Explaining Time Series via Contrastive and Locally Sparse Perturbations
Authors: Zichuan Liu
Yingying ZHANG
Tianchun Wang
Zefan Wang
Dongsheng Luo
Mengnan Du
Min Wu
Yi Wang
Chunlin Chen
Lunting Fan
Qingsong Wen
Venue: ICLR 2024 poster (2024)
Keywords: time series
explainability
perturbation
Primary area: visualization or interpretation of learned representations
TL;DR: A novel perturbation-based method for time series explanation

Abstract: Explaining multivariate time series is a compound challenge, as it requires identifying important locations in the time series and matching complex temporal patterns.
Although previous saliency-based methods addressed the challenges,
their perturbation may not alleviate the distribution shift issue, which is inevitable especially in heterogeneous samples.
We present ContraLSP, a locally sparse model that introduces counterfactual samples to build uninformative perturbations but keeps distribution using contrastive learning.
Furthermore, we incorporate sample-specific sparse gates to generate more binary-skewed and smooth masks, which easily integrate temporal trends and select the salient features parsimoniously.
Empirical studies on both synthetic and real-world datasets show that ContraLSP outperforms state-of-the-art models, demonstrating a substantial improvement in explanation quality for time series data.
The source code is available at \url{https://github.com/zichuan-liu/ContraLSP}.

Published as a conference paper at ICLR 2024
EXPLAINING TIME SERIES VIA CONTRASTIVE AND LOCALLY SPARSE PERTURBATIONS
Zichuan Liu 1.2 Yingying Zh Tianchun , Zefan Wang Dongsheng Luo Mengnan Du Min Wu", Yi Wang", Chunlin Chen't Lunting Fan and Qingsong Wen 1 NNanjing University, "Ailibaba Group, 'Pennsylvania State University. "Tsinghua University, Florida International University,
New Jersey Institute of Technology, 7 **STAR, *The University of Hong Kong
ABSTRACT
Explaining multivariate time series is a compound challenge, as it requires iden- tifying important locations in the time series and matching complex temporal patterns. Although previous saliency-basee methods addressed the challenges, their perturbation may not alleviate the distribution shift issue, which is inevitable especially in heterogeneous samples. We present ContraLSSP, locally sparse model that introduces counterfactual samples to build uninformative perturba- tions but keeps distribution using contrastive learning. Furthermore, we incor- porate sample-specific sparse gates to generate more binary-skewed and smooth masks, which easily integrate temporal trends and select the salient features par- simoniously. Empirical studies on both synthetic and real-world datasets show that Contral .SP outperforms state-of-the-art models, demonstrating substantial improvement in explanation quality for time series data. The source code is avail- able at htttts:////l thub. com/ z chuan- 1 ral.
INTRODUCTION
Providing reliable explanations for predictions made by machine learning models is paramount importance, particularly in fields like finance (Mokhtari et al., (219)), games (Liu et al. (023). and healthcare (Amann et al., 2020). where transparency and interpretability are often ethical and legal prerequisites. T'hese domains frequently deal with complex multivariate time series data, yet the investigation into methods for explaining time series models remains an underexplored frontier (Ro-) jat et al. 2021). Besides, adapting explainers originally designed for different data types presents challenges, as their inductive biases may struggle to accommodate the inherently complex and less interpretable nature of time series data (Ismail et al. 2020). Achieving this requires the identification of crucial temporal positions and aligning them with explainable patterns.
In response, the predominant explanations involve the use of saliency methods (Bachrens et al., 2010 Tjoa & Guan 2020), where the explanatory distinctions depend on how they interact with an arbitrary model. Some works establish saliency maps, e.g., incorporating gradient (Sundararajan et al. 2017] Lundberg et al.) 2018) or constructing attention (Garnot et al.) 2020 Lin et al.) 2020). to better handle time series characteristics. Other surrogate methods, including Shapley (Castro) al. 2009: Lundberg & Lee 2017) or LIME (Ribeiro et al. 20166), provide insight into the predic- tions of a model by locally approximating them through weighted linear regression. These methods mainly provide instance-level saliency maps, but the feature inter-correlation often leads to notable generalization errors (Yang et al.) 2022).
The most popular class of explanation methods is use samples for perturbation (Fong et al., 2019 Leung et al.) 2023] Lee et al. 2022), usually through different styles to make non-salient features uninformative. Two representative perturbation methods in time
series are Dynamask (Crabbé & Van Der Schaar 2021) and Extrmask (Enguehard 2023
Authors contributed equally.
Correspondence qi ggsongedu@@gaa comm and c1 clcchn@nju.edu edu.ccn..

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Published as a conference paper at ICLR 2024
Dynamask utilizes meaningful perturbations to incorporate temporal smoothing. while Extr- mask generates perturbations of less sense close to zero through neural network learning. How- ever, due shifts in shape (Zhao et al., 2022). perturbed time series may be out of distribution for the explained model, leading faithfulness in the generated explanations. For example, time series classified as 1 and its dif- ferent forms of perturbation are shown in Fig- ure I We see that the distribution of all classes moves away from O at intermediate time, while the O and mean perturbations shift in shape. In addition, the blur and learned perturbations are close to the original feature and therefore contain information for classification 1. It may result in a label leaking problem (Jethani et al. 2023), as informative perturbations are introduced. This causes us to think about counterfactuals, i.e., a contrasting perturbation does not affect model inference in non-salient areas.
Original features
Meen perturb.
Zero perturb.
1.0
Blur perturb. (Dynamask)
(Extmaakk
Our perturbations
Distribution of class
0.5
Distribution of class
a loss of
0.0
0.5
Figure I: Illustrating different styles perturba- tion. The red line is sample belonging to class within the two categories, while the dark back- ground indicates the salient features, otherwise non-salient. Other perturbations could be either not uninformative not in-domain, while is counterfactual that is toward the distribution of negative samples.
To address these challenges, we propose a Contrastive and Locally Sparse Perturbations (Con- traLSP) framework based on contrastive learning and sparse gate techniques. Specifically, our ContraLSP learns perturbation function to generate counterfactual and in-domain perturbations through a contrastive learning loss. These perturbations tend to align with negative samples that are far from the current features (Figure [ rendering them uninformative. To optimize the mask, we employ lo- fo-regularised gates with injected random noises in each sample for regularization, which encourages the mask to approach a binary-skewer form while preserving the localized sparse cxpla- nation. Additionally, introduce smooth constraint with trend function to allow the mask to capture temporal patterns. We summarize our contributions as below:
We propose ContraLSP as a stronger time series model explanatory tool, which incorporates coun- terfactual samples to build uninformative in-domain perturbation through contrastive learning.
ContraLSP integrates sample-specific sparse gates as a mask indicator, generating binary-skewed masks on time series. Additionally, we enforce smooth constraint by considering temporal trends, ensuring consistent alignment of the latent time series patterns.
We evaluate method through experiments on both synthetic and real- world time series datasets. These datasets comprise either classification or regression tasks and the synthetic one includes ground-truth explanatory labels, allowing for quantitative benchmarking against other state-of- the-art time series explainers.
2 RELATED WORK
Time series explainability. Recent literature has delved into the realm of eXplainable Artificial In-
telligence (XAI) for multivariate time series (Bento al. 202 Ismail et al., 22200] Zhu al. 2023). Among them, gradient-based methods (Shrikumar et al. 2017; Sundararajan et al. [017]] 7 Lundberg al., 2018) translate the impact of localized input alterations to feature saliency. Attention-based methods (in et al.) 2020; Choi et al., 2016) leverage attention layers to produce importance scores that are intrinsically based on attention coefficients. Perturbation-base
methods, as the most com- mon form in time series, usually modify the data through baseline (Suresh et al.) (017), gener- Leung et al. 2023), or making the data more uninforma- Enguehard 2023). However, these methods provide only an instance-lever saliency map, while the inter-sample saliency maps have been studied little in the existing literature (Gautam et al. 2022). Our investigation performs counterfactual perturbations through inter-sample variation, which goes beyond the instance- saliency methods by focusing on understanding both the overall and specifie model's behavior across groups
ative models (Tonekaboni et al. 2020
tive (Crabbé & Van Der Schaar 2021
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Model sparsification. For better understanding of which part of the features most influential
to the model's 's behavior, the existing literature enforcing sparsity (Fong et al. 2019) to constrain the
model's focus on specific regions. A typical approach is LASSO (Tibshirani 1996). which selects a subset of the most relevant features by adding an & constraint to the loss function. Based on this, several works (Feng& & Simon, [017 [Scardapane et al. 2017 Louizos al. 2018 Yamada
et al. (020)) are proposed to employ distinct forms of regularization to encourage the input features to be sparse. All these methods select global informative features that may neglect the underlying correlation between them. To cope with it, local stochastic gates (Yang et al. (022) consider an instance-wise selector to heterogeneous samples, accommodating cases where salient features vary among samples. [ee et al. (2022) takes a self-supervised way to enhance stochastic gates that encourage the model's 's sparse explainability meanwhile. However, most of these sparse methods are utilized in tabular feature selection. Different from them, our approach reveals crucial features within the temporal patterns of multivariate time series data, offering local sample explanations.
Counterfactual explanations. Perturbation problems, leading to abnormal model behaviors and unreliable explanation (Hase et al.) [02T] Hsieh 1). Previous works (Goyal et al. 2019 Teney et al. 2020) have tackled generating reason-
methods are known to have distribution shift
et al., 2021). able counterfactuals for perturbation-based based explanations, which searches pairwise inter-class pertur- bations in the sample domain explain the classification models. In the field of time series, [Delnnyy eet al. (202T) builds counterfactuals by adapting label-changing neighbors. To alleviate the need for labels in model interpretation. Chuang et al.] (2023) uses triplet contrastive representation learning with disturbed samples to train an explanatory encoder. However, none of these methods explored label-free perturbation generation aligned with the sample domain. On the contrary, our method yields counterfactuals with contrastive sample selection to sustain faithful explanations.
3 PROBLEM FORMULATION
Let ((r,, y1) be a set of multi-variate time series, where x; E R''D is a sample with time steps and D observations, yi y is the ground truth. 2;{4, d denotes feature of æ; in time step t and observation dimension d, where E [] and d E [1: DJ. We let a E Nxxxx y E YN be the set of all the samples and that of the ground truth, respectively. We are interested in explaining the prediction ú = ((x) of pre-trained black-box model f. More specifically, our objective is to pinpoint a subset S C [N x T x D). in which the model uses the relevant selected features x[S] to optimize its proximity to the target outcome. It can be rewritten as addressing an optimization problem: arg ming L (g. f (x())) where L represents the cross-entropy loss for C-classification tasks (i.e., y = .I. C}) or the mean squared error for regression tasks (i.e., y = R).
To achieve this goal, we consider finding masks m 1s {0, NxTxD by learning the samples of perturbed features through $ ((x, m) = m @ x + (1 m) ② x", where x" = Pe, (x) is the counterfactual explanation obtained from perturbation function (e, Nx + E NxTxD
and 0, is a parameter of the function so(.) (e.g., neural networks). Thus, existing literature (Fong
& Vedaldi 2017: (ong et al., 2019; Crabbé & Van Der Schaar 202T) propose to rewrite the above optimization problem by learning an optimal mask as
arg min (f(x), ((x, m)) + R(m) + A(m), m,,;
which promotes proximity between the predictions on the perturbed samples and the original ones in the first term, and restricts the number of explanatory features in the second term (e.g.. R(m) = [[m]]])) The third term enforces the mask's 's value to be smooth by penalizing irregular shapes.
Challenges. In the real world, particularly within the healthcare field, two primary challenges are encountered: (i Current strategies (Fong Vedaldi, 2017 Louizos et al. 2018 Lee et al. 2022 Enguehard| 2023) of learning the perturbation co(.) could be either not counteriactual or out of distributions due to unknown data distribution (Jethani et al.) 2023). (ii) Under-considering the inter-correlation of samples would result in significant generalization errors (Yang et al.) 2022
During training, cross-sample interference among masks {m,} specific predictions, while local sparse weights can remove the ambiguity (Yamada et al. 2017). These challenges motivate us to learn counterfactual perturbations that are adapted to each sample indivicually with localized sparse masks.
I may cause ambiguous sample-
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bp(-)
Contrastive
m
Leamingg
4 (m,;2,;))
0.0
0.0
1.0
0.0
AE(C))
+
0.0
0.0
1.0
Ornfinal Festures
Sporao Cottes
Countestictued
Festubber
RC
Invertad Mark
Cone())
C(f(x;), (x,, m.)) R(x, m.) + Cont((x.))
f())
Figure 2: The architecture of ContraLSP. A sample of features H, RTxx is fed simultaneously to a perturbation function co()) and to a trend function 7--). The perturbation function pp()) uses æ; to generate counterfactuals an that closer other negative samples (but within the sample domain) through contrastive learning. In addition, r(-) learns to predict temporal trends, which together with parameters μe; depicts the smooth vectors μ.: It acts on the locally sparse gates by injecting noises to get the mask m., Finally, the counterfactuals are replaced with perturbed features and the predictions are compared to the original results to determine which features are salient enough.
4
OUR METHOD
We now present the Contrastive and Locally Sparse Perturbations (ContraLSPP, whose overall archi- tecture is illustrated in Figure Specifically, our ContraL learns counterfactuals by means of con- trastive learning to augment the uninformative perturbations but maintain sample distribution. This allows perturbed features toward negative distribution in heterogeneous samples, thus increasing the impact of the perturbation. Meanwhile, a mask selects sample-specific features in sparse gates, which is learned to be constrained with fo-regularization and temporal trend smoothing. Finally, comparing the perturbed prediction to the original prediction, we subsequently backpropagate the error to learn the perturbation function and adapt the saliency scores contained in the mask.
4.1 COUNTERFACTUALS FROM CONTRASTIVE LEARNING
To obtain counterfactual perturbations, we train the per- turbation function yo, (-) through a triplet-based con- trastive learning objective. The main idea is to make counterfactual perturbations more uninformative by in- versely optimizing triplet loss (Schroff et al.] 2015). which adapts the samples by replacing the masked unim- portant regions. Specifically, we take each counterfactual perturbation x = Pe, ) as an anchor, and partition all samples x" into two clusters: positive cluster Ω+ and negative one f based on the pairwise Manhattan simi- larities between these perturbations. Following this parti- tioning, we select the K+ nearest positive samples from the positive cluster 2 denoted as { I== which ex-
Posityes MM D.o
Positives
mwh
D
mmh Anchor ((
Optimizing
triplet loss Centr
Dan
(p(zz))
Aman Negatives
Negatives
Figure 3: Illustration of the impact of triplet loss generate counterfactual perturbations. The anchor is closer to negatives but farther from positives.
K+
hibits similarity with the anchor features. In parallel, we randomly select K subsamples from the negative cluster Ω2,, denoted as {x. M where K- and K- represent the numbers of positive and negative samples selected, respectively. The strategy of triple sampling is similar Li et al. 2021), and we introduce the details in Appendix B
To this end, we obtain the set of triplets T with each element being a tuple T, (xff, (x
1ettkk g 1 {x. ME) Let the Manhattan distance between the anchor with negative samples
be Dan - EK |oc afjih and that with positive samples be Dap RT ΣK |ay| xti--

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As shown in Figure aim to ensure that Dan is smaller than Dap with margin thus making the perturbations counterfactual. Therefore, the objective of optimizing the perturbation function Po, (-) with triplet-based contrastive learning is given by
Centr = max(0, Dan Dap b) b)+ |
(2)
which encourages the original sample and the perturbation af to be dissimilar: The second regu- larization limits the extent of counterfactuals. In practice, the margin b set to 1 following (Balntas)
et al. 2016), and we discuss the effects of different distances in Appendix E.1
4.2 SPARSE GATES WITH SMOOTH CONSTRAINT
Logical masks preserve the sparsity of feature selection but introduce large degree of variance in the approximated Bernoulli masks due to their heavy-tailedness (Yamada et al. 2020). To address this limitation, we apply a sparse stochastic gate each feature in each sample i, thus approximating the Bernoulli distribution for the local sample. Specifically, for each feature x; [t, df, sample- specific mask is obtained based on the hard thresholding function by
m. d] min (1, max(0, p4lt, d) c, ()).
(3)
where ei d] N(0,22) ) is random noise injected into each feature. We fix the Gaussian variance 8 dur- ing training. Typically, μ it. d] is taken as an intrinsic parameter of the sparse gate. However, as a binary- skewed parameter, p4](,, df does not take into account the smoothness, which may lose the underlying trend in temporal patterns. Inspired by Elfwing et al. (2018) and Biswas et al. (2022), adopt siggoid-weighted unit with the temporal trend to smooth n4;- Specifi- cally, we construct the smooth vectors Ju!
hanskmakk
0.8
amooth-naak (c- 2.0)
0.6
amoothh-maa (c- 2.0)
5.0)
smooth mask leamed)
0.2
0.0
Figure 4: Different temperatures for the segmoid-weighted unit. The learned trend function r(-) can be better adapted to smooth vectors (red) hard masks (black).
p4 p4 @ (T:)))) =
(4)
1 e (a)))))
where Tg, NXTXD + NXTxD is trend func- tion parameterized by 02 that plays role in the sig-
moid function as temperature scaling, and μ4; is set of parameters initialized randomly. In practice, use neural network (e.g., MLP) to implement the trend function Te, (-). whose details are shown in Appendix D.4 Note that employing a constant temperature may render the mask continuous. However, for valid mask interpretation, adherence et al. 2023). We illustrate in Figure that a learned temperature (red solid) makes the hard mask smoother and keeps its skewed binary, in contrast to other constant temperatures.
discrete property is appropriate (Queen
To make the mask more informative in Eq. T we follow Yang et al. (2022) by replacing the 41- regularization into an likli constraint. Consequently, the regularization term R(-) can be rewritten using the Gaussian error function (crf) as
R(æ,, m:) = [m 10
Σ t=1
T
Σ
D
+
1
erf [4]it.d]
)
(5)
2
v28
1=1
where ut is obtained from Eq.( 4 The full derivations are given in Appendix A We calculate the empirical expectation over m; for all samples. Thus, masks m are learned by the objective
N
arg min L. (f(z), (ax m)) n.0g
R(a; m.).
(6)
N
where a is the regular strength. Note that the smooth vectors μi: restrict the penalty term A(.) in Eq. (1) for jump saliency over time.
5

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Table 1: Performance on Rare-Time and Rare-Observation experiments w/o different groups.
RARE-TIME
RARE-TIME (DIFFGROUPS)
METHOD
AUP
AUR
Im/10 f
Sm/10²
AUP 1
AUR
1m/10"
Sm/10²
FO
1.00_o.c0
1.13
0,46mmm
17.20
1.00
1.1610.00
1.53
54.89
AFO
1.00 20.00
0.15
0.51
55.6020.85
1.00 1.00
0.16go 0o
0.54
57.76 57.76g0.72
IG
1.0000.00
0.13
0.46+a.01
=0.61
1.00.0.00
0.15 00
0.53+0.01
54.62+0.55
SVS
=0.00
0. 0310.0
0.47+0.11
47.20=n.01
1.00c
0. 0.15+0.00
0.52+0.02
54. 28.4
DYNAMASK
0.99
1..0
1..8
37.24gn.4
1.00
5.75
37.33, g..33
EXTRMASK
1,00 1,00
0.88
16.40
13. 13.10
1.00
0.83
13:37 +0.78
27 27.44
CONTRALSP
1,00 1,00
0.97 10.0:
19.51 Lo:30
4.65.1.77
1.00
0.94
18.92
_.40__oco
RARE-
RARE- OUSERVATION (DuFFgROUPS)
METHOD
AUP
AUR
Im/10" T
Sm/10"
AUP
AUR
Im/10"
Sm/10"
FO
1,00
0.13
0.4610000
47.3920.16
1.00go00
0.14
0.50
13.1990
AFO
1.00
0.16g0.00
0.53+n.01
56.81=0.30
=.00
0.16g0.0z 01
0.54
16.92+1224
IG
1,00
0.13+0.00
0,46+0000
47.82+0.15
1.00=0.00
0,13+0.00
0.47+0.00
49. 19.90)=0.as
SVS
20.0...co
0.13
0.46
47.39
1.00
1.13
0.47
49.53guaa
DYNAMASK
0.97
0.6510.00
8.321..06
22.8710.58
0.98
0.
6.1221.10
30,88 =0.88
EXTRMASK
1.00
g.76
13:25
9.55
1.00
0.70
10.40
32.81
CONTRALSP
1.00 20.00 1.00
20.66 20.68
0.32
1.00g000
0.99 1.99
20.51
0.57
4.3
LEARNING OBJECTIVE
In our method, we utilize the preservation game (Fong & Vedaldi (017). where the aim to maxi- mize data masking while minimizing the deviation of predictions from the original ones. Thus, the overall learning objective is to train the whole framework by minimizing the total loss
N
B N
arg min w (f(x), b(x (( 14.01.02
R(æ,, m.) +
E Coner(()))
N
where {1s, 01, 02) are learnable parameters of the whole framework and {a, B} are hyperparameters adjusting the weight of losses to learn the sparse masks. Note that during the inference phase, we remove the random noises c; from the sparse gates and set m; min(1, max(0, μ4; @ (T((()))) (x)))) for deterministic masks. We summarize the pseudo-code of the proposed ContraL in Appendix
5 EXPERIMENTS
In this section, evaluate the explainability of the proposed method synthetic datasets (where truth feature importance is accessible) for both regression (white-box) and classification (black-box), well on more intricate real-world clinical tasks. For black-box and real-world experiments, use 1-layer GRU with 200 hidden units as the target model fa to explain. All performance results for our method, benchmarks, and ablations are reported using mean + std 5 repetitions. For each metric in the results, we use f to indicate preference for higher values and I to indicate preference for lower values, and we mark bold as the best and underline the second best. More details of each dataset and experiment are provided in Appendix D
5.1 WHITE-BOX REGRESSION SIMULATION
Datasets and Benchmarks. Following Crabbé & Van Der Schaar (2021) ) we apply sparse white- box regressors whose predictions depend only on the known sub-features .1 2] x J, D] salient indices. Besides, extend our investigation by incorporating het- erogeneous samples to explore the influence of inter-samples on masking. Specifically, we con- sider the subset of samples from two unequal nonlinear groups S2) C S, denoted as Diff- Groups. Here, S and S₂ collectively constitute the entire set S, with each subset having a size of |8|] = [S2] / 22- 50. The salient features are represented mathematically as
S x SD c
Eiedees, (2,(t, d)2 (Enndess 2,st.d]
if in S elif in Sy 0 else.
[f(z)), |Σ hass (n(t,d)² in and [f(x)]
0
else,

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Sum perturbed observation ons for each time
Sum origi nal observations for each time
ContraLSP perturb. in St.
Extrmask perturb. in S.
ContraLSP perturb. in Sz.
Extrmask perturb. in Sq.
MM
HMMM
M WW
20 T 40
T 40
Figure 5: Differences between ContraLSP and Extrmask perturbations on the Rare-Observation (Diffgroups) experiment. We randomly select a sample each of the two groups and sum all observations. The background color represents the mask value, with darker colors indicating higher values. ContraL.SP provides counterfactual information, yet Extrmask's perturbation is close O.
In our experiments, we separately examine two scenarios with and without DiffGroups: where set- ting |8" < N x T is called Rare-Time and setting |SD] < N x D is called Rare- Obseevbbeeatioon These scenarios are recognized in saliency methods due to their inherent complexity (Ismail al.) 2019). In fact, some methods are not applicable to evaluate white-box regression models, c.g., DeepLIFT (Shrikumar et al., 2017) and FIT (Tonekaboni et al. 2020). To ensure a fair comparison, compare ContraLSP with several baseline methods, including Feature Occlusion (FO) (Suresh) jet al.] 2017), Augmented Feature Occlusion (AFO) (Tonekaboni et al., 22020), Integrated Gradi- (IG) (Sundararajan al.] (017). Shapley Value Sampling (SVS) (Castro al. 2009), Dyna- mask (Crabbé & Van Der Schaar 2021). and Extrmask (Enguehard, 2023). The implementation details of all algorithms available in Appendix [D.5]
Metrics. Since we know the exact cause, we utilize it as the ground truth important for evaluating explanations. Observations causing prediction label changes receive an explanation of 1, otherwise it is O. To this end, we evaluate feature importance with area under precision (AUP) and area under recall (AUR). To gauge the information of the masks and the sharpness of region explanations, we also use two metrics introduced by Crabbé & Van Der Schaar (202I): the information I =
-Eidde In(1 m.((. [1, dl) and mask entropy 5m (m) = > i,t,d/aa m. [1, d) In [n,,,[(,, d)) +11 mzlt, [n( - m.,tt, d)), where a represents true salient features.
Results. Table summarrzes the performance results of the above regressors with salient fea- tures. AUP does not work as a performance discriminator in sparse scenarios. We find that for all metrics except AUP, our method significantly outperforms all other benchmarks. Moreover, Con- traLSP identifies notably larger proportion of genuinely important features in all experiments, even close to precise attribution, as indicated by the higher AUR. Note that when different groups are present within the samples, the performance of mask-based methods at the baseline significantly deteriorates, while ContraLSP remains relatively unaffected. We present comparison between the perturbations generated by ContraLSP and Extrmask, as shown in Figure [S] This suggests that employing counterfactuals for learning contrastive inter-samples leads to less information in non- salient areas and highlights the mask more compared to other methods. We display the saliency maps for rare experiments, which are shown in the Appendix G Our method accurately captures the important features with some smoothing in this setting. indicating that the sparse gates are working. We also explore in Appendix whether different perturbations keep the original data distribution.
5.2 BLACK-BOX CLASSIFICATION STMULATION
Datasets and Benchmarks. We reproduce the Switch-Feature and State experiments from Tonek aboni et al. (220)) The Switch-Feature data introduces complexity by altering features using Gaus- sian Process (GP) mixture model. For the State dataset, we introduce intricate temporal dynamics using a non-stationary Hidden Markov Model (HMM) to generate multivariate altering observations with time-dependent state transitions. These alterations influence the predictive distribution, high- lighting the importance of identifying key features during state transitions. Therefore, an accurate generator for capturing temporal dynamics essential in this context. For further description the datasets, Appendix D.2 [.2 For the benchmarks, in addition to the previous ones, we also use FIT, DeepLIFT, GradSHAP (Lundberg & Lee 2017). LIME (Ribeiro et al. (016).. and RETAIN (Choi
al. 2016).
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Table 2: Performance on Switch Feature and State data.
SWITCH-FEATURE
STATE
METHOD
AUP
AUR
Im/100 f
Sm/10²
AUP
AUR
/m//10
Sm/10
FO
0.89_6.0
1..m
1.861a1
15.60
0.M0_e..s
1..0
2.731uus
28. 07
AFO
0.82_0.06
0.41
2.00g0.14
17.32g0.0 30
0.84
D.36 03
3.16
14.0
IG
0.91 0.90-0.02
0.44
2.21
16.87=0.52
0.93 go.oz
0.34 os
3.17=0.28
30.19
GRADSHAP
0.88-0.02
0,38+0.32
1.92+9.18
15. 15.85=n..4
0.85e0.00
0.30+0.02
2.76+0.22
28.. 18-11800.
DEEPLIFT
0.91_p.02
1..4
2.231
16.861n.52
2.93
0.35 1o.us
3.20
30.21
LIME
0.94-0.02
0.40+0.02
2.01+0.13
16.09+0.58
=.95=
0.32+0.08
2.94+0.29
28.55=1.68
FIT
0.48_.0.0
0.43
1.99
17.16gu.au
go.45.o.ozz
0.50 2.50....u
7.922u..0
33.50
RETAIN
0.93_..01
0.33
1.541a.a0
15.08
0.52
1.56gn.84
25.01
DYNAMASK
0.35==0.00
0.77+0.02
5. 5.22+n.26
12.85go.5e
0.36g0.01
0.79 0.79+0.02
10.59
25. 20..00
0.97 0..01
0.65
8. 10.5 10.51
6.90 11.44
0.87
0.77+0..0
29.71 11.59
10.46
CONTRALSP
2.98
0.80
24.23=1.27
0.91
g.90
g.81
50.09
0.50=0:05
Table Effects of contrastive perturbations (using the triplet loss) and smoothing constraint (using the trend function) on the Switch-Feature and State datasets.
SWITC--FEATH FEATURE
STATE
METROD
AUP
AUR
1m/100
Sm,/00
AUP
AUR
f,,/10''
Sm//10
AL
0.92
0.70 1.70220.2
g.08
0.78
0.76ga.m
g.74
42.26
0.14
CONTRAL w/o TRIPLET LOSS
B.97 20.0
0.79
22 22.90_as ga
1.00
0.88 0.88
0.80
0.76
CONTRALSP woo TRUND TUNCTION
0.022000:
0.50 ...
24.16
0.65
0.77
0.50
42.224450
0.15
CONERALSS
0.98
0.50
24.23
0.91.0.36
0.90
0.81
50.09.0.x
0.50.0m
Metrics. We maintain consistency with the ones previously employed.
AFO
Gredtinap
Results. The performance results on simu-
Deoplit
lated data are presented in Table 2 Across Switch-Feature and State settings, ContraLSP is the best explainer on 7/8 (4 metries in two datasets) over the strongest baselines. Specif- ically, when AUP is at the same level, method achieves high AUR results from its emphasis producing smooth masks over time, favoring complete subsequence patterns over sparse portions, aligning with human in- terpretation needs. The reason why Dyna- mask has a high AUR is that the failure pro- duces smaller region of masks, shown in Figure 6 ContraLSP also has an average 94.75% improvement in the information content Im and an average 90.24% reduction in the entropy Sm over the strongest baselines. This indicates that the contrastive perturbation is superior to perturba- tion by other means when explaining forecasts based on multivariate time series data.
LIME
RETAIN
Dynamask
Extmank
Control
Lubwi
Figure 6: Saliency maps produced by various meth- ods for Switch-Feature data.
Ablation study. We further explore these two datasets with the ablation study of two crucial com- ponents of the model: (i) let Centr to cancel contrastive learning with the triplet loss and (ii) without the trend function Ta. (-) that μı' μ.. As shown in Table 3 the ContraLSP with both components performs best. Whereas without the use of triplet loss, the performance degrades as the method fails to learn the mask with counterfactuals. Such perturbations without contrastive optimization not sufficiently uninformative, leading to a lack of distinction among samples. Moreover, equipped with the trend function, ContraL improves the AUP by 0.06 and 0.13 the two datasets, respec- tively. It indicates that temporal trends introduce context as smoothing factor, which improves the explanatory ability of our method. To determine the values of a and 8 in Eq. (7). we also show different values for parameter combination, which are given in more detail in the Appendix E.2
5.3 MIMIC-III MORTALITY DATA
Dataset and Benchmarks. We use the MIMIC-III dataset (Johnson et al. 2016). which is a com- prehensive clinical time series dataset encompassing various vital and laboratory measurements. It extensively utilized in healthcare and medical artificial intelligence research. For more details, please refer Appendix D.3 We use the same benchmarks before the classification.
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Table 4: Performance report on MIMIC-III mortality by masking 20% data.
AVERAGE SUBSTITUTION
ZERO SUBSTITUTION
METHOD
ACc 4
CE
SUFF-10" L
COMP-10"
ACC 1
CE
SUFP
COMP<10" 1
FO
2.968
0,084
0:455
-0 20
0.97]
0. 0.121
-0 -0.529
-0 -0.523atvar
AFO
0.989
0.007
0.185
0.008
0.972-000
0.120
-0.5406-m-
-0. -0.160
0.988-1008
0.096gomms
0.08044
0.971ga.mm
0.1222g.00
-0.385.00
GRADSHAP
4008
0.400_...m in
0.219
g.128g0.015
D.00Gaa.ccm
0.628 anar
DuseLerr
0.987 20.02
a000
0.303 c.
0.115
0.972
0.119.c.omm ec.ces
0.119
-0.427 10.100
-0 .0.
LIME
0.118 2.094
-0 -0.028
0.988
0.0:99c..00
19.577
0.254
FIT
0. 0.
0.008g0mm
-0.139
0.375
0.957=00001
g.108
-0.
-0.74554.00
1,053
0.088.0..01
0.002:0000
-0.155.0..0
0.971
20.00m
0.07240.304
-0.984an.00
DYNAMASK
10050
20009s
-0.063
0.9788-0.00
0.114ec.oo
-0.422 0.000
EXTRMASK
0 0.982
0
-1157
1,50
0.963
0.318
6.942-a051
10. 10.847..
CONTRALSP
0.980
0.127
1..92
2.386
0.928.00.00
0.357 g0.0s
6.636 0.315
17.442,a.54
FO
FIT
RETAIN
Dynamask
Extrmask
ContraL5P
Comprehunsivenns
0.03
0.15
Accurocy
Swifie Meleeyyyyy
0.00
0.02
0.990
0.955
Cross
0.11
-0.03
0.01
0.00
0.09
-0.02
6.1 0.2 0.3
0.4 0.5 0.6
0.3
0.2
0.3
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.3
0.2
0.3
0.4
0.5 0.0
Fraction of the average perturbed
Fraction of the average perturbed
Praction of the average perturbed
Fraction of the average peraubed
Figure 7: Quantitative results on the MIMIC-III mortality experiment, focusing on Accuracy 4. Cross Entropy 1. Sufficiency J. and Comprchensiveness 1. We mask a varying percentage of the data (ranging from 10% to 60%) for each patient and replace the masked data with the overall average over time for each feature: [,,(,d] d] Σi æ; d]. Since some curves are similar, we show representative baselines for clarity.
Metrics. Due to the absence of real attribution features in MIMIC-III, we mask certain portions of the features assess their importance. We report that performance evaluated using top mask substitution, as is done in Enguehard (2023). It replaces masked features either with an average over time of this feature (ar d] = T Ei= =1 Li(t, d)) or with zeros (z. d] 0). The metrics we select are Accuracy (Acc, lower is better), Cross-Entrops (CE, higher is better), Sufficiency (Suff, lower is better), and Comprehensiveness (Comp, higher is better), where the details are in Appendix D.3
Results. The performance results on MIMIC-III mortality by masking 20% data are presented in Table 4 We can see that our method outperforms the leading baseline Extrmask on 7/8 metrics (across 4 metrics in two substitutions). Compared to other methods on ceature-removal (FO, AFO, FIT) and gradient (IG, DeepLift, GradShap), the gains are greater. The reason could be that the local mask produced by ContraL-SP is sparser than others and is replaced by more uninformative perturbations. We show the details of hyperparameter determination for the MIMIC-III dataset, which is deferred to Appendix E Considering that replacement masks different proportions of the data, we also show the average substitution using the above metrics in Figure where 10% 60% of the data is masked for each patient. Our results show that our method outperforms others in most cases. This indicates that perturbations using contrastive learning are superior to those using other perturbations in interpreting forecasts for multivariate time series data.
6 CONCLUSION
We introduce ContraLSP, a perturbation-base model designed for the interpretation of time series models. By incorporating counterfactual samples and sample-specific sparse gates, ContraLSP not only offers contractive perturbations but also maintains sparse salient areas. The smooth constraint applied through temporal trends further enhances the model's ' ability to align with latent patterns in time series data. The performance of ContraL.PP across various datasets and its ability to reveal essential patterns make it a valuable tool for enhancing the transparency and interpretability of time series models in diverse fields. However, generating perturbations by the contrasting objective may not bring counterfactuals strong enough, since it is label-free generation. Besides, an inherent lim- itation of method is the selection of sparse parameters, especially when dealing with different datasets. Addressing this challenge may involve the implementation of more parameter-e efficiente tuning strategies, it would be interesting to explore one of these adaptations salient areas.

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Published as a conference paper at ICLR 2024
ACKNOWLEDGMENTS
This work was supported by Alibaba Group through Alibaba Research Intern Program.
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A REGULARIZATION TERM
Let erf be the Gaussian error function defined as crf = 2 -0 d- and let the mask m; be obtained with the sigmoid gate output uí and an injected noise e; from NNO,, 8²). Thus, the regularization term for each sample R(9) can be expressed by
R (zt m.) E a (mm/lll
=a E d= IP (nilt, + et d) 0)
a E
[ P (1/ df + Eilt, d s 0)
=a aa E E
1 - vp (-ujledd) }
(8)
El= El=1
V/ (Kilt.c)
=a E2
(itt )) (2 erf(
v26
= a Eb
( + erf( 14 (11 ))
where (-) is the cumulative distribution function, and will, d] is computed by Eq. (4
B TRIPLE SAMPLES SELECTED
In this section, we deseribe how to generate positive and negative samples for contrastive learning- For each sample our goal is to generate the counterfactuals æ! via the perturbation function sp(.). optimized to be counterfactual for an uninformative perturbed sample. The pseudo-code of the triplet sample selection is shown in Algorithm and elaborated follows. (i) We start by clustering samples in each batch into the positives S and the negatives ! with 2-kmeans, (ii) we anchor, along with K+ nearest samples from the
select the current sample from each cluster same cluster as the positive samples, (iii) and we select K random samples from the other cluster yielding negative samples. Note that to select positive and negative samples, respectively.
Sp and Sn, auxiliary variables representing two sets
Algorithm Selection of a triplet sample
Input: The set of perturbation time series Ω {x 1 and the current perturbation x;. ** {.;;,))<>
Output: Triple sample T; (æ!' {
Initialize positive set Sp = O} and negative set S, = 0
Clustering positive and negative samples (2+, [ <- 2-kmeans(
for Ω* in {2+, do
Select Anchor x ?
Ω² + Ω {xr)
for l <- to K do
L = 02" Top(")))
Ω + Ω² \ (.]t)) Sp + Sp U u
end for
for & + 1 to K do
x = random(S) \ 12")
Ω¹ + Ω* (a[jec Sn + Sn a
end for end for Output: Triple sample (æf, ( {a
(
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C
PSEUDO CODE
Algorithm 2 The pseudo-code of our ContraLSP
Input:
Multi-variate time series (æ; J 1= black-box model f. sparsity hyper-parameters {a, Gaussian noise 6, total training epochs E, learning rate 7
Output: Masks to explain Training:
Initialize the indicator vectors μ4 ) of sparse perturbation
Initialize perturbation function yo, (.) and a trend function Te, (.) for 1 to E do for + 1 to N do
Get time treads {Te, (2: d in each observations 2f(;; d]
Compute μ4: + f4; @ o (Tx;))
Sample e, from the Gaussian distribution (O, 8)
Compute instance-wise masks m, <- min (1, max(0, /4/ + 6;))
Get counterfactual features x < 90; (x.)
Compute the triplet loss Lentr via Alg. and Eq. 2
Compute the regularization term R(o, m.) via Eq. end for
Get perturbations (<x, m) t m @ x + (1 m) 3 x
Construct the total loss function:
L (xx), J (xx, m)) + N Σ R(x; m.) + &t N
Lentr
Update 14 1 1 -V 0, 01 Vo, E, 0g t 02 ---Vo.6 v
end for
Store μl, Pe, (-), To2(.) (-)
Inference: Compute final masks m <- min(1, max max(0, Return: Masks m
D EXPERIMENTAL SETTINGS AND DETAILS
D.1 WHITTE-BOX REGRESSION DATA
As this experiment relies on a white-box approach, our sole responsibility is create the input sequences. As detailed by Crabbé & Van Der Schaar (2021), each feature sequence is generated using an ARMA process:
x [t, d] = 0.252 [t- 1, d. + 0.1æ,(t 2, d] + 0.05æ, 3, d] c
(9)
where e: (N(0,)) 1). We generate 100 sequence samples for each observation d within the range of d E [1 50] and time t within the range of t E [1 50), and set the sample size |S = =| |S) 50 in different group experiments.
In the experiment involving Rare-Time, we identify 5 time steps as salient in each sample, where consecutive time steps are randomly selected and differently for different groups. The salient ob- servation instances are defined as D [:, 13 38] without different groups and as SP = |. 1 25), SP = [:, 13 38] with different groups
In the experiment involving Rare- Pare-Observation, we identify 5 salient observations in each sample without replacement from 50), whereas in different groups SP and SP are different obser- vations randomly selected respectively. The salient time instances are defined ST [t. 13 38] without different groups, and as Sf = [t, 1 25), ST = [t, 13 : 38) with different groups.
D.2 BLACK-BOX CLASSIHCATION DATA
Data generation on the Switch-Feature experiment. We generate this dataset closely following Tonekaboni al. 2020), where the time series states are generated via two-state HMM with equal
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initial state probabilities of [. 3 al and the following transition probabilities
r0.95
0.02
0.03
0.02
0.95
0.03
00.03
0.02
0.95
The emission probability is GP mixture, which is governed by RBF kernel with 0.2 and uses means 141 = [0.8, -0.5, -0.2), ( = [0.0, -100, 0.0), /4a = [-0.2, -0.2, 0.8) in each state. The output y; at every step is designed
if [
1tc a
clif s; [t) 1 and yil4 Bernoull(pp:()).
elif s,
14e7% 1,63
where si[ is a single state each time that controls the contribution of single feature to the output, and we set 100 states:
[1 100). We generate 1000 time series samples using this approach. Then we employ single-layer GRU trained using the Adam optimizer with learning rate of 10-4 for 50 epochs to predict yi based on
Data generation on the State experiment. We generate this dataset following Tonekaboni et al. (2020) and Ennguehard (2023). The random states of the time series are generated using a two-state (0.5, 0.5] and the following transition probabilities
HMM with
T. 0.9
0.1 0.9
The emission probability a multivariate Gaussian, where means are μn = 1.6,, 0.5] and #2 = [-0.1, -0.4, -.5].. The label yi[t] is generated only using the last two observations, while the first one is irrelevant. Thus, the output yi at every step is defined as
if s [t]
p.d
Tte
and y:((] Bernoulli(p.(]).
elif 1. =
Itc ..
where s,[t] is either at each time, and we generate 200 states: E [1 200]. We also generate 1000 time series samples using this approach and employ single-layer GRU with 200 units trained by the Adam optimizer with a learning rate of 10-4 for 50 epochs to predict yi based on æ;,
D.3 MIMIC-III DATA
For this experiment, we opt for adult ICU admission data sourced from the MIMIC-III dataset (John- son et al. 2016). The objective is to predict in in-hospital mortality of each patient based on 48 hours of data (T 48), and we need to explain the prediction model (the true salient features are unknown).
For each patient, used features and data processing consistent with Tonekaboni al. (2020) We summarize all the observations in Table 5 with a total D 31. Patients with complete 48-hour blocks missing for specific features are excluded, resulting in 22.988 ICU admissions. The predicted model we train is single-layer RNN consisting of 200 GRU cells. undergoes training for 80 epochs using the Adam optimizer with learning rate of 0.001.
Table 5: List of clinical observations at each time for the risk predictor model.
DATA CLASS
NAME
STATIC OBSERVATIONS
AGE, GENDER, ETHNICITY. FIRST ADMISSION TO THE ICU LACTATE, MAGNESIUM, PHOSPHATE, PLATELET, POTASSHIM, Prr, INR, Pr. SODIUM, BUN, WBC HEARTRATE, DIASBP,
LAB OBSERVATIONS
RESPRATE, SPO2, GLUCOSE,
In this task, introduce the same metrics Enguchard (202)), which detailed follows: (i) Accuracy (Acc) means the prediction accuracy while salient features selected by the model are removed, so lower value is preferable. (ii) Cross-Entropy (CE) represents the entropy between
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Table 6: Experimental settings for ContraLSP across all datasets.
PARAMETUR
RATE-TIME
RATE-OBSERVATION
SWITCH-PENNTRE
STATE
MIMIC-III
LEARNING RATE
0.1
0.1
0.01
0.01
0.1
OPTIMIZER
ADAM
ADAM
ADAM
ADAM
ADAM
MAX EPOCHS
200
200
500
500
200
0.1
0.1
1.0
2.0
0.005
0.5
0.5
0.8
0.5
0.5
[0 1/5
|251/5
1051/5
| 1/5
50
1/5
[2 1/5
1/5
[02 1/5
Table 7: The specific structure of the trend function.
No.
STRUCTURE
ORS. 2ND OBS.
MI.P(LINEAR(T: 32), L32, 7) MLP[LINEAR(T) 32), RELU, L3N,AR(32, 7)]
DTH OBS.
MLP[LINEAR(T; 32), RELU, LINEAR(32. 2)]
the predictions of perturbed features with the original features. It quantifies the information loss when crucial features omitted, with higher value being preferable. (iii) Sufficiency (Suff) is the average change in predicted class probabilities relative to the original values, with lower values being preferable. (iv) Comprehensiveness (Comp) the average difference of target class prediction probability when most salient features are removed. It reflects how much the removal of features hinders the prediction, so higher value is better.
D.4 DETAILS OF OUR METHOD
We list hyperparameters for each experiment performed in Table 6 and for the triplet loss, the marginal parameter b is consistently set to 1. The size K and are chosen to depend on the number of positive and negative samples ((2+1 and [S2 (). In the perturbation function (e,, (+), use a single-layer bidirectional GRU, which corresponds to a generalization of the fixed perturbation. In the trend function To₃ (-), employ independent MI.P for each observation d find its trend, whose details are shown in Table 7 Please refer to our codebase" for additional details on these hyperparameters and implementations.
D.5 DETAILS OF BENCHMARKS
We compare our method against ten popular benchmarks, including FO (Suresh et al., 2017),
AFO (Tonekaboní et al. 2020), IG (Sundararajan et al. 2017). GradSHAP (1 (Lundberg Lee 2017)
(SVS (Castro et al., 2009) in regression). FIT (Tonekaboni et al. 2020 DeepL.IFT (Shrikumat
ctt al. 2017). LIME Shriikuaar et al. 2017). RETAIN (Choi et al. 2016). Dynamask (Crabbé &
Van Der Schaar 2021), and Extrmask (Enguchard, 2023), whereas the implementation of bench-
marks is based on open source codes time interpre and DynaMask All hyperparameters follow the code provided by the authors.
E ADDITIONAL ABLATION STUDY
E. EFFECT OF DISTANCE TYPE IN CONTRASTIVE LEARNING.
For the instance-wise similarity, we consider various losses maximize the distance between the anchor with positive or negative samples Eq. @2). We evaluate three typical distance metrics in Rare-Time and Observvisnvttion datasets: Manhattan distance, Euclidean distance, and cosine
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Table Performance of SontraL with different contrastive loss types on rare experiments.
PARE-TIME
AARF-ORSERVATION
DISTANCE IN Cente
A
AUR f
Im/10*
Sm/100
AUP
AUR
Im/10' f
Sm/100
TAN DISTANCE
1.00.0.00
0.97.0.01
19.51
4.65 20.71
1.00
1.00.0.00
20. 20.08-0.08
0.32
BUCLIDEAN DISTANCE
1.00=0.00
0.97+0.02
19.67
1.97=0.05
=.00
1.00-0.01
20.72+0.00
0.69+0.17 19.22_0.00
COSINE SIMILARITY
1.00
0.9620.02
18.41
6.87.0.4
1.00
0.98_0.01
0.98
similarity. The results presented in Table 8 indicate that the Manhattan distance is slightly better than the other evaluated losses.
E.2 EFFECT OF REGULARIZATION FACTOR.
We conduct ablations on the black-box classification data using our method to determine which values of and 3 should be used in Eq. 7 For each parameter combination, we employed five distinct seeds, and the experimental results for Switch-Feature and State are presented in Table D and Table 10 respectively. Higher values of AUP and AUR are preferred, and the underlined values represent the best parameter pair associated with these metrics. Those Tables indicate that the L- regularized mask m is most appropriate when a is set to 1.0 and 2.0 for both Switch-Feature and State data, allowing for the retention of small but highly valuable subset of features. Moreover, to force Po, (-) to learn counterfactual perturbations from other distinguishable samples, / is best set to 2.0 and 1.0, respectively. Otherwise, the perturbation may contain crucial features of the current sample, thereby impacting the classification.
We also perform ablation on the MIMIC-III dataset for parameters a and using our method. We employ Accuracy and Cross-Entropy as metrics and show the average substitution in Table [T] This Table shows that (8 is best set 0.01 to learn counterfactual perturbations. Note that the results are better when lower values of a are used, but over-regularizing m close to O may not be beneficial. Notably, lower values of a yield superior results, but excessively regularizing m toward may prove disadvantageous (Enguehard, 2023). Therefore, we select 0.005 and 3 0.01 as deterministic parameters on the MIMIC-III dataset.
Table Effects of a and /3 on the
data. Underlining is the best.
0.1
0.5
1.0
2.0
5.0
AUP
AUR
AUP
AUP
AUR
AUP
3= 0.1
0.28
0.26
0.01ga.00
0.18
0.01
0.12
0.01
0.14ga.06
0.01
3 0.5
0.56
0.97 nn
0.91go0s
0.44g0.2s
0.52
0.02
0. 0.19
0.02
0.16
0.01
3 1.0
0.55
0.97
0.80
0.87
0.98
0.56
0.7
0.09gaue
0.28
0.02-aum
2.0
0.54g
0.97
0. 1.86
0.80
0.80
0:00
0.68
0.50
0.05
5.0
0.54gaoe
0.97 jom
0.87 1000
0.89
0.97 0.97
0.80
0.
0.69
0.99....v 0o.00
0.37
Table 10: Effects of and ,3 on the State data. Underlining is the best.
a 0.1
a=
0.5
=
1.0
a= 2.0
==
AUP
AUR
AUP
AUR
AUP
AUR
AUP
AUR
AUP
AUR
3 3=0.1 0.1
0.
0m90gam
0.67
0.79
0.00
0.01:00m
0,32 14
0.01g000
0.50
0.01gam
8= 0.5
0.962000
0.66gg0
0.90g.o01
0.77ga.0
0.86:00m
0.
0.70ga
0.77ga.1
0.08_.
3= 1.0
0.52
0.962000
0.66220m
0.91
0.77
0.87.mm
0. 0z90gg
0.82
0.8%
0.23
==0
0.52axo0
0.96amm
0.6520az
0.92aa.00
0.77aa.2
0.88
0. 0.
0.82pa.2
0.97.9.11
0.70=..0
5.0
0:90
0.60ga0
0.91ga.00
0.70gga.o
0.88_.om
40 oa
0.82gam1
0.97
0.700g0m
F DISTRIBUTION ANALYSIS OF PERTURBATIONS
To investigate whether the perturbed samples are within the original dataset's distribution, we first compute the distribution of the original samples by kernel density estimation (KDE). Subsequently,
htttps://ccikii 1earn www.ieerrrrrreeee....e.. wtgg/ttalllllooooooooo sttablemmodui http://oooiieeeeeeeeeeeeeee es/generated///e lear learn nei ghbora.
Kernel Diaeeelennttty..e
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Published as a conference paper at ICLR 2024
Table 11: Effects of and 3 MIMIC-III mortality. We mask 20% data and replace the masked data with the overall average over time for each feature. Underlining is the best.
0,001
0.1
Auz:
CF
Aux
CF
Auzi
Acd
CB
CR
(1000001
0.00 aar
0.122
0.964 fusu
0.120
0,0015
0.00 Rus
0.007
0,057
0:98 Lovnn
Lov
2.125_...00
La.300
0.121 0.121_a.07
0.088 902
0.085
0.000
0.057 10
0:980
0.080
0.127 uv.
0.004_...00
0.004
0.90f
0.057.a
0.127
an our
0,003
0.123
0,002 002
GUM8 nos
3.0
0.128.0.07
0.106
Table 12: Difference between the distribution of different perturbations and the original distribution.
RARE-TIME
RARE-OBSEAVATION
PERTURBATION TYPE
KDE-SCORE
KL KL-DIVERGENCE
IDE-SCORE
KI-DIVERGENCE
ZERO PERTURNATION
-25.242
-23.377
MEAN PERTURBATION
-30,805
0.0731
0.0589 -26.121
-22.332
CONTRALSP PERTURBATION
-23,290
0.0393
-22.732
0.0386
Dynamask
Extmask
ContraLSP
Label
Figure 8: Saliency maps produced by various methods for Rare-Time experiment.
assess the ligeliioloood of each perturbed sample under the original distribution, called as KDE- score, where closer to ( indicates a higher likelihood of perturbed samples originating from the orig- inal distribution. Additionally, we quantify the KL-divergence between the distribution of perturbed samples and original samples, where a smaller KL means that the two distributions are closer. We conduct experiments on the Rare-Te Time and Observatton datasets and the results are shown in Table 12 It demonstrates that ContraLSP's perturbation is more akin to the original distribu- tion compared to the zero and mean perturbation. Furthermore, Extrmask performs hest because generates perturbations only from current samples, and therefore the generated perturbations guaranteed to be uninformative. This conclusion aligns with the visualization depicted in Figure
G ILLUSTRATIONS OF SALIENCY MAPS
Saliency maps represent valuable technique for visualizing the significance of features, and pre- vious works (Alqaraawi et al. 2020 Tonekaboni et al.) 2020; Leung et al.) 2023), particularly in multivariate time series analysis, have demonstrated their utility enhancing the interpretative pects the results. We also demonstrate the saliency maps of the benchmarks and our method for each dataset: (i) the saliency maps for the rare experiments shown in Figure g 9 and TO (ii)
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Published as a conference paper at ICLR 2024
FO
AFO
SVS
Dynamask
Figure 9: Saliency maps produced by various methods for Rare-Observation experiment,
AFO
SVS
Dynamask
Extrmask
ContraLSP
Label
Group Sj
Group $
Group-S2
Group
Figure 10: Saliency maps produced by various methods for Rare-Time (Diffgroups) experiment.
the Switch-Feature and State saliency maps are shown in Figure 12 and Figure respectively, (iii) and the saliency maps for the MIMIC-III mortality in Figure 14
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Published as a conference paper at ICLR 2024
FO
AFO
1G
SVS
Dynamask
Extmask
ContraLSP
Label
Group S
Group
Group S
Group S2
Figure 11: Saliency maps produced by various methods for Care-Observation (Diffgroups) experi- ment.
FO
AFO
IG
GradShap
Desplit
LIME
RETAIN
Dynemask
Extmask
Con
Label
Figure 12: Saliency maps produced by various methods for Switch-Feature data.
20

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Published as a conference paper at ICLR 2024
FD
AFO
10
GradShap
Desplif
RETAIN
Dynamask
Eximask
ContraLSSP
Label
Figure 13: Saliency maps produced by various methods for State data.
FO
AFO
IG
DoepLift
LIME
FIT
RETAIN
Dynamask
Extmask
ContraLSP
Figure 14: Saliency maps produced by various methods for MIMIC-III Mortality data.
21


Reviews:
[{"review_id": "SAhYf5i20Q", "reviewer": "Reviewer_mcnc", "summary": "The paper presents a tool for time series explanations, which is challenging as it requires matching complex temporal patterns and features. Perturbations have been among popular approaches to identify counterfactuals, but the paper argues, in time series these can be particularly challenging since perturbations can make samples OOD, rendering the resulting explanation meaningless to the original goal (i.e., finding a counterfactual). This is especially the case when considering the label-free perturbation scenario, which is less studied in literature. \n\nIn order to address this, the paper proposes a label-free Contrastive, and locally sparse perturbation approach that is more likely to generate in-domain perturbations. \n\nContraLSP has two main components -- first a contrasting objective that seeks to ensure perturbations are dissimilar from the the original time series and are \"more distracting\". There is also a sparse, stochastic gate for each feature to ensure sparsity in feature selection. The final objective contains 3 terms -- contrasting loss, a regularizer on the mask, and a proximal loss to ensure predictions are close to the original, un perturbed input.", "questions": "Please see above, I have listed several questions.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* **Problem statement and motivation**: Time series explainability is an important topic, that has received relatively lesser attention. The paper correctly identifies the trouble with OOD perturbations in time varying data, which are poorly understood in comparison with image and language modalities. The tool is capable of working with both blackbox and whitebox models, as well as working with regression and classification tasks-- which are positives.\n* **Problem formulation**: The contrasting approach to time series explainability appears to be novel as far as I know. \n* **Evaluation**: Extensive empirical evaluations are conducted on synthetic benchmarks with available ground truth on feature importance, as well as real world clinical data. ContraLSP appears to be outperforming several related baselines in both scenarios.", "weaknesses": "* **Counterfactuals**: The paper generously uses counterfactuals in the text to indicate perturbations produced by their model, whereas this is a label free approach and the mask is learned to minimize the gap between the original and unperturbed samples. The contrasting objective is the only source for potential counterfactual generation, that too it is not guaranteed to do so --  this distinction should be made more explicit in the text, and reduce the usage of perturbations being called counterfactuals. The experiments mostly only measure the ability of ContraLSP on identifying salient features, so this claim should be tempered down. \n* In this context, can the authors elaborate on the failures or weaknesses of ContraLSP? Specifically, when is it expected to fail, perhaps in comparison to techniques that work with labeled data?\n* **The contrasting objective** :  Since negatives are chosen at random, they are likely going to be weak negatives, and claiming these will be \"more counterfactual\" is probably not true. It must also be defined what \"more counterfactual\" means here -- more than what? How does the random negative selection ensure perturbations are crossing over class boundaries? Why is an L1 edit distance the right distance metric to do this? \n* **OOD Perturbations**  how does this objective _guarantee_ or at least ensure lack of OOD perturbations? Is the training of the perturbation function with contrastive loss sufficient to ensure this?\n* **Sparse gating and stochasticity**: Please define what the heavy-tailed nature of the sparse feature selection is, and how it is relevant to ContraLSP. The hard thresholding function in eqn (3) is only needed due to the random noise injected in the masking, since $\\mu'$ is a sigmoid function already.. why is the noise needed in the first place? \n* The paper's writing is not easy to follow, and this makes it hard to assess the core contribution of the work more rigorously. There are a lot of vague statements which are not stated clearly. Some of these are listed below:\n\t* \".. perturbation may not alleviate the distribution shift issue..\" (in the abstract)\n\t* \".. unregulated data distribution ..\" (in Sec 3)\n\t* \".. allows perturbed features to perceive heterogenous samples, thus increasing the impact of the perturbation..\" (Sec 4)\n\t* \".. counterfactual perturbations more distracting..\" (Sec 4.1)\n\t* \".. due to their heavy tailed nature..\" (Sec 4.2)\n* **Illustrations**: I recognize time series explanations are more challenging than visual data like imagery. However, the current set of illustrations are not very clear. For e.g. in Fig 5 why is the sum of salient observations shown? What is the inference from this figure? its very unclear, please make the key observations more explicit, perhaps with the help of a simpler dataset or time series and more consistent with Fig 1, which is easier to follow.", "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": "wgvUjkkDMb", "reviewer": "Reviewer_zXTo", "summary": "This paper presents ContraLSP, a locally sparse model that introduces counterfactual samples to build uninformative perturbations but keeps distribution using contrastive learning.\n\nNote that this paper does not quite match the expertise of my research and I have made the comments to AC.", "questions": "see above", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The idea of using contrastive loss seems to be a new idea\n2. In the experiment section, the authors provide a comprehensive comparison with multiple baseline models\n3. The paper is well written.", "weaknesses": "I mainly have some questions to the author:\n1. I curious about if the method is scalable to high dimension data. For example, video sequences?\n2. What is the $\\alpha$ and $\\beta$ values you use for each dataset? and how do you determine their values?\n3. In section 4.1, I wonder why you choose Manhattan distance rather than more conventional Euclidean distance? Optionally, other metrics like cosine distance might work better for contrastive learning?", "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": "2EYmA1w80v", "reviewer": "Reviewer_9mjJ", "summary": "This manuscript presents a new method in the explainability of time series predictions. The task here is given a multivariate time series of factors to predicting an output variable to identify the regions of the input that are most predictive of the output, here defined by a binary mask. The presented technique uses a perturbative approach to compute the binary mask on the input factors. While perturbative approaches have been considered, it differs from other approaches in how it produces these perturbations. They use a contrastive (triplet) loss across samples  a smoothed sparse gate. They provide a series of experiments comparing performance to other perturbative and other approaches, such as Dynamask and Shapley Features. They use a synthetic white-box experiment with rare observation or time salience and show improved recall with their method compared to others, although all methods showed high precision. Similarly on a synthetic state-switching task they find improved recall, and perform ablations to show how  different inputs vary. They provide further examples using classification and with a real-world mortality task. There is a comprehensive supplement giving further documentation for the methods and experiments.", "questions": "* The authors mention treatment of inter-sample correlations as an important component of the technique, but I do not see clear evidence of this. \n\n* Can you explain what in-domain and negative samples refer to “Other perturbations could be either not uninformative or not in-domain, while ours is counterfactual that is toward the distribution of negative samples “\n\n* “ To cope with it, locally stochastic gates Yang et al. (2022) consider an instance-wise selector that employs heterogeneous samples. Lee et al. (2022) takes a self-supervised way with unlabeled samples to enhance stochastic gates that encourage the model explainability meanwhile.” The terms introduced here (stochastic gates, heterogeneous samples) are not defined. The writing is unclear as well. \n\n* I found the description of the ‘Datasets and Benchmarks’ in 5.1 WHITE-BOX REGRESSION SIMULATION very unclear, making it hard to follow the experiments. \n\n* “our method significantly outperforms all other benchmarks.” I do not see any tests of significance. \n\n* Figure 5 I found unclear.", "limitations": "", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "* The approach is original and I believe a good contribution to existing methodologies.\n\n* They present a comprehensive set of experiments that are well motivated and the result achieves SOTA performance on many of them. \n\n* While the writing and motivation is often unclear, the math behind the method is very clearly explained.", "weaknesses": "* The advance feels somewhat incremental and the experiments performed are near-identical to the Dynamask paper (cited in text).\n\n* It was unclear to me how hyperparameters were selected for each experiment. This is important as changing the expected sparsity could have a dramatic effect on recall performance. More generally there are now a family of approaches for interpretability and it is not clear what the respective strengths and weaknesses are of each. This manuscript suggests their method is superior to all others, but a discussion of which types of data each method is suited to would be helpful. \n\n* The manuscript is hard to follow the text as the writing and motivation is not clear in a number of points. Terms are not always introduced in order and it is hard to appreciate the innovations is. One of my reservations about this manuscript is even if the algorithm is novel it will be hard for others to appreciate. \n\n* In the white box experiments I had trouble appreciating the experimental design, which made it difficult to evaluate. Moreover the largest difference between methods was in the information-based metrics, which seemed to scale quite nonlinearly with recall  (fine tuning/hyperparameters).", "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": "YdiuJBmaBZ", "reviewer": "Reviewer_MZY5", "summary": "-\tThe paper proposes a Contrastive and Locally Sparse Perturbations (ContraLSP) framework, which utilizes contrastive learning techniques to render non-salient features uninformative during training. The sparse gate with $\\ell_0$ regularization can aid in feature selection. The proposed method exhibits strength in both with-box and black-box scenarios.", "questions": "I will happily raise the score if the authors can address the following questions:\n\n-\t1. Although the authors discuss the selection of positive and negative samples in Appendix B, the selection of positive and negative pairs in time series is quite controversial because the proximity of data samples does not guarantee similarities [1,2,…]. The method in Appendix B appears too naive and may pose a risk of incorrect sampling for time series pair selection.\n-\t2. Can you provide a more specific explanation of why the counterfactual of non-salient features is superior to ignoring that part (e.g., setting it to zero), as shown in Figure 1? Even though a zero value of $x$ does not affect the training to minimize the loss of prediction with weight $w$ as $wx$, using counterfactuals can have adverse effects.\n-\t3. The learned mask in Figure 4 appears to exhibit similar behavior to a hard mask rather than other smooth masks. Can you clarify how the learned function $\\tau(\\cdot)$ behaves in a multi-dimensional context? I have read the ablation study in Table 3.\n-\t4. What is the difference in using the $\\ell_0$ norm in Section 4.2 of your methods compared to previous methods that use the $\\ell_0$ norm?\n\n[1] Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding, ICLR 2021.\n[2] TS2Vec: Towards Universal Representation of Time Series, AAAI 2022.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "-\tThe paper demonstrates its novelty by incorporating contrastive learning techniques into explainable time series tasks. Contrastive learning is a suitable solution for distinguishing informative and non-informative components.\n-\tThe paper is well-written and easy to read, and the figures effectively aid in comprehending the main ideas.\n-\tThrough the use of perturbation methods, ContraLSP remains relatively unaffected by noise and uninformative parts.\n-\tThe paper shows the performance enhancement of ContraLSP across a wide range of datasets, surpassing existing methods. The authors cover various tasks in Rare-Time, Rare-Observation, and various real-world datasets.", "weaknesses": "-\tPlease refer to questions.", "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)