Going Beyond Static: Understanding Shifts with Time-Series Attribution
Authors: Jiashuo Liu
Nabeel Seedat
Peng Cui
Mihaela van der Schaar
Venue: ICLR 2025 Poster (2025)
Keywords: distribution shifts
performance drop
attribution
time-series data
Primary area: alignment, fairness, safety, privacy, and societal considerations
TL;DR: We propose a time-series shift attribution framework that attributes performance degradation from various types of shifts to each temporal data property in a detailed manner, supported by theoretical analysis and empirical results.

Abstract: Distribution shifts in time-series data are complex due to temporal dependencies, multivariable interactions, and trend changes. 
However, robust methods often rely on structural assumptions that lack thorough empirical validation, limiting their practical applicability. 
In order to support an empirically grounded inductive approach to research, we introduce  our **T**ime-**S**eries **S**hift **A**ttribution (TSSA) framework, which analyzes *problem-specific* patterns of distribution shifts. Our framework attributes performance degradation from various types of shifts to each *temporal data property* in a detailed manner, supported by theoretical analysis of unbiasedness and asymptotic properties. Empirical studies in real-world healthcare applications highlight how the TSSA framework enhances the understanding of time-series shifts, facilitating reliable model deployment and driving targeted improvements from both algorithmic and data-centric perspectives.

Published as a conference paper at ICLR 2025
GOING BEYOND STATIC: UNDERSTANDING SHIFTS WITH TIME-SERIES ATTRIBUTION
Jiashuo Liul; Nabeel Seedat Peng Cui & Mihaela der Schaar! TTinggua University, UUniversity of Cambridge
(a com, ns741 @cam. ac. uk cuip@tsinghua edu. mv4 720 cam ac. uk
ABSTRACT
Distribution shifts in time-series data are complex due temporal dependencies, multivariable interactions, and trend changes. However, robust methods often rely on structural assumptions that lack thorough empirical validation, limiting their practical applicability. In order to support an empirically grounded inductive approach to research, we introduce our Time-Series Shift Attribution (TSSA) framework, which analyzes problem-specific patterns of distribution shifts. Our framework attributes performance degradation from various types of shifts to each temporal data property in a detailed manner, supported by theoretical analysis of unbiasedness and asymptotic properties. Empirical studies in real-world healthcare applications highlight how the TSSA framework enhances the understanding of time-series shifts, facilitating reliable model deployment and driving targeted improvements from both algorithmic and data-centric perspectives.
INTRODUCTION
Machine learning models are increasingly deployed in high-stakes settings such as healthcare with a variety of applications such as early discase screening (Cohn et al., 2003; Soriano et al.. 2009) or patient risk assessment (Naghavi et al., 2003; Twetman & Fontana, 2009). While model reliability is vital in such stakes settings, ML model performance often degrades when faced with distribution shifts. This challenge becomes particularly pronounced in time-series data, where unlike static data, the non-stationary properties of time-sereis such trends, seasonality and inherent temporal dynamics add additional complexity to the nature of these distribution shifts. In particular, we refer unique challenge manifested in time series namely "shifts in stationary properties", where the patterns themselves evolve over time.
In critical fields such as healtheare, ignoring these temporal distribution shifts can have thcetthre consequences, posing risks to patient safety and care quality. For instance, predictive models trained on patient data prior to a major public health crisis, such as the COVID-19 pandemic, may exhibit significant performance drops when deployed in post-pandemic settings (Roland et al., 2022). For example, during the COVID-19 pandemic, not only did static features like the proportion of high-risk patients change (Ngiam et al., 2023; Singh et al., 2023), but also temporal relationships between vital signs like heart rate and respiratory rate or trends in blood oxygen levels also changed in complex ways time. Consequently, understanding the changes beyond just static shifts is crucial not just to maintain model performance, but also to ensure patient safety and maintain trust Al-assisted decision-making systems.
Addressing this problem of understanding distribution shifts in time series remains underexplored and particularly challenging. Exisiting approaches (Lu et al., 2023; Liu et al., 2024b) draw on methods similar to those used for general static out-of-distributiin (OOD) generalization, such as distributionally robust optimization (DRO) (Sagawa al.; Duchi & Namkoong, 2021; Liu al., 2022) and causal invariant learning (Peters et al., 2016: Kuang et al., 2018; Arjovsky et al., 2019). These methods, although theoretically compelling, typically overlook the inherent temporal dynamies of time-series data. Moreover, they frequently rely on structural assumptions about distribution
Research conducted while visiting the der Schaar lab the University of Cambridge.

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Understanding Performance Degradation
For Future Improvements
Truining Population? ?
(i) What data properties we interested
(ii) Why such performance degradation?
Flw to reliably deploy the model?
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4 Case Study
Identity safe and risk regions
Prediction Model fo
performance degradation
Temporal Property Charactorization
Attribution
Performance Degradation
④ Case Study
Hos to improve the model?
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sufficioncy measure
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effective algorithmic Interveation
Identifly influential features for
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How to efficiently collect frature & data? 9
Population
denographics, living habote trand,, frequoory sorr diomns sings...
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Figure I: Overview of our TSSA framework.
shifts without rigorous empirical validation, potentially limiting their practical utility (Gulrajani & Lopez-Paz; Yang al., 2023; Gagnon Audet al., 2023; Liu et al., 2023a).
In response to these limitations, we emphasize the importance of adopting an inductive approach that is grounded in understanding cemne-srres-sppccffee patterns of distribution shifts- to effectively address real-world distribution shifts. Rather than arbitrarily applying robust methods or fine-tuning models when performance drops on new test data, we argue for first identifying the specific temporal factors driving the decline. This targeted understanding can guide more effective model adjustments or data collection (Liu et al., 2023a) and enable more judicious model deployment. Recent works (Cai et al., 2023; Feng et al., 2024) propose decomposition approaches to understand and attribute performance drop to different factors. However, they focus on "static" settings and cannot deal with the "shifts in temporal dynamics" problem for time-series data, which necessitates modeling the changes in temporal data properties for time series. Hence, the key question of this work is: How to attribute performance degradation between populations to temporal data properties?
To tackle this problem, we propose Time-Series Shift Autribution (TSSA) framework, which analyzes distribution shifts for time-series data from a data-centric perspective. As shown in Figure 1, our framework involves two parts: (i) Define metrics that characterize the behavioral properties of time- series data, along with a sufficiency measure that reflects the optimal predictive power in estimating the deployed model's 'ss prediction error for each sample using these metrics; (ii) Attribute performance degradation to each data property in detailed manner. We derive an unbiased doubly robust estimator, incorporating sample-efficiee model architecture for attribution.
Contributions: TSSA a framework which to the best of our knowledge is the first to address the issue of time-series distribution shift understanding and attribution bringing several con- tributions: ! Technically: we explicitly model and decompose time-series into interpretable properties and link them to shifts using the TSSA framework, providing doubly robust estima- tor for a nuanced attribution and understanding of why and how model performance changes across distributions for time-series predictors. ② Theoretically: we characterize the unbiased- ness and asymptotic properties for the attribution estimator.
3 Emprically: we demonstrate through 4 case studies in real-world health-care applications how our TSSA framework en- hances the understanding of time-series shifts and informs both reliable model deployment and targeted improvements MI. models as well as data collections.
2 PRELIMINARIES
In the context of time-series classification, let X = [U, E X represent the input covariates, where U E dRdv denotes static features and Vi.... E Rd.xtt denotes multi-variate time-series data up to time step f. Let Y E y represent the target prediction outcome. Consider a time-series prediction model f. which aims to predict the outcome Y based on the covariates X. Suppose f is trained on data pairs (X, Y) sampled from a training distribution IP. Let ((f(x), y) be a loss function quantifying the prediction error, such as cross-entropy loss 0-1 loss.
In this work, we consider a situation where we observe a performance degradation from P to a target population Q, i.e. Eg (e(((f(X), Y)] Ex (x)e(f(X), Y)]. In time-series data, performance degradation can arise from several factors, including changes in the distribution of input variables such as and V alterations in the temporal properties of the time series Vi..t, and the presence of missing
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variables. Understanding and attributing these shifts is crucial for effectively improving model robustness and ensuring accurate predictions in new settings.
Consider time-series model designed to predict patient mortality risk based on demographic features and various health metrics monitored in a hospital. The model may have been trained on data collected from the patient population prior to major public health event but deployed during or after the event, where there could be a significant shift in patient demographics or the emergence of new factors influencing mortality. Additionally, the model may need to be deployed across diverse settings, such as different countries or hospitals. In such cases, we may have sufficient labeled data during the event evaluate the model, but not enough to train a new one, as investigated in Section 5. Given that collecting new data is extremely costly and could delay patient care, we aim to understand and attribute the performance drop in order to determine in a principled manner the best way to adapt our model or collect the targeted data. Before presenting our methodology, we first discuss the challenges associated with time-series data, and then review the literature on performance drop attribution.
Challenges in time-series data Distribution shifts in time-series data are complex, involving both temporal shifts within distributions (e.g.. trends, seasonality) and changes between distributions, a challenge we call the "shifts in shifts" problem. Unlike static data, time-series requires addressing these evolving patterss. For instance, pre tre-pandemic blood oxygen levels in healthy individuals were stable, but during COVID-19, they dropped significantly and continued fluctuating in recovered patients. This highlights the need to consider temporal shift patterns alongside standard shifts.
Attributing performance drops Cai et al. (2023) propose decomposing performance drops into two general sources: covariate shifts (X) and concept shifts (Y) Building on this, Feng et al. (2024) employ Shapley values for more detailed decomposition. However, designed for static data, they cannot directly applied to time-series data, where, as discussed above, the distribution shifts are much more complicated. Furthermore, since we only concerned with the contribution of single data property to the model's performance degradation while all other properties (or features) remain constant, comprehensive calculation of Shapley values may be unnecessary and less appropriate. Additionally, there are studies that quantify the importance of shifts in individual features within (partially) known causal or problem structure (Wu et al., 2021; Thams et al., 2022; Zhang et al., 2023). However, these methods rely heavily on expert knowledge, and any misspecification could introduce significant risks in practice.
To the best of our knowledge, our work is the first to analyze detailed shift patterns in time-series data. While extensive research on time-scries forecasting addresses temporal shifts within a single distribution (Kim et al., 2021; Fan et al., 2023), our work focuses on the more general problem of shifts in temporal dynamics. This work primarily aims to understand performance drops in time-series classification models. In the following sections, we will introduce metrics to quantify these temporal shifts (Section 3.1) and develop a framework to attribute performance degradation to specific shift patterns (Section 3.2), to address the aforementioned challenges and limitations. More related works on distribution shifts, Shapley Value, and time-series anomaly detection can be found in Appendix A.
METHOD
In this section, we introduce our Time-Series Shift Attribution (TSSA) framework, designed to pro- vide detailed analysis of model performance degradation in time-series data. The key challenges are two-fold: capturing the temporal properties of time-series data and attributing the overall performance degradation individual features or properties. Corresponding with these two challenges, as shown in Figure 1, our framework contains two parts: (1) Temporal Property Characterization: We define and extract temporal properties, such as global, local and structural properties of the time series, that influence predictive performance. The sufficiency of these metrics is assessed through novel Sufficiency Measure, designed to quantify the extent to which each temporal feature contributes to model performance degradation. (2) Performance Attribution: We attribute model performance deterioration to individual temporal properties. This attribution is conducted with a doubly robust estimator, ensuring both unbiasedness and asymptotic consistency under mild assumptions. We also leverage a shared representation space to efficiently estimate risk models and propensity scores, particularly in scenarios with limited target population data, thereby improving estimation reliability.
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3.1 DESIDERATA FOR TIME-SERIES METRICS
To systematically capture the complex nature of distribution shifts in time series data, we propose the following desiderata for metrics to attribute performance shifts, which cover various aspects of time series behavior subjected to distribution shift. We categorize these desiderata into four main groups:
Global Characteristics Capture the overall, long-term behavior of the time series. These could encompass: (1) Overall Statistics: The overall statistics of a sequence of data, like the average value and standard deviation. (2) Trends: Metries to capture long-term di- rectional movements in the data. (3) Frequency: Metrics to identify and quantify cycli- cal patterns or periodic components. (4) Noise level: Metrics to quantify the signal-to- noise ratio. In this work, we introduce 8 metrics to capture the global characeteristics, including the average, max, min, standard deviation values, standardized trend, smoothed trend, maximum frequency, and signal-to-noise ratio.
Local Dynamics Assess short-term behaviors and local patterns within the time series. These could encompass: (1) Variability Assessment: Metrics to measure the degree and nature of fluctuations in the time series. (2) Local Non-stationarityy Metrics to detect short-term shifts. (3) Outlier and Anomaly Detection: Metrics to identify outlier or unusual values. In this work, metrics are included to capture the local dynamies, namely short-term variability, high-frequency energy, normalized Jitter index, relative strength index, KPSS non-stationary test, and the number of breakout points.
Identify significant shifts or changes in the underlying data data-generating process. These could encompass (1) Metrics to detect abrupt shifts in the statistical properties of the time series. (2) Metrics to capture the shifts in local trends associated with abrupt shifts. We introduce 2 metrics to capture the structural changes, including the number of change points, and the trend variability.
Structural Changes
Inter-series Relationships Address the interactions between multiple time series. These could encompass metrics to capture relationships and dependencies between different time series. We introduce the covariance variability among multiple time series to capture this.
These desiderata are motivated by the multifaceted nature of distribution shifts in time series data. Global characteristics can reveal shifts in overall patterns, while local dynamics can capture more subtle changes that might be masked in aggregate measures. Structural changes are crucial for identifying significant alterations in the underlying process, and inter-series relationships are essential for understanding shifts in complex, multivariate time series. While not exhaustive, as shown in Table 1, these metrics are drawn from various fields, and represent a comprehensive attempt to instantiate each desideratum, and more metries can be added in future developments. The detailed definitions can be found in Appendix F.
Table 1: Various metrics to quantify temporal properties from different aspects.
Temporal Property
Name
Meuie
Domain
Overall Statisties
Average, Standard Deviation, Max, Min values
Statistics
Standardized Trend
Equation (16)
Statistics
Global Characteristics
Smoothed Trend
Savitzky-Gool Golay Filter (Savitzky & Golay, 1964) Dominant frequency by FFT
Analyticul Chemistry
Maximum Frequency
Signal Processing
Signal-to- No-Nois Ratio
Equation (17)
Signal Processing
Short-Term Variability
Equation (19)
Signal Processing
High-Frequency Energy
Equation (20)
Sigmal Processing
Normalized Jitter Index
Equation (21)
Signal Processing
Local Dynamics
Relative Strength Index
Equation (22)
Finance
KPSS Non-Stutionary Test
p- Value from KPSS Test
Economics
Breakout Points
Equation (18) (Hollinger Hands (Rollinger, 1992))
Finance
Structural Changes
Change Points
PELT (Killick et 2012)
Statistics
Tread Variability
Standard deviation local trends
Statistics
Multivariate Interaction
Covariance Variahility
Equation (23)
Finance
With these metrics, we combine the static features U with the metrics of all time-series features Vi....> collectively referred to as in the following sections of this paper.
Sufficiency Measure Before moving on to the attribution, one natural question is whether the designed metrics are good enough to capture the temporal properties of time series. Since the ultimate goal is to understand the predictive performance drop, the primary requirement for these metrics is that they should relate to predictive performance. Therefore, we propose sufficiency measure to
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evaluate the optimal predictive power of the metrics, defined as:
Suff.(X) = min EE Loss (()), (((())
gEg
where Loss(;-)) denotes some loss functions (e.g., mean squared error, 0-1 loss) to measure the gap between the predicted error and the real error of the deployed (and fixed) model J. 9 can be chosen as any model classes (e.g., neural networks, XGBoost, etc.). This metric measures the optimal power in predicting the deployed model's prediction error for each sample using the data property metrics. The smaller it is, the more predictive the metrics become. Therefore, it can serve as guideline to measure the quality of the metrics. In Proposition we demonstrate how this sufficiency measure affects the asymptotic properties of our attribution estimation (introduced in Section 3.2). Moreover, in our first case study (Section 5. we demonstrate how temporal property metrics can help to effectively identify, in highly interpretable manner, both the "safe region", where the model performs reliably, and the "risk region", where is less reliable. In Appendix D, we discuss more about the utility of our sufficiency measure.
3.2 PERFORMANCE DROP ATTRIBUTION
Based on the collection X of static features and temporal data properties in Table 1, we propose to attribute the performance drop, i.e., (e((([(X),) - Ep (X),,, Y)] to each component in X. To assess how a specific data property contributes to the performance drop, inspired by treatment effect estimation, we control for the distribution of all other features except the data property of interest. For instance, if we we could first control for the distribution of all other features like demographics, blood oxygen level, heart rate, to be the same across both populations. The remaining performance drop, after controlling for other factors, could then be attributed to the effect of blood pressure. Additional demonstrations on the relationship between our TSSA approach and average treatment effect (ATE) estimation can be found at Appendix C.
interested in understanding the effect of blood pressure the performance decline,
Objective of Attribution For specific data property S of interest, let (x)) denote all other properties/features in X, abbreviated as X-s in the remainder of this work. To "control" for the effects of X X-s. we define the conditional risks under distributions and Q as follows:
Rp(8-s = Ex(e(s(X), Y) &-sl, Ra(X-s) = EEl((((X),)))))) [Xss).
(2)
where {((()), Y) denotes the deployed model's original prediction error on the sample (X, Y). Note that when measuring prediction error (X))), Y),, we use the original samples rather than the extracted temporal properties. Building on this, we define the attribution score of feature as:
ASt == E ( s) Rr(X-s))-
which quantifies the performance gap between Q and IP, while holding the marginal distribution of all features except the feature of interest, X-s, constant. From distribution shift perspective, Attr. quantifies the performance drop introduced by (Y, (Y.5))XA1)) -shiiss between IP and Q
-siffts
Furthermore, in cases where we do not isolate a specific feature (i.e. feature of interest is set to the empty set), i.e., Attr. (0). the attribution score captures the "systematic" (and unavoidable) difference between IP and Q potentially caused by missing information. For example, in predicting patient risk, individuals from two populations may have similar health indices yet experience vastly different outcomes due to missing information, such as differing living habits across regions or the absence of key health metrics in the records. Note that this term reduces to the concept of "Y|X-shiff X-shift" introduced by Cai et al. (2023). To effectively estimate Equation (3), we propose a doubly robust estimator for our objective Equation (3) is resilient to misspecification, ensuring reliable attribution even when some assumptions might be violated.
Doubly Robust Estimation for Attribution Consider the original data (U+, Vi. Y ~ P and (U', VL. y3) Q we first calculate the temporal properties in Table 1 for Vi...,, and convert the data into (X" Yi ~ IP and (X², Y') Q. To estimate the attribution, i.e. Equation (3), we first learn two predictors Rer(-), (i(()) to approximate the conditional risk function Rs((.,, Ro(+) in Equation (2) respectively from the observation data. Then we fit domain classifier +-) as (propensity score estimator):
* #( s) 2 (x)=)) = Pr(s-s from & = x-s)
(4)
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We use non- non-parametrii models for Rp(-), Ro(+).(()) ensuring flexibility in learning the relationships between variables without relying on strong parametric assumptions. Throughout the theoretical analysis in this paper, we consider generic nonparametric regression estimators, and all strategies could be used directly with different ML models, e.g. tree-ensembles. Then we formulate the Augmented IPW (AIPW) (Robins et al., 1994) estimator as:
(St =
Σ (po(X -xo
np nQ
(5)
Re(X2g) pe((_ss) up R=(X jr (X=2s)) x(iis)
1 (x=
where Re(X2s) denotes the ground-truth value on sample X that can be calculated from our observation data (the same for Rr(X=s)) We also demonstrate the compatibility of our attribution with Shapley Value in Appendix B.
This aforementioned formulation ensures double robustness, meaning that our attribution remains consistent and unbiased as long as either the conditional risk predictors or the propensity score estimator is correctly specified. With the propensity score estimator +(-) in use, we rely the overlap assumption between P and Q common requirement in causal inference (Wager. 2020). There are several approaches to address potential non-overlap in practice (Cai et al., 2023). In this work, we adopt a simpler strategy to mitigate the effects non-overlap by excluding samples with propensity scores that extremely close to 0 or 1. Furthermore, in Section 4, prove the unconfoundedneess, unbiasedness, and the asymptotic properties of our estimator in Equation (5).
Gample-Efficiees Estimation of (ip(-), (a()), and +-)) with Neural Networks In non-parametric estimation, we generally have sufficient samples for (-) (from the training population PP.. However, in worl-world applications, data from the target pop-
ulation Q is often scarce, making challenging to estimate ir(()) and f--) accurately. To mitigate
this, given the functions share the same input X-s- we propose to learn a shared representation space, thereby sharing information between the two popu- lations, and improving the sample efficiency of our estimates. Motivated by Shi et al. (2019), we adopt the model architecture as shown in Figure 2. Note that more advanced architectures (Curth & Van der Schaar, 2021) can be adopted here, and this is not the focus of this work. Through this model, share information between samples from I' and Q learn the representation space, which helps for the estimation of (-)()) and (-). Specifically, the loss function is:
(Rl -?
a(-)
(Ria -9
4
Figure 2: Sample-efficient estimation with neural networks. Ri denotes the conditional risk associated with i-th sample drawn from TP
(similar for (2)). h-)()) represents the shared representation learner, and wa. Waz: Wog de- note three separate predictors.
min d.
Σ (wo, (X' yt)2
wo, ( x
far(wo, (ha (X)s))
for (.)
Ag(-)
for 5
where (c denotes the cross-entropy loss.
4 THEORETICAL ANALYSIS
In this section, we characterize the unbiasedness and asymptotic properties for our estimation.
Proposition 1 (Unconfoundedness! & Unbiasedness). Denote T E {0, as an indicator variable:
T= 0, if X-s is from P; T= x is from Q
(6)
which can be likened to treatment variable. For any attribute S E X, we have:
[R((X_s), Ro( 11 T &-s.
(7)

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Based on this, assume that for all X-s, the overlap assumption holds, i.e., 0 xx(-s) < then the estimator in Equation (3) is consistent if either the pr((),, ( are consistent or ft()) is consistent.
Proof can be found in Appendix H. In addition to the unconfoundedness and unbiasedness, based on Wager (2020), we quantify the consistency between our estimator and the oracle one follows.
Proposition (Consisteney).. Consider the oracle estimator that uses the true up(+) RR (-),
(+(+) = (c).), and (-) rather than the estimates thereof:
RP uP+nQ
Attr. (S) np + QQQ
Σ -R(( (X
(8)
Assume that all samples are independent, fnr all 8-9, the overlap assumption holds, then: |Aure()) Attr." (S) =Op max (E(P.Q)
EE [((1-(8-)) Rr ()) E [ -==(===x_- ==(X {({=))))+})
sufficiency measure in Equation (1)
Proof can be found in Appendix H.
Remark 1. Proposition 2 quantiftes how closely our estimator approximates the oracle. We can make the following observations: (i) The first term, (P.O) E ( (X-s))
R,
characterizes the prediction error jupl)) and fiz(-). This term directly corresponds the sufficiency measure in Equation (1), which represents the objective of our designed temporal data properties thereby linking the two stages of our framework. (ii) For any op(n 1er1////cosssseeeeee machine learning methods to estimate puz, Pi. R. i.e.
$ (#(X ()( - -x( R s)) max E ((((((X-s) - ( (E(F.Q)
then we have (9)
Vn
vTl (T(AArr(S) - -Atr. As)) -tp O.
(10)
5 EXPERIMENTS
We design case studies comprehensively demonstrate the effectiveness and usage of our TSSA framework, including different real-world shift patterns and prediction tasks. Through our exper- iments, we use the Medical Information Mart for Intensive Care (MIMIC) (Johnson et al., 2016) dataset. It is representative of complex real-world medical time series and contains 23,100 patients from which static demographic features (such as age, gender, admission type etc) and 53 time-series health indexes (such as blood pressure, Braden mobility, temperature etc) have been measured.
5.1 CASE STUDY 1: TEMPORAL. PROPERTIES GUIDING RELIABLE MODEL DEPLOYMENT
In the first case study, we demonstrate the importance of our time-series data properties (Appendix F) through the interpretable guidance for model safe deployment. Consider typical intensive-care scenario where the classifier, fo()), is trained on historical data but is deployed across different patients and various stages of their care. Since different patients are likely to exhibit varying feature patterns, it is challenging for a single model to perform consistently well across all incoming patients. Therefore, high-stakes scenarios like this, is crucial identify in advance the types of data where the model performs reliably and clinicians can trust its predictions ciadicttioss-efferred to as the safe region. Similarly, important to recognize the data patterns where the model performs poorly and should not be relied upon, referred to as the risk region.
Experiment Setup The task is to predict patient mortality based on 24-hour recordings. We follow the standard design outlined by Jarrett et al., randomly splitting the patients in the MIMIC-II dataset into a training set (18,49) 490 patients, IP) and a test set (4,610 patients, Q), ensuring no patient overlap between the two sets. For the validation set, we use the same patients as the training set but select different time segments for their time- series features, denoted as Poal- We train a Transformer model, fo(.), on the training set, perform region analysis based on the validation data, and use the test set to verify the effectiveness of the identified regions.
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Figure 3: Region Analysis. (a)-(b): Visualizations of the safe and risk regions, defined by interpretable decision rules based on the extracted temporal properties. (c) The enror rates on the validation set, the entire test set, the safe region, and the risk region. Error rates in the risk region exceed overall test error, while error in the safe region is much lower than overall test error, thereby guiding safe model deployment by identifying and avoiding usage for patients in the risk region. Note that the regions are learned on validation set Pval with no access of the test set in advance.
Methodology in Region Analysis Given the high-stakes nature of the task, these regions must be highly interpretable, rather than relying on opaque, non-interpretable parametric models. Inspired by Lim et al. (2021); Liu et al. (2023a), we fit decision tree model, Ix() on the validation set (Pva)), to predict the prediction error (X)) Y) of the trained model fo()). using the extracted data properties and static demographic features X (Appendix F). The decision tree partitions the data into distinct regions, each defined by interpretable decision rules and corresponding to unique leaf node. By analyzing the samples within each leaf, we can identify regions with the highest and lowest risk, as the label assigned by the decision tree represents the original prediction error.
Analysis In Figure 3a and Figure 3b, we visualize the safe and risk regions identified based on temporal properties, defined by interpretable and sasy-to-understand decision rules. To demonstrate how this guides safe model deployment, we calculate the error rates for the entire test set, the safe region, and the risk region separately. From Figure 3c, while the overall error rate on the test set relatively reasonable (22.4%), the error rate in the risk region much higher (52.0%), nearing the level of random guessing. In contrast, the error rate in the safe region is significantly lower (3.7%). Our region analysis offers not only interpretability by design, but also a tool for reliable model deployment. Clinicians can confidently apply the model on patients in the safe region while avoiding use for patients in the risk region, thus ensuring reliable model deployment, which is important from the perspective of trustworthy ML in high stakes settings like healthcare. Further results in Appendix G.3 reinforce the superiority of our Take-away 1: regions, ensuring the reliable and smart deployment of ML models in critical care.
region analysis. Temporal properties enable accurate and interpretable identification of safe and risk
5.2
CASE STUDY 2: AGE SHIFTS IN MORTALITY RISK PREDICTION
In real-world healthcare settings, shifts in population distribution are commonly observed. For instance, significant variations in patient age distributions often arise across different hospitals and regions. To rigorously assess the effectiveness of our attribution method, we design scenarios reflecting these variations in patient age on MIMIC-III, and verify that our framework attributes the observed performance degradation to the appropriate features or properties.
Experiment Setup: Shifts in Patient Age The task is to predict patient mortality based on 24-hour recordings. We consider a data collection process that oversamples patients under the age of 65, where the average age of the patients in training is 57, while in the test set, the average age is 77. The training set contains 1 11,476 patients (training distribution I"), and the test set contains 6,408 new (but older) patients (target distribution Q). For the validation data, similar with Case Study I (Section 5.1), we choose the same patients as in the training set but select different time segments for their time-series features. We train Transformer model fe(-) on P and evaluate it on Q, where we observe a performance drop of 13.9pp on accuracy (from 87.7% to 73.8%), and 8.8pp on Macro-F1 score (from 72.5% 63.7%) In the subsequent analysis, we keep the model So (-) fixed during evaluation and apply our TSSA framework to attribute its performance drop to various features. More details can be found in Appendix G.6.
Analysis We begin by presenting the feature attribution results in Figure 4a, which show the average attribution scores along with standard deviation errors from 10 random runs. The findings reveal that the top features identified by our framework are predominantly demographic variables (yellow bars), with the "Age" feature correctly attributed as the most influential to the performance
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(a) Feature Attribution.
(b) Accuracy.
(c) Macro-F1 Score.
Figure 4: Results for Case Study 2: (a) We visualize the top 10 most important features, which are mainly demographic features (yellow bars), with age being the most prominent. This corresponds with our "prior" knowledge and verify that framework attributes to the appropriate features. (b)-(c) We do some balancing the top three features respectively during the training phase and plot the accuracy and Macro-F1 score for each model. The results show significant improvement in performance over original model and simple finetuning when we intervene on these top features.
drop. Other key features, such as Admission Location (c.g., emergency room, referral, transfer from other hospitals) and Previous ICU Stay Duration, have a relatively strong correlation with the Age feature. This aligns well with our problem setting, where we perform oversampling based on the "Age" feature. Furthermore, can we use the attribution to guide actions to remedy model performance. For each of the top 3 identified features (i.e., Age, Admit Location, and Previous ICU Stays), we apply simple balancing by reweighting the data based solely on the inverse density ratio of that specific feature to achieve uniform distribution. As shown in Figure 4b and Figure 4c, observe significant improvements in both test accuracy and Macro-F1 score. This demonstrates that the top features identified by framework directly influence the performance drop observed between the training and test patients. Additionally, this highlights how our attribution results can inspire further algorithmic interventions. In this case study, this inductive approach shows that even simple algorithmic modifications can lead to significant improvements.
Our attribution framework accurately attributes the performance drop to relevant demographic features and inspires straightforward yet effective algorithmic interventions, such as data balancing (as done in our intervention), and targeted data augmentation.
Take-away 2:
5.3 CASE STUDY 3: PREEMPTIVE DIAGNOSIS UNDER TEMPORAL SHIFTS
Beyond shifts in patient age, temporal variations in patients' conditions represent another prevalent type of shift in healthcare data. In preemptive diagnostic scenarios, our target is for the model to detect mortality risks at the earliest possible stage (Filippin et al., 2015). This proactive approach not only enhances patient outcomes by facilitating timely interventions but also underscores the importance of adapting models to account for the dynamic nature of patient health over time. In this case study, we explore how our attribution framework can offer valuable insights for this.
Experiment Setup: Preemptive Diagnosis under Temporal Shifts To evaluate reliability in the early detection of mortality risk, we examine the temporal shifts between the training and test patients. Specifically, for the training set P. we utilize the last 24-hour time segments for all time-series features, while for the test set Q we select the first 24-hour time segments for all features. This setup allows us to assess whether the model can effectively withstand these temporal shifts and accurately identify patients at high risk of mortality in the early stage. We train a Transformer model so (-) on IP, which comprises 12,574 patients, and validate it on an additional 5,547 patients. To control for other shifts, we use the same set of patients for both the validation and test sets Q; the only difference lies in the time segments used: the last 24 hours for validation and the first 24 hours for testing. In this case, we observe a performance drop of 13.8pp in accuracy (from 90.0% to 76.2%) and 24.8pp in Macro-F1 score (from 64.1% to 39.3%), highlighting the necessity to investigate the reasons behind this significant decline. Then for the subsequent analysis, we keep the model fo() fixed during evaluation and apply our TSSA framework to attribute its performance drop to various features.
Analysis In Figure 5a, we present the average attribution scores along with standard deviation errors from 10 random runs. In contrast to Figure 4a, which displays attribution based on age shifts, the prominent features in this analysis are primarily temporal properties, including the smoothed slope, high-frequence energy, and break points. For instance, for the top feature- the smoothed slope of Braden Activity- we randomly selected ten patients and visualized the last 24-hour (blue) and the first ho- (red) time series for Braden Activity in Figure 5b. Here, we observe that the trends, as indicated by the smoothed slope metric (top feature). and break points (sixth feature) of this time series differ significantly. As demonstrate by Valiani al. (2017), mobility status during

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(a) Attribution (Case Study 3). (b) Braden Activity Curve.
(c) Attribution (Case Study 4).
Figure 5: Results of Case Study 3&4: (a) We visualize the top 10 most important features for Case that the performance drop is primarily driven by extracted temporal properties. (b) We randomly select 10 patients to compare the curves of the top feature (Braden Activity). A significant difference in both the slope and breakpoints is observed. (c) We visualize the top 10 most important features for Case Study 4, where they are all temporal properties.
Study 3. We
hospitalization provides substantial prognostic value in hospitalized older adults. The Braden Activity score could be an efficient and valuable source of information about mobility status for targeting post-hospital care of older adults. Our attribution results provide valuable insights for clinicians. First, it is essential to monitor changes in the Braden Activity feature closely. Second, as illustrated on the right side of Figure 5b, many of these changes may go unrecorded or unmeasured during the early stages of patient care. To enable timely detection, clinicians should prioritize the assessment of this feature from the outset. Overall, these findings underscore the potential of our results to enhance clinical practices and improve feature collection.
Take-away 3: Our attribution framework provides valuable insights guide ML engineers and clinicians, like implementing timely and effective feature monitoring and collection.
5.4 CASE STUDY 4: VENTILATOR PREDICTION
We focus on predicting the use of mechanical ventilation in intensive care- a procedure that is both invasive and uncomfortable, requiring the induction of artificial coma and carrying significant risk of mortality. Accurate predictions are crucial, as errors can lead to serious consequences.
Experiment Setup The task is to predict whether a patient requires mechanical ventilation. We consider realistic scenario in which model trained on historical data (12,574 patients, first 24-hour time series, denoted as P) must be deployed for new patients and future time segments (an additional 5,547 patients, second 24-hour time series, denoted as Q). This scenario accounts for shifts in both demographics (across different patients) and temporal factors (across various time periods, such as the first day versus the second day). We train Transformer model, and observe a performance drop of 12.4pp in accuracy (from 93.7% to 31.3%) and 10 in Macro-F1 score (from 62.4% to 52.3%). highlighting the necessity investigate the reasons behind this significant decline.
Analysis We present the feature attribution results in Figure Sc. Notably, all top 10 features are temporal properties, indicating that the expected demographic shifts among patients are unexpectedly minor. To further explore this phenomenon, we exclude temporal shifts and build a new test set denoted as Q' where the time-series features are also derived from the first 24 hours (the same as P). After evaluation, the drop from P to Q' is only 0.6pp in accuracy and 0.3pp in Macro-Fl score. Thus, this drop can be primarily attributed to demographic shifts among different patients. This further supports our attribution results that indicate minor shifts among patients in this scenario. Furthermore, our identified top features are closely related to the ventilator prediction. For example, Platelet Count (Top-1) is recognized as significant prognostic marker in intensive care (Mackay al.. 2010: Ilban& & Simsek, 2023). Therefore, our attribution results offer valuable insights for ensuring reliable deployment and aiding clinicians in making more informed decisions.
Take-away 4: Our attribution framework effectively identifies the primary sources of distributional shifts, providing actionable insights for guiding subsequent algorithmic interventions.
6 CONCLUSION
This paper presented the Kime-Series Shift Attribution (TSSA) framework, which effectively attributes performance degradation due to distribution shifts in time-series data, with a focus healthcare applications. Our empirical and theoretical results demonstrate its potential to enhance model reliability and inspire both algorithmic and data-centric interventions in the future.
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ACKNOWLEDGEMENTS
The authors are grateful to the anonymous ICLR reviewers for their useful comments and feedback. Peng Cui is supported by NSFC (No. 62425206, 62141607) and Beijing Municipal Science and Technology Project (No. Z241100004224009) NS is funded by the Cystic Fibrosis Trust.
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A RELATED WORK
Besides the works introduced Section 2, we will briefly review other methods related to our topic in this section.
Distribution Shifts To tackle the challenge of distribution shifts (Liu et al., 2021b), several methods have been proposed, with distributionally robust optimization (DRO) (Sagawa et al.: Duchi & Namkoong, 2021: Duchi et al., 2023; Liu et al., 2023a) and invariant learning (Arjovsky et al., 2019; Koyama & Yamaguchi, 2020; Liu et al., 2021a; 2024a) being among the most prominent approaches. DRO techniques involve perturbing the data distribution within predefined uncertainty set and optimizing for the worst-case prediction risk. However, these uncertainty sets often selected based on theoretical considerations rather than empirical evidence, which can lead to overly pessimistic outcomes in practice (Liu al., 2023a). Invariant learning methods, on the other hand, aim to discover representations that maintain a consistent relationship with the outcome variable across different domains. Nevertheless, these methods depend heavily on the availability of high-quality environments (Liu et al., 2021a), and the assumption of invariance may not hold in real-world settings. For instance, unobserved confounders or missing Periables-commen scenarios- can prevent the existence of a robust invariant representation. Our work addresses the distribution shift problem through an inductive approach, first aiming to understand the shift patterns. This understanding can then inform targeted interventions from both algorithmic and data-centric perspectives.
practical
Time-Series Anomaly Detection In time-series anomaly detection, several works have addressed concept drifts over time, developing both supervised and unsupervised methods (Le & Papotti, 2020; Braci & Wagner, 2020; Liu al., 2023b). Our approach differs from these methods in several key ways: (i) our goal is to understand why a model's performance declines in a prediction task by attributing this drop to specific properties of interest, whereas anomaly detection methods focus primarily on reliably detecting breakpoints; (ii) the shifts considered in time-series anomaly detection are typically associated with breakpoints, whereas our work covers a broader range of temporal properties (as shown in Table 1). Additionally, our attribution framework can be applied to diagnose performance drops in anomaly detection methods as well.
Furthermore, in the following Appendix B, demonstrate in detail the related works with Shapley Value (Lundberg & Lee, 2017), as well as the compatibility of our approach with Shapley Value.
B SHAPLEY VALUE
One typical attribution method the SHapley Additive exPlanations (SHAP) (Lundberg & Lee, 2017), which uses cooperative game theory to compute explanations of model predictions. However, our work differs from previous ones in the following aspects:
Different goals: Previous works focus attributing model predictions to input features, whereas our work aims to understand the performance degradation of the model when transferring from one distribution to another.
Different philosophies: Shapley values compute the average contribution of feature across all possible subsets of features. In contrast, our approach focuses on the impact of a single data property on the model's performance degradation, while keeping all other properties (or features) constant. As result, a full calculation of Shapley values may be unnecessary and less suitable for our objectives.
Different settings: Previous works typically address static settings, where models can be refit with any subset of features. Our work, however, deals with time-series data, where each time series involves multiple temporal properties, making it infeasible to "remove" one property and refit the model to estimate SHAP values.
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Furthermore, our proposed attribution method is compatible with SHAP values, attribution score can be integrated into SHAP as the "effect" function. In the following, we would like to first demonstrate why currently do not Shapley Value, and then illustrate how our approach can be integrated with Shapley Value.
Why we do not use Shapley Value One typical attribution method is the SHapley Additive exPlanations (SHAP) (Lundberg & Lee, 2017). which uses cooperative game theory to compute explanations of model predictions. However, our work differs from previous ones in the following aspects:
Previous works focus on attributing model predictions to input features, whereas our work aims to understand the performance degradation the model when transferring from one distribution to another.
Different goals:
Different philosophies: Shapley values compute the average contribution of feature across all possible subsets features. In contrast, our approach focuses on the impact of single data property the model's performance degradation, while keeping all other properties (or features) constant. As a result, a full calculation of Shapley values may be unnecessary and less suitable for our objectives.
Different settings: Previous works typically address static settings, where models can be refit with any subset of features. Our work, however, deals with time-series data, where each time series involves multiple temporal properties, making it infeasible to "remove" one property and refit the model to estimate SHAP values.
Compatibility with Shapley Value Furthermore, our proposed attribution method is compatible with SHAP values, as attribution score can be integrated into SHAP as the "effect" function.
First, recall the definition of Shapley Value: for a player i, the Shapley value (v( calculated as:
SHUM - S - 1)! (v(SU (0) - v(S)
(.()) = Σ
(11)
WI
SCAVOC
Where N is the set of all players, S is subset of players that does not include i, |S| and [W] are the sizes of sets S and N, respectively, vSS) is the value function for coalition S, representing the payoff that the players in S can generate. v(S U (i)) v(S) is the marginal contribution of player i when joining coalition S.
Second, we demonstrate how our TSSA approach can be integrated with Shapley Value. Denote the attribution results of feature S given by our original approach as (St. Then can define the Shapley Value as:
DIa 11 -111 (Attr. (VUS) - -Attt))
SHAP.Attr. (S)
Σ
(12)
d!
VEX-S
where d denotes the number of extracted features, X-s denotes the set of all features except S. Therefore, our TSSA approach is compatible with Shapley Value, which we leave promising way of future extension of this work.
C DISCUSSION ON THE RELATIONSHIP WITH AVERAGE TREATMENT EFFECT
Relationship with Average Treatment Effect (ATE) First, we would like to clarify that our TSSA
attribution approach, which is not designed estimate ATE solve causal problems. And only "interpret" our objective function as special kind of ATE. That is, denote E (0, 1) as an indicator variable:
T= 0, if x from P. T= if X- is from Q
(13)
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which can be likened treatment variable. And our attribution objective then be rewritten as: [[())=B[((X() 1) R..-RR =)],
(14)
where R( 1) denotes Rg(-). and R(.. T 0) denotes Rp(-) that can be viewed as two outcome function (like in causal literature). Therefore, when studying the effect of one feature to the performance drop, our attribution approach controls all the other attributes (to be identical between group T = 1 and group I' = 0), and then calculate its effect. Note that we are not studying original ATE estimation problems.
Thcoretical Analysis Beyond ATE Unlike in causal inference literature, where verifying the unconfoundedness assumption can challenging, our problem formulation enables us prove the unconfoundedness directly in Proposition I, highlighting key advantage of this approach. Based on this, it follows naturally that the double robustness property, as characterized in Proposition 1, ensures the unbiasedness of our estimator.
D UTILITY OF SUFFICIENCY MEASURE
In this section, we would like to clarify the utility of the sufficiency measure by addressing it from the following two aspects.
Experiment Perspective First, for case study (see Section 5.1), select top- features with K E {10, 20, 30, all), calculate the sufficiency measure as well as the worst-accuracy (among up(.), (.).), and xT-)) of our attribution model. The results in Table 2 show clear trend: better sufficiency (corresponding to lower sufficiency score, which is the MSE) correspond to improved prediction performance and more precise attribution, thereby highlighting the practical utility of this measure. Note that lower sufficiency score represents better sufficiency, since the measure is defined as mean-square error.
Theory Perspective Second, as demonstrated in Proposition 2, the attribution estimation error is derived as:
Op max (E(P.Q (
(A(8_s) -
(15)
sufficioncy measure Equation (1), of pp.
(T-)
which is directly controlled by the sufficiency measure. This theoretical result further underscores the importance and relevance of this metric in ensuring robust and reliable attribution.
Why to report the worst accuracy? The attribution estimation error in Equation (15) is the product of (1) the worst error of (=(-), po(-) and (2) the error of 7--). Therefore, we care about the performance of all three predictors (up(-), (a(+) and T--). Thus, we report the worst accuracy among (up().He()) and (-) reflect the sufficiency of extracted features.
Table 2: Utility of sufficiency measure, where lower sufficiency score represents better sufficiency, since the measure is defined as mean-square error.
Top- 10 Features
Top-20 Features
Top-30 Features
All Features
Sufficiency,
0.202
0.182
0.176
0.166
Worst-Acet
68.9
72.8
73.4
76.0
(among Pp, HQ; n)
E VALUE OF OUR ATTRIBUTION ON INTERVENTIONS
In this section, we would like demonstrate how attribution can guide further interventions.
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What can TSSA provide Our attribution results designed to provide comprehensive frame- work to understand the distribution shifts responsible for performance drops. Specifically, the interpretability of both static features and extracted non-stationary properties allows clinicians to identify the underlying reasons behind model failures.
How to leverage Our results provide a basis for both model-centric and data-centric intervention, and can also inform smart deployment.
When the model can be finetuneedre-trainee, our TSSA can guide target model interventions. For example, our results can be incorporated with distributionally robust optimization to form some directed/targted uncertainty set, as shown Liu al. (2023a). Also, results guide more data-driven algorithmic design for better robustness or fairness among demographic groups (c.g., defined by the identified feature "Age").
Model Intervention:
Data-Centric Intervention: Our results can guide efficient data collection (for exam- ple, collect more data from the risk region), data balancing (as done our case study in Section 5.2), and targeted data augmentation (only perturb sensitive features).
Smart Deployment: When the model cannot be changed, our safe/risk regions can guide engineers/clinicians about where (not to) deploy the model, as demonstrated in our case study in Section 5.1 and Appendix G.3.
How to choose practice, these three aspects should be incorporated together so as to further improve the model. And we acknowledge that further efforts can be made on how to select better algorithms in each kind based on the specific situations one face, which to the best our knowledge still untouched field.
F DETAILS OF TEMPORAL PROPERTIES
In this section, we first clarify the guidance and transparency in our metric selection, and then introduce the metrics we used in detail.
F.1 GUIDANCE AND TRANSPARENCY IN METRIC SELECTION
Before introducing metrics used for extracting non-stationarity, we would like to clarify the guidance and transparency in our metric selection.
Desiderata for metries To provide a principled and transparent basis for metric selection, introduce desiderata for the types of metrics (Section 3.1). Specifically, our desiderata define the properties that metrics should capture in time-series data, grouped into four categories:
Global Characteristics: Capturing long-term trends, averages, and periodicities.
Local Dynamics: Measuring short-term variability and anomalies.
Structural Changes: Identifying abrupt shifts in data generation processes.
Multivariate (Inter-Series) Relationships: Quantifying dependencies between multiple
time series.
By organizing metries into these categories, we offer a structured framework guide practitioners in selecting or tailoring metrics for their specific datasets. To systematically assess the quality and rele- vance of metrics, we employ sufficiency measure, which quantifies the predictive power of selected metrics in explaining performance degradation. As theoretically demonstrated by Proposition 2, metrics with better sufficiency (lower sufficiency score, experiments see Appendix D) contribute enable more reliable attribution. We believe such measure provides data-driven measure to evaluate and refine metric selection in addition.
While acknowledge that current set of metrics is not exhaustive, TSSA a framework permits users to extend it with additional metrics that align with the defined desiderata. By linking sufficiency predictive performance, this then ensures that newly added metrics have utility for attribution.
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F.2 PROPERTY DEFINITION
To address the non-stationarity of time series, inspired from various fields, such as finance, statistics, and signal processing, identify numerous data property metries. Specifically, for sequence Vi... of length I, we define metrics corresponding to different temporal properties: Global Characteristics:
Overall Statistics: We calculate the average, standard deviation, maximum, and minimum values of each time-series feature.
Standardized Slope: Widely used in financial and climate analysis, the standardized slope is defined as:
Standardized Slope (V.... //tr..))/S((VVi.... (Vi.......)
(16)
which quantifies the strength of a sequence relative to its variability.
Drawing inspiration from analytical chemistry, we use the Savitzky- Golay filter (Savitzky & Golay, 1964) to characterize the smoothed trend. This filter smooths the data by fitting a polynomial to each segment data points, effectively extracting the underlying trend.
Smoothed Trend:
We calculate the dominant frequency for each time series using the Fast Fourier Transform (FFT) i.e. we extract the dominant frequency (with the maximal amplitude) from positive frequencies, where the positive frequency values are real numbers, calculated as fu N (T's 1 in our experiments).
Frequency:
Signal-to-Noise Ratio:
We compute the Signal-to- -egnal-o-NNise Ratio (SNR) for each feature in a time-series dataset by using moving average estimate the signal and residuals noise. The metric is defined as:
B[[
SNR
(17)
B[J[V - -
where V represents the original time-series feature, and V/ is the smoothed data (estimated signal).
Local Dynamics:
Breakout points: Inspired by the Bollinger Bands (Bollinger, 1992) widely applied in financial analysis, we calculate the number of breakout points within the sequence Vi... as:
p(Vi...) Ki [ [Mean(V.....) + Std(Vi....) for i I......)
(18)
which identifies the number of points that fall outside the 2-standaard-deviation bands to capture its local non-stationarity.
Short-term Variability: We first calculate first differences AV; V; V.-1. and the short-term variability can be defined as:
σAV Std (kd(AV, AVi),
(19)
which the standard deviation of first differences, and larger standard deviation indicates greater short-term fluctuation.
To capture the figh-frequency components, based on Discrete Fourier Transform, define the high-frequency energy as:
niggh-Frequenyy Energy:
Enigh
Σ A= k=
Vye
12nkj/t
(20)
which calculates the squared magnitudes of the upper half of the frequency spectrum.
Normalized Jitter Index: To provide a comprehensive characteristic of variability, we design the normalized Jitter index as:
Jitter Index : 00 + (1 az) Frigh
(21)
mean( Vi....)
where a E (0, 1) the parametrt to adjust the information from time and frequency domains to provide comprehensive measure of fluctuation in time series.
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Relative Strength Index: In order to capture the speed and change of signal, the relative strength index (RSI) defined as:
RS En I(V V2-1) (V- Σi=I(V I(V, Vi-)) (V--1-V,
100
RSI = 100
(22)
1 RS
where RS captures the ratio of average gains to average declines of V Thus, the RSI measures the momentum strength of signal, particularly the relative magnitude of recent gains versus declines.
KPSS Non-Statinn -tatiioan Test: We calculate the p-value from the KPSS test (Kwiatkowski- Phillips-Schmidt-Shie test), which is used to assess the stationarity of time series.
3. Structural Changes
Change points: From statisties, we utilize Pruned Exact Linear Time (PELT (Killick et al., 2012)) to capture the optimal change point set for sequence Vi..., which identifies multiple change points in the sequence such that the statistical properties (e.g., mean, variance) remain consistent within each segment.
Trend Variability: We calculate the local trend changes associated with the change points.
4. Multivariate Interaction
To capture the varying relationships (w.rt. time) among multiple time-series features, inspired by literatures local covariance (Papadimitriou et al., 2006; Chen et al., 2010), we design a covariance variability for time-series features V VI..TT E RdxT
Covariance Variability:
follows:
Cov. Var(V == Std(A Amsx (C(t)))
(23)
where C(t) denotes the local covariance matrix at time t.
We list the metrics in Table 1, and more details as well as some other metrics are provided in the Appendix. With these metrics, we combine the static features with the metrics of all time-series features Vi..., collectively referred as X in the following sections of this paper.
G ADDITIONAL EXPERIMENT RESULTS
In this section, we add more details of our experiments.
G.1 DATASET DESCRIPTIONS
Through our experiments, we use the Medical Information Mart for Intensive Care (MIMIC) (Johnson al., 2016) dataset, which is representative of complex real-world medical time series. The whole dataset contains 23, 100 patients, from which static demographic features- including insurance status, marital status, ethnicity, gender, age, previous admission, previous ICU stay time, admission type, and admission location- and 53 time-series health indexes, including BUN, Braden activity, Braden friction/shear, Braden mobility, Braden moisture, Braden nutrition, GCS (eye opening), GCS (motor response), GCS (verbal response), HCO3, MCH, MCHC, MCV, 02 fraction, 02 pressure, 02 saturation, PTT, RDW, anion gap, arterial line, bicarbonate. calcium, chloride, cordis/introducer,, creatinine, dialysis catheter. diastolic blood pressure, glucose, heart rate, hematocrit, hemoglobin, magnesium, mean airway pressure, mean arterial blood pressure. multi lumen, norepinephrine, pCO2, pH, pO2, phenylephrine, phosphate, PICC line, platelet count, potassium, red blood cells, respiratory rate, sodium, systolic blood pressure, temperature, tidal volume, urea nitrogen, ventilator usage, and white blood cell counts. The time-series features are measured every hour, and the average length 85.4.
Dataset Details
In case studies 1 ~ 3, the outcome variable is mortality, and in case study 4, the outcome variable is ventilator usage (where we exclude the mortality feature).
Advantages of the MIMIC Dataset The MIMIC dataset offers several advantages, making especially suitable for our study:
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Real-World Complexity: MIMIC represents real-world clinical settings, including data from a diverse set of patients across different demographics and medical conditions. This is crucial for developing models that generalize well to actual hospital environments, where variability is high and patient trajectories are complex.
The 53 time-series features in MIMIC cover wide array of physiological signals, lab measurements, and treatments. This granularity allows for more comprehensive modeling of patient health. In comparison, many other datasets may focus a narrower subset of features, limiting their ability capture nuanced patient dynamics.
Granularity and Richness of Time-Series Data:
Diverse Outcome Variables: The dataset supports the study of multiple clinical outcomes, such as mortality and ventilator usage, which are critical in the context of ICU care. This allows for different case study designs and enables us to explore various clinical scenarios and broaden the scope of potential applications.
Longitudinal Data with High Temporal Resolution: MIMIC provides high-resolution, time-stamped data that tracks patients throughout their ICU stays. This temporal depth allows for the detailed study of health trajectories over time, which essential for building predictive models that anticipate patient outcomes based on continuous monitoring capability that many smaller or less detailed datasets lack.
Widely Used and Well- Validated: MIMIC has been extensively validated in the research community and is a well-established benchmark dataset for various tasks in medical machine learning. Its widespread use ensures the reliability and comparability of our results with those of previous studies. Additionally, its consistent presence in peer-reviewed research provides confidence in its data quality and facilitates benchmarking
Justification of the Temporal Shift Setting Then we would like further clarify the early diagnosis setup in case study 3. This partition reflects practical clinical scenario where early-stage predictions are critical in healthcare to identify patients at risk. Note, we are not predicting the past but rather assessing how well model trained on later-stage data can generalize and perform on earlier data (which temporally shifted). This is important in healthcare since while later-stage data may eventually become available, clinicians often need to make decisions based on the first 24 hours of patient data to prevent adverse outcomes or to take actions. Hence, our setup evaluates the model's 's ability perform early predictions and correctly identify patients risk, which is essential for preemptive and early care in clinical practice.
G.2 MODEL TRAINING DETAILS
As for the original model (under evaluation), hidden.dim:32), learning rate is le the total epoch number is 200, batch size 256, and the early stop is used during training (according to last 10 epoch). As for the attribution model: The model architecture is shown in Figure 2, where we use two-layer MIP with hidden size selected from 116,22,64,11 128) for each part according to the validation results, learning rate 1e-3 and batch size 64.
Transformer model (n.head:4, layer:3,
G.3 DIFFERENT TEMPORAL PROPERTIES MATTER FOR DIFFERENT TIME SERIES
To illustrate the necessity of incorporating various temporal properties, as discussed in Section 3.1, we compute the feature importance scores within the conditional risk predictor (ap()). The importance score for each feature is determined using the gradient norm of that feature, given by:
Er (X)x
where higher score indicates that the feature plays more significant role in predicting the error of the deployed model f-)). We visualize the feature importance in Figure 6. The results reveal that different temporal metrics are important for different time-series features, highlighting the intricate
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Th:: Booio Puat
Ingrctane Soom
Importance Stuce
Figure 6: Feature Importance. In case study 1, we visualize the top 30 most important features for (p).). The results highlight that different temporal characteristics are significant for different time series, demonstrating the complex nature of time series.
nature of time-series data. This not only highlights the complexity of the MIMIC dataset, but also justifies the necessity of the temporal property characterization stage in our framework.
G.4 COMPARISON WITH "STATIC" REGION ANALYSIS
In Case Study I, straightforward approach would be to treat all time-series features as static features and then apply the existing static region analysis method (Liu al., 2023a). This approach offers a natural baseline for comparison, as it simplifies the temporal aspect of the data. However, this simplification may overlook important dynamic patterns inherent in the time-series data.
Table 3: Comparison of Region Analysis Methods on Test Set.
Safe Region
Risk Region
Error Rate + # Samples f
Error Rate t
Samples
Static
8.8%
215
36.7%
30
Ours
3.7
241
52.0%
296
In Table 3, we present the error rate and the number of test samples falling within each region for both the static method and proposed method. A lower error rate indicates better safe region, while a higher error rate corresponds to a more effective risk region. Regarding sample size, larger number test samples in a region suggests that the region more robust and reliable.
From the results, it is evident that our region analysis method significantly outperforms the static feature-based approach. Additionally. the risk region in our method encompasses a much larger sample size, suggesting that our method, by incorporating temporal properties, captures more reliable and generalizable regions.
G.5 SAMPLE EFFICIENCY OF OUR ARCHITECTURE
In case study 2, we examine the performance of our proposed architecture (Figure 2) fitting the functions (-). (a()) (-). and #()) across different target sample sizes. Since the outcome variables are binary, we compute the worst balanced accuracy of our model, using XGBoost as a baseline for comparison. For XGBoost, Note that we mainly compare with XGBoost here since has shown superior prediction power on tabular data, and
train three independent models, one for each of the three functions.
outperforms neural networks (Gardner et al., 2022; McElfresh et al., 2024).
As shown in Figure 7, when the target sample size exceeds 30% of the training data, our proposed model consistently outperforms XGBoost, highlighting the effectiveness of the shared representation
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XcBoout
Balanced Accuracy
Figure 7: The worst balanced accuracy under different target sample sizes.
Table Intervention results. We compare our attribution-guided simple intervention with simple finetuning.
Original
Finetune
Age Intervention
Admit Loc. Intervention
ICU Stay Time Intervention
Accuracy
73.8
77.0
83.9
79.2
84.3
Macro-F1
63.7
65.7
68.4
67.0
69.3
space. However, as the target sample size decreases further, our model performs similarly to XGBoost. This outcome is expected, tree-ensemble models like XGBoostt are known to excel on tabular data, even low-data regimes. Additionally, for our attribution objective, a wide range of models can be employed to estimate jiz (-), (e(+), and f(-), offering flexibility in model selection.
G.6 COMPARISON WITH SIMPLE FINETUNING
For case study 2, we add the results of finetuning, where we use 50% samples (3200) from the original test set for finetuning, and test the remaining 50% test samples. For model intervention, mix the original training set with the finetuning samples, and then retrain a classifier with balanced weights according to the identified features (age, ICU stay time, etc.). The results are shown in Table where we can see that our intervention can significantly outperform simple finetuning.
H PROOFS
Proof for Proposition 1.
for unconfoundednesss the core is to prove that Rp xx(X-s) and Ry(X_
are both functions relying solely on X-s. S. Since X_ is derived from the original input X via some kind of transformations, we define g(X) = X-s. We first prove that Rp(X-s) = (x)) =
Ep (P)((Jo(X) Y) (x) is function of (XX). From measure theory, the conditional expectation
Ep ())(()) ()))) (X)) is defined with respect to the o-algebra (g(X)) and satisfies:
()) = h(g(X)).
(24)
where h()(X)) is measurable function of gXX). This implies that for any event A (g((X)) we have:
(E) -|((])
LA].
(25)
which implies that the conditional expectation (X), gX)). Note that here we use the Tower property (Billingsley, 2017), which states that E E|x], where G is sub-o-algebra. This means that when taking the conditional expectation of a random variable X, and then the result is equal to the total expectation of X. For the above equation, the inner conditional expectation Ep( [XX] can be viewed function of g(X). denoted as {X)())) And the outer expectation considers the expectation of ((g(X)) over some event A x()(X).. Thus, by tower property, the result of LHS equals to EJ Y) IAl because In is measurable with respect to (g(())), the o-algebra generated by g(X). And this ensures that [x((((X V) X)) is well-defined and depends only g(X)
depends only on the value of
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Based this, we re-write (x(X-s) and (X hx(9(X)) and h2(g( Then have:
Pr(T, ((x)
(26)
- -Pr(T, (,
(27)
PX(TT//L(((()))xxxx()))))))))) Pr(h) (2(o(x)))o( (((2)))))))))))))) -Pr(TTg(X)) (r(b)((((x))))xx(((()))))
(28)
(29)
which proves the conditional independence. Note that the last equation holds because h (g(X)) and (x))(( are both functions of g(X).
Then we proceed to proving the unbiasedness (also known as the double robustness). Note that the SUTVA assumption holds naturally in our problem setting. First, if jip(-) and (a(() are consistent, i.e.
(.p(.) R-(-) and (.p(.) = R-(-), it is easy to show the consistency of our estimator (by plugging-in pip and po)) Second, if # (-) is consistent, i.c. (-) (-), denote the indicator
1,
F is from Q
T
(30)
0,
if X is from P.
our estimator can be re- ce-written as:
1 ao+ap
T.Ro s)
(1 - R:)Rp(( s)
Attr.
o.p + nQ
TT m({is)
optimal IPW estimator
(31)
ng tnp
Tj n (x'ss)
T, (822))
(Ro(X s)(1
pip(X s)((1
np nQ
additioona
To complete the proof, need to show (i) the optimal IPW estimator is consistent, and (ii) the additional term is equal to 0. The proof of consistency of the optimal IPW estimator is standard and one can refer Wager (2020, Chapter 2). For the additional term, we have:
T.
E
X Xisl 0,
(32)
T(==))
and therefore complete the proof of unbiasedness.
Proof of Proposition 2. Our proof builds on the established techniques presented in (Wager, 2020,
Chapter 3), with tailored adaptations and simplifications specific our problem setting.
First, since in our problem setting, (P(()) = Rg(c) and po(+) = Ro(c), the oracle estimator is simplified to:
up+nQ
Attr. (S)
1
Σ
(Ra(X_s) Rr( Rx(X2s))
(33)
np + nq
where we do not have the propensity score term. Then we decompose Altr.()) Attr. (S) as:
Rp+nQ
Attr.(S) Attr." (S) = np + nQ
Σ
(
f - Ro ( [ss) + Rx((
(34)
i=1
Ro (x 5) (x 8)
R²(X 3) Pup (Xi
+
(1 T:)
(35)
*(X's)
1- -xx(X's)
A ug
(36)
where we define
no+nQ
(po(Xis)= s)( + Ro( - -igg(" -
13).
A
(37)
uQ
np nQ
A *(}!s)
E=
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and define An analogously. In order to prove Proposition 2, it suffices to show that Aug satisfies that conclusion. To prove this, we decompose Au as follows:
noona
1
Ap
(pQ(X"s) Ro( s))(1
(38)
np + nQ
*(X=s)
netnQ
1
(no(X_s) - RR(
T; T xX-=s)
(39)
np +
nQ
-=1
ap+na
1
- s)) # #(
)
(40)
up + nQQ
* x(X s)
We first deal with the first term. Note that in practice, we typically use cross-fitting and therefore (+)()) can be viewed as deterministic in the following. From Equation (32), the summands used to build the first term become mean-zera Therefore, we have:
ag+nQ
27
E
Σ
(0o(Xis) Ro(82s)) T(Xis)
(41)
nP + nQ
nntnoe
1
Ti T
=Var
(No(X's) - Re(
(42)
np + nQ
+nQ
x(2's)
1=1
1
Tj
Var
(Ra(Xis) -Ro(X (1)ss)(
(independent terms)
(43)
nP + nQ
x(X-3'
1
E
(Po(X 5) (
(44)
1PP + nQ
T (X
1
(Ro(X 5) -Ra( s))²(
T( 1)
(45)
P + no
where the last equality is because of:
EI(1
T
118 = E[[
2T,
T
Xi = (1- 1). (46)
T ((8'))
(X-s)
((82s)
Then from the overlap assumption, we assume that for all X 5. 1) < m(()) gives that
< 1 n7 which
E ( - Ho(("s)))
x(22s) 1)
(47)
np + ni
1
Bl(ie((21)) Ro((
(48)
(np + nQ)
Then for the second term, we have:
ap+no
(((o(X()s) - Ro(x__)) *(xis) क (X22s)
(49)
np nq
(0o(8 {
)2 (50)
V up + +nQ
1pp + na s:fi=1
T(X2s)
(X{
ad:=1
( RR =}]}] + T (#(8 - - = =(
(51)
25


Reviews:
[{"review_id": "oNvhGwL2Kv", "reviewer": "Reviewer_WGSf", "summary": "The paper proposes a data-driven framework to mitigate the distribution shift in time series data. The framework is designed based on characterizing metrics for behavioral properties of time series and attributing the performance degradation to those metrics. Paper provides empirical and theoretical analysis of the proposed method.", "questions": "1)  Why is the proposed method based on analyzing \"application-specific\" patterns? What does the paper mean by \"application-specific\"?\n\n2) What is the reason behind selecting metrics in each category of desiderata?  Can different metrics be selected?", "limitations": "", "rating": 5, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1) The paper addresses a very important yet underexplored problem. Not many existing works are designed to study and mitigate the distribution shift in time series data, despite the importance of time series models in real-world applications.\n\n2) The paper provides both theoretical and empirical analysis of the proposed method, which makes the model trustworthy and desirable for deployment in real-world applications.\n\n3) The proposed method demonstrates good performance.", "weaknesses": "1) The paper is not well-structured. It introduces many ill-defined concepts, without introducing them or justifying what they mean. For instance, what does the paper mean by \"shift within shift\"? \n\n2) As a follow up to the previous point, the paper also makes several claims which is not justified throughout the paper. For example, the paper claims the the proposed approach analyzes \"application-specific\" patterns. However, it is unclear why the proposed metrics are application-specific, as they seem to be mostly focused on general properties of time series.\n\n3) In the first part of the framework, the paper introduces four categories of desiderata for time series metrics and proposed different metrics for each category. It is not clear what are the criteria for selecting metrics in each category? Can different metrics be used?  \n\n4) The contribution of the paper is incremental to some extent, as it is mainly built upon similar frameworks designed for the static setting[1,2].\n\n[1]Tiffany Tianhui Cai, Hongseok Namkoong, and Steve Yadlowsky. Diagnosing model performance\nunder distribution shift. arXiv preprint arXiv:2303.02011, 2023\n\n[2]Jean Feng, Harvineet Singh, Fan Xia, Adarsh Subbaswamy, and Alexej Gossmann. A hierarchical\ndecomposition for explaining ml performance discrepancies. arXiv preprint arXiv:2402.14254,\n2024.", "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": "6NrF37pfYC", "reviewer": "Reviewer_36tU", "summary": "This paper builds a distribution shift explainer based on a rigorous Double Robustness estimator, applied to various extracted statistics. They provide theoretical justification of the estimator formulation, and experiments show how causes of shifts can be correctly identified and how the risk regions of the original model can be assessed.", "questions": "Wouldn't the shared representation space of the neural network compromise the double robustness by associating estimation of Pi and mu? It is likely that if one is wrong, the other is also due to their association ; hence negating the double robustness benefit. Would it be possible to test the reliability of double robustness in such conditions?\n\n(39) assumes iid data ==> It would be good to make explicit in the main body of the paper the assumption (X,Y) iid. As the work deals with time series, I wasn't sure if repeated measures for a patient, for instance, could be used as several samples. It appears that it is not the case, and should be put in preliminaries paragraph 1.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "The paper is very clear, with adequate contextualization (with both reference to ML community studies and medicine-focused studies), easy to understand preliminaries and properties, precise experiment protocol and separate experiments takeaways.\n\nThe experiments are strong evidences of the method relevance, as correct domain knowledge on well known datasets is infered.\n\nThe theory is sound and easy to verify (concise, clear, and refers to the relevant reference).", "weaknesses": "My understanding is that no code was provided for results reproducibility.\n\nOtherwise, I can only say that the weakness of this paper are beyond my abilities to review. The only weakness I could think of would be how much of a strong evidence the risk assessment would be to a medical practitioner. But I do not focus on the medical field, so I cannot be sure if this is an actual limitation.", "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": "3COeNcgNsk", "reviewer": "Reviewer_itss", "summary": "In this paper, the authors propose a novel approach, Time-Series Shift Attribution (TSSA), to address distribution shift issues in time-series data. This method is designed to analyze application-specific patterns of distribution shifts. The authors begin by outlining desirable characteristics for time-series metrics, examining factors such as Global Characteristics, Local Dynamics, Structural Changes, and Inter-series Relationships. Following this, they introduce a performance drop attribution strategy based on the Augmented IPW and prove that their estimator is unconfounded, unbiased, and consistent. The paper concludes with case studies that validate the effectiveness of the TSSA approach.", "questions": "1. Is Equation (21) derived using the tower property?\n2. The frequency is involved as discrepancy metric in Section 3.1. Is it justified in the proposed framework. For example, the distribution discussed in this paper is supported on $\\mathbb{R}$.", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The topic is highly relevant to the themes of the ICLR conference.\n2. The problem addressed is critical for real-world applications and holds substantial potential for future use.\n3. The proposed attribution strategy is intuitive and well-suited to the problem.", "weaknesses": "1. **Insufficient Baseline Comparisons**: The experimental section lacks sufficient baseline comparisons, which would further validate the effectiveness of the proposed approach.\n2. **Convergence Property**: In optimization, demonstrating uniqueness (and potentially consistency) is often followed by a proof of convergence properties [1]. It appears that convergence analysis is missing in this manuscript.\n3. **Font Size**: Some font sizes in Figure 5 are too small, making the content difficult to read.\n4. **Error Bars in Figure 7**: The presentation of Figure 7 is inconsistent with Figures 4 and 5(a), where error bars are provided. Should this discrepancy be addressed?\n\n---\n\nReferences:  \n[1]. { Euclidean, Metric, and Wasserstein } Gradient Flows: an overview", "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": "EQsNG9WC0D", "reviewer": "Reviewer_WKbg", "summary": "The paper presents methods for understanding and attributing predictive performance drops in time series classification models due to temporal data properties.", "questions": "Questions:\n1. Case Study 2: The authors mention reweighting the data based solely on the inverse density ratio. Which dataset is this applied to? \n2. The paper mentions prior work on performance drop attribution using Shapley values designed for static data (line 127). However, if the temporal properties discussed include summary statistics of a time series, such as mean, variance, or trend, could Shapley values then be used?\n\nSuggestions:\n- Clinical expert feedback on the relevance and actionability of identified temporal data properties would help motivate the proposed approach in practice.\n- Including distribution plots of the training and test set features could help illustrate the distribution shifts for readers.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The paper gathers and systematizes metrics to attribute performance shifts in time series.\n- The paper present four different case studies on clinical scenarios with distribution shifts.\n- The paper uses real-world healthcare data with a large patient population.\n- The paper discusses methods to identify the specific temporal factors driving prediction error, providing interpretability and guidance for targeted domain adaptation methods.", "weaknesses": "1. Clarity Regarding Prior Work: This paper introduces a Sufficiency Measure and a method for performance drop attribution, claiming to be the first to analyze detailed shift patterns in time-series data. However, distribution shifts in time series are not a new topic. A clearer discussion of prior work, specifically addressing how this study differs from existing approaches, would better position and motivate the contribution.\n\n2. Novelty Concerns: The novelty of the methods appears limited. For instance, neither the metrics predicting classification error nor the models used are new. The primary innovation seems to lie in the combined use of these metrics to predict and understand performance drops (i.e., using them as inputs to a model that estimates the prediction error of another model).\n\n3. Utility of the Sufficiency Measure: The Sufficiency Measure is introduced to assess the optimal predictive power of the metrics, with empirical studies reporting values of around 0.16 for mean squared error and 0.25 for mean balanced 0-1 loss. This information would be better suited to the results or case study sections. Additionally, it is unclear what constitutes a \"good\" sufficiency measure. Experiments comparing various sufficiency measures and their ability to identify ‘safe’ and ‘risk’ regions (Case Study 1) would help motivate this proposed measure.\n\n4. Clarity in Case Studys: \n- The case studies lack clear explanations of key methodological details, such as the transformer model architecture, model, hyperparameters, and evaluation metrics. Including summary paragraphs in the Methods section for the patient cohort, models/model training, and evaluation used across all four case studies would enhance clarity.\n- Case Study 3: The data partition strategy is unusual, with the validation set (the last 24 hours) occurring temporally after the test set (the first 24 hours). The practicality of this experiment is unclear, given the unrealistic and artificial temporal shift.\n\n5. Utility of the Approach/Lack of Baselines: \n- The lack of baseline comparisons or ablations studies makes it challenging to evaluate the contributions of the proposed methods.\n- The work advocates for identifying specific temporal factors that contribute to performance decline, as opposed to solely applying robust methods or fine-tuning on new test data. However, the results do not compare this approach with other common methods, such as fine-tuning, used to adapt data to new distributions. Including such comparisons would strengthen the motivation for this approach, particularly by illustrating potential computational benefits and performance trade-offs relative to fine-tuning. \n- Additionally, the interpretability of performance drop attribution appears valuable for guiding data reweighting or balancing techniques for certain features (e.g., demographic features in Case Study 2). However, it remains unclear what interventions would be applied to address these temporal factors or whether these identified factors would be deemed clinically useful by experts.", "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)