Out-of-distribution Representation Learning for Time Series Classification
Authors: Wang Lu
Jindong Wang
Xinwei Sun
Yiqiang Chen
Xing Xie
Venue: ICLR 2023 poster (2023)
Keywords: Domain generalization
out-of-distribution generalization
time series classification

Abstract: Time series classification is an important problem in the real world. Due to its non-stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper, we propose to view time series classification from the distribution perspective. We argue that the temporal complexity of a time series dataset could attribute to unknown latent distributions that need characterize. To this end, we propose DIVERSIFY for out-of-distribution (OOD) representation learning on dynamic distributions of times series. DIVERSIFY takes an iterative process: it first obtains the ‘worst-case’ latent distribution scenario via adversarial training, then reduces the gap between these latent distributions. We then show that such an algorithm is theoretically supported. Extensive experiments are conducted on seven datasets with different OOD settings across gesture recognition, speech commands recognition, wearable stress and affect detection, and sensor-based human activity recognition. Qualitative and quantitative results demonstrate that DIVERSIFY significantly outperforms other baselines and effectively characterizes the latent distributions. Code is available at https://github.com/microsoft/robustlearn.

Published as a conference paper at ICLR 2023
OUT-OF-DISTRIBUTION REPRESENTATION LEARNING FOR TIME SERIES CLASSIFICATION
Wang Lu Jindong Wanga1, Xinwei Sun Yiqiang Xhng Xie²
Institute of Comput. Tech., CAS "Microsoft Research Asia
*Fudan University
ABSTRACT
Time series classification is an important problem in the real world. Due to its non- stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper, we propose to view time series classification from the distribution perspective. We argue that the temporal complexity of time series dataset could attribute to unknown latent distributions that need characterize. To this end, we propose DIVERSIFY for out- of-distribution (OOD) representation learning series. DIVERSIFY takes an iterative process: it first obtains the 'worst-case' latent distribution scenario via adversarial training, then reduces the gap between these latent distributions. We then show that such an algorithm is theoretically supported. Extensive experiments are conducted on seven datasets with different OOD settings across gesture recognition, speech commands recognition, wearable stress and affect detection, and sensor-based human activity recognition. Qualitative and quantitative results demonstrate that DIVERSIFY significantly outperforms other baselines and effectively characterizes the latent distributions. Code available https: wttt://.ccoooocccoccccee htt.://ww.......ooooooooooooooaa
dynamic distributions of times
INTRODUCTION
Time series classification is one of the most challenging problems in the machine learning and statistics community (Fawaz et al. 2019 Du et al.) 2021). One important nature of time series is the non-stationary property. indicating that its statistical features are changing over time. For years, there have been tremendous efforts for time series classification, such as hidden Markov models (Fulcher &
Jones 2014), Rased methods (Hüsken & Stagge 2003), and Transformer-bant approaches (Li
al. 2019 Drouin al. 2022).
We propose to model time series from the distribution perspective to handle its dynamically changing distributions; more precisely, to learn out-of-distribution (OOD) representations for time series that generalize to unseen distributions. The general OOD/domain generalization problem has been extensively studied (Wang al.. 2022 Lu et al., 2022, Krueger et al.. [022]] Rame al. 2022), where the key is to bridge the gap between known and unknown distributions. Despite existing efforts, OOD in time series remains less studied and more challenging. Compared to image classification, the dynamic distribution of time series data keeps changing over time, containing diverse distribution information that should be harnessed for better generalization.
Figure I shows an illustrative example. OOD generalization in image classification often involves several domains whose domain labels are static and known (subfigure (a)), which can be employed to build OOD models. However, Figure (b) shows that in EMG time series data (Lobov et al. 2018). the distribution is changing dynamically over time and its domain information is unavailable. If no attention is paid to exploring its latent distributions (i.e., sub-domaa sub-domains), predictions may fail in face of diverse sub-domain distributions (subfigure (c)). This will dramatically impede existing OOD algorithms due to their reliance on domain information.
In this work, we propose DIVERSIFY, an OOD representation learning algorithm for time series classification by characterizing the latent distributions inside the data. Concretely speaking, DI-
Work done when Wang Lu (luwang@ine (itaann@cct.accm)) was an intern at Microsoft Research Asia. Correspondence to: Jindong Wang (jindong, wang microsoft.com).

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Published as a conference paper at ICLR 2023
(a) Image:
Domain la bel known (b) Time series: Domain label unknown
(c) Misclassified sub-domains if we treat it as one distribution
(d) Latent distributions of domain leamed by our method
scributionn
Pa
Paalnting
Px
Figure Illustration of DIVERSIFY: (a) Domain generalization for image data requires known domain labels. (b) Domain labels unknown for time series. (c) If treat the time series data as one single domain, the sub-domains are misclassified. Different colors and shapes correspond to different classes and domains. Axes represent data values. (d) Finally, our DIVERSIFY can effectively learn the latent distributions. X-axis represents data numbers while Y-axis represents values.
VERSIFY consists min-max adversarial game: on one hand, it learns to segment the time series data into several latent sub-domains by maximizing the segment-wise distribution gap to preserve diversities, i.e,, the 'worst-case' distribution scenario; on the other hand, it learns representations reducing the distribution divergence between the obtained latent domains. Such latent distributions naturally exist in time series, e.g., the activity data from multiple people follow different distributions. Additionally, our experiments show that even the data of one person still has such diversity: it can also be split into several latent distributions. Figure (d) shows that DIVERSIFY can effectively characterize the latent distributions (more results are Sec. 3.5).
To summarize, our contributions are four-fold:
We propose to view time series classification from the distribution perspective to learn OOD representation, which is challenging than the traditional image classification due to the existence of unidentified latent distributions.
Novel perspective:
Novel methodology: DIVERSIFY is novel framework to identify the latent distributions and learn generalized representations. Technically, we propose pseudo domain-class labels and adversarial self-supervised pseudo labeling to obtain the pseudo domain labels.
Theoretical insights: We provide the theoretical insights behind DIVERSIFY to analyze its design philosophy and conduct experiments to prove the insights.
Superior performance and insightful results: Qualitative and quantitative results using various backbones demonstrate the superiority of DIVERSIFY in several challenging scenarios: diffi- cult tasks, significantly diverse datasets, and limited data. More importantly, DIVERSIFY can successfully characterize the latent distributions within a time series dataset.
2 METHODOLOGY
A time-series training dataset DAr can be often pre-processed using sliding window to N inputs: D {(x,, yx) N where x; X C R2 is the p-dimensional instance and 3/s E )²= {1,....... C) is its label. We use (x. y) on X' x Y to denote the joint distribution of the training dataset. Our goal is to learn a generalized model from Der to predict well on an unseen target dataset, D which inaccessible in training. In our problem, the training and test datasets have the same input and output spaces but different distributions, i.c., X = Xte. y = = but ppt [ (x, y) a Ip'e(x (x, y). We aim to train model h from Dd to achieve minimum error D
2.1 MOTIVATION
What are domain and distribution shift in time series? Time series may consist of several unknown latent distributions (domains), even if the dataset is fully labeled. For instance, data collected by sensors of three persons may belong to two diffferent distributions due to their dissimilarities. This can be termed as spatial distribution shift. Surprisingly, we even find temporal distribution shifts in
Sliding window is common technique to segment one time series data into fixed-size windows. Fach window is minimum instance. We focus on fixed-size inputs for its popularity in time series (Das et al. 1998).
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Concept
Raw input
Fine-grained feature update
Latent distribution characterization
Domaiin-nvariant feature learning
Preprocessing
Algorithm
Copy
Copy
Feature
Feature
Feature extractor
Bottleneck
Bottleneck
Bottleneck
Classifior
Caaster
Linear
Closa for
Linear
8 Rx C
1, -.
Lusi/ Self-sueerviied proudo comaain label.
Forward
Backward
Louger
fussie Class labol
Loss
Pieuudo domain dlass label
Domain
Figure 2: The framework of DIVERSIFY.
experiments (Figure 6 that distributions of one person can also change at different time. Those shifts widely exist in time series, as suggested by (Zhang et al. 2021 Ragab et al. 2022).
OOD generalization requires latent domain characterization. Due to the non-stationary property, naive approaches that treat time series as one distribution fail to capture domain-invarian (OOD) features since they ignore the diversities inside the dataset. In Figure (c). we assume the training domain contains two sub-domains (cirele and plus points). Directly treating as one distribution via existing OOD approaches may generate the black margin. Red star points misclassified to the green class when predicting on the OOD domain (star points) with the learned model. Thus, multiple diverse latent distributions in time series should be characterized learn better OOD features.
brief formulation of latent domain characterization. Following above discussions, a time series may consist of K unknown latent domain MI rather than fixed one, i.c., pprr y)
K
T TPPP' (x, y). where (x. y) is the distribution of the i-th latent one with weight π.. Σ =
There could be infinite ways to obtain P's and our goal is to learn the 'worst-case' distribution scenario where the distribution divergence between each IP* and P] is maximized. Why the "worst- case' scenario? will maximally preserve the diverse information of each latent distribution, thus benefiting generalization. For illustration, these obtained latent distributions are shown in Sec. 3.5
2.2 DIVERSIFY
In this paper, we propose DIVERSIFY learn OOD representations for time series classification. The core of DIVERSIFY is to characterize the latent distributions and then minimize the distribution divergence between each two. DIVERSIFY utilizes an iterative process: first obtains the 'worst-case' distribution scenario from a given dataset, then bridges the distribution gaps between each pair of latent distributions. Figure describes its main procedures, where steps 2 4 are iterative:
1. Pre-processing: this step adopts the sliding window to split the entire training dataset into fixed-size windows. We argue that the data from one window the smallest domain unit.
2. Fine-grained feature update: this step updates the feature extractor using the proposed pseudo domain-class labels as the supervision.
3. Latent distribution characterization: it aims identify the domain label for each instance obtain the latent distribution information. It maximizes the different distribution gaps to enlarge diversity.
4. Domain-invariant representation learning: this step utilizes pseudo domain labels from the last step to learn domain-invarian representations and train generalizable model.
We assume K E (1, .N) smaller K may be too coarse to show the diversities in distributions while larger K brings difficulties optimization. K is suned in this work but expect learn in the future.
A domain a set of data samples following certain distribution and we use them interchangeably hereafter.
We use the notations n; and p only deseribe the problem, but do not formalize it.
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Published as a conference paper at ICLR 2023
Fine-grained Feature Update. Before characterizing the latent distributions, we perform fine- grained feature updates to obtain fine -r-ignain representation. As shown in Figure 2 (blue), we propose new concept: pseudo domain-class label to fully utilize the knowledge contained in domains and classes, which serves as the supervision for feature extractor. Features are more fine-grained w.r.t. domains and labels, instead of only attached domains labels.
At the first iteration, there is no domain label d' and we simply initialize d' = 0 for all samples. We treat per category per domain as a new class with label {1, 2........ ,S.. We have S K C where K is the pre-defined number of latent distributions that can be tuned in experiments. We perform pseudo domain-class label assignment get discrete values for supervision: s d' x CCyy
Let h hig _! be feature extractor, bottleneck, and classifier, respectively (we use superscripts to denote step number). Then, the supervised loss is computed using the cross-entropy loss t:
(2) Super E(x.)) (1(2) (hg (n) (x))).
(2)
(1)
Latent Distribution Characterization. This step characterizes the latent distributions contained in (green),
one dataset. As shown in Figure (green), we propose adapted version of adversarial training to disentangle the domain labels from the class labels. However, there are no actual domain labels
provided, which hinders such disentanglement. Inspired by (Caron et al. 2018), we employ self-supervised asseudo-labelinn strategy to obtain domain labels.
First, we attain the centroid for each domain with inssriinvrriant features: (
j.g: ExExx dk (hg ( (xx (x))))) (he (3) (x:)) (8)
(3)
Ex,ex (he (n, (h (xx))))
(3) (3)
where ( 1ig (3) are feature extractor, bottleneck, and classifier, respectively. as is the initial centroid of the 5tth latent domain while dg is the htth element of the logit soft-max output. Then, obtain the pscudo domain labels via the nearest centroid classifier using a distance function D:
(3) d; arg min Dhh (h (x:)),ūx)
(3)
Then, we compute the centroids and obtain the updated pseudo domain labels: (3)
Exex, I(d; k)h, (h) (3) (x))
d = arg min D(h (3) (h
(4)
Exexx I(d) k)
k
where I(a)= = when a true, otherwise 0. After obtaining d', we can compute the loss of step 2:
(3) Lsotf + Less -E e(h (8) (N, (1, (x))), d') + E(h (Rx, (li (3) (h (x))),
(5)
where h add is the discriminator for step 3 that contains several linear layers and one classification layer. RX, is the gradient reverse layer with hyperparameter À (Ganin al. 2016). After this step, we can obtain pseudo domain label d' for x.
Domain-invariant Representation Learning. After obtaining the latent distributions, we learn domain-invarian representations for generalization. In fact, this step (purple in Figure 2 is simple: we borrow the idea from DANN (Ganin et al.) (016) and directly use adversarial training to update the classification loss Lote and domain classifier loss Ldom using gradient reversal layer (GRL) (a
common technique that facilitates adversarial training via reversing gradients) (Ganin et al. 2016);
Lots + Letom -Ex.)))FF ((M(4) (1g.
(4) (h (x))).)
(Ro (1. (h)) (x)))),
(4) (4)
(6)
where is the cross-entropy loss and Rx, is the gradient reverse layer with hyperparameter X (Ganin al. 2016). We will omit the details of GRL and adversarial training here since they are common
techniques in deep learning. More details are presented in Appendix B.2
Training, Inference, and Complexity. We repeat these steps until convergence or max epochs. Different from existing methods, the last two steps only optimize the last few independent layers but not the feature extractor. We perform inference with the modules from the last step. Most of the trainable parameters are shared between modules, indicating that DIVERSIFY has the same model size existing methods and can reach quick convergence in experiments (Figure
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2.3 THEORETICAL INSIGHTS
We present some theoretical insights to show that our approach is well motivated in theory. Proofs can be found in Appendix A
Proposition 2.1. Let X' be space and H. be a class of hypotheses corresponding to this space. Let Q and the collection {P,} be distributions over and let { be a collection of non-negative
coefficient with Ei fss 1. Let O be set of distributions s.1. 4/S E O, the following holds
dHSH E S) S max (P.,
13
Then, for any h E H,
EQ(h) S X E (1)r,(1) + min (HHHH(. Q)
1
max dHAH Py); 6.
(8)
SEO
where X is the error of an ideal joins hypothesis. Er(h) is the error for a hypothesis h on a distribution P. (TA Q) is H-divvrgence which measures differences in distribution (Ben-David et al. 2010)
The first item in Eq. (8), X. is often neglected since it is small in reality. The second item, Σ: (PEE,, (h), exists in almost all methods and can be minimized via supervision from class la- bels with cross-entrope loss in Eq. (6). Our main purpose is to minimize the last two items in Eq. (8) Here Q corresponds the unseen cattoo-diisribution target domain.
The last term Y max4, duwn (P... 12) is common in OOD theory which measures the maximum differences among source domains. This corresponds to step 4 in our approach.
Finally, the third item, 2 minseo dH (8, Q), explains why we exploit sub-domains in step 3. Since our goal is learn a model which can perform well on an unseen target domain, we cannot obtain Q. To minimize & minsso dHAH((, Q). we can only enlarge the range of O. We have to maxi.j d (Pi, F2) according to Eq. (7), corresponding to step 3 in our method which tries to segment the time series data into several latent sub-domains by maximizing the segment- distribution gap to preserve diversities, i.c., the 'worst-case' distribution scenario.
3 EXPERIMENTS
We perform evaluations on four diverse time series classification tasks: gesture recognition, speech commands recognition, wearable &tress& detection, and sensor-based activity recognition.
Time series OOD algorithms are currently less studied and there are only two recent strong approaches
for comparison: GILE (Qian et al. | 1 and AdaRNN (Du et al. 2021 Fl We further compare with
7 general OOD methods from DemainBed (Gulrajani Lopez-Pau Paz 2021 : ERM, DANN (Ganin
et al. 2016), CORAL (un & Saenko 2016), Mixup (Zhang et al. 2018). GroupDRO Sagawa
et al. 2020). RSC (Huang et 20.22202),, and ANDMask (Parascandolo et al. 2021). More details of these methods in Sec. B.2 and B.3 For faimess,, all methods (except GILE and AdaRNN)
use a feature net with two blocks and each block has one convolution layer, one pooling layer, and one batch normalization layer, following (Wang al. 2019). We also use Transformers (Vaswani let al. 2017) for backbone. Detailed data pre-processing, architecture, and hyperparameters are in Appendix C.5 and D Ablations with various backbones are in Figure X and Appendix F.4
Most OOD methods require the domain labels known in training while ours does not, which is more challenging and practical. We conduct the training-domann dolaiin-alliaatonn strategy and the training data are split by 8 2 for training and validation. We tune all methods to report the average best performance of three trials for fairness. Note that the "target" in experiments is unseen and only used for testing. K" in DIVERSIFY is treated as a hyperparameter and we tune it to record the best OOD performance Per-segment accuracy the evaluation metric. Time complexity and convergence are in Sec. F55
showing its quick convergence.
'There are recent approaches purely time series, but not for OOD,
TThere could he recent OOD methods, but according to DomainBed (Gulrajani Lopez-Paz (2021), most approaches do not significantly outperform ERM. DANN, CORAL, and Mixup are also strong baselines. 'There might be optimal K for dataset. We perform grid search in [2, 10] to get the hest performance.
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3.1 GESTURE RECOGNITION
First, we evaluate DIVERSIFY on EMG for gestures Data Set (Lobov al., 2018). It contains data of 36 subjects with 7 classes and we select 6 common classes for our experi- ments. We randomly divide 36 subjects into four domains (i.e.. 0, 1, 2, 3). More details on EMG and domain splits can be found in Sec. C. respectiivv. EMG data is affected by many factors since it comes from bioelectric signals. EMG data are scene and device-dependent, which means the same person may generate different data when performing the same activity with the same device at a different time (i.e., distribution shift across time (Wilson et al. [2200] Purushotham et al. 2016)) or with the different devices at the same time. Thus, the EMG benchmark is challenging. Table [ssows that with the same backhone, our method achieves the hest average performance and is 4.3% better than the second-best method. DIVERSIFY even outperforms AdaRNN which has a stronger backbone.
Table 1: Results on EMG dataset.
"Target" 0 ~ 4 denotes unseen test
distribution that is only for testing.
Target
HRM
62.6
69.9
67.9
69.3
67.4
DANN
62.9
70.0
66.5
68.2
66.9
71.4
74.2
Mixup
60.7
69.9
70.5
68.2
67.3
GreupDRO
67.6
77.4
73.7
72.5
72.8
RSC
70.1
72.4
71.9
ANDMask
06.5
69.1
71.4
68.9
59.0
AdaRNN
68.8
81.1
75.5
78.1
75.8
DIVERSIFY
71.7
76.9
27.3
3.2
SPEECH COMMANDS
Then, we adopt a regular speech recognition task, the Speech Com- mands dataset (Warden] 2018). consists of one-sccond audio recordings of both background noise and spoken words such as 'left' and 'right'. It is collected from more than 2,000 persons, thus is more complicated. Following (Kidger et al. 2020), we use 34,975 time series corresponding to ten spoken words to produce a balanced classification problem. Since this dataset is collected from multiple persons, the training and test distributions are different, which is also an OOD problem with training domain. There many subjects and each subject only records a few audios. Thus, we do not split each sample. Figure shows the results two different backbones. Compared with GroupDRO, DIVERSIFY has over 1% improvement with a basic CNN backbone and over 0.6% improvement with a strong backbone MatchBoxNet3-1-666 (Majumdar& & Ginsburg 2020). It demonstrates the superiority of our method on a regular time-series benchmark containing massive distributions.
98
NazchBoNNct:
97
Accuracy (25)
96
45
94
93
BRM
GroupORO
ANDMask
Ours
Figure 3: Results on Speech commands with two different backbones.
3.3 WEARABLE STRESS AND AFFECT DETECTION
We further evaluate DIVERSIFY larger dataset, Wearable Stress and Affect Detection (WESAD) (Schmidt et al. 2018). WESAD is public dataset that contains physiological and motion data of 15 subjects with 63, 000, 000 instances. We utilize sensor modalities of chest-worn devices including clectrocardiogram, electrodermal activity, electromyogram, respiration, body temperature, and three axis acceleration. We split 15 subjects into four domains (details are in Sec. Sec. Results Figure 4 showed that our method achieves the best performance compared to other state-of-the-art methods with an improvement of over 8% on this larger dataset.
80
ERM
ANDMask Ours
GroupDRo
Accirscy (8))
70
6u
30
40
AVG
Unseen test set
Figure 4: Results WESAD. Here, O ~ in x-axis denotes the unseen test dataset.
3.4 SENSOR- BASED HUMAN ACTIVITY RECOGNITION
Finally, we construct four diverse OOD settings by leveraging four sensor-based based human activity recognition datasets: DSADS (Barshan & Yüksek, 2014). USC-HAD (Zhang & Sawchuk, 2012). UCI-HAR (Anguita et al. 2012), and PAMAP (Reiss & Stricker 2012). These datasets are collected from different people and positions using accelerometer and gyroscope, with 11, 741, 000 instances in total. (1) Cross-person generalization aims to learn generalized models for different persons. (2) Cross-position generalization aims to learn generalized models for different sensor positions. (3) Cross-dataset generalization aims to learn generalized models for different datasets. (4) One- Person-To- To-Another aims to learn generalized models for different persons from data of single

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Published as a conference paper at ICLR 2023
Table 2: Accuracy cross-person generalization. "Target" denotes the unseen test
DSADS
USC-HAD
PAMAP
ALL.
Target
ERM
83.1
79.3
87.8
71.0
80.3
81.0
57.7
74.0
65.9
69.7
90.0
78.1
55.8
84.4
77.1
75.7
DANN
89.1
84.2
85.9
83.4
85.6
81.2
57.9
76.7
70.7
71.6
82.2
78.1
15.4
87.3
75.7
77.7
86.2
Mixup
89.6
82.2
89.2
86.9
$7.0
80.0
64.1
74.3
61.3
69.9
89.4
80.3
58.4
87.7
79.0
78.6
GrvaDRRO
91.7
35.9
87.6
78.1
85.9
80.1
$5.5
74.7
60.0
67.6
85.2
77.7
56.2
85.0
76.0
76.5
RSC
77.7
87.8
ANDMask
85.0
75.8
87.0
77.6
81.4
79.9
55.3
74.5
65.0
68.7
86.7
76.4
43.6
85.5
73.1
74.4
GILE
81.0
75.0
77.0
66.0
74.7
78.0
62.0
77.0
63.0
70.0
83.0
68.0
42.0
76.0
67.5
70.7
75.5
73.7
81.6
82.7
DIVERSIFY
90.4
86.5
90.0
86.1
88.2
82.6
63.5
78.7
21.3
74.0
91.0
84,3
60.5
87.7
80.8
81.0
Table Classification accuracy on cross-position, cross-dataset, and one-to-another generalization.
Cross pasition generalization
Cross
Cross-dataset dotaset generalization
One Person-Tr- Amother
Tagget
2
AVG
3
AVG
DSADS
USC-HAD
PAMAP
AVG
DANN
15.4
25.3
38.1
28.9
25.1
32.6
29.7
45.3
16.1
43.8
11.2
CORAL
33.2
25.2
25.8
22.3
20.6
25.4
39.5
41.8
39.1
36.6
39.
Mixup
48.8
34.2
37.5
29.5
29.9
36.0
57.3
47.4
402
23.1
37.0
62.7
46.3
58.6
55.8
GrophDR
27.1
24.8
53.1
50.8
46.6
27.4
35.9
27.0
29.8
55.9
ANDMask
47.5
31.1
39.2
31.2
29.9
35.6
41.7
33.8
43.2
40.2
30.7
57.2
45.9
$4.3
52.5
DIVERSITY
47.7
32.9
44.5
31.6
30.4
37.4
48.7
46.9
49.0
99.9
$1.1
67.6
55.0
62.5
61.7
person For simplicity, we use 0, ... to denote different domains. More details on datasets information, setting construction, and domain splits can be found in Sec. C.3
C.4 and C.6).
Table and Table 3 show the results on four settings for HAR, where our method significantly outperforms the second-best baseline by 2.4%, 1.4%, 9.9%, and 5.8% respectively. All results demonstrate the superiority of DIVERSIFY. More results using Transformer can be found in F.4
We observe more insightful conclusions. (1) When the task is difficult: In the Cross Person setting, USC-HAD may be the most difficult task. Although it has more samples, it contains 14 subjects with only two sensors on one position, which may bring more difficulty learning. The results prove the above argument that all methods perform terribly this benchmark while ours has the largest improvement. (2) When datasets are significantly more diverse: Compared to Cross-Person and Cross-Position settings, Cross-Datased may be difficult since all datasets are totally different and samples are influenced by subjects, devices, sensor positions, and some other factors. In this setting, method is substantially better than others. (3) Limited data: Compared with Cross-Person setting, One-Person -ee----eroo-------o To-Another is more difficult since it has fewer data samples. In this case, enhancing diversity bring a remarkable improvement and our method can boost the performance.
3.5 ANALYSIS
Ablation study We present ablation study to answer the following three questions. (1) Why obtain- ing pseudo domain labels with class-invariant features in step 3? If obtain pseudo domain labels with common features, domain labels may have correlations with class labels, which may introduce
In One-Person- To-tohe setting, we only report average accuracy of four tasks on each dataset. Since only one domain exists in training dataset for this setting, DANN and CORAL cannot he implemented here.
FAM
76
Arquery (44)
Updata Faature
Updkta
75
70
16
76
LRG
(a) Class-ivvarin feat.
(b) Update feat. with d'
(c) Update feature with y
(d) #Domain K (EMG)
Figure 5: Ablation study of DIVERSIFY.
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34
D D.
1.00
0.68
1.71
1.68
13
1.08
0.90
1.71
1.50
04
0.68
1.68
(a) USC-HAD
(b) EMG
(c) Initial splits
(d) Our splits
Figure 6: (a) (b) Latent distributions obtained by our method on two datasets. X-axis data numbers while Y-axis is its values. (c) (d) H-divergence among domains with initial splits and splits PAMAP. Axes are domain numbers.
(a) Initial domain split (b) Our domain split
(c) ANDMask
(d) Our classification
Figure 7: t-SNE visualizations for domain splits ((a) (b)) and classification ((c) (d) on EMG data.
contradictions when learning domain invariant representations and lead to common performance. This is certified by the results in Figure (2) Why using fine-grained domain-class labels in step 2? If we utilize pseudo domain labels update the feature net, may make the representations seriously biased towards domain-related features and thereby leads to terrible performance on classification, which proved in Figure 5(b) If only utilize class labels update the feature net, it may make representations biased to class reaaseeelated features, thus DIVERSIFY is unable to obtain true latent sub-domains, as shown in Figure 5(c) Hence, we should employ fine- onn-graieed domain -laass labels to obtain representations with both domain and class information.
(3) The more latent domains, the better? More latent domains may not bring better results (Figure since a dataset may only have few latent domains and introducing more may contradict its intrinsic data property. Plus, more latent domains also make it harder to obtain pseudo domain labels and Iearn domain-invarian features.
Existence of latent distributions What exactly can our DIVERSIFY learn? In Figure 6(a) for subject in USC-HAD, there is more than one latent distribution for his walking activities, showing the existence of temporal distribution shift: the distribution of the same activity could change. For spatial distribution shift, Figure 6(b) on EMG dataset shows that our algorithm found three latent distributions from the EMG data multiple people. These results indicate the existence of latent distributions with both temporal and spatial distribution shifts. More results are in Appendix F.1
Quantitative analysis for 'worst-case' distributions We present quantitative analysis by com- puting the H--iiergeence distribution'. As shown in Figure and compared to initial domain splits, latent sub-domains generated by our method have larger H--iieegencce among each other. According larger H-divergence among domains brings better generalization. This again shows the efficacy of DIVERSIFY in computing the 'worst-case" distribution scenario. More results are in Appendix F.3
et al.] 2010) to show the effectiveness of our 'worst-case
Prop. 2.1
Visualization study We present some visualizations to show the rationales of DIVERSIFY. Data points with different initial domain labels are mixed together in Figure (aa while DIVERSIFY can characterize different latent distributions and separate them well in Figure 7 Figure 7 and show that DIVERSIFY can learn better Nomain-invarian representations compared to the latest method ANDMask. To sum up, DIVERSIFY can find better latent domains to enhance generalization. More results are Appendix F.T
Varying backbones Figure 8 shows the results using small, medium, and large backbones. respec- tively (we implement them with different numbers of layers.). Results indicate that larger models tend
Figure ((c) ((d) and the experimental results above prove that paying attention to shifts comprchensively bring larger divergence and better results.
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to achieve better OOD generalization performance. Our method outperforms others in all backbones, showing that DIVERSIFY presents consistently strong OOD performance in different architectures. More results with Transformer are in Appendix F.4 Parameter sensitivity is in Appendix
ANDMask
4 RELATED WORK
AVG Accurscy (%)
nn
GroupDRo
75
Time series classification is a challenging problem. Researches mainly focus temporal relation modeling via specially-designed methods [Dempster et al. 2021), RNN-based networks (Dennis et al.
70
65
2019), or Transformer architecture (Drouin et al. 2022). To our best knowledge, there is only one recent work (Du et al. (021) that studied time series from the distribution level. However, AdaRNN is a two-stage non-differential method that is tailored for RNN.
60
Smalll
Madium size
Latge
Figure 8: Results with differ- ent backbones on EMG. typically assumes the availability of domain labels for training. Specifically, Matsuura & Harada (2020) also studied DG without domain labels by clustering with the style features for images, which is not applied to time series and is not end-to-end trainable. Disentanglement (Peng et al. 2019 Zhang et al. 2022b) tries to disentangle the domain and label information, but they also assume access to domain information. Single domain generalization is similar to problem setting which also involves one training domain (Fan et al.) [022 1] Li et al. 2021: Wang et al.) 2021 Zhu Li (022). However, they treated
Domain OOD generalization (Wang et al. 2022
et al., 2022)
the single domain one distribution and did not explore latent distributions.
Multi-domain learning is similar to DG which also trains on multiple domains, but also tests on training distributions. Deecke al. (2022) proposed sparse latent adapters to learn from unknown domain labels, but their work does not consider the min-max worst-case distribution scenario and optimization. In domain adaptation, Wang et al. (2020) proposed the notion of domain index and further used variational models to learn them (Xu et al. 2023), but took different modeling methodology since they did not consider min-max optimization. Mixture models (Rasmussen et al., 1999) are models representing the presence of subpopulations within an overall population, e.g.. Gaussian mixture models. Our approach has a similar formulation but does not use generative models. Subpopulation shift is new setting (Koh et al. 2021) that refers to the case where the training and test domains overlap, but their relative proportions differ. Our problem does not belong to this setting since assume that these distributions do not overlap.
Distributionally robust optimization (Delage Ye 2010) shares a similar paradigm with our work, whose paradigm is also to seek distribution that has the worst performance within range of the raw distribution. GroupDRO (Sagawa et al.) (020)) studied DRO at a group level. However, we study the internal distribution shift instead of seeking global distribution close the original one.
5 LIMITATION AND DISCUSSION
DIVERSIFY could be more perfect by pursuing the following avenues. 1) Estimate the number of latent distributions K automatically: we currently treat it as hyperparameter. 2) Seek the semantics behind latent distributions (c.g., Figure 6(a) : can adding more human knowledge obtain better latent distributions? 3) Extend DIVERSIFY beyond classification, but for forecasting problems.
Moreover, we argue that dynamic distributions not only exist in time series, but also in general machine learning data such as images and text (Deecke al., 2022, Xu al., 2023). Thus, it is of great interest to apply our approach to these domains to further improve their performance.
6 CONCLUSION
We proposed DIVERSIFY to learn generalized representation for time series classification. DIVERSIFY employs adversarial game that maximizes the 'worst-case' distribution scenario while minimizing their distribution divergence. We demonstrated its effectiveness in different applications. We are surprised that not only mixed dataset, but dataset from single person also contain several latent distributions. Characterizing such latent distributions will greatly improve the generalization performance unseen datasets.

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ACKNOWLEDGEMENT
This work is supported by National Key Research & Development Program of China (No. 2020YTC000,) Natural Science Foundation of China (No. 61972383), the Strategic Priority Re- search Program of Chinese Academy of Sciences ( No. XDA28040500), Science Research Foundation of the Joint Laboratory Project on Digital Ophthalmology and Vision Science (No.SZYK202201).
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CONTENTS
Theoretical Insights
14
Background
14
A.2
Proof of Proposition 2.1.
15
Method Details
15
B.
Domain-invariant Representation Learning
15
B.2
Method Formulation and Implementation
16
B.3
Comparisons to Other Latest Methods
16
Dataset
16
Datasets Information
16
More details on EMG
17
C.3
Details Sensor-basee Human Activity Recognition Dataset
17
Details on Different Settings for Human Activity Recognition
17
Data Preprocessing
17
C.6
Details on Domain Splits
18
D Network Architecture and Hyperparameters
18
Evaluation Metries
19
More Experimental Results
20
Visualization Study
20
Parameter Sensitivity
20
F3
H-divergence
20
The Influence of Architectures
20
F5
Time Complexity and Convergence Analysis
21
A THEORETICAL INSIGHTS
A.1 BACKGROUND
For distribution IP with an ideal binary labeling function h" and hypothesis h, define the error (h) in accordance with (Ben-David et al. 2010)) as:
Ep (h) = Ex-=/ - (x)).
We also give the definition of H-divergence according with (Ben-David al. 2010). Given two distributions IP, Q over space X' and hypothesis class H.
dx (P. Q) = 2 sup PPr((In) - Pro(I.),
(10)
heh
where I, fx xx((x)= 1). We often consider the 7 -ivveiiveeeee in (Ben-David al. 2010) where the symmetric difference hypothesis class HAH is the set functions characteristic to disagreements between hypotheses.
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Theorem A.1. (Theorem 2.1 in (Sicilia al. 2021), modified from Theorem 2 in (Ben- David et al. 2010)). Let X be space and H. be class of hypotheses corresponding to this space. Suppose P and Q are distributions over X. Then for any h E H. the following holds
(q(h) S X" + ce(h) + SHHAH (Q.
(11)
with X" the error of an ideal joint hypothesis for Q, P.
Theorem A. provides an upper bound on the target-error. X" is a property of the dataset and hypothesis class and is often ignored. Theorem A. demonstrates the necessity learn domain invariant features.
A.2 PROOF OF PROPOSITION 2.1.
Proposition 2.1. Let be a space and H. be a class of hypotheses corresponding to this space. Let Q and the collection [P,)K, be distributions over X and let { be a collection of non-nege non-negative coefficient with Σ; PP: = 1. Let the object O he a set of distributions such that for every S E O the following holds
dHAH Σ (iPP, S max NHAn (P,,
(12)
Then, for any E H.
1
(h(h) S X Σ PIER, (h)
min dHAH Q) + max (I (P,,, SEO
(13)
2 1.j
where X/ the error of an ideal joint hypothesis.
Proof. On one hand, with Theorem A.I we have
(h) < X; + (h) + (S,), e H, e O.
(14)
On the other hand, with Theorem A.1 we have
cs(h)= X/2 + Exi, p.P,
P.P, (h) + duwml E S), wh E H.
(15)
Since ex, p.P. (h) = E, (,pp,(h), and dz p.P,, S maxis dHaH Py), we have
ch(h)= S X Σ pier, (h) dRaH (S, ++++
max dHAM E S),,, 4h H. (16)
in
where = Xi + X/. Equation 16 for all holds. Therefore, we complete the proof.
B METHOD DETAILS
B.
REPRESENTATION LEARNING
Domain-invarian representation learning utilizes adversarial training which contains feature work, a domain discriminator, and classification network. The domain discriminator tries its best discriminate domain labels of data while the feature network tries its best to generate features to confuse the domain discriminator, which thereby obtains domain-invariant representation. Therefore, is adversarial process, and in our setting, it can be expressed follows,
min (4) (4))
E ( E(h (1)
(4) (4) (4) (4) (h) (x))). v) (( (h) (h (x))), d'),
(17)
((x.)) ((0 ((1 (1) (1 (x))), d').
min addo
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need iterative process to optimize hib (4) and h (ad iteratively, which is cumbersome. It is better to optimize hi ((4) and h hade at the same time. It is obvious that the key is solve the problems caused by the negative sign in Eq. (17). Therefore, a special gradient reversal layer (GRL), a popular implementation of the adversarial training in training several domains as suggested by (Ganin al. 2016), came. GRL acts as an identity transformation during the forward propagation while it takes the gradient from the subsequent level and changes its sign before passing it to the preceding layer during the backpropagation. During the forward propagation, the GRL can be ignored. During the backpropagation, the GRL makes the sign of gradient on hg reverse, which solves the problems caused by the negative sign in Eq. 177
To optimize Eq.
B.2 METHOD FORMULATION AND IMPLEMENTATION
While it is common to use some probability or Bayesian approaches for formulation when one mentions distributions, we actually do not formulate the latent distributions: we are not generative or parametric method. In fact, the concept of latent distribution is just notion to help understand our method. Our ultimate goal to infer which distribution a segment belongs to for best OOD performance. Thus, we do not care what distribution exactly looks like it is not our focus. As long as we can obtain diverse latent distributions, things are all done.
parameterize it since
In real implementation, the latent distributions are just represented as domain labels: latent distribution i is also a domain that certain time scries segments belong to, as we stated in the introduction part. Additionally, also acknowledge that parameterizing the latent distributions may help get better performance, which can be left for future research.
B.3 COMPARISONS OTHER LATEST METHOOS
Here, offer more details on comparisons to other latest methods utilized in the main paper.
DANN (Ganin et al. 2016) is method that utilizes the adversarial training to force the discrimi- nator unable to classify domains for better ionain-invariant features. It requires domain labels and splits data in advance while ours is universal method.
CORAL (Sun Saenko 2016) method that utilizes the covariance alignment in feature layers for better
features. It also requires domain labels and splits data in advance.
Mixup Zhang al. 2018 is method that utilizes interpolation generate more data for better generalization. Ours mainly focuses on generalized representation learning.
GroupDRO (Sagawa et al. 2020) is a method that seeks global distribution with the worst performance within a range of the raw distribution for better generalization. Ours study the internal distribution shift instead of seeking a global distribution close the original one.
RSC (Huang et al. 2020) a self-challenging training algorithm that forces the network to activate features as much possible by manipulating gradients. It belongs to gradient operation-basee DG while ours is to learn generalized features.
ANDMask (Parascandolo et al., 2021 is another gradient- based optimization method that belongs to special learning strategies. Ours focuses on representation learning.
GILE QQan et al. 202T is a disentanglement method designed for cross-persee human activity recognition. It is based on VAEs and requires domain labels.
AdaRNN (Du et al. (02T) a method with two-stage that is non-differential and it tailored for RNN. A specific algorithm is designed for splitting. Ours is universal and is differential with better performance.
C DATASET
C.1 DATASETS INFORMATION
Table 4howw the statistical information each dataset.
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Table 4: Information datasets.
Dataset
Subjects
Sensors
Classes
Samples
EMG
36
7
33,903,472
SPCMD
2618
35
105,829
WESAD
8
63,000,000
DSADS
8
1,140,000
USC-HAD
5,441,000
UCI-HAR
1,310,000
PAMAP
9
3
18
3,850,505
C.2 MORE DETAILS ON EMG
Electromyography (EMG) is typical time-series data that is based on bioelectric signals. We use EMG for gestures Data Set (Lobov al. (018) that contains EMG data recorded by MYO Thalmic bracelet. The bracelet is equipped with eight sensors equally spaced around the forearm that simuitaneously acquire myographic signals. Data of 36 subjects collected while they performed series of static hand gestures and the number of instances is 40, 000 - 50, 000 recordings in each column. It contains classes and we select 6 common classes for our experiments. We randomly divide 36 subjects into four domains (i.e., 0, 1,2, 2, 3) without overlapping and each domain contains data of 9 persons.
C.3 DETAILS ON SENSOR-BASED HUMAN ACTIVITY RECOGNITION DATASET
UCI daily and sports dataset (DSADS) Barshan & Yüksek 2014) consists of 19 activities collected from subjects wearing body-worn sensors on body parts. USC-SIPI human activity dataset (USC-HAD) (Zhang & Sawchuk 2012) is composed of 14 subjects (7 male, female, aged 21 to 49) executing 12 activities with a sensor tied on the front right hip. UCI-HAR (Anguita et al. 2012) is collected by 30 subjects performing 6 daily living activities with waist-mounted smartphone. PAMAP (Reiss & Stricker 2012) contains data of 18 activities, performed by 9 subjects wearing 3 sensors.
C.4 DETAILS DIFFERENT SETTINGS FOR HUMAN ACTIVITY RECOGNITION
We construct four different settings representing different degrees of generalization: (1) Cross- person generalization: This setting utilizes DSADS, USC-HAD, PAMAF datasets to construct three benchmarks. Within each dataset, randomly split the data into four groups and then use three groups as training data to learn a generalized model for the last group. (2) Cross-positton generalization: this setting uses DSADS dataset and data from each position denotes different domain. Each sample contains three sensors with nine dimensions. We treat one position as the test domain while the others are for training. (3) Cross-dataset generalization: this setting uses all four datasets, and each dataset corresponds to different domain. Six common classes are selected. Two sensors from each dataset that belong the same position are selected and data is down-sampled to have the same dimension. (4) and PAMAP datasets. In each dataset, we randomly select four pairs of persons where one is the training and the other is the test.
To-on-TTT-noher This setting adopts DSADS, USC-HAD,
C.5 DATA PREPROCESSING
will introduce how we preprocess data and the final dimension of data for experiments here. We mainly utilize the sliding window technique, common technique in time-series classification, to split data. As its name suggests, this technique involves taking a subset of data from a given array or sequence. Two main parameters of the sliding window technique are the window size, describing subset length, and the step size, describing moving forward distance each time.
For EMG, set the window size 200 and the step size 100, which means there exist 50% overlaps x min X between two adjacent samples. We normalize each sample with & max X min X contains all x. The final dimension is 1 x 200.
We do UCI-HAR in cross-person setting since its haseline is gond enough.
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For Speech Commands, we follow (Kidger et al. 2020).
For WESAD, we utilize the same preprocessing as EMG.
Now give details on all datasets in Cross-person setting. For DSADS, we directly utilize data split by the providers. The final dimension shape 45 x 125. 45 = 5 x x 3 where means five positions, the first means three sensors, and the second means each sensor has three axes. For USC-HAD, the window size is 200 and the step size is 100. The final dimension shape is 6 x x 200. For PAMAP, the window size is 200 and the step size is 100. The final dimension shape is 27 x x 200. For UCI-HAR, we directly utilize data split by the providers. The final dimension shape is 6 x 1 128.
For Cross-position, we directly utilize samples obtained from DSADS Cross-person setting. Since each position corresponds one domain, sample is split into five samples in the first dimension. And the final dimension shape is 9 x X 125.
For Cross-dataset, directly utilize samples obtained in Cross-person setting. To make all datasets share the same label space and imput space, we select six common classes, including WALKING, WALKING UPSTAIRS, WALKING DOWNSTAIRS, SITTING, STANDING, LAYING. addition, we down-sample data and select two sensors from each dataset that belong to the same position. The final dimension shape x 50.
For One-Person-Dle PeeeoeeTT-AAootheeeee Toothe, we randomly select four pairs of persons from DSADS, USC-HAD, and PAMAP respectively. Four tasks are 1 - 0,3 + 2, 5 + 4, and 7 - 6. Each number corresponds
to one subject. And the final dimension shape is 45 x 1 x 125, 6 x x 200, and 27 1 x 200 for DSADS, USC-HAD, and PAMAP respectively.
As we can see, samples in EMG, WESAD, and HAR all have more than one channel (the first dimension shape), which means they are all multivariate.
C.6 DETAILS ON DOMAIN SPLITS
We introduce how split data here.
Since Speech Commands is a regular task, we just randomly split the entire dataset into a training dataset, validation dataset, and testing dataset.
We mainly focus on EMG, WESAD, and HAR, and we construct domains for OOD tasks. We denote subjects of dataset with 0 Sn, where 8n is the number of subjects in the dataset. For example, there are 36 subjects in EMG and we utilize 0, 1,2, 2.. ..... 355 to denote data of them respectively.
Table 5 shows the initial domain splits of EMG, WESAD, and all datasets for HAR in Cross-person setting. We just want to make each domain has a similar number of samples in one dataset. As noted in the main paper, we also utilize 1, 2, and 3 to represent different domains but they have different meanings with subjects. When conducting experiments, we take one domain as the testing data and the others as the training data. Our method is not influenced by the splits of the training data since do not need the domain labels.
Table 5: Initial domain splits.
Dataset
1
2
3
EMG
0-8
9-17
18-26
27-35
WESAD
0-3
4-7
8-11
12-14
DSADS
0.1
2,3
4,5
6.7
USC-HAD
0,1,2,11
3,5,6,9
7,8,10,13
4,12
PAMAP
2,3,8
1.5
0.7
4,6
D NETWORK ARCHITECTURE AND HYPERPARAMETERS
For the architecture, the model contains two blocks, and each has convolution layer, pooling layer, and one batch normalization layer. A
layer is used as the bottleneck layer while another fully-connected layer serves as the classifier. All methods are implemented with
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PyTorch (Paszke et al. 2019). The maximum training epoch is set to 150. The Adam optimizer
with weight decay 5 x 10 is used. The learning rate for GILE is 10 The learning rate for the
rest methods is 10 or 10 (For Speech Commands with MatchBoxXeet3-1666 we also try the learning rate, 10-1. We tune hyperparameters for each method.
For the pooling layer, utilize MaxPool2d in PyTorch. The kernel size is (1,2) ad the stride is 2. For the convolution layer, we utilize Conv2d in PyTorch. Different tasks have different kernel sizes and Table TJbleesssowss the kernel sizes.
Table 6: The kernel size of each benchmark.
EMG
(1.9)
DSADS
(1.9)
SPEECHCOMMANDS
(1,9)
Cross-Person
USC-HAD
(1,6)
WESAD
(1.9)
PAMAP2
(1,9)
Cross-position
(1.9)
One-Person- Trn-PPeson-To-Amooeeee To-Another
The same as Cross-Person
Cross- dross-dataset
E EVALUATION METRICS
We utilize average accuracy the testing dataset evaluation metrics for all benchmarks. Average accuracy is the most common metric for DG and it can computed as the following,
Acc E(x.)e TU*)
#[
(18)
1 = arg max l(x).
(y+) is indicator function. If y y+, it equals 1, otherwise it equals O. #1 represents the number of the set. is the model to learn. Please note that a has different distribution from X for EMG and HAR. And has been preprocessed and each sample is segment.
(a) ERM
(b) RSC
(c) ANDMask
(d) Ours
Figure 9: Visualization of the t-SNE embeddings for classification EMG. Different colors corre- spond to different classes while different shapes correspond to different domains.
(a) Initial splits USC
(b) Our splits USC
(c) Initial splits EMG (d) Our splits on EMG
Figure 10: Visualization of the t-SNE embeddings for domain splits where different colors represent different domains.
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F MORE EXPERIMENTAL RESULTS
F.1 VISUALIZATION STUDY
We show more visualization study in this part. As shown in Figure ((a) and Figure 9b) both ERM and RSC also cannot obtain fine domain- invariinn representations and method still achieves the best domain-invariant representations. As shown in Figure [0, compared with initial domain splits, latent sub-domains generated by our method better separated.
F.2 PARAMETER SENSITIVITY
sccurscy INN
ERM
30
Dur BRM
Out EAN
Dus BRM
74
10
0.1
0.1
1:50
3:30
5:30
19:35
335
Aa
spochsround
(a) Latent domains K
(b)
(c) X2
(d) Local epoch Round
Figure 11: Parameter sensitivity analysis (EMG).
There are mainly four hyperparameters in our method: K which the number of latent sub-domains, A for the adversarial part in step A2 for the adversarial part in step and local epochs and total rounds. For fairness, the product of local epochs and total rounds is the same value. We evaluate the parameter sensitivity of our method in Figure [I where we change one parameter and fix the other to record the results. From these results, we can see that our method achieves better performance in wide range, demonstrating that our method robust.
F.3 H-DIVERGENCE
0.48
0-
0.78
0.60
0.45
0.38
0.78
0.78
2
0.48
0.38
2
0.60
0.78
0
2
(a) Initial splits
(b) Our splits
Figure 12: H-divergence among domains with initial splits and our splits on EMG.
Figure 12 shows H-divergence among domains with initial splits and our splits on EMG, which demonstrates splits have larger H-divergence and thereby bring better generalization.
F.4 THE INFLUENCE OF ARCHITECTURES
To ensure that method work with different sizes of models, add some experiments with more complex or simpler architectures. As shown in Table where small, medium, and large indicate the different model sizes (our paper uses the medium), we see clear picture that model sizes influence the results, and our method also achieves the best performance. Small corresponds to the model with one convolutional layer, Medium corresponds the model with two convolutional layers, and Large corresponds to the model with four convolutional layers. For most methods, more complex models bring better results.
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Table 7: Results EMG dataset with different model sizes.
Model Size
Small
Medium
Large
Target
AVG
AVG
2
AVG
ERM
56.6
65.7
65.3
61.8
62.3
62.6
69.9
67.9
69.3
67.4
61.2
78.8
68.8
64.6
68.4
DANN
65.3
69.3
63.6
62.9
65.3
62.9
70.0
66.5
68.2
66.9
63.0
72.7
69.4
68.5
68.4
CORAL
66.9
74.9
70.8
73.2
71.4
66.4
74.6
71.4
74.2
71.7
67.7
77.0
72.7
71.8
72.3
Mixup
56.8
61.0
67.2
60.7
69.9
70.5
67.3
81.1
71.2
69.6
72.0
GroupDRO
64.9
69.1
70.1
73.7
72.5
72.8
66.3
79.3
71.3
73.0
RSC
62.7
73.2
67.6
64.0
66.9
70.1
74.6
72.4
71.9
72.2
65.1
76.8
72.2
67.7
70.4
ANDMask
62.4
66.0
66.3
65.6
65.1
66.6
69.1
71.4
68.9
69.0
65.7
78.1
72.1
71.2
71.9
DIVERSIFY
69.8
77.3
74.4
74,4
74.0
71.7
82.4
76.9
77.3
77.1
72.0
86.6
78.5
79.0
Table 8: Results EMG dataset with Transformer.
Target
2
3
AVG
ERM
71.7
83.8
76.
78.0
77.4
DANN
72.7
82.3
77.6
77.3
77.5
GroupDRO
72.1
84.4
77.5
78.3
78.1
RSC
72.1
83.7
77.6
78.2
77.9
Ours
75.6
86.2
79.4
79.7
80.2
We also try Transformer (aaswani et al. 2017) as the backbone for comparisons. As shown in (Zhang et al. 2022a), Transformer often has better generalization ability compared to CNN, which implies improving with Transformer is more difficult. From Ta- ble(]] we can see that each method with Transformer has a remark- able improvement
CNN
Transformer
EMG. Compared ERM, DANN almost has no improvement but ours still has further improvements and achieves the best performance. To further validate the advantage of our method, we perform the experiments on more difficult task, i.. the first task of cross-dataset where distribution gaps are larger. As shown in Figure [.4] our method still achieves the best performance in this more difficult situation while DANN even performs worse than ERM, which demonstrates the importance of more accurate sub-domain labels.
ERM
DANN
RSC
Figure 13: Results the first task in Cross-dataset generaliza- tion using Transformers.
Overall, for all architectures, our method achieves the best per- formance.
Table 9: Time costs of different methods (s).
method
ERM
DANN
CORAL
Mixup
GroupDRO
RSC
ANDMask
Ours
time
305.98
328.62
357.54
2042.93
340.03
321.51
379.87
356.8
F.5
TIME COMPLEXITY AND CONVERGENCE ANALYSIS
We also provide some analysis on time complexity and convergence. Since we only optimize the feature extractor in Step 2, our method does not cost too much time. And the results in Table prove this argument empirically.
0.4
0.3
0.2
The convergence results are shown in Figure F.5
Our method convergent. Although there are some little fluctuations, these fluc- tuations exist widely in all domain generalization methods due to different distributions of different samples.
60
80
100 120 140
epoch
Figure 14: Convergence re- sults on EMG.
21


Reviews:
[{"review_id": "mxwGoX-RAN", "reviewer": "Reviewer_x6zY", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper propose a method for representation learning robust to out of distribution cases for the times series classification cases.", "summary_of_the_review": "Even with the propose method end2end and extensive real data experimetns, the contribution is marginal, not strong connection of OOD motivation and supporting evidences. Many things the author claimed 'novel', like perspetive and methodology is variant of existing works and thus marginal, or if not, authors should more thoroughly examine and point out the differences. ", "strength_and_weaknesses": "## Strength\n- consider worst-case scenario and develop the algorithm and modeling end to end.\n- extensive real-data experiments to demonstrate the superiority of the method.\n\n\n## Weakness\n- lack of motivation and weak examiniation on the method \n - why OOD is important in time series? \n - how was OOD defined in the time series formally? at least reference? these definition can be different from static data \n - What if all real dataset do not fall in OOD categories the authors defined? any synthetic experiments to support the necessity of the method?\n - the theoretical results is adopted from existing one, why is this specially applicable to time series setting beyond static setting? Without it, it is just OOD method in image classification and need more thoroughly to be compared with those literatures? \n - similary, why existing methods in static classification are not applicable to time series setting?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "XeVSUB8b9Dv", "reviewer": "Reviewer_SWyN", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a domain generalization method for time series classification to\nimprove the generalization on new unseen target domain without using domain labels.\nMoreover, an identification approach of the sub-distributions inside the data is\nproposed. Last, a min-max adversarial approach is presented to find domain invariant\nfeatures among the predicted domains and sub-domains. Experimental results on four\ndifferent time series datasets show the superiority of the proposed approach.", "summary_of_the_review": "The paper addresses a challenging yet an important problem of distribution shift for time\nseries data . The main weaknesses are the incomplete support of some claims, while\nmissing some important baselines in the related works and experiments.", "strength_and_weaknesses": "Strength:\n\nThe problem of domain generalization for time series classification is significant\nand important\n\nA new perspective for the inherit sub-distributions inside the time series data is\ninsightful\n\nTheorical insights are also provided.\nWeaknesses:\n\nThe technicality of the idea, while assuming there exists sub-distributions\nwithin each well-defined domain is plausible, it is not clear how the method\ndifferentiates between the class-distributions within each domain (which is also\ncan be detected as sub-domains) and the original sub-distributions.\n\nOverclaims and Novelty:\n\nThe authors claimed that domain generalization for time series\nclassification is that “under explored” without mentioning in time series\ndomain generalization methods. However, the exist some domain\ngeneralization methods for time series data such as [1,2]\n\nThe authors claim novelty for working and using pseudo domain labels.\nHowever, some domain generalization methods exist that use peudo\ndomain labels such as [3].\n\nThe authors claim “Finally, our work is not a direct application of DG due\nto the non-existence of domain labels ” to distinguish their methods from\ndomain generalization approach. Nevertheless, there exist some\napproaches that also doesn’t require domain labels [1, 2, 3]\n\nExperiments:\n\nOne key motivation for the paper is the detection of sub-distributions\nwithin each domain. However, all the tested domain generalization\nscenarios are clearly usually mapping across clearly separated domains\nsuch as different humans where each human is one domain. Thus, I\ncannot see any experiment that support their claim of the existence of\nsub-domains.\n\nMissing Time series domain generalization baselines [1,2].\n\n[1] Zhang, Wenyu, Mohamed Ragab, and Ramon Sagarna. &quot;Robust domain-free domain generalization\nwith class-aware alignment.&quot; ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech\nand Signal Processing (ICASSP). IEEE, 2021.\n\n[2] Ragab, Mohamed, et al. &quot;Conditional Contrastive Domain Generalization for Fault Diagnosis.&quot; IEEE\nTransactions on Instrumentation and Measurement 71 (2022): 1-12.\n\n[3] Matsuura, Toshihiko, and Tatsuya Harada. &quot;Domain generalization using a mixture of multiple latent\ndomains.&quot; Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 34. No. 07. 2020.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "CbdilkANxy", "reviewer": "Reviewer_oHGw", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "In this work, the authors propose DIVERSIFY, an OOD representation learning algorithm for time series classification. It has two iterative steps: (i) learn to segment the time series data into several latent sub-domains by maximizing the distribution gap and (ii)  learn domain-invariant representations by reducing the distribution divergence between the obtained latent domains. The experiments on several time series classification tasks showed that the proposed method outperforms other baselines.", "summary_of_the_review": "Overall I think it is a good work, though there are some flaws in experiment section should be addressed.", "strength_and_weaknesses": "* Strength\n\n(i) The work is clearly written and easy to follow.\n\n(ii) The design is sensible, as it is widely seen from other OOD work beyond time-series data.\n\n(iii) Sec 2.3 is insightful, esp. linking Eq. (7) to the step 3 of the proposed algorithm.\n\n* Weakness\n\n(i) The novelty is quite limited, as the techniques used here are largely adapted from existing work.\n\n(ii) For the experiment, it is not clear why such a simple feature net (two-conv) is used, given that stronger backbones exist.\n\n(iii) Why there is an inconsistency over methods for different datasets? i.e., some methods are not evaluated for certain datasets/tasks. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "8mfIYR_TcX2", "reviewer": "Reviewer_EJKA", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper presents a representation learning model for OOD timeseries data. By building on top of DANN, it applies clustering in order to identify domains along with pseudo domain-class labels and adversarial self-supervised pseudo labeling to obtain the pseudo domain labels. Extensive experiments are conducted on various datasets with different OOD settings showing that the proposed framework outperforms two closely related baselines and other baselines from the domain generalization literature.", "summary_of_the_review": "This is a very well designed paper with strong results. My only concerns are about exploring different backbone architectures such as Transformers and lack of code.", "strength_and_weaknesses": "S\n+ Strong results in an array of diverse timeseries tasks\n+ Extensive experimentation with different settings across people/positions/datasets\n+ Intuitive explanation of why the components of the method should be there (along with ablations)\n\nW\n- Lack of comparisons with other backbones like Transformers", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "2VzaMfL20X4", "reviewer": "Reviewer_MfQf", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a new machine learning model, and training objective, for classifying signal data from speech, wearables, EMG, and sensors. I don't fully understand the proposed model (see questions for clarification below). But it outperforms previous methods in the field.\n\n\"While most efforts have predominantly resided in image classification, OOD in time series remains underexplored and more challenging.\" I don't think it's underexplored, there's entire research fields dedicated to sequential extrapolation. Look up DYCK languages or most of the papers published by Michael Hahn in 2019-2020. Moreover, if the OOD is in reference to signal processing, I am sure the field of reinforcement learning and robotics are dealing with similar challenges of OOD.\n\nAfter reading the introduction, I still don't understand what \"DIVERSIFY\" does, other than it's adversarial and models the underlying distribution.\n\n\"Surprisingly, we even find temporal distribution shifts in our experiments (Figure 6) that distributions of one person can also change at various times\" Do you collect your own dataset? What kind of experiments are you referring to?\n\n\"a time series may consist of K2 unknown latent domains3 rather than a fixed one\" The way the citation works make it seems like it says K squared.\n\nWhat are Hc, Hb, and Hf - do you have more detailed explanations of them somewhere? Also, please give a more elaborate explanation of (2).\n\n\"At the first iteration, there is no domain label d′ and we simply initialize d′ = 0 for all samples. We treat per category per domain as a new class with label s ∈ {1, 2, · · · , S}. We have S = K × C where K is the pre-defined number of latent distributions that can be tuned in experiments. We perform pseudo domain-class label assignment to get discrete values for supervision: s = d′ × C + y.\"\nI don't understand this. Do you choose a set of sub-sequences by hand, and then force your model to iteratively use more finegrained subsequences?\n\n\"Latent Distribution Characterization\" Is this some type of hard attention?\n\nFigure 7 is not covered enough, I don't have a strong intuition for why your model works. I would like to see specific examples of data where your model performs better.\n\n", "summary_of_the_review": "I am not familiar with this field and the paper does not make it easier to understand. The authors argue that their focus on OOD on sequences is novel, however, I don't see how OOD signal processing is a new field of research. I need a better motivation. It is not clear to me from the text if the models they are testing against are state-of-the-art, or if they are reimplementations.", "strength_and_weaknesses": "Strength\nImproved performance\n\nWeakness\nUnclear how the model works\nLack of visualizations\nMotivation is not completely correct\nUnclear if improved performance is state-of-the-art", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster