indices.
Revised: Our full model, Gated BERT-UNet augments BERT-UNet with multiple predictive heads to adapt the model’s prediction to different medical indices.

Original: It is important for boosting the model’s performancesince the relationship between breathing and oxygen saturation has been shown related to manymedical indices.
Revised: It is important for boosting the model’s performance since the relationship between breathing and oxygen saturation has been shown related to many medical indices.

Original: For example, gender is an influential factor as men and women have differences intheir oxygen transport systems [34].
Revised: For example, gender is an influential factor as men and women have differences in their oxygen transport systems [36].

Original: Another example is that sleep stage affects a person’s restingoxygen levels [8].
Revised: Another example is that sleep stage affects a person’s resting oxygen levels [8].

Original: To do the adaptation, our Gated BERT-UNet selects the most suitable head for a person via a gatecontrolled by the subject’s categorical indices.
Revised: To do the adaptation, our Gated BERT-UNet selects the most suitable head for a person via a gate controlled by the subject’s categorical indices.

Original: Specifically, as shown in Figure 1(b), it has a gatefunction G ( v, u ) :
Revised: Specifically, as shown in Figure 1(b), it has a gate function G ( v, u ) :

Original: V × U → { 1 , 2 , · · · , N } where v ∈ V and u ∈ U are accessible/inaccessiblevariables, N is the number of gate statuses.
Revised: V × U → { 1 , 2 , · · · , N } where v ∈ V and u ∈ U are accessible/inaccessible variables, N is the number of gate statuses.

Original: We use the term accessible variable for variables easilyavailable during inference time (e.g., gender, race) and the term inaccessible variable for informationthat is not available during inference, but available during training, like a person’s sleep stages.
Revised: We use the term accessible variable for variables easily available during inference time (e.g., gender, race) and the term inaccessible variable for information that is not available during inference, but available during training, like a person’s sleep stages.

Original: Theprediction for inaccessible variable is learned concurrently with the main task under full supervision.
Revised: The prediction for inaccessible variable is learned concurrently with the main task under full supervision.

Original: The model has N heads { F i } Ni =1 that adapt the prediction ˆ y i
Revised: The model has N heads { F i } Ni =1 that adapt the prediction ˆ y i

Original: = F i ( E ( x )) to the gate status.
Revised: = F i ( E ( x )) to the gate status.

Original: Italso has an extra predictor F u to infer inaccessible variables u .
Revised: It also has an extra predictor F u to infer inaccessible variables u .

Original: During testing time, based on theaccessible variables v and estimated inaccessible variables ˆ u , we evaluate the gate status s =
Revised: During testing time, based on the accessible variables v and estimated inaccessible variables ˆ u , we evaluate the gate status s =

Original: G ( v, ˆ u ) .
Revised: G ( v, ˆ u ) .

Original: Please see Appendix D for the details of (1) the loss function used to train our full model; (2) theexact construction of the gate function G ( v, u ) .
Revised: Please see Appendix D for the details of (1) the loss function used to train our full model; (2) the exact construction of the gate function G ( v, u ) .

Original:  Experiments and Results
Revised:  Experiments and Results

Original: Dataset and Metrics.
Revised: Dataset and Metrics.

Original: We conduct experiments on three medical datasets: SHHS [44], MrOS [5] and
Revised: We conduct experiments on three medical datasets: SHHS [51], MrOS [5] and

Original: MESA [7], and a self-collected RF dataset.
Revised: MESA [7], and a self-collected RF dataset.

Original: We consider three evaluation metrics: correlation (Corr),mean-absolute error (MAE) and rooted mean-squared error (RMSE).
Revised: We consider three evaluation metrics: correlation (Corr), mean-absolute error (MAE) and rooted mean-squared error (RMSE).

Original: Please refer to Appendix E formore details on datasets and metrics.
Revised: Please refer to Appendix E for more details on datasets and metrics.

Original: Baselines.
Revised: Baselines.

Original: We compare our model with the following baselines: (a) CNN , a fully convolutionalmodel; (b) CNN-RNN , an augmentation of CNN with RNN units in the bottleneck; (c) BERT-UNet+ VarAug , which takes BERT-UNet as the backbone and uses medical variables as extra inputs oroutputs.
Revised: We compare our model with the following baselines: (a) CNN , a fully convolutional model; (b) CNN-RNN , an augmentation of CNN with RNN units in the bottleneck; (c) BERT-UNet + VarAug , which takes BERT-UNet as the backbone and uses medical variables as extra inputs or outputs.

Original: Appendix F explains more details of the baselines.
Revised: Appendix F explains more details of the baselines.

Original: Training and Evaluation Protocols.
Revised: Training and Evaluation Protocols.

Original: Since the RF dataset is too small for training, we train modelson breathing signals from the medical datasets, and test them directly on the respiration signalsextracted from the RF dataset as well as medical datasets’ test sets.
Revised: Since the RF dataset is too small for training, we train models on breathing signals from the medical datasets, and test them directly on the respiration signals extracted from the RF dataset as well as medical datasets’ test sets.

Original: More details are in Appendix G.
Revised: More details are in Appendix G.

Original: 3.1 Results on Medical Datasets
Revised: 3.1 Results on Medical Datasets

Original: Quantitative.
Revised: Quantitative.

Original: The results on medical datasets are shown in Table 1.
Revised: The results on medical datasets are shown in Table 1.

Original: Since there is no past work thatpredicts oxygen from breathing or radio signals, all models in the table refer to variants of our neuralnetwork.
Revised: Since there is no past work that predicts oxygen from breathing or radio signals, all models in the table refer to variants of our neural network.

Original: The table shows that all variants achieve relatively low prediction errors with an average
Revised: The table shows that all variants achieve relatively low prediction errors with an average

Original: MAE that ranges from 1.58 to 1.73 percent, and an average RMSE that ranges from 1.70 to 1.78percent.
Revised: MAE that ranges from 1.58 to 1.73 percent, and an average RMSE that ranges from 1.70 to 1. percent.

Original: Such a relatively low RMSE shows our model rarely has predictions that largely deviatefrom the ground truth.
Revised: Such a relatively low RMSE shows our model rarely has predictions that largely deviate from the ground truth.

Original: All variants also achieve reasonable high correlations ranging from 0.47 to0.53.
Revised: All variants also achieve reasonable high correlations ranging from 0.47 to 0.53.

Original: Such a correlation level indicates our model’s prediction capture the dynamics of the groundtruth SpO2 which is also visually shown in Figure 2.
Revised: Such a correlation level indicates our model’s prediction capture the dynamics of the ground [Figure] [Figure] [Table]

Revised: [Figure]

Revised: truth SpO2 which is also visually shown in Figure 2.

Original: These quantitative results highlight that oursystem can be useful for continuous monitoring of patients’ oxygen at home.
Revised: These quantitative results highlight that our system can be useful for continuous monitoring of patients’ oxygen at home.

Original: The upper rows in the table show the variants that do not leverage side variables.
Revised: The upper rows in the table show the variants that do not leverage side variables.

Original: The table showsthat the BERT-UNet model consistently outperforms the CNN model and the CNN-RNN model onall datasets, in all metrics.
Revised: The table shows that the BERT-UNet model consistently outperforms the CNN model and the CNN-RNN model on all datasets, in all metrics.

Original: This indicates that BERT-UNet is a preferable architecture for this task.[Figure] [Figure] [Table]
Revised: This indicates that BERT-UNet is a preferable architecture for this task.

Original: [Figure]

Original: [Table]

Original: [Figure] [Table] [Figure] The bottom rows in the table show the results of models leveraging accessible and inaccessiblemedical variables.
Revised: The bottom rows in the table show the results of models leveraging accessible and inaccessible medical variables.

Original: The table shows that BERT-UNet + VarAug and Gated BERT-UNet outperformmodels that do not leverage physiological indices, demonstrating the benefit of leveraging suchvariables.
Revised: The table shows that BERT-UNet + VarAug and Gated BERT-UNet outperform models that do not leverage physiological indices, demonstrating the benefit of leveraging such variables.

Original: In addition, Gated BERT-UNet outperforms VarAug on all three datasets, demonstratingthat a gated multi-head approach works best for such categorical side variables.
Revised: In addition, Gated BERT-UNet outperforms VarAug on all three datasets, demonstrating that a gated multi-head approach works best for such categorical side variables.

Original: Qualitative.
Revised: Qualitative.

Original: Figure 2 visualizes the predicted oxygen saturation of the Gated BERT-UNet model andthe VarAug model on a male subject in the SHHS dataset.
Revised: Figure 2 visualizes the predicted oxygen saturation of the Gated BERT-UNet model and the VarAug model on a male subject in the SHHS dataset.

Original: As the ground-truth oxygen saturationare integers, we round the predicted oxygen values.
Revised: As the ground-truth oxygen saturation are integers, we round the predicted oxygen values.

Original: The background color indicates different sleepstages.
Revised: The background color indicates different sleep stages.

Original: The ‘dark grey’, ‘light grey’ and ‘white’ correspond to non-REM ‘Sleep’, ‘REM’ and ‘Awake’stage, respectively.
Revised: The ‘dark grey’, ‘light grey’ and ‘white’ correspond to non-REM ‘Sleep’, ‘REM’ and ‘Awake’ stage, respectively.

Original: We observe that Gated BERT-UNet consistently outperforms VarAug over thewhole night.
Revised: We observe that Gated BERT-UNet consistently outperforms VarAug over the whole night.

Original: The small panel focuses on different sleep stages.
Revised: The small panel focuses on different sleep stages.

Original: In general, different sleep stages tendto show different behavior and hence the importance of using a gated model.
Revised: In general, different sleep stages tend to show different behavior and hence the importance of using a gated model.

Original: Specifically, oxygen istypically more stable during non-REM ‘Sleep’ than during REM and Awake stages.
Revised: Specifically, oxygen is typically more stable during non-REM ‘Sleep’ than during REM and Awake stages.

Original: The figures showthat Gated BERT-UNet can track the ups and downs in oxygen and is significantly more accuratethan VarAug.
Revised: The figures show that Gated BERT-UNet can track the ups and downs in oxygen and is significantly more accurate than VarAug.

Original: This experiment demonstrates that the way we incorporate the sleep stages into themodel improves performance across different sleep stages.
Revised: This experiment demonstrates that the way we incorporate the sleep stages into the model improves performance across different sleep stages.

Original: 3.2 Results on RF Dataset
Revised: 3.2 Results on RF Dataset

Original: The results on the RF dataset are shown in Table 2.
Revised: The results on the RF dataset are shown in Table 2.

Original: All model variants have low prediction errorand high correlation.
Revised: All model variants have low prediction error and high correlation.

Original: Among the models that do not leverage physiological variables, CNN-RNNand Bert-UNet perform better than the vanilla CNN, which shows the importance of modelingtemporal information.
Revised: Among the models that do not leverage physiological variables, CNN-RNN and Bert-UNet perform better than the vanilla CNN, which shows the importance of modeling temporal information.

Original: When using physiological variables, the performance of BERT-UNet+VarAugis similar to that of BERT-UNet, while Gated BERT-UNet is better than all other variants.
Revised: When using physiological variables, the performance of BERT-UNet+VarAug is similar to that of BERT-UNet, while Gated BERT-UNet is better than all other variants.

Original: Thisdemonstrates that the gating design leverages auxiliary variables better.
Revised: This demonstrates that the gating design leverages auxiliary variables better.

Original: Overall, the MAEs, RMSEsand correlations on the RF dataset are comparable to those on the medical datasets.
Revised: Overall, the MAEs, RMSEs and correlations on the RF dataset are comparable to those on the medical datasets.

Original: This indicates thatour model is directly applicable to respiration signals from RF.
Revised: This indicates that our model is directly applicable to respiration signals from RF.

Original: We have also visualized the predictionresults in Figure 3.
Revised: We have also visualized the prediction results in Figure 3.

Original: As shown, our model can accurately track the fluctuation of ground truth SpO2. 
Revised: As shown, our model can accurately track the fluctuation of ground truth SpO2. [Figure] [Table]

Revised: 3.3 Visualization of Breathing-Oxygen Patterns

Original: More results are in the Appendix: Section I shows  different  breathing patterns and correspondingtrue/predicted oxygen levels; Section H analyzes (predicted) oxygen value distributions in differentrace groups; Section J compares our method with prior camera-based methods; Section K hasmore visualization on our model’s performance on different datasets, patients with different relevantdiseases.
Revised: We demonstrate several visual results on different patterns of breathing signals and the corresponding ground truth/predicted oxygen saturation, as shown in Figure 4. Figure 4(a) shows a normal breathing pattern, which leads to constant oxygen saturation. In contrast, Figure 4(b,c) present two different abnormal breathing signals and the resulting fluctuated oxygen predictions. These figures show the diversity of the oxygen and breathing patterns as well as the complexity of their relationship.

Revised: The model however is able to capture this relationship for highly diverse patterns

Revised: 3.4 Comparison with Past Works

Revised: We compare our approach with two recent deep-learning camera-based SpO2 monitoring methods.

Revised: The first method [11] asks the user to press his/her finger against a smartphone camera, and uses a

Revised: CNN to estimate SpO2 from the video.

Original: A Related Work
Revised: The second method [27] uses a CNN to estimate oxygen from a video of the person’s hand. The input of these systems is different from ours (camera vs. RF); so to compare them we follow the setup in [27]. In their setting, test samples are 180-240 seconds and vary between normal breathing to no or minimal breathing. Similarly, we divide the RF test dataset into non-overlapping 240-second segments containing both regular breathing and shallow breathing (i.e., apnea or hypopnea) and compute metrics on them.

Revised: Table 3 reports the output of the three models.

Revised: The results of the baselines are taken from [27], and the results of our RF-based model are computed as described.

Revised: The results show that our model improves the correlation and reduces the MAE and

Revised: RMSE in comparison to past work.

Revised: More results are in the appendix: Section H analyzes (predicted) oxygen value distributions in different race groups; Section I has more visualization on our model’s performance on different datasets, patients with different relevant diseases.

Revised:  Concluding Remarks

Revised: This paper introduces the new task of inferring oxygen saturation from radio signals.

Revised: It develops a new gated transformer architecture to deliver this application and adapt deep models to auxiliary categorical variables.

Revised: We note the work have some limitations.

Revised: First, the paper focuses on special use cases (e.g., at-home oxygen monitoring in very old adults or during sleep), but is not suitable for other use cases (e.g., measuring oxygen to optimize performance during exercise).

Revised: Second, the results in the paper provide an initial proof of concept that the shape and dynamics of the breathing signal include sufficient clues to infer a useful estimate of oxygen saturation.

Revised: However, before this system can be used in clinical care, one needs clinical studies to quantify the performance for different disease conditions.

Revised: A Related Work

Original: Monitoring Oxygen Saturation.
Revised: Monitoring Oxygen Saturation.

Original: The most accurate measurements of oxygen saturation areinvasive and require arterial blood samples.
Revised: The most accurate measurements of oxygen saturation are invasive and require arterial blood samples.

Original: The non-invasive and widely-used method for measuringoxygen saturation (SpO2) uses a pulse oximeter, a small device worn on the finger.
Revised: The non-invasive and widely-used method for measuring oxygen saturation (SpO2) uses a pulse oximeter, a small device worn on the finger.

Original: To enable remote
Revised: To enable remote

Original: SpO2 measurements, past work has investigated the use of cameras [41, 42, 37, 3, 16].
Revised: SpO2 measurements, past work has investigated the use of cameras [43, 44, 39, 3, 16].

Original: Howeverthose methods have limitations like susceptibility to noise, sensitivity to motion, and a need forambient light.
Revised: However those methods have limitations like susceptibility to noise, sensitivity to motion, and a need for ambient light.

Original: Recently, deep learning has been considered to aid SpO2 monitoring using cameras.[11] tried to monitor SpO2 using smartphones.
Revised: Recently, deep learning has been considered to aid SpO2 monitoring using cameras. [11] tried to monitor SpO2 using smartphones.

Original: But their solution requires the fingertip to be pressedagainst the camera, and hence cannot provide continuous overnight measurements.
Revised: But their solution requires the fingertip to be pressed against the camera, and hence cannot provide continuous overnight measurements.

Original: A more recentwork [25] has estimated SpO2 in a contactless way with regular RGB cameras.
Revised: A more recent work [27] has estimated SpO2 in a contactless way with regular RGB cameras.

Original: Their method firstextracts the region of interest from the video of the person’s palm, then uses a CNN model to estimate
Revised: Their method first extracts the region of interest from the video of the person’s palm, then uses a CNN model to estimate

Original: SpO2.
Revised: SpO2.

Original: While this approach is contactless, it still requires the user to keep their hand in front of thevideo camera for the duration of the monitoring, which is not practical for continuous or overnightmonitoring.
Revised: While this approach is contactless, it still requires the user to keep their hand in front of the video camera for the duration of the monitoring, which is not practical for continuous or overnight monitoring.

Original: Our work differs from all of these prior works in that we predict oxygen values frombreathing or radio waves, which allows for continuous oxygen sensing in a contactless and passivemanner.
Revised: Our work differs from all of these prior works in that we predict oxygen values from breathing or radio waves, which allows for continuous oxygen sensing in a contactless and passive manner.

Original: Contactless Health Sensing with Radio Signals.
Revised: Contactless Health Sensing with Radio Signals.

Original: The past decade has seen a rapid growth inresearch on passive sensing using RF signals.
Revised: The past decade has seen a rapid growth in research on passive sensing using RF signals.

Original: Early work has demonstrated the possibility of sensingone’s breathing and heart rate using radio signals [1].
Revised: Early work has demonstrated the possibility of sensing one’s breathing and heart rate using radio signals [1].

Original: Later, researchers have shown that by analyzingthe RF signals that bounce off the human body, they can monitor a variety of health metrics includingsleep, gait, falls, and even human emotions [46, 19, 40, 45, 12, 23].
Revised: Later, researchers have shown that by analyzing the RF signals that bounce off the human body, they can monitor a variety of health metrics including sleep, gait, falls, and even human emotions [53, 19, 42, 52, 12, 25, 47, 24].

Original: We build on this work to enable SpO2 monitoring with radio waves.
Revised: We build on this work to enable SpO2 monitoring with radio waves.

Original: Adaptation of ML Models to Medical Indices.
Revised: Adaptation of ML Models to Medical Indices.

Original: Prior deep learning models  do not adapt toa person’s medical indices.
Revised: Prior deep learning models [46, 45, 23, 49, 48] do not adapt to a person’s medical indices.

Original: For example, the literature has models that infer sleep stages fromrespiration [46], detect arrhythmia from ECG [20], and classify emotion from EEG signals [28].
Revised: For example, the literature has models that infer sleep stages from respiration [53], detect arrhythmia from ECG [20], and classify emotion from EEG signals [30].

Original: A recent survey [35] collected 147 papers about learning with physiological signals.
Revised: A recent survey [37] collected 147 papers about learning with physiological signals.

Original: None of thedeep models therein adapt to a person’s medical indices.
Revised: None of the deep models therein adapt to a person’s medical indices.

Original: The deep learning literature includes a fewapproaches for leveraging auxiliary variables.
Revised: The deep learning literature includes a few approaches for leveraging auxiliary variables.

Original: If the variable is available at inference time, typicallyit is taken as an extra input [29, 38].
Revised: If the variable is available at inference time, typically it is taken as an extra input [31, 40].

Original: Variables accessible only during training are typically usedas extra supervisors to regularize the model via multi-task learning [24, 26].
Revised: Variables accessible only during training are typically used as extra supervisors to regularize the model via multi-task learning [26, 28].

Original: We propose a gatingmechanism to handle categorical variables and show that it performs better.
Revised: We propose a gating mechanism to handle categorical variables and show that it performs better.

Original: B Extracting Breathing Signals from RF Signals
Revised: B Extracting Breathing Signals from RF Signals

Original: We leverage past work on extracting breathing from the RF signals.
Revised: We leverage past work on extracting breathing from the RF signals.

Original: Specifically, our system isequipped with a multi-antenna Frequency-Modulated Continuous-Wave (FMCW) radio, which iscommonly used in passive health monitoring [33, 43, 13].
Revised: Specifically, our system is equipped with a multi-antenna Frequency-Modulated Continuous-Wave (FMCW) radio, which is commonly used in passive health monitoring [35, 50, 13].

Original: The radio transmits a very low power
Revised: The radio transmits a very low power

Original: RF signal and captures its reflections from the environment.
Revised: RF signal and captures its reflections from the environment.

Original: We process these reflections using thealgorithm in [43] to infer the subject’s breathing signal.
Revised: We process these reflections using the algorithm in [50] to infer the subject’s breathing signal.

Original: Past work shows that breathing signalsextracted in this manner are highly accurate.
Revised: Past work shows that breathing signals extracted in this manner are highly accurate.

Original: Specifically, their correlation with an FDA-approvedbreathing belt on the person ranges from 91% to 99% , depending on the distance from the radio andthe distance between people [43].
Revised: Specifically, their correlation with an FDA-approved breathing belt on the person ranges from 91% to 99% , depending on the distance from the radio and the distance between people [50].

Original: C Backbone Model: BERT-UNet
Revised: C Backbone Model: BERT-UNet

Original: Our backbone model a combination of a BERT module [9] and UNet [36].
Revised: Our backbone model a combination of a BERT module [9] and UNet [38].

Original: As shown in Figure 1(a),our BERT-UNet model consists of an encoder E ( · ; θ e ) and an oxygen predictor F ( · ; θ f ) .
Revised: As shown in Figure 1(a), our BERT-UNet model consists of an encoder E ( · ; θ e ) and an oxygen predictor F ( · ; θ f ) .

Original: The encoderis composed of a fully convolutional network (FCN) followed by a bidirectional-transformer (BERT)module [9].
Revised: The encoder is composed of a fully convolutional network (FCN) followed by a bidirectional-transformer (BERT) module [9].

Original: The FCN extracts local features from the raw respiration signals, then the BERT modulecaptures long-term temporal dependencies based on those features.
Revised: The FCN extracts local features from the raw respiration signals, then the BERT module captures long-term temporal dependencies based on those features.

Original: The predictor F is composed ofseveral deconvolutional layers, which up-sample the extracted features to the same time resolution ofoxygen saturation.
Revised: The predictor F is composed of several deconvolutional layers, which up-sample the extracted features to the same time resolution of oxygen saturation.

Original: Formally, we have E : R 1 × f b T → R n × αf b T and F : R n × αf b T → R 1 × f o T wheren is the dimension of the respiration feature and α is the down-sampling factor ( α = 1 / 240 in ourexperiments).
Revised: Formally, we have E : R 1 × f b T → R n × αf b T and F : R n × αf b T → R 1 × f o T where n is the dimension of the respiration feature and α is the down-sampling factor ( α = 1 / 240 in our experiments).

Original: The model is trained with a combination of the L 1 loss and the correlation loss given below:L (ˆ y, y ) = ∥
Revised: The model is trained with a combination of the L 1 loss and the correlation loss given below:

Original: ˆ y − y ∥ 1 f o T − λ (cid:80) i (ˆ y i − µ ˆ y ) ( y i − µ y ) √ (cid:80) i
Revised: [Equation]

Original: (ˆ y i − µ ˆ y ) 2 (cid:80)

Original: i ( y i − µ y ) 2 . Here ˆ y = F ( E ( x ; θ e ); θ f ) is the model prediction, y is the ground truth oxygen, µ y and µ ˆ y are themean values of y and ˆ y , and λ is a hyper-parameter to balance the two loss terms.
Revised: Here ˆ y = F ( E ( x ; θ e ); θ f ) is the model prediction, y is the ground truth oxygen, µ y and µ ˆ y are the mean values of y and ˆ y , and λ is a hyper-parameter to balance the two loss terms.

Original: We choose the L 1loss over other regression loss functions, since it is more robust to outliers and empirically has betterperformance.
Revised: We choose the Lloss over other regression loss functions, since it is more robust to outliers and empirically has better performance.

Original: We also use the correlation loss to help in matching the fluctuations in the predictedoxygen with the fluctuations of the ground truth.
Revised: We also use the correlation loss to help in matching the fluctuations in the predicted oxygen with the fluctuations of the ground truth.

Original: Architecture Specifications.
Revised: Architecture Specifications.

Original: The encoder has nine 1-D convolutional layers (Conv-BatchNormRReLU) that shrink the features’ temporal dimension by 240 times.
Revised: The encoder has nine 1-D convolutional layers (Conv-BatchNormRReLU) that shrink the features’ temporal dimension by 240 times.

Original: It is then followed by severalbi-directional multi-head self-attention layers (BERT) [9] to aggregate the temporal informationat the bottleneck.
Revised: It is then followed by several bi-directional multi-head self-attention layers (BERT) [9] to aggregate the temporal information at the bottleneck.

Original: We use 8 layers, 6 heads with hidden-size of 256, intermediate-size of 512 forself-attention, and the max position embeddings is 2400.
Revised: We use 8 layers, 6 heads with hidden-size of 256, intermediate-size of 512 for self-attention, and the max position embeddings is 2400.

Original: The decoder contains 7 layers of 1-D deconvolutional layers (DeConv-Norm-RReLU).
Revised: The decoder contains 7 layers of 1-D deconvolutional layers (DeConv-Norm-RReLU).

Original: We also use a skip connection [36] by concatenatingthe convolutional layers in the encoder to the de-convolutional layers in the predictor.
Revised: We also use a skip connection [38] by concatenating the convolutional layers in the encoder to the de-convolutional layers in the predictor.

Original: Figure 4illustrates the overall network architecture. 
Revised: Figureillustrates the overall network architecture. Conv Conv Conv

Original: [Figure]
Revised: Conv Conv Conv 𝐸 ! 𝐸 " …

Original: [Equation]
Revised: [Equation]

Revised: +

Original: [Figure]
Revised: [Figure]

Original: PositionEmbeddings
Revised: PositionEmbeddings

Original: BERT
Revised: BERT

Original: [Equation]
Revised: DeConv DeConv

Original: Temporal-
Revised: DeConv DeConv DeConv DeConv

Original: [Figure]
Revised: [Table]

Revised: Encoder

Original: Predictor
Revised: Predictor

Original: [Figure]
Revised: Input Output

Original: D Full Model: Gated BERT-UNet
Revised: D Full Model: Gated BERT-UNet

Original: In medical applications, there are useful side variables.
Revised: In medical applications, there are useful side variables.

Original: Adapting to such variables will likely improveperformance and make the results more personalized.
Revised: Adapting to such variables will likely improve performance and make the results more personalized.

Original: In many cases, the relevant variables are binaryor categorical.
Revised: In many cases, the relevant variables are binary or categorical.

Original: For example, the relevant variables for oxygen saturation include gender, whether theperson is a smoker, whether they have asthma, etc.
Revised: For example, the relevant variables for oxygen saturation include gender, whether the person is a smoker, whether they have asthma, etc.

Original: The categorical nature of these variables inducesdiscontinuity in the learned function over the physiological indices.
Revised: The categorical nature of these variables induces discontinuity in the learned function over the physiological indices.

Original: Specifically, consider oxygensaturation y =
Revised: Specifically, consider oxygen saturation y =

Original: g s ( x ) as a function of respiration x and gender s ( 0 for male and 1 for female).
Revised: g s ( x ) as a function of respiration x and gender s ( 0 for male and 1 for female).

Original: g 0 ( x )and g 1 ( x ) can be two different functions since men and women have differences in their oxygentransport systems [34].
Revised: g 0 ( x ) and g 1 ( x ) can be two different functions since men and women have differences in their oxygen transport systems [36].

Original: To handle such discontinuity for better leveraging the categorical variables, we propose Gated BERTUNet , a new model that augments BERT-UNet with multiple predictive heads.
Revised: To handle such discontinuity for better leveraging the categorical variables, we propose Gated BERTUNet , a new model that augments BERT-UNet with multiple predictive heads.

Original: It selects the mostsuitable head for a person via a gate controlled by the subject’s categorical indices.
Revised: It selects the most suitable head for a person via a gate controlled by the subject’s categorical indices.

Original: The modelsupports both variables available at the time of inference (e.g., gender), as well as dense categoricalvariables concurrently learned from the input signals (e.g., sleep stages).
Revised: The model supports both variables available at the time of inference (e.g., gender), as well as dense categorical variables concurrently learned from the input signals (e.g., sleep stages).

Original: Figure 1(b) illustrates the model.
Revised: Figure 1(b) illustrates the model.

Original: It has a gate function G ( v, u ) :
Revised: It has a gate function G ( v, u ) :

Original: V × U → { 1 , 2 , · · · , N } wherev ∈ V and u ∈ U are accessible/inaccessible variables, N is the number of gate statuses.
Revised: V × U → { 1 , 2 , · · · , N } where v ∈ V and u ∈ U are accessible/inaccessible variables, N is the number of gate statuses.

Original: We use theterm accessible variable for variables easily available during inference time, e.g., gender, and theterm inaccessible variable for information that is not available during inference, but available duringtraining, like a person’s sleep stages.
Revised: We use the term accessible variable for variables easily available during inference time, e.g., gender, and the term inaccessible variable for information that is not available during inference, but available during training, like a person’s sleep stages.

Original: Inaccessible variables are typically dense time series (e.g., sleepstages).
Revised: Inaccessible variables are typically dense time series (e.g., sleep stages).

Original: Their prediction are learned concurrently with the main task under full supervision.
Revised: Their prediction are learned concurrently with the main task under full supervision.

Original: Theconstruction of the gate function G ( v, u ) is described in the next sub-section.
Revised: The construction of the gate function G ( v, u ) is described in the next sub-section.

Original: The model has N heads { F i } Ni =1 that adapt the prediction ˆ y i
Revised: The model has N heads { F i } Ni =1 that adapt the prediction ˆ y i

Original: = F i ( E ( x )) to the gate status.
Revised: = F i ( E ( x )) to the gate status.

Original: Italso has an extra predictor F u to infer inaccessible variables u .
Revised: It also has an extra predictor F u to infer inaccessible variables u .

Original: During testing time, based on theaccessible variables v and estimated inaccessible variables ˆ u , we evaluate the gate status s =
Revised: During testing time, based on the accessible variables v and estimated inaccessible variables ˆ u , we evaluate the gate status s =

Original: G ( v, ˆ u ) .
Revised: G ( v, ˆ u ) .

Original: In the case of oxygen prediction, ˆ y i and the gate status s are time series.
Revised: In the case of oxygen prediction, ˆ y i and the gate status s are time series.

Original: As shown in Figure 1(b),the final prediction at each time step, is the gated combination of every head’s output, i.e. ∀ t =1 , . .
Revised: As shown in Figure 1(b), the final prediction at each time step, is the gated combination of every head’s output, i.e. ∀ t = 1 , . .

Original: , f o T, ˆ y t =
Revised: , f o T, ˆ y t =

Original: (cid:80) Ni
Revised: (cid:80) Ni

Original: =1 1 [ s t = i ]
Revised: =1 1 [ s t = i ]

Original: ˆ y ti .
Revised: ˆ y ti .

Original: We train Gated BERT-UNet (GBU) with the following loss,
Revised: We train Gated BERT-UNet (GBU) with the following loss,

Original: [Equation]
Revised: [Equation]

Original: where L is the main loss defined in Equation 1, L CE is the cross-entropy loss to train the branch forpredicting inaccessible variables and λ u is a balancing hyperparameter.
Revised: where L is the main loss defined in Equation 1, L CE is the cross-entropy loss to train the branch for predicting inaccessible variables and λ u is a balancing hyperparameter.

Original: Mapping Variables to Heads.
Revised: Mapping Variables to Heads.

Original: The number of heads in a Gated BERT-UNet model puts an upperbound on the number of possible gate states.
Revised: The number of heads in a Gated BERT-UNet model puts an upper bound on the number of possible gate states.

Original: For example, if the model has 6 heads, the gate can takeonly 1 of 6 states.
Revised: For example, if the model has 6 heads, the gate can take only 1 of 6 states.

Original: Typically, we have many more variable states than gate states.
Revised: Typically, we have many more variable states than gate states.

Original: To find a propermapping G ( v, u ) from variable state to gate state, we rely on gradient similarity.
Revised: To find a proper mapping G ( v, u ) from variable state to gate state, we rely on gradient similarity.

Original: For example, ifwe want to check whether male smokers should be in the same group as female smokers, we take apretrained backbone BERT-UNet and compute its averaged gradient (w.r.t the loss function) over allmale smokers and all female smokers in the dataset.
Revised: For example, if we want to check whether male smokers should be in the same group as female smokers, we take a pretrained backbone BERT-UNet and compute its averaged gradient (w.r.t the loss function) over all male smokers and all female smokers in the dataset.

Original: Then we check the cosine similarity between thetwo gradients.
Revised: Then we check the cosine similarity between the two gradients.

Original: If the gradients are similar, which means the two categories move the loss function inthe same direction, we can use the same predictor for them.
Revised: If the gradients are similar, which means the two categories move the loss function in the same direction, we can use the same predictor for them.

Original: On the other hand, if the gradients arevastly different, it is preferable to separate such categories and assign them to different gate statuses.
Revised: On the other hand, if the gradients are vastly different, it is preferable to separate such categories and assign them to different gate statuses.

Original: E Datasets and Metrics
Revised: E Datasets and Metrics

Original: Medical Datasets.
Revised: Medical Datasets.

Original: We leverage three public medical datasets: Sleep Heart Health Study( SHHS ) [44], Multi-Ethnic Study of Atherosclerosis ( MESA ) [7], and Osteoporotic Fractures in
Revised: We leverage three public medical datasets: Sleep Heart Health Study ( SHHS ) [51], Multi-Ethnic Study of Atherosclerosis ( MESA ) [7], and Osteoporotic Fractures in

Original: Men Study ( MrOS ) [5].
Revised: Men Study ( MrOS ) [5].

Original: The datasets were collected during sleep studies.
Revised: The datasets were collected during sleep studies.

Original: For each subject, theyinclude the respiration signals throughout the night along with the corresponding blood oxygen timeseries.
Revised: For each subject, they include the respiration signals throughout the night along with the corresponding blood oxygen time series.

Original: The breathing signals are collected using a breathing belt around the chest or abdomen, andthe oxygen is measured using a pulse oximeter.
Revised: The breathing signals are collected using a breathing belt around the chest or abdomen, and the oxygen is measured using a pulse oximeter.

Original: The datasets also contain side variables includingsleep stages, which for every time instance assign to the subject one of the following: Awake, Rapid
Revised: The datasets also contain side variables including sleep stages, which for every time instance assign to the subject one of the following: Awake, Rapid

Original: Eye Movement (REM) or non-REM stage.
Revised: Eye Movement (REM) or non-REM stage.

Original: We note that the subjects in these studies have an age range between 40 and 95, and some of themsuffer from a variety of diseases such as chronic bronchitis, cardiovascular diseases, and diabetes.
Revised: We note that the subjects in these studies have an age range between 40 and 95, and some of them suffer from a variety of diseases such as chronic bronchitis, cardiovascular diseases, and diabetes.

Original: This allows for a wider range of oxygen variability beyond the typical range of healthy individuals.
Revised: This allows for a wider range of oxygen variability beyond the typical range of healthy individuals.

Revised: [Figure]

Original: RF Datasets.
Revised: RF Datasets.

Original: We collected a dataset of RF signals paired with
Revised: We collected a dataset of RF signals paired with

Original: SpO2 measurements.
Revised: SpO2 measurements.

Original: The data is collected from two sleep labs.
Revised: The data is collected from two sleep labs.

Original: Intotal, there are 400 hours of data from 49 overnight recordings of32 subjects.
Revised: In total, there are 400 hours of data from 49 overnight recordings of 32 subjects.

Original: The dataset contains subjects of different genders andraces.
Revised: The dataset contains subjects of different genders and races.

Original: Some subjects are healthy volunteers while others are patientswith sleep problems.
Revised: Some subjects are healthy volunteers while others are patients with sleep problems.

Original: Thus, the ground truth oxygen saturationdistribution is wider than normal ranges.
Revised: Thus, the ground truth oxygen saturation distribution is wider than normal ranges.

Original: A radio device is installedin the room to collect RF signals, as shown in Fig.
Revised: A radio device is installed in the room to collect RF signals, as shown in Fig.

Original: The radiosignals are synchronized with the SpO2 measurements and processedwith the algorithm in [43] to extract the person’s breathing signals.
Revised: The radio signals are synchronized with the SpO2 measurements and processed with the algorithm in [50] to extract the person’s breathing signals.

Original: Metrics.
Revised: Metrics.

Original: Let ˆ y , y denote the predicted and ground truth oxygen saturation.
Revised: Let ˆ y , y denote the predicted and ground truth oxygen saturation.

Original: Following the previouswork [25], we use three standard metrics for evaluation: (1) Correlation: (cid:80) t ( y t − µ y )
Revised: Following the previous work [27], we use three standard metrics for evaluation: (1) Correlation: (cid:80) t ( y t − µ y )

Original: (ˆ y t − µ ˆ y ) √ (cid:80) t ( y t − µ y ) 2 (cid:80) t (ˆ y t − µ ˆ y ) 2 ,where µ y and µ ˆ y are the averaged oxygen saturations; (2) MAE: 1 T (cid:80)
Revised: (ˆ y t − µ ˆ y ) √ (cid:80) t ( y t − µ y ) 2 (cid:80) t (ˆ y t − µ ˆ y ) 2 , where µ y and µ ˆ y are the averaged oxygen saturations; (2) MAE: 1 T (cid:80)

Original: Tt =1 | y t − ˆ y t | ; and (3) RMSE:403 (cid:113) 1 T (cid:80)
Revised: Tt =1 | y t − ˆ y t | ; and (3) RMSE: (cid:113) 1 T (cid:80)

Original: Tt =

Revised: Tt =

Original: ( y t − ˆ y t ) 2 .
Revised: ( y t − ˆ y t ) 2 .

Original: The models take a night of breathing as input and predict the corresponding oxygenlevels.
Revised: The models take a night of breathing as input and predict the corresponding oxygen levels.

Original: During the evaluation, we divide the model’s prediction and ground truth oxygen into 240second segments to compute the metrics.
Revised: During the evaluation, we divide the model’s prediction and ground truth oxygen into 240second segments to compute the metrics.

Original: We note that those metrics are sensitive to the segment’slength.
Revised: We note that those metrics are sensitive to the segment’s length.

Original: For a fair comparison, we follow [25] and use 240-second intervals.
Revised: For a fair comparison, we follow [27] and use 240-second intervals.

Original: F Baselines.
Revised: F Baselines.

Original: We compare the following neural network architectures for our backbone model: (a) CNN is a fullyconvolutional model composed of eight 1-D convolutional layers and seven 1-D deconvolutionallayers; (b) CNN-RNN augments the CNN model with a recurrent unit  in the bottleneck to bettercaptures the long-term temporal relationships of the data.
Revised: We compare the following neural network architectures for our backbone model: (a) CNN is a fully convolutional model composed of eight 1-D convolutional layers and seven 1-D deconvolutional layers; (b) CNN-RNN augments the CNN model with a recurrent unit (one layer LSTM) in the bottleneck to better captures the long-term temporal relationships of the data.

Original: (c) BERT-UNet further makes two improvements on the CNN-RNN model.
Revised: (c) BERT-UNet further makes two improvements on the CNN-RNN model.

Original: First, it uses an attention module to replace recurrent unit fortemporal modelling.
Revised: First, it uses an attention module to replace recurrent unit for temporal modelling.

Original: Second, it adds skip links between encoding convolutional layers and decodingdeconvolutional layers at the same temporal scale to better capture the signal’s local information.
Revised: Second, it adds skip links between encoding convolutional layers and decoding deconvolutional layers at the same temporal scale to better capture the signal’s local information.

Original: To evaluate our design for incorporating side information, we compare the following models: (a)
Revised: To evaluate our design for incorporating side information, we compare the following models: (a)

Original: BERT-UNet + VarAug , which uses BERT-UNet as backbone and takes accessible variables as extrainputs and inaccessible variables as auxiliary tasks.
Revised: BERT-UNet + VarAug , which uses BERT-UNet as backbone and takes accessible variables as extra inputs and inaccessible variables as auxiliary tasks.

Original: (b) Our Gated BERT-UNet model, which uses amulti-head model gated by physiological variables.
Revised: (b) Our Gated BERT-UNet model, which uses a multi-head model gated by physiological variables.

Original: G Training and Evaluation Protocols
Revised: G Training and Evaluation Protocols

Original: Train/Valid/Test Spilt.
Revised: Train/Valid/Test Spilt.

Original: Due to the limited data amount in the RF dataset, the RF data is all holdout for testing.
Revised: Due to the limited data amount in the RF dataset, the RF data is all hold out for testing.

Original: In our study, all models are trained on the medical datasets and evaluated on both themedical datasets and the RF dataset.
Revised: In our study, all models are trained on the medical datasets and evaluated on both the medical datasets and the RF dataset.

Original: Collectively, the medical datasets have about 48,000 hours ofdata from 5,765 subjects in total.
Revised: Collectively, the medical datasets have about 48,000 hours of data from 5,765 subjects in total.

Original: We randomly split subjects, 70% for training and validation, and30% for testing, and fix the splits in all experiments.
Revised: We randomly split subjects, 70% for training and validation, and 30% for testing, and fix the splits in all experiments.

Original: We train each model on the union of the trainingsets from the three medical datasets, and tested on each test set.
Revised: We train each model on the union of the training sets from the three medical datasets, and tested on each test set.

Original: Side Variable Specifications.
Revised: Side Variable Specifications.

Original: For models that incorporate side variables, we use gender as theaccessible variable and sleep stages as the inaccessible variable.
Revised: For models that incorporate side variables, we use gender as the accessible variable and sleep stages as the inaccessible variable.

Original: In Gated BERT-UNet, we usegradient similarity to map gate status as described in the method section, which results in thefollowing 6 categories: (male, awake), (male, REM sleep), (male, non-REM sleep), (female, awake),(female, REM sleep), (female, non-REM sleep).
Revised: In Gated BERT-UNet, we use gradient similarity to map gate status as described in the method section, which results in the following 6 categories: (male, awake), (male, REM sleep), (male, non-REM sleep), (female, awake), (female, REM sleep), (female, non-REM sleep).

Original: The sleep stages themselves are learned from theinput since they are an inaccessible variable.
Revised: The sleep stages themselves are learned from the input since they are an inaccessible variable.

Original: In the baseline VarAug, the gender variable is providedas an additional input and the sleep stages are used as an auxiliary task in a multitask model.
Revised: In the baseline VarAug, the gender variable is provided as an additional input and the sleep stages are used as an auxiliary task in a multitask model.

Original: Implementation Details.
Revised: Implementation Details.

Original: We implement all models in PyTorch.
Revised: We implement all models in PyTorch.

Original: All experiments are carried outon a NVIDIA TITAN
Revised: All experiments are carried out on a NVIDIA TITAN

Original: Xp GPU with 12 GB memory.
Revised: Xp GPU with 12 GB memory.

Original: The number of parameters for the Gated
Revised: The number of parameters for the Gated

Original: BERT-UNet model is 26,821,113 and the model size is 107.28MB.
Revised: BERT-UNet model is 26,821,113 and the model size is 107.28MB.

Original: In the training process, we usethe Adam optimizer with a learning rate of 2 × 10 − 4 , and train the model for 500 epochs.
Revised: In the training process, we use the Adam optimizer with a learning rate of 2 × 10 − 4 , and train the model for 500 epochs.

Original: Due to thevarying input length, we set the batch size for all models to 1 (i.e., one night of respiration signal andthe corresponding oxygen time series).
Revised: Due to the varying input length, we set the batch size for all models to 1 (i.e., one night of respiration signal and the corresponding oxygen time series).

Original: H Results for Different Skin Colors
Revised: H Results for Different Skin Colors

Original: Since pulse oximeters rely on measuring light absorbance through the finger, they are known tobe affected by skin color and tend to overestimate blood oxygen saturation in subjects with darkskin [14, 39].
Revised: Since pulse oximeters rely on measuring light absorbance through the finger, they are known to be affected by skin color and tend to overestimate blood oxygen saturation in subjects with dark skin [14, 41].

Original: A large study that looked at tens of thousands of white and black COVID patientsfound that the “reliance on pulse oximetry to triage patients and adjust supplemental oxygen levelsmay place black patients at increased risk for hypoxaemia"[39].
Revised: A large study that looked at tens of thousands of white and black COVID patients found that the “reliance on pulse oximetry to triage patients and adjust supplemental oxygen levels may place black patients at increased risk for hypoxaemia"

Original: In contrast, breathing and RF signalshave no intrinsic bias against skin color.
Revised: In contrast, breathing and RF signals have no intrinsic bias against skin color.

Original: Figure 6 shows the distributions of the oximetry-basedground-truth oxygen and the Gated BERT-UNet prediction for different races, for the union of alldatasets.
Revised: Figure 7 shows the distributions of the oximetry-based ground-truth oxygen and the Gated BERT-UNet prediction for different races, for the union of all [Figure]

Original: The ground-truth measurements from oximetry show a clear discrepancy between black and
Revised: O xy g e n S a t u r a t i o

Original: [Figure]
Revised: [Figure]

Original: Our Prediction
Revised: datasets.

Original: [Figure] [Figure] white subjects.
Revised: The ground-truth measurements from oximetry show a clear discrepancy between black and white subjects.

Original: In particular, black subjects have higher average blood oxygen.
Revised: In particular, black subjects have higher average blood oxygen.

Original: This is compatiblewith past findings that pulse oximeters overestimate blood oxygen in dark-skinned subjects [14].
Revised: This is compatible with past findings that pulse oximeters overestimate blood oxygen in dark-skinned subjects [14].

Original: Incontrast, the breathing-based oxygen prediction corrects or reduces this bias, and shows more similaroxygen distributions for the two races.
Revised: In contrast, the breathing-based oxygen prediction corrects or reduces this bias, and shows more similar oxygen distributions for the two races.

Original: I Visualization of Different Breathing-Oxygen Patterns.

Original: We demonstrate several visual results on different patterns of breathing signals and the correspondingground truth/predicted oxygen saturation, as shown in Figure 7.

Original: Figure 7(a) shows a normal breathingpattern, which leads to constant oxygen saturation.

Original: In contrast, Figure 7(b,c) present two differentabnormal breathing signals and the resulting fluctuated oxygen predictions.

Original: These figures show thediversity of the oxygen and breathing patterns as well as the complexity of their relationship.

Original: Themodel however is able to capture this relationship for highly diverse patterns.

Original: J Comparison with Past Works

Original: We compare our approach with two recent deep-learning camera-based SpO2 monitoring methods.

Original: The first method [11] asks the user to press his/her finger against a smartphone camera, and uses a

Original: CNN to estimate SpO2 from the video.

Original: The second method [25] uses a CNN to estimate oxygen froma video of the person’s hand.

Original: The input of these systems is different from ours (camera vs. RF); so tocompare them we follow the setup in [25].

Original: In their setting, test samples are 180-240 seconds and varybetween normal breathing to no or minimal breathing.

Original: Similarly, we divide the RF test dataset intonon-overlapping 240-second segments containing both regular breathing and shallow breathing (i.e.,apnea or hypopnea) and compute metrics on them.

Original: Table 3 reports the output of the three models.

Original: The results of the baselines are taken from [25], and the results of our RF-based model are computedas described.

Original: The results show that our model improves the correlation and reduces the MAE and

Original: RMSE in comparison to past work.

Original: [Table]

Original: K Extra ResultsK.1 Example of Same Breathing Rate but Different Oxygen Level
Revised: I Extra Results I.1 Example of Same Breathing Rate but Different Oxygen Level

Original: One might wonder whether our model predicts oxygen merely by the breathing frequency.
Revised: One might wonder whether our model predicts oxygen merely by the breathing frequency.

Original: We showit is not the case.
Revised: We show it is not the case.

Original: Our model understands that the same breathing frequency does not translate tothe same oxygen level.
Revised: Our model understands that the same breathing frequency does not translate to the same oxygen level.

Original: Figure 8 shows two people breathing at the same frequency of 14 BPM, butthe model correctly realizes that one of them has high and stable oxygen of 98 while the other hasa relatively low oxygen level of 93.
Revised: Figure 8 shows two people breathing at the same frequency of 14 BPM, but the model correctly realizes that one of them has high and stable oxygen of 98 while the other has a relatively low oxygen level of 93.

Original: The model even follows the dynamic change in their oxygenlevels from one second to the next.
Revised: The model even follows the dynamic change in their oxygen levels from one second to the next.

Original: This is possible because the model analyzes the full detailsof the breathing signal and its dynamics, which is a dense 1D input, not just one variable like therhythm.
Revised: This is possible because the model analyzes the full details of the breathing signal and its dynamics, which is a dense 1D input, not just one variable like the rhythm.

Original: To see that, consider again the example in Figure 8.
Revised: To see that, consider again the example in Figure 8.

Original: While the two people breathe at thesame frequency, the person whose breathing is plotted in blue suddenly starts taking deeper breaths.
Revised: While the two people breathe at the same frequency, the person whose breathing is plotted in blue suddenly starts taking deeper breaths.

Original: This is an indication that the person is low on oxygen and is trying to increase his oxygen intake.
Revised: This is an indication that the person is low on oxygen and is trying to increase his oxygen intake.

Original: When the person takes such deep breaths, the oxygen level increases.
Revised: When the person takes such deep breaths, the oxygen level increases.

Original: In contrast, the person whoseoxygen is plotted in orange is not struggling with low oxygen and his breathing is steady.
Revised: In contrast, the person whose oxygen is plotted in orange is not struggling with low oxygen and his breathing is steady.

Original: [Figure]
Revised: [Figure]

Revised: but different oxygen saturation.

Revised: [Figure]

Original: K.2 Qualitative Results in Different Datasets
Revised: I.2 Qualitative Results in Different Datasets

Original: We include more visualizations of the breathing signals and the corresponding oxygen saturationpredicted by the Gated BERT-UNet model for the medical datasets: MESA (Figure 9 and Figure 10),
Revised: We include more visualizations of the breathing signals and the corresponding oxygen saturation predicted by the Gated BERT-UNet model for the medical datasets: MESA (Figure 9 and Figure 10),

Original: MrOS (Figure 11 and Figure 12).
Revised: MrOS (Figure 11 and Figure 12).

Original: We also visualize the model’s prediction on unhealthy subjectswith various diseases including chronic obstructive pulmonary disease (COPD), asthma, diabetes.
Revised: We also visualize the model’s prediction on unhealthy subjects with various diseases including chronic obstructive pulmonary disease (COPD), asthma, diabetes.

Original: Inthe plots, The background color indicates different sleep stages.
Revised: In the plots, The background color indicates different sleep stages.

Original: The ‘dark grey’, ‘light grey’ and‘white’ correspond to ‘Non-REM sleep’, ‘REM’ and ‘Awake’, respectively. 
Revised: The ‘dark grey’, ‘light grey’ and ‘white’ correspond to ‘Non-REM sleep’, ‘REM’ and ‘Awake’, respectively. [Figure]

Original: MESA.
Revised: MESA.

Original: The example in Figure 9 shows our model’s ability to capture the fluctuations of oxygensaturation.
Revised: The example in Figure 9 shows our model’s ability to capture the fluctuations of oxygen saturation.

Original: At the same time, the example in Figure 10 shows that our model accurately detects theregion of low oxygen saturation, which highlights its usefulness in monitoring patients.[Figure] [Figure]
Revised: At the same time, the example in Figure 10 shows that our model accurately detects the region of low oxygen saturation, which highlights its usefulness in monitoring patients.

Original: MrOS.
Revised: MrOS.

Original: From the zoomed-in regions (a) and (b) in Figure 11, we see that the model exhibits a largererror when the ground truth SpO2 reading is very low.
Revised: From the zoomed-in regions (a) and (b) in Figure 11, we see that the model exhibits a larger error when the ground truth SpO2 reading is very low.

Original: It is mainly caused by the imbalanced labelsin the training set since subjects usually experience much less time of having low oxygen level (e.g.,below 90%) than having a normal oxygen level between 94% to 100%.
Revised: It is mainly caused by the imbalanced labels in the training set since subjects usually experience much less time of having low oxygen level (e.g., below 90%) than having a normal oxygen level between 94% to 100%.

Original: Figure 12 shows anotherexample of the dynamics.
Revised: Figure 12 shows another example of the dynamics.

Original: As shown in the zoomed range, oxygen fluctuations correlate with one’ssleep stage: in ‘REM’ (colored by light gray), the oxygen fluctuates drastically while in ‘Non-REMsleep’ (colored by dark gray), the oxygen is much more stable and fluctuates in a small range.
Revised: As shown in the zoomed range, oxygen fluctuations correlate with one’s sleep stage: in ‘REM’ (colored by light gray), the oxygen fluctuates drastically while in ‘Non-REM sleep’ (colored by dark gray), the oxygen is much more stable and fluctuates in a small range.

Original: Ourmodel makes accurate predictions since it leverages the sleep stage information.
Revised: Our model makes accurate predictions since it leverages the sleep stage information.

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: K.3 Results for Relevant Diseases
Revised: I.3 Results for Relevant Diseases

Original: As we mentioned earlier, using breathing as the input to the neural network model allows us to bothtrain and test on large respiration dataset from past sleep studies.
Revised: As we mentioned earlier, using breathing as the input to the neural network model allows us to both train and test on large respiration dataset from past sleep studies.

Original: Since these datasets contain diversepeople with a variety of diseases, it makes it possible to check how the model generalizes to unhealthyindividuals.
Revised: Since these datasets contain diverse people with a variety of diseases, it makes it possible to check how the model generalizes to unhealthy individuals.

Original: Particularly we are interested in diseases that interact with oxygen saturation includingpulmonary diseases such as chronic obstructive pulmonary disease (COPD), chronic bronchitis,asthma, emphysema, and others like diabetes and coronary heart disease.
Revised: Particularly we are interested in diseases that interact with oxygen saturation including pulmonary diseases such as chronic obstructive pulmonary disease (COPD), chronic bronchitis, asthma, emphysema, and others like diabetes and coronary heart disease.

Original: Diabetes is a disease in which the patient’s blood sugar levels are too high.
Revised: Diabetes is a disease in which the patient’s blood sugar levels are too high.

Original: Research has shownthat diabetes is a risk factor for severe nocturnal Hypoxemia in obese patients [22].
Revised: Research has shown that diabetes is a risk factor for severe nocturnal Hypoxemia in obese patients [22].

Original: Further diabeticpatients tend to have 3% to 10% lower lung volumes than adults without the disease.
Revised: Further diabetic patients tend to have 3% to 10% lower lung volumes than adults without the disease.

Original: Figure 13 showsan example of a diabetic patient who has an oxygen level that keeps oscillating between 85% and95%.
Revised: Figure 13 shows an example of a diabetic patient who has an oxygen level that keeps oscillating between 85% and 95%.

Original: From the zoomed-in region, we can see our model captures the oscillating oxygen dynamicsand accurately predicts the oxygen values.
Revised: From the zoomed-in region, we can see our model captures the oscillating oxygen dynamics and accurately predicts the oxygen values.

Original: Chronic obstructive pulmonary disease (COPD) refers to a chronic inflammatory lung disease thatobstructs airflow from the lungs.
Revised: Chronic obstructive pulmonary disease (COPD) refers to a chronic inflammatory lung disease that obstructs airflow from the lungs.

Original: Severe COPD can cause hypoxia, an extremely low oxygen level.
Revised: Severe COPD can cause hypoxia, an extremely low oxygen level.

Original: Figure 14 shows an example of a COPD patient who experiences several oxygen droppings during 
Revised: Figure 14 shows an example of a COPD patient who experiences several oxygen droppings during the REM period (indicated by the orange box). As we can see, our model successfully predicts the events of oxygen dropping.

Original: [Figure]
Revised: [Figure]

Original: Chronic bronchitis refers to long-term inflammation of the bronchi.
Revised: Chronic bronchitis refers to long-term inflammation of the bronchi.

Original: Chronic bronchitis patients canhave shortness of breath which affects oxygen levels.
Revised: Chronic bronchitis patients can have shortness of breath which affects oxygen levels.

Original: Figure 15 is an example of a chronic bronchitispatient whose oxygen level keeps osculating between normal and low during the night.
Revised: Figure 15 is an example of a chronic bronchitis patient whose oxygen level keeps osculating between normal and low during the night.

Original: Our modelcaptures the trend well.
Revised: Our model captures the trend well.

Original: Asthma is a condition in which a person’s airways narrow, swell, and produce extra mucus.
Revised: Asthma is a condition in which a person’s airways narrow, swell, and produce extra mucus.

Original: Anasthma patient’s oxygen levels can be irregular due to the breathing difficulty caused by the disease.
Revised: An asthma patient’s oxygen levels can be irregular due to the breathing difficulty caused by the disease.

Original: As shown in the example in Figure 16, the patient has a normal oxygen level for most of the time,but the oxygen occasionally drops to low levels.
Revised: As shown in the example in Figure 16, the patient has a normal oxygen level for most of the time, but the oxygen occasionally drops to low levels.

Original: Our model works well on detecting those abnormaloxygen levels from the person’s respiration.
Revised: Our model works well on detecting those abnormal oxygen levels from the person’s respiration.

Original: Emphysema refers to a lung condition in which the air sacs in the person’s lung are damaged.
Revised: Emphysema refers to a lung condition in which the air sacs in the person’s lung are damaged.

Original: Patientswith emphysema usually have breathing issues that affect oxygen saturation.
Revised: Patients with emphysema usually have breathing issues that affect oxygen saturation.

Original: Figure 17 shows anexample of an emphysema patient.
Revised: Figure 17 shows an example of an emphysema patient.

Original: The patient experiences a long period of low oxygen during sleep(as highlighted by the orange box).
Revised: The patient experiences a long period of low oxygen during sleep (as highlighted by the orange box).

Original: Our model successfully predicts such unusual oxygen dynamics.
Revised: Our model successfully predicts such unusual oxygen dynamics.

Original: Coronary heart disease develops when the arteries of the heart are too narrow to deliver enoughoxygen-rich blood to the heart.
Revised: Coronary heart disease develops when the arteries of the heart are too narrow to deliver enough oxygen-rich blood to the heart.

Original: A deficiency in providing oxygen-rich blood can lead one’s oxygensaturation to deviate from normal level.
Revised: A deficiency in providing oxygen-rich blood can lead one’s oxygen saturation to deviate from normal level.

Original: Figure 18 is an example of a person with coronary heartdisease who experiences several severe oxygen drops during sleep.
Revised: Figure 18 is an example of a person with coronary heart disease who experiences several severe oxygen drops during sleep.

Original: Our model accurately tracks theiroxygen level and detects the oxygen reduction events.
Revised: Our model accurately tracks their oxygen level and detects the oxygen reduction events.

Original: [Figure] [Figure]
Revised: [Figure] [Figure]

Original: L Concluding Remarks
Revised: J Concluding Remarks

Original: This paper introduces the new task of inferring oxygen saturation from radio signals.
Revised: This paper introduces the new task of inferring oxygen saturation from radio signals.

Original: It developsa new gated transformer architecture to deliver this application and adapt deep models to auxiliarycategorical variables.
Revised: It develops a new gated transformer architecture to deliver this application and adapt deep models to auxiliary categorical variables.

Original: The paper empirically shows the superiority of the proposed gated transformermodel over the common approach of taking categorical variables as inputs.

Original: We believe the proposeddesign for adapting deep models to auxiliary categorical variables is generally applicable to other tasksto leverage categorical side information.

Original: We also believe the work has a broader impact because it canhelp in tracking oxygen saturation in older adults during sleep, and providing an initial notificationto a caregiver if excessively low oxygen is detected.

Original: More extensive measurements with a medicaldevice can then be performed to confirm the results and take medical decisions.

Original: The work also has some limitations.
Revised: We note the work have some limitations.

Original: First, the paper focuses on special use cases (e.g., at-homeoxygen monitoring in very old adults or during sleep), but is not suitable for other use cases (e.g.,measuring oxygen to optimize performance during exercise).
Revised: First, the paper focuses on special use cases (e.g., at-home oxygen monitoring in very old adults or during sleep), but is not suitable for other use cases (e [Figure] g., measuring oxygen to optimize performance during exercise).

Original: Second, the results in the paper providean initial proof of concept that the shape and dynamics of the breathing signal include sufficient cluesto infer a useful estimate of oxygen saturation.
Revised: Second, the results in the paper provide an initial proof of concept that the shape and dynamics of the breathing signal include sufficient clues to infer a useful estimate of oxygen saturation.

Original: However, before this system can be used in clinicalcare, one needs clinical studies to quantify the performance for different disease conditions.
Revised: However, before this system can be used in clinical care, one needs clinical studies to quantify the performance for different disease conditions.

Original: Finally, all studies in this paper that involve human subjects have obtained IRB approval.

Original: [Figure]
Revised: [Figure]

Original: [Figure] [Figure]
Revised: [Figure] [Figure]