Towards Enhancing Time Series Contrastive Learning: A Dynamic Bad Pair Mining Approach
Authors: Xiang Lan
Hanshu Yan
Shenda Hong
Mengling Feng
Venue: ICLR 2024 poster (2024)
Keywords: Time Series Contrastive Learning
Healthcare
Self-Supervised Representation Learning
Primary area: representation learning for computer vision, audio, language, and other modalities

Abstract: *Not all positive pairs are beneficial to time series contrastive learning*. In this paper, we study two types of bad positive pairs that can impair the quality of time series representation learned through contrastive learning: the noisy positive pair and the faulty positive pair. We observe that, with the presence of noisy positive pairs, the model tends to simply learn the pattern of noise (Noisy Alignment). Meanwhile, when faulty positive pairs arise, the model wastes considerable amount of effort aligning non-representative patterns (Faulty Alignment). To address this problem, we propose a Dynamic Bad Pair Mining (DBPM) algorithm, which reliably identifies and suppresses bad positive pairs in time series contrastive learning. Specifically, DBPM utilizes a memory module to dynamically track the training behavior of each positive pair along training process. This allows us to identify potential bad positive pairs at each epoch based on their historical training behaviors. The identified bad pairs are subsequently down-weighted through a transformation module, thereby mitigating their negative impact on the representation learning process. DBPM is a simple algorithm designed as a lightweight **plug-in** without learnable parameters to enhance the performance of existing state-of-the-art methods. Through extensive experiments conducted on four large-scale, real-world time series datasets, we demonstrate DBPM's efficacy in mitigating the adverse effects of bad positive pairs.

Published as a conference paper at ICLR 2024
TOWARDS ENHANCING TIME SERIES CONTRASTIVE LEARNING: A DYNAMIC BAD PAIR MINING APPROACH
Xiang Lan', Hanshu Yan?, Shenda Hong"* Mengling Feng 1 Saw Swee Hock School of Public Health & Institute of Data Science, National University Singapore
BayteDance, National Institute of Health Data Science, Peking University (ephlanx, ephfm) @nus edu. .g hanshu. yan@bytedance com, hongsheenda@pku.eduu en
ABSTRACT
Not all positive pairs are beneficial time series contrastive learning. In this paper, study two types of bad positive pairs that can impair the quality of time series representation learned through contrastive learning: the noisy positive pair and the faulty positive pair. We observe that, with the presence of noisy positive pairs, the model tends to simply learn the pattern of noise (Noisy Alignment). Meanwhile, when faulty positive pairs arise, the model wastes considerable amount effort aligning non-representative patterns (Faulty Alignment). To address this problem, we propose Dynamic Bad Pair Mining (DBPM) algorithm, which reliably identifies and suppresses bad positive pairs in time series contrastive learning. Specifically, DBPM utilizes memory module dynamically track the training behavior of each positive pair along training process. This allows to identify potential bad positive pairs each epoch based their historical training behaviors. The identified bad pairs are subsequently down-weighted through a transformation module, thereby mitigating their negative impact on the representation learning process. DBPM is a simple algorithm designed as a lightweight plug-in without learnable parameters enhance the performance of existing state-of-the-arr methods. Through extensive experiments conducted on four scale, real-world time series datasets, we demonstrate DBPM's efficacy in mitigating the adverse effects of bad positive pairs.
Still good positive pair?
Still good positive pair?
Original signal
Augmented view
Original signal
Augmented
Noisy Positive Pair
Faulty Positive Pair
(a)
(b)
Two types of bad positive pair identified in real-world time series contrastive lcarning: Noisy Positive Pair: The presence of excessive noise the original signal and the augmented view Icads to the contrastive model predominantly learning patterns from noise (i.e., Noisy Alignment). Faulty Positive Pair: The augmented view no longer has the same semantic meaning as the original signal due to the destruction of important temporal patterns during augmentation (the red part highlighted in the original signal), causing the contrastive model learns align non-representative patterns (i.c., Faulty Alignment).
Figure 1: Motivation:
"Corresponingg authors
Codes available GitHub

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Published as a conference paper at ICLR 2024
1 INTRODUCTION
Self-supervised contrastive learning has shown remarkable efficacy in learning meaningful represen- tations from unlabeled time series data, thereby improving the performance of downstream tasks (e.g., time series classification) (Oord et al., 2018; Tonekaboni al., 2021; Eldele et al., 2021; Yèche et al., 2021; Lan et al., 2022; Yue et al., 2022; Yang & Hong, 2022; Zhang et al., 2022b; Ozyurt et al., 2023). The key concept of time series contrastive learning is to capture the meaningful underlying information shared between views (usually generated by random data augmentation), such that the learned representations are discriminative among time series. To accomplish this objective, existing contrastive methods comply with an assumption that the augmented views from the same instance (i.e.. positive pair) share meaningful semantic information (Chen et al., 2020; He al., 2020a; Chen & He, 2021a; Wen & Li, 2021).
But what happens if this assumption violated? Some recent studies (Morgado et al., 2021; Chuang et al., 2022) have investigated the effects of the faulty view problem in image contrastive learning. was discovered that the effectiveness of the contrastive learning models will indeed suffer when two views generated from the same image actually do not share meaningful information (e.g., an unrelated cat-dog pair cropped from the same image). In other words, not all positive pairs are beneficial to contrastive learning. We extend this line of work to time series by investigating whether time series contrastive learning encounters similar challenges, and explore what kind of positive pairs are detrimental the learning process. Specifically, when applying commonly used contrastive learning methods to time series applications, we observe two extreme cases of positive pairs that violate the assumption and consequently vitiate the quality of the learned time series representation:
Noisy Positive Pairs: As shown in Figure 1 (a), real-world example from the Sleep-EDF dataset (Goldberger al., 2000) (EEG signal). These pairs can arise when the original signal exhibits substantial noise, which could be attributed to improper data collection in real-world scenarios. This results in noisy contrasting views, where the shared information between views is predominantly noise. In the given example, the low voltage EEG is interfered by other electrical signals such as the electrooculogram (EOG) from eye movement, which makes some subtle EEG spikes indicative of early stage epilepsy being overwhelmed by noise. As result, noisy alignment occurs, in which the model simply learns the pattern of noise rather than the true signal.
Faulty Positive Pairs: As shown in Figure 1 (b), a real-world example from the PTB-XL dataset (Wagner et al., 2020) (ECG signal). Due to the sensitivity of time series, data augmentation may inadvertently impair sophisticated temporal patterns contained in the original signal and thus produce faulty views. In the example, the unique temporal pattern exhibited by ventricular premature beat (red part) for diagnosing ECG abnormality has been destroyed after augmentation. Consequently, the augmented view is no longer has the same semantic meaning as the original ECG, leading to a faulty alignment where the model learns to align non-representative patterns shared between views.
For clarity, we refer to these two extreme cases as bad positive pair problem in time series contrastive learning. An intuitive solution is suppress bad positive pairs during contrastive training. however, directly identifying bad positive pairs in real-world datasets is challenging for two reasons. First, for noisy positive pairs, it often infeasible to measure the noise level given a signal from real-woril dataset. Second, for faulty positive pairs, one will not be able to identify if the semantic meaning of augmented views are changed without the ground truth.
Therefore, in this work, we start by investigating the training behavior of contrastive learning models with the presence of bad positive pairs using simulated data. As shown in Figure 3, we find noisy positive pairs exhibit relatively small losses throughout the training process. In contrast, faulty positive pairs are often associated with large losses during training.
Inspired by these observations, we design dynamic bad pair mining (DBPM) algorithm. The proposed DBPM algorithm addresses the bad positive pair problem with a simple concept: identify and suppress. Specifically, DBPM aims for reliable bad positive pair mining and down-weighting in the contrastive training. To this end, DBPM first utilizes a memory module to track the training behavior of each pair along training process. The memory module allows to dynamically identify potential bad positive pairs at each epoch based on their historical training behaviors, which makes the identification more reliable. In addition, we design a transformation module to estimate suppressing
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weights for bad positive pairs. With this design, DBPM reliably reduces negative effects of bad positive pairs in the learning process, which in turn improves the quality of learned representations.
Overall, the contributions of this work can be summarized in three aspects. First, to the best of our knowledge, this is the first study to investigate the bad positive pair problem exists in time series contrastive learning. Our study contributes to deeper understanding of important issue that has not been thoroughly explored. Second, we propose DBPM, a simple yet effective algorithm designed as a lightweight plug-in that dynamically deals with potential bad positive pairs along the contrastive learning process, thereby improving the quality of learned time series representations. Third, extensive experiments over four woaldworld large-scale time series datasets demonstrate the efficacy of DBPM in enhancing the performance of existing ofute-of-th-aa art methods.
2
RELATED WORKS
2.1 SELF-SUPERVISED CONTRASTIVE LEARNING
Contrastive learning aims to maximize the agreement between different yet related views from the same instance (i.e., positive pairs), since they are assumed to share the meaningful underlying seman- ties (Chen et al., 2020; He et al., 2020a; Zbontar et al., 2021; Grill et al., 2020). By minimizing the InfoNCE loss (Oord et al., 2018), the contrastive model forces positive pairs to align in representation space. Therefore, the success of contrastive learning heavily relies on the view design, while training on inappropriate views can be detrimental to model performance (Wang & Qi, 2022a; Tian et al., 2020; Wen & Li, 2021).
few prior works in vision domain explored potential faulty positive pairs problem. RINCE (Chuang et al., 2022) alleviated this problem by designing a symmetrical InfoNCE loss function that is robust to faulty views. Weighted xID (Morgado et al., 2021) then down-weighted suspicious audio-visual pairs in audio-visual correspondence learning. Our DBPM differs from image-based solutions in following aspects. First, DBPM is designed for time series contrastive learning, in which not only faulty positive pairs arise, but also noisy positive pairs exist. The particular challenge of addressing two different types of bad positive pairs is unique to time series data and distinguishes them from image data. Adapting methods directly from image data may not effectively address the challenges posed by these pairs in the time series context. Our DBPM is designed based on the unique characteristics of these pairs within time series data, thus capable of handling both two types of bad pair simultaneously. Furthermore, DBPM identifies bad positive pairs based on their historical training behaviors in a dynamic manner, which allows more reliable identification of potential bad positive pairs.
2.2 TIME SERIES CONTRASTIVE LEARNING
Several recent studies have demonstrated that contrastive learning is prominent self-supervised approach for time series representation learning. For example, TSTCC (Eldele et al., 2021) proposed temporal and contextual contrasting that worked with a weak-strong augmentation strategy to learn discriminative time series representation. BTSF (Yang & Hong, 2022) presented bilinear temporal- spectral fusion module that utilized the cemporal-spectrer affinities to improve the expressiveness of the representations. CoST (Woo et al., 2022) applied contrastive learning to learn disentangled seasonal-trent representations for long sequence time series forecasting. TS2Vec (Yue et al., 2022) utilized hierarchical contrasting over augmented context views such that the learned contextual representation for each timestamp is robust. TF-C (Zhang et al., 2022b) leveraged fime-freyuency consistency mechanism in the pre-training to facilitate knowledge transfer between datasets.
2.3 LEARNING WITH LABEL ERROR
Based on the fact that contrasting views provide supervision information to each other (Wang et al., 2022), we relate the bad positive pair problem to the label error problem in supervised learning. Works in Swayamdipta et al. (2020); Shen & Sanghavi (2019) showed that data with label error exhibits different training behaviors compared to normal data. Inspired by these observations, we analyzed the training behavior (e.g., individual pair loss and its variance during training) of bad positive pair using simulated data in the context of time series contrastive learning, and further design DBPM to dynamically deal with bad positive pairs based observations.
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Time Series Contrastive Learning Framework
Dynamic Bad Pair Mining
G(D)
Raw Signal x
(i.e)
M
T
(1e) (i.e)
G(
r
Memory Module
Lg.1)
L(12)
L.222)
Me = (mar))
T ML,)
(i))
L(L3)
l(23)
k(3))
L(.e-1))
Lia-1
(ite) S Eup
t/p Mute
Noisy Positive Pairs
Faulty Positive Pairs
Figure 2: Graphical illustration of time series contrastive learning with DBPM. DBPM consists of memory module M and rransormation module T. records the training behaviors of cach positive pair along training procedure (i.e., m(se)), and generates a global statistic Mr for identifying potential bad positive pairs at cach epoch. These pairs are then down-weighted using ((.e)) estimated from T. DBPM is simple yet effective, and can be easily integrated into existing frameworks to improve their performance (as shown in upper orange box).
3 METHODS
In this section, we start by theoretically analyzing the drawbacks of current time series contrastive learning with the presence bad positive pairs. Then, we verify our hypothesis and study the training behaviors of bad positive pairs using specially crafted simulated dataset. We next introduce the DBPM algorithm, designed to alleviate the detrimental impacts of potential bad positive pairs in real-world datasets. An overview of the proposed DBPM algorithm is presented in Figure 2.
3.1 PROBLEM DEFINITION
We represent the original time series as x E RCCK where C' is the number channels and K the length of the time series. Given set of time series X, the goal of time series contrastive learning is to learn an encoder G(0) that projects each æ from the input space to its representation r E Rd where H is the dimension of the representation vector.
We use the well-accepted linear evaluation protocol (Chen et al., 2020; Eldele et al., 2021; Yue et al., 2022) to evaluate the quality of learned time series representations. Specifically, given the training dataset Xeaain = {aaaan Yuainn and the test dataset Nest = {Xeest Yest the encoder G(0) is first trained on training data (Xurain): ). G(0) parameters are then fixed and only used generate training representations Rirain = {G(X 10)}. Following this, linear classifier F F(Oic) is trained using [arinn Ymain }. Lastly, the quality of representations is evaluated with predefined metrics on the test dataset, i.e., Metric(F(C
Yeea).
3.2 ANALYSIS: TIME SERIES CONTRASTIVE LEARNING
Here we theoretically analyze how noisy positive pairs and faulty positive pairs could affect the representation learning process. For simplicity, learning framework (as shown the grey box Figure 2) for analysis.
simple InfoNCE-based time series contrastive
Preliminaries. Consider training time series E C'x K in training set Xuzain with N instance, the time series contrastive learning framework first applies a random data augmentation function r(-) to generate two different views from original data (u, 02) 7 T(2x) (i.c., positive pair). These two views are then projected to representation space by the time series encoder (r r"") (G(u,() ()) G(v, The time series encoder is learned to maximize the agreement between positive pair (u,, 0)) by
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minimizing the contrastive loss (i.e., InfoNCE):
exp(s(r), rr()))
((s))))) =-logg -log
(I)
exp(s(ri) //0 + exp(s(r)' r )/1))
where rr""T"")/ll |||r"] || is a score function that calculates the dot product between lg normalized representation r and r". (r.: r) denotes representations from different time series (i.e., negative pairs). is a temperature parameter.
Noisy Alignment. Let us consider the noisy positive pair problem. According to Wen & Li (2021), each input data can be represent in the form of x; 2, + f., where 2; D3 denotes the true signal that contains the desired features we want the encoder G(#)) to learn, and & ~ De is the spurious dense noise. We hypothesize that the noisy positive pair problem likely to occur on T; when & >> Zi. because noisy raw signals will produce noisy views after data augmentation. Formally, we define (u4,") v;) as a noisy positive pair when e >> 2 and ş > z!" Further, we know that minimizing the contrastive loss is equivalent to maximize the mutual information between the representations
two views (Tian et al., 2020). Therefore, when noisy positive pairs present, arg max, ( (u; (0); (()) is approximate to arg max, ( (G(E)))) 10); G(E))0))). This results in noisy alignment, where the model predominantly learning patterns from noise.
Faulty Alignment. Now, we consider the faulty positive pair problem. In view of the sensitivity of time series, it is possible that random data augmentations (e.g., permutation, cropping (Um et al., 2017)) alter impair the semantic information contained in the original time series, thus producing faulty views. Formally, we define (us, vt) as a faulty positive pair when T T(zz) ~ D Dunknown. where D Punknown * D.. Take partial derivatives of ((ur,s) w.I.t r, (full derivation in Appendix A.4), we have
ac 0r
1 r
N
exp(r /()
(2)
Σ exp(r? T (5)/t))
-=
2 reveals that the representation of augmented view u4 depends the representation of augmented view uú and vice versa. This is how alignment of positive pairs happens in contrastive learning: the two augmented views u, and U; provide supervision signal to each other. For example, when o; is faulty view (i.e., 2²" ~ Dz, z ~ Dunknown),, r provides a false supervision signal to G(O) to learn r. In such case, arg max, ((r";r r"") is approximate arg maxx
O); G(z))0))). where G()) extracts faulty or irrelevant information shared between uq and U; leading to a faulty aligmment. This analysis can also be applied situations where u, is a faulty view, or where both u, and v are faulty views. Moreover, we hypothesize that representations from faulty positive pairs often exhibit low similarity (i.e., s(r", rf') 4), as their temporal patterns are different. This means the encoder will place larger gradient on faulty positive pairs, which exacerbates the faulty alignment.
3.3 EMPIRICAL EVIDENCE
We build a simulated dataset to verify our hypoth- esis and observe training behaviors of bad positive pairs. In particular, we focus on the mean and vari- ance of training loss for bad positive pairs across training epochs. We pre-define three types of posi- tive pair in our simulated dataset: normal positive pair, noisy positive pair, and faulty positive pair. In order simulate noisy positive pairs, we as- sume that the noise level of signal depends on its Signal-to-Non
3.0
Type Normal
25
Faulty
Variance
Naiky
2.0
Ratio (SNR). By adjusting the SNR, we can generate time series with varying levels of noise, from clean (i.e., SNR>1) to ex- tremely noisy (i.e., Il.<1). To simulate faulty positive pairs, we randomly select a portion data and alter their temporal features to produce faulty views. See Appendix A.5 for detailed bad positive pairs simulation process.
0.0
3.5
5.0
Mean Training Loss
Figure 3: Observation: tive pairs (green cluster) exhibit relatively small con- trastive losses, whereas faulty positive pairs (orange cluster) tend to have large contrastive losses.
During training, noisy posi-
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Our main observation is illustrated in Figure 3. We find that noisy positive pairs exhibit a relatively small loss and variance throughout the training process (the green cluster). In Appendix A.6, we further demonstrate that representations learned from noisy positive pairs fall into small region in the latent space, which means the model collapses to a trivial solution. These evidence confirm our hypothesis regarding noisy alignment. It reveals that, unlike supervised learning, small contrastive loss does not always imply that the model learns an useful pattern, but rather it may simply extract information from noise. In contrast, faulty positive pairs are often associated with large contrastive loss and small variance during training (the orange cluster), which implies that the faulty positive pair difficult align. This supports our hypothesis regarding faulty alignment, where the model expends considerable effort trying to align the irrelevant patterns.
3.4 DYNAMIC BAD PAIR MINING
Based the theoretical analysis and empirical observations, propose Dynamic Bad Pair Mining (DBPM) algorithm to mitigate negative effects caused by bad positive pairs. The idea behind DBPM is simple: dynamically identify and suppress bad positive pairs to reduce their impact on the representation learning process.
Identification. For the purpose of identifying possible bad positive pairs in real-world datasets, we first employ memory module M to track individual training behavior at each training epoch. Specifically, M E IR Nx is look-up table, where N is the number of training samples and E is the number of maximum training epoch. For i-th positive pair (u, v4), (o.e) is updated with its contrastive loss (i.e) e-th training epoch, which is calculated by Eq. Then, we summarize the historical training behavior of i-th pair by taking the mean training loss of (u,, v,) before e-th epoch (e > 1):
Σ (3,d") e'=1
m(iee)
Therefore, at e-th training epoch, M will generate global statistic Me = (m,,,e) N describing historical training behaviors of all positive pairs. Once the Me is obtained, we use its mean and standard deviation as the descriptor for the global statistic at e-th epoch:
Σ (m(ae) Me)
m(,e)) Oe
N
N
In order to identify potential bad positive pairs, we must determine threshold that differentiates them from normal positive pairs. We define the threshold for noisy positive pair and faulty positive pair as:
tmp = pe= Smp tsp = pe + 3yyge.
(5)
At e-th training epoch, we identify noisy positive pairs with a mean historical contrastive loss (i.e) lower than fup. while pairs with mean historical contrastive loss m(i.)) larger than typ are identified as faulty positive pairs. Note that Sup and B5p are practice, simple heuristic, we set 8mp and Byp within the range [1,3] 3] and find it generally works well. See Appendix A.8 for further analysis on effects of 3ap and f5p- In this way, we are able to dynamically identify potential bad positive pairs at each training epoch according their historical training behavior, which in turn makes the identification more reliable. For example, a pair that has high contrastive losses throughout the training procedure is more likely be faulty positive pair than one that occasionally shows a high contrastive loss at just few training epochs.
that determine thresholds. In
Weight Estimation. Next, we design transformation module T to estimate suppression weights for bad positive pairs at each training epoch. We formulate the weight estimation from the transformation module T as:
[1. W(.e) (o))
1: =
(6)
if 1,
where 1; is indicator that is set to if i-th pair is bad positive pair, 0 otherwise. T maps the training loss of i-th positive pair at e-th epoch into a weight W(..) E (0, 1). Inspired by the mean training loss distribution from empirical evidence, we set T as Gaussian Probability Density Function. Therefore,

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when i-th pair is identified bad positive pair e-th epoch, its corresponding weight ((iee) is estimated by:
1 exp (-
(L(the))-e) 20?
T ((C()
Ve
By using this function, we assume the global statistic M, at each epoch follows a normal distribution with mean [r, and variance o². As such, the weight of a bad positive pair is the probability density of N ~ (Me; o²) that is approximately proportional to the pair loss. This ensures bad positive pairs receive a smooth weight reduction, thereby suppressing their effects. Additionally, the transformation module provides flexibility in the selection of weight estimation functions. See Appendix A.7 for the performance comparison of DBPM equipped with other weight estimation functions.
3.5 TRAINING
With DBPM, the contrastive model is optimized with a re-weighted loss. Formally, after initial warm-up epochs, the re-weighted loss for i-th positive pair at e-th training epoch is formulated as:
[(ie) ((.e):
if I1 =
(it.e) =
(8)
if I1; 1.
See Appendix A.1 for the algorithm of contrastive learning procedure with DBPM.
4 EXPERIMENTS
4.1 DATASETS, TASKS, AND BASELINES
Our model is evaluated on four real-world benchmark time series datasets: PTB-XL (Wagner et al., 2020) is to-date largest freely accessible clinical 12-lead waveforeoorm dataset. Based on ECG annotation method, there are three multi-label classification tasks: Diagnostic (44 classes), Form (19 classes), and Rhythm (12 classes). HAR (Anguita et al., 2013): multi-class classification for different activities. Sleep-EDF (Goldberger et al., 2000): multi-class classification for 5 sleep stages. Epilepsy (Andrzejak et al., 2001): binary classification identify epileptic seizure. We use AUROC as test metric for PTB-XL as in Strodthoff et al. (2020), Accuracy and AUPRC for HAR, Sleep-EDF, and Epilepsy as in Eldele et al. (2021). See Appendix A.2 for detailed descriptions of each dataset.
We examine the performance improvement by integrating DBPM into six state-of-the-an contrastive learning frameworks, including three
et al., 2020), MoCo (CC.cCCCPR22 et al., 2020b), and SimSiam (ICC & He, 2021b); and three methods tailored for time series: USCCIJUA1121), TF-C NeurIP))))) and B also compare DBPM with view problem in image contrastive learning. Note that RINCE is not applicable to SimSiam, which has no negative pairs. For each experiment, we run it five times with five different seeds, and report the mean and standard deviation of the test metrics. See Appendix A.3 for implementation details.
methods:
We which is robust InfoNCE loss to deal with the faulty
4.2 LINEAR EVALUATION
Table 1 and 2 demonstrate that the integration of DBPM consistently leads to superior test AUROC and lower performance fluctuation under different tasks and datasets, compared to both original state-of-the-art methods and their variants with RINCE. For instance, by integrating DBPM, the performance of BTSF in the diagnostic classification task significantly improves from 69.48 to 73.32, while the performance of TF-C in the rhythm classification task rises from 80.46 to 82.10. We further examine the per-class AUROC on PTB-XL dataset. Figure 4 shows the top 15 categories with the largest improvements by integrating DBPM into SimCLR. It is evident that DBPM not only considerably enhances AUROC for these categories, but also contributes to a more stable training than the original SimCLR. This is observed in the reduced performance variation across different runs for the most categories upon DBPM integration. The results suggest that the bad pair problem is more likely to occur in certain time series, and DBPM can effectively alleviate its adverse effects. Additionally, the minimal run-time and memory overheads indicates that DBPM is a lightweight plug-in, adding only negligible complexity to the model. See Appendix A. for complexity analysis.
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When comparing DBPM with RINCE, we observed that DBPM is more reliable and consistently out- performs RINCE across most experiments, providing larger performance enhancements to baselines. This is largely because: first, RINCE only addresses the problem of faulty positive pairs, whereas in the context of time series contrastive learning, noisy positive pairs can also undermine the models' performance; second, RINCE simply penalizes all positive pairs with large losses each training iteration, which could result in an over over-penalization. For example, some pairs generated by stronger augmentation while maintaining their original identity can indeed benefit contrastive learning (Tian et al., 2020; Wang & Qi, 2022b), though they may have relatively larger losses at certain training iterations. Penalizing such pairs could lead to sub-optimal performance. In contrast, DBPM takes both types of bad pairs into account and dynamically identifies them based historical training behaviors. Therefore, DBPM more reliable in mitigating negative impacts of bad pairs and thus consistently performs well across all datasets. See Appendix A.8 for ablation analysis on M and T.
SimCLR
100
Per AUROO AUROC
80
20
2AVB
PRCTS]
SaWY
SVTAC
ISCAH
IPLM!
BAVB
RVHl
ANEUR
LPPB
INVOLT
BGGU
LAGRAE
Lau
AELT
PTB-XL Categories
Figure 4: Per-class AUROC (%) on PTB-XL dataset. The integration of DBPM not only brings significant
performance improvements, but also contributes to more consistent model performance across different runs.
Table I: Test AUROC (%) of linear evaluation on PTB-XL dataset with three different tasks.
Task
Diagnostic Classification
Form Classification
Rhythm Classification
SimCLR
80.5012.16
17.16_1.88
80.18
RINCE
78.6443.65
77.97-1.22
80.82
DBPM
81.56=1.84
78.07
80,89 +3.85
run-time
(+0.70s/epoch)
(-0. (-0.122/eppock)
(+0:5tte/epoch)
MoCo
76.41
67.98_2.69
77.99
RINCE
72.85
68.49+1.82 +1.82
74.98
DBPM
77.32
68.28_1.16
80.31 10.47
extra run-time
(+0.40x/vpuch)
(-0.37x/<ponck)
(40. S0e/spoc))
SimSiam
63.95
63.77_0.48
68.5712.25
RINCE
NM
N61
DBPM
67.00
63.9041.31
69.1421.58
extra Fun-time
(40.924/epock)
(-0.64x/cpooh)
(+0.93s/<poch))
TSTCC
77.3420.52
69.75_o.40
84.58g0.22
+ RINCE
76.91 +0.22
69.35-0.68
84.49+0.33
DBPM
77.46=0.37
69.8149.42
84.70+0.17
extra run-time
(+0.27%/xpock)
(-0.31x/epocch)
(40-73</epoch)
TF-C
71.31
70.98
80.4612.0
RINCE
73.63
71.18
78.38
DBPM
74.04
72.03
82.10
extra ron-time
(40.94s/spock)
(+0.30x/cpoch)
(211/22//)poch)
BTSF
69.4812.52
70.61
67.7543
RINCE
69.37
70.02-2.28
68.22+3.41
DBPM
73.32=3.08
71.67+0.71
67. 77.900
extra run- non-time
(+1.34x/epmck)
(-0.26x/<pocc)
(4x0/lxx/)oock)
memory
+1.00M9
+0.37MB
+1.40MB
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Table 2: Test Accuracy (%) and AUPRC (% of linear evaluation three real-world time series datasets.
Dataset
HAR
Sleep-EDF
Epilepsy
Metric
Accuracy
AUPRC
Accuracy
AUPRC
Accuracy
AUPRC
SimCLR
20.20
95.00
77.25
73.26
97.15.0.16
38.97
+ RINCE
20.07
90.07
77.60
72.85
96.9920.19
98.91 98.9140.05
+ DBPM
90.42
95.16
77.59
43.55
97.27
98.97 =0.01
MoCo
85.48
90.82 1.60
69.
70
64.57 1.005
96.77.00.2
98. 0,
+ RRNCE
85.56
1..8
69.02
18.44
64.0011..6
96.6410.25
98.67 1:0.1
+ DBBPM
86.39 10.59
91.80 1.63
70.04 10.83
65.10 20.98
96.77 10.14
98.73
SimSiam
17.44
93.44
67.20
61.30
96.61
98.6010.23
RINCE + DBPM
47.78 11.31
93.72
67.50
61.65
96.71 20.23
98.65-0.14
TSTCC
87.51 40.90
92.63+1..
83.
$3.9940.aa
79.45.0.12
97.46+0.08
99.21 09.004
RINCE
88.7640.58
93.07 +1.71
84.03
79.47 +0.28
40.47
97.37
99.22
DBPM
88.11 20.85
93.22 1.18
84.17 2.026
79.68
97.46
99.25_0.om
TF-C
87.16
93.9240.61
77.71 #0.66
73.69
96.01
98.4331..1
RINCE
92.93 27.43
77.7110.78
74.22
96.50_0.34
98.43
+ DBPM
88.43 00.89
94.42 1.08
78.85
20.28
96.37
98.58_0010
BTSF
04.24
89.4 89.4441.00 1.00
72.75 g0.32
67 17.4004..4x
95.2 95.26.0.20
97. +0.00
RINCE
83.96
89.4 89.41+1.08
72. g0.20
t0.41
95.37
+0.00
+ DBPM
85.70 10.74
92.97 0.58
74.37 10.21
69.10 20.37
95.85 :0.14
98.15_0.10
extra memory
+0.58MB
+2.60MR
+0.72MB
4.3 ROBUSTNESS AGAINST BAD POSITIVE PAIRS
We conduct controlled experiments to assess the impact of bad positive pairs and DBPM's robust- ness to increasing numbers of such pairs. Besides using Sleep-EDF that already contains an un- known number of bad positive pairs, also a clean simulated dataset for better observation. See Appendix A.5 for the design of controlled ex- periments. Figure 5 illustrates that performance decreases in both datasets with an increase in bad positive pairs, indicating their negative impact on time series contrastive learning. Our DBPM shows stronger resistance to bad positive pairs in both datasets, consistently outperforming the baseline by non-trivial margin. The results demonstrate that DBPM effectively mitigates the negative impacts of bad positive pairs, thus enhancing the robustness of learned representations.
Sleep-EDF dataset
Simulated datasel
DEPM
70
DEPN
InfoNCE
05-
Moan Accurasy
50
Acaunity
25
56
35
5%
30%
35.
20%
10%
20%
Injected Bad Positive Pain
Injected Bad Positive Pairs
Figure 5: Robustness against bad positive pairs.
CONCLUSION
In this paper, we investigated the bad positive pair problem time series contrastive learning. We theoretically and empirically analyzed how noisy positive pairs and faulty positive pairs impair the quality of time series representation learned from contrastive learning. We further proposed a Dynamic Bad Pair Mining algorithm (DBPM) to address this problem and verified its effectiveness in four real-world datasets. In addition, we empirically demonstrated that DBPM can be easily integrated into state-of-the-e methods and consistently boost their performance. Moving forwards, there are two promising directions to improve DBPM. The first to develop an automatic thresholds selection strategy with the help of pocision-making methods (e.g., Reinforcement Learning). Further, also plan to apply DBPM to more time series applications such as forecasting and anomaly detection. We believe that our methods pose novel direction for developing better time series contrastive learning.

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ACKNOWLEDGMENTS
This research is also supported by A*SAR, CISCO Systems (USA) Pte. Ltd and National University of Singapore under its Cisco-NUS Accelerated Digital Economy Corporate Laboratory (Award 12100150002). This research is supported by the National Research Foundation Singapore under its AI Singapore Programme grant number AISG2-TC-2022-004.
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Towards Enhancing Time Series Contrastive Learning: A Dynamic Bad Pair Mining Approach Appendix
A.1DBPM Algorithm
14
A. A.2asst Descriptions
15
I.Implementttion and Technical Details
16
A.4Gradient Derivation of InfoNCE Loss
16
A.5Bad Positive Pair Simulation
16
A.6Representations of Noisy Positive Pairs
18
A.7DBPM with Other Weight Estimation Functions
19
A.8Ablation Analysis
19
A.9 Broader Impacts and Limitations
21
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A.1 DBPM ALGORITHM
Algorithm 1: Dynamic Bad Pair Mining
Input:Time series encoder G(O),
Training dataset Xrain with N instance, Memory module M.
Transformation module T,
Data augmentation function r(.).
8mp for noisy positive pairs identification, 3fp for faulty positive pairs identification, Temperature t for contrastive loss.
Output: Learnt G()).
while MaxEpoch do
e > WarmupEpoch then for i to N do (i.e) c- Ee= (a.o') end
11
12
13
14
Pe Mean(Me)
Oe StandardDeeviation lnp Pe Be
16
18
tsp = pe + Byyge
19
end
for i
to N do
21
ui ; + T(x;)
r - G(x;10)
22
23
r - G( 0)
((.,)) + InfoNCE(r" r),
24
25
Update M(re)) with ((.e)
26
if WarmupEpoch then if m((e) & Imp or maae) 2 fr then W(i.e) + ((C
27
((.)) (i,e)
end
end
32
0 + Optimizer(4((e))
33
end
34 end
Algorithmic Complexity Analysis. We conducted a detailed analysis on algorithmic complexity. Suppose we have N instance that generate N positive pairs:
The parts of the algorithm that cause extra runtime:
1. Calculation of the mean and standard deviation: For each positive pair, the mean mi.e) is updated based on the previous means, which is an O(1) operation per instance since it is based on pre- computed values. The overall mean u, across all positive pairs at each epoch requires summing up N mean values and dividing by N, which is O(N) operation. Once the overall mean u, is calculated, the a. requires a pass over the N mean values to calculate the sum of the squared difference from the Me, which is an O(N) operation. Then the calculation of actual oe involves dividing by N and taking the square root, both are (11) operations. Therefore, calculating the mean and standard deviation will result in runtime complexity of O(N).
2. Conditions check: Each comparison is an O(1) operation, so for all N instance, the condition check is O(N) per epoch.
3. Calculation of weights: Calculating the weights for each pair is a constant constant-time operation O(1). Therefore, for all N instance, the calculation of weights is O(N).
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In summary, the runtime complexity of DBPM is O(N).
The parts of the algorithm that cause extra memory:
In our algorithm, memory module M serves look-up table for storing the training loss for each instance along the training epochs, therefore original M is the size x E. Here we show the M can be optimized size N x 1 in practical implementation:
For positive pair at e-th epoch, its training behavior is calculated by averaging the training losses before e-th epoch:
1
(i.e))
Σ c'=l
(9)
The above equation can be rewritten as:
((te)) [[ [-11_-1 Σ (o,2)) (e- +((e)) E
e-2
1
(10)
E 2
((,e)) = [mfsee1) (e- + ((i.e))
(11)
e-1
This means that, for calculating the mean training loss of positive pair at e-th epoch, we only need to store the mean training loss of sample i at (e 1) epoch. Therefore, the memory size can be reduced to size N x 1 in the practical implementation. Assuming a 16-bit foating-point number for each loss, the total extra memory required is 2N bytes.
A.2 DATASET DESCRIPTIONS
PTB-XL (Wagner et al., 2020) is currently the largest publicly available clinical 12-lead ECG dataset, consisting of 21,837 records from 18,885 patients. Annotations of each ECG are assigned based on its statements, which are categorized into three non-mutually exclusive groups: Diagnostic (clinical diagnostic statements), Form (associated with significant changes in specific ECG segments), and Rhythm (involving particular changes in rhythm). Altogether, there are 71 distinct statements, comprised of 44 diagnostic, 12 rhythm, and 19 form statements, with 4 of these also serving as diagnostic ECG statements. Based on the ECG annotation method, there are three multi-label classification tasks: Diagnostic Classification (44 classes), Form Classification (19 classes), and Rhythm Classification (12 classes). We follow the data prepceseesing steps from Strodthoff et al. (2020) for this dataset. Table provides summarization of PTB-XL dataset.
HAR. In the UCI Human Activity Recognition dataset (Anguita et al., 2013), data is collected from wearable sensors installed on 30 subjects participating different activities, where each recording contains 9 time series with length of 128. Epilepsy. The Epileptic Seizure Recognition dataset (Andrzejak al., 2001) consists of brain activity recordings from 500 subjects, where each recording contains single time series with length of 178. Sleep-EDF (Goldberger al., 2000) contains whole- night Polysomnography (PSG) sleep recordings categorized into 5 sleep stages. Each recording contains single time series with length of 3,000. We follow the data pre- pre-processing steps from Eldele et al. (2021) for these three datasets. Table provides a summarization of HAR, Epilepsy, and Sleep-EDF.
Table Summarization of PTB-XL.
Task
Train
Val
Test
Channels
Categories
Diagnostic Classification
13,715
3,429
4,286
12
44
Form Classification
5,752
1,438
1,798
12
19
Rhythm Classification
13,481
3,371
4.214
12
12
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Table 4: Summarization of HAR, Epilepsy, and Sleep-EDF.
Dataset
Train
Val
Test
Channels
Categories
HAR
5,881
1,471
2.947
6
Epilepsy 7,360
1,840
2,300
2
Sleep-EDF
25,612
7,786
8,910
5
A.3 IMPLEMENTATION AND TECHNICAL DETAILS
Data Augmentations. We refer to Um al. (2017) and design the data augmentation function T(-) to include five data augmentation methods. Specifically, Jittering adds additive Gaussian noise the imput time series. Scaling alters the magnitude of time series by multiplying its data by random factor. Permulation randomly changes the temporal position of time windows, where the input time series is first divided into segments, and then positions of these segments are randomly permuted. JitterPernutaion is combination of jittering and permutation, in which the jittering is applied to a permuted time series. ScalePermuttiion is a combination of scaling and permutation, where the scaling is applied to permuted time series. We refer Eldele al. (2021) for setting the hyper-parameters of abovementioned data augmentations.
Training. As DBPM is general algorithm designed to function plug-in for enhancing the performance of existing methods, we mainly refer to our baselines' implementations when setting up pre-training. We use single full-connected layer the linear classifier F(0ic), and train it for 40 epochs for the linear evaluation task for all datasets. The Adam optimizer (Kingma Ba, 2015) with fixed learning rate of 0.001 is used optimize the linear classifier for all datasets. The temperature t is set to 0.2 for the contrastive loss defined in Eq. Experiments are conducted using Py PyToch 1.11.0 (Paszke et al., 2019) on NVIDIA A100 GPU.
A.4 GRADIENT DERIVATION OF INFONCE Loss
With r and ry denote the lg normalized representations from i-th positive pair, express its InfoNCE loss as
cxp(r:TT Tr(
C log
(12)
exp(r T /t/
exp(r? rij
To simplify the notation (Zhang et al., 2022a), let us denote exp(r." TT "ō" -///t) exp(r (xp/r(TT://)) Therefore, Eq. 12 can be expressed as:
log exp(r? /tt))
(13)
Σ exp(r? TT ry /t)
1=0
Then, the negative gradient of L on r is calculated by Eq. 14:
0L
exp(r." TT 11/1) r(//1)
N
exp(r. r3 /t)
t
Σ exp(r. T -1)
Σn exp(r:" 1/)
(14)
N
exp(r.:T TT r5 /t) En exp(r.' r5 /t)
r
1=0
A.5 BAD POSITIVE PAIR SIMULATION
Time Series Generation. We generate time series data with three different temporal patterns, and assume that the ground truth of each time series only depends on its temporal pattern. Specifically,
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use Sine waveform, Square waveform, and Sawtooth waveform basic temporal patterns, and each time series is assigned with one type of basic temporal pattern only. We set the length of each time series to 500, in which two segments each of length 100 randomly selected and padded with the temporal pattern, while other locations are padded with zeros. The two segments that contain the temporal pattern scaled with random factors, such that each generated time series is different. Figure provides examples of the simulated time series.
||
W
M
0-
0.0
00.
-1
-1
-10-
-15
100
300
400
500
100
200
300
500
0
100
300
400
500
Sine waveform
Square waveform
Sawtooth waveform
Label:
Label: 2
Label:
Figure 6: Examples of simulated time series with different temporal patterns.
Noisy Positive Pair Simulation. Noisy positive pairs may arise when the original signal contains substantial noise, where it results in noisy contrasting views. To simulate noisy positive pairs, we assume that the noise level of time series depends on its Signal-to-Noise Ratio (SNR). By adjusting SNR, we can generate time series with varying levels of noise. In our simulated dataset, signals with SNR>1 are defined as clean signals, while signals with SNR<1 are defined as noisy signals. Specifically, we generate time series data with different SNRs (i.e., 50, 40, 30, 20, 10, -30), and analyze the training behavior of time series with SNR of -30 that produce noisy views. Figure 7 provides examples of simulated time series with different SNR.
Faulty Positive Pair Simulation. We simulate faulty positive pair by randomly altering the temporal pattern of the contrasting view. Specifically, we keep the temporal pattern of one view unchanged from the original signal, while randomly altering the temporal pattern of the other view a different one. For example, we artificially create a faulty view for time series with Sine waveform by changing its temporal pattern Square waveform. Figure 8 provides example of simulated faulty positive pair.
Simulated Dataset.
Our simulated dataset contains 3,600 training samples and 1,800 test samples. In the training set, there are a total of 600 simulated noisy positive pairs and 600 simulated faulty positive pairs. Table provides summarization of our simulated dataset used for observation. Codes and the simulated dataset will be made publicly available.
Table 5: Statistics of the simulated dataset used for observation.
Temporal Pattern
Train
Noniyy (Train)
Nauity (Train)
Test
Sine Waveform
1,200
600
Square Waveform
1,200
600
Sawtooth Waveform
1,200
600
Total
3,600
600
600
1,800
Controlled Experiments. In our controlled experiments to evaluate DBPM robustness against bad positive pairs Figure 5, we control the number of bad positive pairs by randomly sampling a fraction of positive pairs and manually convert them into bad positive pairs. Specifically, we create the noisy positive pair by adding strong Gaussian noise to the signal, such that the noise overwhelms the true signal. The faulty positive pair is generated by applying over-augmentation (e.g., strong random scaling) to the signal, which impairs its temporal pattern. We increase the number of bad positive pairs and see how performance changes.
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SNR=50
SNR=40
SNR=30
W
-2
100
300
400
500
200
300
400
500
100
200
300
100
500
SNR=20
SNR=10
SNR=-30
20
0-
-1
-10
-60
600
200
300
300
600
500
Figure 7: Examples of simulated time series with different SNR.
Normal Positive Pair
Faulty Positive Pair
00
Figure 8: Example of simulated faulty positive pair.
A.6 REPRESENTATIONS OF NOISY POSITIVE PAIRS
We support our hypothesis regarding noisy alignment Section 3.3 (in main text) by visualizing the representations learned from noisy positive pairs in our simulated dataset. The t-SNE visualization (Van der Maaten & Hinton, 2008) is shown in Figure 9. We can observe that the representations learned from noisy positive pairs close each other and fall into a small region in the latent space (orange cluster). This indicates the contrastive model collapses to trivial solution on these pairs (i.c., simply learns patterns from noise instead extracting discriminative information).
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Pair Type
Not Noisy
Noisy
Figure 9: L-SNE visualization of representations learned from noisy positive pairs (orange dots) in simulated datasct.
A.7 DBPM WITH OTHER WEIGHT ESTIMATION FUNCTIONS
Here we show that our DBPM provides flexibility in selecting weight estimation functions. We test DBPM with two different weight estimation functions: Constant. We use constant weight for all identified bad positive pairs; GMM. We use the Gaussian Mixture Model (GMM) to estimate the weight for identified bad positive pairs. Specifically, when i-th pair is identified as bad positive pair at e-th epoch, its corresponding weight ((..)) estimated from GMM is:
(C(i.e) -(p.e))
W(iee) Σ ((p.e) p=1 (p.e) V 2m
exp
(15)
20 (p.e)
where P is the number of mixture components, >(p.e) is the weight for p-th mixture component, M(p.e) and (p.e) are mean and standard deviation for p-th mixture component, respectively. It is worth noting that when P the weight estimation function is the same as defined in main text Eq. 7 (i.e., Gaussian Probability Density Function). Test results of DBPM using different weight estimation functions are shown in Table 6. Baseline refers to the simplest InfoNCE-based contrastive learning framework as described in Section 3.2.
From the results we can see that both Constant and GMM can improve the performance, which demonstrates the effectiveness of DBPM in identifying potential bad positive pairs. Meanwhile, GMM shows more stable performance improvements across datasets. For example, accuracy of Constant is lower than the InfoNCE baseline when 0.50 in Sleep-EDF. We also find the performance of GMM is not sensitive to P. and the Gaussian Probability Density Function (i.e., GMM(P 1)) provides better weight estimation than GMM(P 1) in most cases. Therefore, for simplicity and computational efficiency, we equip DBPM with Gaussian Probability Density Function in this work.
A.8 ABLATION ANALYSIS
Effects of Thresholds. We conduct experiments to study the effects of Bmp and Byp in Eq. 5 that determine the thresholds for identifying bad positive pairs. Here we use the simplest InfoNCE-baal baseed contrastive learning framework as described in Section 3.2. Table 7, 8 and Table 9 show the results of DBPM with different 8ap and 3,, on HAR, Sleep-EDF. and Epilepsy, respectively. As we can from the results, DBPM is not excessively sensitive 3ap and Bip- We find that there is risk
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Table 6: Test results of DBPM with different weight estimation functions.
Datasct
HAR
Sleep-EDF
Epilepsy
Metric
Accuracy
AUPRC
Accuracy
AUPRC
Accuracy
AUPRC
Baseline
82.95:11.93
86.1842.44
82.82:10.74
78.30=0.224
97.03110.09
98.85:10.04
Constant
0.00
83,34+:1.85
86.32++..85
02.8
78.36=0.21
97.03=+0.08
98.82:00005
w 0.25
83,31
86.41+2.08
82. 02.8
78 78.36=00.2
97.07:10.10
98.82=0.055
w 0.50
83.12++1.88
86.30++2.18
82.80
78.34
97.06-+0.06
98.84+00.44
GMM
=
83.29.11.79
86.35.11.89
82.90.10.72
78.36.10.20
97.04.10.09
98.87110.04
P P=3 2
83.26.11.79
86.37111.2
82.87
78.37
97.0710.008
98.82.10.07
P p= 83.27+1.77
8..33+1.88
82.87=0.69
78.37=0.21
97.03+00.09
98.81=0.07
P 83.27
86.34
82.65
78.35=0.22
97.08
98.76=0018
of unsatisfactory results if fp is too small, For example, when 3pp 1, the accuracy of DBPM is lower than the InfoNCE baseline (82.95 for [w/o tup. w/o fpl)). The reason that small Bjp means more positive pairs are identified as faulty positive pairs, which could potentially penalize normal positive pairs that are helpful to model's performance. Meanwhile, we find that smaller 8ap works better in the HAR dataset, which may due to there are more noisy data in the dataset. In practice, we set 8op and Brp within the range [1, 3] and find it works well for most datasets.
Table 7: Mean accuracy (%) of DBPM with different 9mp and Brr on HAR dataset.
Thresholds
Bap
Bup
Bup
w/o Exp
3rp
82.10
81.86
81.55
31p
83.22
83.06
82.93
82.92
31p = 3
83.29
83.05
82.95
82.95
w/o typ
83.28
83.02
82.97
82.95
Table 8: Mean accuracy of DBPM with different 3up and Byp on Sleep-EDF dataset.
Thresholds
Snp
Bap 2
8mp 3
w/o fxp
35p = 82.41
82.64
82,68
82.71
3rr 2
82.58
82.89
82.87
82.79
3rp
82.56
82.87
82.90
82.83
w/o typ
82.56
82.87
82.90
82.82
Table Mean accuracy DBPM with different Bap and 3,p on Epilepsy dataset.
Thresholds
9mp 1
Buy
Bup
w/o tup
3fp
97.02
97.03
97.06
97.07
3fp
97.01
97.09
97.06
97.05
35p =
97.01
97.04
97.04
97.04
w/o 1pp
97.01
97.04
97.04
97.03
Effects of M and T. We conducted an ablation study on PTB-XL dataset to analyze the individual effects of memory module and transformation module on the overall model performance, In w/o M. directly identify bad positive pairs each epoch without using the historical information. In w/o T, we remove the transformation module and set the weight of identified bad pairs to zero. The results are shown in Table 10.
We can observe from the results that both the memory module M and transformation module are important for ensuring consistent improvements of model performance. M plays crucial role in
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Published as a conference paper at ICLR 2024
Table 10: Individual effects of M and T..
Rhythm Classification
Form Classification
Diagnostic Classification
SimCLR +DBPM (w/o M)
80.18 5.22
77.16 = 1.58
80.50 + 2.16
79.94 + 3.75
77.62 + 1.83
81.54 + 1.82
+DBPM (w/o T)
80.54 3.69
77.72 = 1.08
81.21 + 2.05
+DBPM
80.89 + 3.85
78.07 + 1.01
81.56 + 1.84
reliably identifying potential bad positive pairs. For instance, we do not use historical information in the Rhythm classification task. performance can be adversely affected. While T ensures smooth weight reduction which contributes more stable training process. This can be seen from the suboptimal model performance when removing T.
A.9 BROADER IMPACTS AND LIMITATIONS
The bad positive pair problem in self-supervised time series contrastive learning that we explored in this work presents unique challenges and opportunities for the growing body of research on this topic. We envision that this work will inspire the community and promote more studies designing self-supervised contrastive learning methods that better suited for time series data.
Our proposed DBPM serves as lightweight plug-in without learnable parameters enhance existing state-of-the thet---rt methods, ensuring only a minimal increase in computational overhead. Additionally, the data used for study are publicly available, further encouraging transparency and accessibility in this area of research. We have carefully considered the ethical and social aspects of our work and do not foresee any clear negative impacts stemming from it.
worth noting that, although most time series contrastive learning methods are based on data augmentation, there An example is Te2Vec, which treats the representations at the same timestamp in two augmented contexts as positive pairs. This approach defining positive pairs in TS2Vec is quite different from that in augmentation- based time series contrastive learning. To provide clearer analysis of the bad positive pair problem, we focused on augmentation- based time series contrastive learning in this work. We plan to investigate non-augmentation methods further and explore how we can extend our proposed methods to broader problem setups in future works.
few methods that generate positive pairs by utilizing temporal information.
On the other hand, it is important to note that the techniques investigated in this study are still at very early stages. Therefore, the proposed approach should not yet be utilized to make critical clinical decisions. For instance, although our method demonstrates performance improvement in ECG data, it should only be used as an assistant tool rather than a standalone solution for crucial clinical decisions.
21


Reviews:
[{"review_id": "EzCGb7c13o", "reviewer": "Reviewer_gEVT", "summary": "This paper explores the challenges faced by contrastive learning in the context of time series data due to the presence of noisy and faulty positive pairs. It introduces a novel Dynamic Bad Pair Mining (DBPM) algorithm that dynamically identifies and mitigates the influence of these bad positive pairs, aiming to enhance the performance of existing contrastive learning methods. The paper demonstrates the effectiveness of DBPM through extensive experiments on a suite of real-world time series datasets.", "questions": "What are other potential applications (e.g. forecasting) where DBPM could be beneficial? Would be good to see evaluation beyond just classification.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. **Novel Problem Identification:** The paper introduces a previously unrecognized issue in time series contrastive learning—the challenge of 'bad' positive pairs. The authors convincingly illustrate two variants of such pairs: noisy and faulty, which arise due to augmentation on certain data inputs. The paper provides a persuasive and logical explanation for the emergence of these pairs, marking a significant observation for the time series contrastive learning community.\n\n2. **Empirical Observations:** Through empirical research on a simulated dataset, the authors observed that noisy positive pairs exhibit very low training loss, whereas faulty positive pairs show high training loss. Remarkably, both types display consistently low loss variances. Hence, on a plane plotting mean against variance of training loss, these two classes stand out as outliers from the bulk of good positive pairs. This finding is not only intriguing and insightful but also interpretable and plausible.\n\n3. **Algorithm Development:** Building upon these observations, the authors suggest utilizing the statistics (mean and variance) of training losses of positive pairs to flag the bad ones. This process includes a memory module that records the loss of all positive pairs over several epochs, followed by an algorithm that then downweights the bad pairs identified through this mechanism.\n\n4. **Presentation Clarity:** The paper is well-structured and articulate in detailing the problem, the proposed resolution, and the experimental framework. The inclusion of illustrative figures and tables effectively contributes to the reader's comprehension of the concepts and validates the significance of the proposed approach.", "weaknesses": "1. **Ablation Study Limitations:** The presented ablation studies are notably limited, which constrains the understanding of each component's unique effects on the overall system performance. Particularly, the roles of the memory module and the transformation module have not been analyzed independently. Distinct investigations into how each module contributes to the suppression of bad pairs, the efficiency of the learning process, and the final model accuracy would greatly enhance the transparency of the results. \n\n2. **Algorithmic Complexity:** The discussion on the algorithm’s additional computational complexity is mentioned but lacks depth. A detailed exploration of the computational costs, including an assessment of trade-offs, would be instructive. Further analysis on the scaling behavior, particularly concerning large datasets and the associated runtime and memory implications in comparison to baseline methods, would greatly benefit the paper.\n\n3. **Parameter Sensitivity Analysis:** The method for selecting the hyperparameters critical for identifying bad positive pairs (specifically, the two $\\beta$ parameters) seems to be heuristic-based. A thorough sensitivity analysis of these hyperparameters, with an emphasis on how they influence model performance, could substantiate the robustness of the paper. Although the preset heuristics for setting thresholds perform adequately, an adaptive strategy for threshold selection could potentially be more effective than manual tuning of the β values.", "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": "", "extra_scores": {}}, {"review_id": "L0Pi34ZZbo", "reviewer": "Reviewer_iore", "summary": "This paper delves into the challenges of time series contrastive learning, specifically focusing on two types of detrimental positive pairs that can degrade the quality of time series representations. Initially, the authors articulate the characteristics of these pairs and elucidate how their presence can adversely impact the contrastive learning process. To address this issue, the paper introduces the DBPM algorithm, designed to detect and mitigate these harmful pairs. DBPM employs a memory module to monitor the training behavior of each pair throughout the learning process, enabling the identification of potential negative pairs. Once identified, these pairs are assigned a lower weight in the loss function to diminish their influence. The efficacy of this approach is substantiated through empirical testing on multiple datasets, demonstrating its effectiveness in enhancing time series contrastive learning.", "questions": "Please see the strengths and weaknesses sections.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. This paper examines a largely underexplored yet practically significant problem with wide-ranging applications. It addresses the issues of noisy and faulty positive pairs, which are common in real-world scenarios and can adversely affect the efficacy of contrastive learning processes.\n\n2. The structure and presentation of this paper are commendably clear and accessible. The method proposed is articulated well, and the empirical evaluation provided is thorough and comprehensive.", "weaknesses": "1. The paper zeroes in on contrastive learning techniques specific to time series data. A key issue it tackles is the identification of noisy and faulty positive pairs. However, the authors could further clarify why these types of pairs pose a unique challenge within the context of time series, distinguishing them from other data types.\n\n2. There is a potential need for the authors to address the assumptions underlying their model, particularly the noisy alignment assumption that $\\xi_i \\gg z_i$. This assumption might be overly stringent for real-world scenarios where noise typically represents a smaller fraction of the overall signal.\n\n3. The methodology presented, while clear and direct, does not seem to offer substantial technical innovation. It primarily revolves around monitoring historical training statistics and down-weighting samples with elevated contrastive losses. Additionally, the empirical results, though solid, do not demonstrate a marked improvement over existing baselines.", "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": "", "extra_scores": {}}, {"review_id": "umk3ZBspWP", "reviewer": "Reviewer_Cugc", "summary": "This paper investigates issues in time series contrastive learning caused by \"bad\" positive pairs violating the assumption of shared semantic information between views. It identifies two types of bad pairs: noisy positive pairs mainly sharing noise patterns when original signal is noisy, and faulty positive pairs where data augmentation alters important temporal patterns, resulting in views no longer sharing meaning. Through analysis and observing a simulated dataset, the paper shows these bad pairs degrade representations via noisy alignment or faulty alignment during training. To address this, the authors propose a Dynamic Bad Pair Mining (DBPM) algorithm that tracks training loss of each pair over time to identify potential bad pairs based on statistics of historical losses. DBPM estimates weights to suppress identified bad pairs, mitigating their detrimental impacts. Experiments show integrating DBPM into various contrastive learning frameworks consistently improves linear evaluation performance on time series benchmarks. Controlled tests also demonstrate DBPM provides greater robustness against injected bad pairs versus baseline contrastive learning. Overall, this paper provides first investigation of the bad pair problem in time series contrastive learning and proposes the DBPM solution to reliably identify and suppress bad pairs as a simple plug-in enhancing existing methods.", "questions": "1. Did the authors conduct ablation experiments to distinguish the individual impacts of noisy versus faulty positive pairs on the model's performance? It would be insightful to determine if specific datasets are predominantly influenced by one over the other. Is it possible to isolate certain features and then forecast based on them?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Identifies and provides the first study of an important issue in time series contrastive learning - the problem of bad positive pairs - that has not been thoroughly explored before. Provides both theoretical analysis and empirical observations on simulated data to demonstrate the detrimental effects of noisy and faulty positive pairs on representation learning.\n\n- Proposes a simple solution (DBPM) that is model-agnostic and can work as a plug-in to boost various existing contrastive learning methods for time series.\n\n- Evaluation on multiple real-world time series benchmarks demonstrates clear and consistent improvements from integrating DBPM across different datasets and models. Additional experiments validate DBPM's ability to confer greater robustness against injected bad pairs compared to baseline contrastive learning.\n\n- Thorough ablation studies analyze the effects of different design choices and hyperparameters\n\n- The code and simulated dataset will be made publicly available to facilitate future research", "weaknesses": "1. The identification of bad pairs is based on heuristically set thresholds. Could more principled statistical methods could be explored to automatically determine optimal thresholds?\n2. All evaluations were studied with the InfoNCE loss, does this approach generally work for other losses, for e.g., the supervised contrastive (SupCon) loss Khosla et. al, NeurIPS 2020.", "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": "", "extra_scores": {}}, {"review_id": "YXzOQQGKW9", "reviewer": "Reviewer_DxUx", "summary": "This paper investigates an important but unexplored problem in contrastive learning for time series applications: the challenge of bad positive pairs. The study reveals two distinct types of time series pairs that violate the positive pair assumption, leading to suboptimal representations learned from contrastive learning. To address this special challenge, the paper introduces a simple yet effective algorithm: dynamic bad pair mining (DBPM). The key idea of DBPM is to track the training loss of individual time series pair, and use historical information to identify and suppress bad positive pairs. DBPM has the advantage of being a lightweight plug-in that does not require trainable parameters to enhance existing methods. Extensive evaluations validate DBPM's effectiveness in addressing the challenge, and its integration consistently boosts the performance of SOTA methods.", "questions": "Apart from positive pairs, did the authors consider negative pairs? Would it be possible to extend the proposed methods to account for false negatives (e.g. similar time series but treated as negative samples)?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "Significance: As far as I know, this study is the first attempt to examine the bad positive pair problem, which is clearly important yet has not been thoroughly examined. The main findings regarding noisy/faulty alignment will certainly provide valuable insights to future researchers working on contrastive learning for time series applications. The proposed DBPM is a simple plug-in that is easy to implement in existing methods, thus holding potential for broad application impact.\n\nNovelty: The study and proposed methods are novel. First, it's smart to connect the unexplored issue of bad positive pairs in self-supervised learning with the more familiar problem of label errors in supervised learning. Second, the design of DBPM aligns well with empirical observations, and its dynamic identification techniques make the algorithm more reliable. It is also a plus that the method does not have any trainable parameters, and introduces minimal memory overheads to the model.\n\nQuality: The submission is of high quality. The authors present a detailed theoretical analysis of noisy/faulty alignment, supported by empirical evidence using synthetic data. The evaluation is quite comprehensive, encompassing four large time series datasets and various tasks, compared with popular baselines. Experimental results are impressive and validate the proposed method’s effectiveness.  \n\nClarity: The paper is well organized and clearly written. The motivation is clearly illustrated and is convincing. The problem and evaluation are clearly defined. The tables and figures are well made and informative. The appendix is well-structured and contains sufficient information. Overall, the paper is very exhaustive, but is still quite clear and easy to follow.\n\nReproducibility: The submission included an anonymized github link to the source code. Therefore, I believe this submission contains sufficient information that helps in reproducibility.", "weaknesses": "1. The identification may not be accurate during the early stages of training when the model hasn't been well trained. It is possible that these errors propagate through the training process and accumulate. \n\n2. Since hard samples that are beneficial may also experience large losses, they could potentially be misidentified as faulty pairs. Could the authors explain how to avoid this problem? \n\n3. In Eq3, it is unclear why the mean loss is calculated using e-1 epochs instead of e epochs (the current epoch). Could the authors explain the rationale behind this design?", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)