CaDrift: A Time-dependent Causal Generator of Drifting Data Streams

Eduardo V. L. Barboza; Jean Paul Barddal; Robert Sabourin; Rafael M. O. Cruz

cs.LGFeb 23, 2026

CaDrift: A Time-dependent Causal Generator of Drifting Data Streams

Authors: Eduardo V. L. Barboza, Jean Paul Barddal, Robert Sabourin, Rafael M. O. Cruz

Organizations: LIVIA, École de Technologie Supérieure (ÉTS), Université du Québec, Montreal, QC, Canada · Graduate Program in Informatics (PPGIa), Pontifícia Universidade Católica do Paraná (PUCPR), Curitiba, PR, Brazil

Abstract

This work presents Causal Drift Generator (CaDrift), a time-dependent synthetic data generator framework based on Structural Causal Models (SCMs). The framework produces a virtually infinite combination of data streams with controlled shift events and time-dependent data, making it a tool to evaluate methods under evolving data. CaDrift synthesizes various distributional and covariate shifts by drifting mapping functions of the SCM, which change underlying cause-and-effect relationships between features and the target. In addition, CaDrift models occasional perturbations by leveraging interventions in causal modeling. Experimental results show that, after distributional shift events, the accuracy of classifiers tends to drop, followed by a gradual retrieval, confirming the generator's effectiveness in simulating shifts. The framework has been made available on GitHub.

Figures & tables

Method	Causal	Generates drift	No source
STAGGER ( Schlimmer & Granger, 1986 )		X	X
SEA ( Street & Kim, 2001 )		X	X
Sine ( Gama et al., 2004 )		X	X
RandomRBF ( Bifet et al., 2009b )		X	X
TabPFN ( Hollmann et al., 2025 )	X		X
Drift-resilient TabPFN ( Helli et al., 2024 )	X	X	X

Table 1: Concept matrix of state-of-the-art synthetic generators.

Panel of Figure 1 — Figure 1: Representation of a node in a causal graph and how interventions are included to the feature $x_{3}$ .

Figure 2: Samples generated by CaDrift using a DAG with six nodes – five features and one target. Each color refers to a different class.

Dataset	IncA-DES	TabPFN ${}^{\text{Stream}}$	ARF	LevBag	OAUE	HT	LAST
1	86.69 $\pm 0.17$	68.83 $\pm 0.13$	87.78 $\pm 0.18$	78.08 $\pm 1.59$	62.38 $\pm 0.00$	59.08 $\pm 0.00$	86.17 $\pm 0.00$
2	70.73 $\pm 1.17$	67.18 $\pm 0.22$	73.82 $\pm 0.43$	72.94 $\pm 0.80$	45.33 $\pm 0.00$	53.00 $\pm 0.00$	67.67 $\pm 0.00$
3	87.33 $\pm 0.11$	75.44 $\pm 0.07$	84.50 $\pm 0.23$	82.23 $\pm 0.20$	75.04 $\pm 0.00$	76.92 $\pm 0.00$	78.21 $\pm 0.00$
4	67.49 $\pm 0.27$	86.00 $\pm 0.16$	66.99 $\pm 0.09$	65.06 $\pm 2.24$	67.23 $\pm 0.00$	45.51 $\pm 0.00$	66.43 $\pm 0.00$
5	91.61 $\pm 0.12$	96.85 $\pm 0.06$	94.91 $\pm 0.03$	94.47 $\pm 0.15$	88.99 $\pm 0.00$	88.08 $\pm 0.00$	91.17 $\pm 0.00$
6	73.80 $\pm 0.30$	80.26 $\pm 0.08$	76.75 $\pm 0.13$	75.17 $\pm 0.21$	72.36 $\pm 0.00$	66.23 $\pm 0.00$	69.58 $\pm 0.00$

Table 2: Average accuracy and standard deviation of baselines on datasets generated by CaDrift and popular synthetic benchmarks.

Panel of Figure 3 — Figure 3: Prequential accuracies on tested datasets. Dashed vertical lines indicate shift points. Shaded areas refer to the length of incremental and gradual shifts. Letters refer to the distributional shifts applied to the datasets. D stands for distributional, S for severe, C for covariate, and L for local shifts.

	iid		EWMA		AR		EWMA+AR
	p-value	Reject $H_{0}$	p-value	Reject $H_{0}$	p-value	Reject $H_{0}$	p-value	Reject $H_{0}$
x1	0.194	N	$<0.001$	Y	$<0.001$	Y	$<0.001$	Y
x2	0.444	N	$<0.001$	Y	$<0.001$	Y	$<0.001$	Y
x3	0.716	N	$<0.001$	Y	$<0.001$	Y	$<0.001$	Y
x4	0.412	N	$<0.001$	Y	$<0.001$	Y	$<0.001$	Y
x5	0.386	N	0.612	N	$<0.001$	Y	$<0.001$	Y

Table 3: Ljung-Box test (20 lags) on synthetic data streams generated by CaDrift with different strategies for time dependence.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Mapper	Hyperparameters
Learned MLP	$hidden\_layers=1$ , $neurons=10$ , $optimizer=adam$ , $max\_iter=10$ , $activation=relu$ , $learning\_rate=0.001$
Random MLP	$hidden\_layers=1$ , $neurons=10$
Decision Tree	$max\_depth\in[5,25]$ , $criterion=^{\prime}squared\_error^{\prime}$
Regression w/ SGD	$max\_iter=10$ , $penalty=l2$ , $alpha=0.0001$

Appendix

Table 4: Hyperparameters of mapping functions that map cause-and-effect relationships in the SCM. All mappers were implemented with scikit-learn ).

Figure 4: EWMA evolution with different

\alpha

values. The lines show the raw values generated with autoregressive noise, and the impact of EWMA on the value depending on the parameter

\alpha

assigned.

Dataset	IncA-DES	TabPFN ${}^{\text{Stream}}$	ARF	LevBag	OAUE	HT	LAST
1	77.50 (9.19)	43.71(25.12)	75.54(12.24)	64.88(13.20)	27.63(34.75)	55.67(3.41)	74.25(11.92)
2	61.25(9.48)	52.33(14.85)	61.29 (12.53)	58.00(14.94)	21.75(23.58)	49.17(3.83)	54.79(12.88)
3	79.08 (8.25)	74.29(1.15)	77.29(7.21)	76.17(6.06)	75.20(-0.16)	75.96(0.96)	75.96(2.25)
4	61.75 (5.74)	29.98(56.02)	57.23(9.06)	59.05(8.01)	56.45(10.78)	42.70(2.81)	63.86(2.57)
5	90.04(1.57)	72.37(24.48)	92.63 (2.28)	91.11(3.36)	81.61(7.38)	83.49(4.59)	87.36(3.81)
6	71.11(2.69)	76.51 (3.75)	72.94(3.81)	71.19(3.98)	67.18(5.18)	64.33(1.90)	67.10(2.48)

Appendix

Table 5: Average accuracy of baselines with limited label availability. Values in parentheses refer to the difference in accuracy compared to the experiments performed in a test-then-train manner.

Figure 5: The impact of the

\alpha

and

\rho

variables on the lagged autocorrelation function. Each row refers to a different value for

\alpha

, and each column a different feature (

x_{1}

x_{3}

and

y

	RandomRBF		SEAConcepts		Sine
	p-value	Reject $H_{0}$	p-value	Reject $H_{0}$	p-value	Reject $H_{0}$
x1	0.011	Y	0.299	N	0.387	N
x2	0.012	Y	0.626	N	0.324	N
x3	0.192	N	0.337	N	–	–
x4	0.612	N	–	–	–	–
y	0.723	N	0.083	N	0.547	N

Appendix

Table 6: Ljung-Box test (20 lags) on synthetic data streams generated by popular synthetic generators for data streams.

	Electricity		NOAA
	p-value	Reject $H_{0}$	p-value	Reject $H_{0}$
x1	$<0.001$	Y	$<0.001$	Y
x2	$<0.001$	Y	$<0.001$	Y
x3	$<0.001$	Y	$<0.001$	Y
x4	$<0.001$	Y	$<0.001$	Y
x5	$<0.001$	Y	$<0.001$	Y

Appendix

Table 7: Ljung-Box test (20 lags) on real-world datasets.

Panel of Figure 6 — Figure 6: Maximum Mean Discrepancy Heatmaps on datasets.

Panel of Figure 7 — Figure 7: Prequential mean absolute error on datasets. Letters refer to the distributional shifts applied to the datasets. D stands for distributional, and C for covariate.

Node	Mapper	Target Function
Dataset 1
$x_{1}$	Normal Distribution	–
$x_{2}$	Uniform Distribution	–
$x_{3}$	MLP	Sine
$x_{4}$	Random MLP	–
$x_{5}$	Linear Reg.	Checkerboard

Appendix

Table 8: Information of Mappers and Target Functions of nodes in the sample DAG. Normal and Uniform distributions carry no target function, as well as the random MLP and the prototype-based categorical mapper.

Dataset	# dim.	# classes	# concepts	% min. class	# samples	% Missing	% Interventions
1	5	4	5	16.48%	2,500	0	0
2	5	5	5	8.76%	2,500	0	0
3	5	3	5	10.4%	2,500	0	0
4	10	10	10	1.98%	10,000	0	10%
5	25	2	10	33.53%	10,000	10%	10%
6	100	3	20	13.46%	10,000	10%	10%

Appendix

Table 9: Information on the datasets used in the experiments. Datasets were generated using

\alpha=0.05

and

\rho=0.5

Shift	Type	$\Delta$	Description
Dataset 1
1	Abrupt Covariate Shift	1	Mean of Normal distribution in $x_{1}$ changed.
2	Abrupt Distributional Shift	1	Position of centroids changed; Target function of node $x_{5}$ changed to a Sine Function.
3	Abrupt Severe Shift	1	The outcome between two classes was swapped.
4	Abrupt Distributional Shift	1	Position of centroids changed; Target function of node $x_{3}$ changed to a Step Function.
Dataset 2

Appendix

Table 10: Information regarding shift events on the datasets used as examples in the paper.

\Delta

refers to the shift length.

Panel of Figure 8 — Figure 8: Class distribution across batches for datasets sampled by CaDrift.

Method	Source	Category
HT	Domingos & Hulten (2000)	Online Learner
LAST	Assis et al. (2025)	Online Learner
LevBag	Bifet et al. (2010b)	Ensemble
OAUE	Brzezinski & Stefanowski (2014)	Ensemble
ARF	Gomes et al. (2017)	Ensemble
IncA-DES	Barboza et al. (2025)	Dynamic Ensemble Selection

Appendix

Table 11: Baseline methods for drifting data streams.

Method	Hyperparameters
HT	$grace\_period=200$
LAST	$change\_detector:ADWIN$
LevBag	$change\_detector:ADWIN$ , $ensemble\_size=10$
OAUE	$ensemble\_size=10$ , $window\_size=500$
ARF	$change\_detector:ADWIN$ , $ensemble\_size=100$
IncA-DES	$change\_detector:RDDM$ , $pool\_size=75$

Appendix

Table 12: Baselines’ hyperparameters. All ensemble methods use a HT as base classifier.

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Concept Drift from a Causal Perspective

Eduardo V. L. Barboza, Jean Paul Barddal, Robert Sabourin, Rafael M. O. Cruz

LIVIA, École de Technologie Supérieure · Graduate Program in Informatics (PPGIa), Pontifícia Universidade Católica do Paraná (PUCPR)

Concept Drift Drifting Models Synthetic Data Evaluation

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Concept drift is a common phenomenon in real-world data streams, in which changes in the data-generating distribution can degrade predictive model performance. Most existing definitions characterize drift as changes in the joint distribution

P(\mathbf{x}, y)

, without distinguishing which component of the data-generating process has changed. In this work, we introduce a causal perspective on concept drift based on Structural Causal Models (SCMs). We propose a taxonomy that categorizes drift events by their causal origin, including changes in exogenous variables, endogenous mechanisms, confounders, and target-generating processes. Building on this framework, we develop an SCM-based data stream generator that simulates controlled mechanism-level drift events. Our experiments empirically characterize the distributional effects of each drift type and show that drifts with different causal origins induce distinct patterns of distribution shift and predictive behavior. Furthermore, by integrating causal discovery methods, we use our framework to construct data streams grounded in real-world dependency structures, enabling more realistic and informative evaluation scenarios. We also demonstrate that leveraging the generated data can improve downstream performance. These results highlight the importance of accounting for causal structure when studying and evaluating adaptive learning methods, and establish a foundation for causally-aware evaluation in non-stationary environments.

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