No $D_{train}$: Model-Agnostic Counterfactual Explanations Using Reinforcement Learning
Authors: Xiangyu Sun
Raquel Aoki
Kevin H. Wilson
Venue: Accepted by TMLR ()

Abstract: Machine learning (ML) methods have experienced significant growth in the past decade, yet their practical application in high-impact real-world domains has been hindered by their opacity. When ML methods are responsible for making critical decisions, stakeholders often require insights into how to alter these decisions. Counterfactual explanations (CFEs) have emerged as a solution, offering interpretations of opaque ML models and providing a pathway to transition from one decision to another. However, most existing CFE methods require access to the model's training dataset, few methods can handle multivariate time-series, and none of model-agnostic CFE methods can handle multivariate time-series without training datasets. These limitations can be formidable in many scenarios. In this paper, we present NTD-CFE, a novel model-agnostic CFE method based on reinforcement learning (RL) that generates CFEs when training datasets are unavailable. NTD-CFE is suitable for both static and multivariate time-series datasets with continuous and discrete features. NTD-CFE reduces the CFE search space from a multivariate time-series domain to a lower dimensional space and addresses the problem using RL. Users have the flexibility to specify non-actionable, immutable, and preferred features, as well as causal constraints. We demonstrate the performance of NTD-CFE against four baselines on several datasets and find that, despite not having access to a training dataset, NTD-CFE finds CFEs that make significantly fewer and significantly smaller changes to the input time-series. These properties make CFEs more actionable, as the magnitude of change required to alter an outcome is vastly reduced. The code is available in the supplementary material.

Published in Transactions on Machine Learning Research (06/2025)
No Dtrain: Model-Agnostic Counterfactual Explanations Using Reinforcement Learning
Xiangyu Sun RBC Borealis
zionggu.sum@rrccoorolls..om
Raquel Aoki RBC Borealis
rapuel.cokk.@rbccoraaa.cccm
Kevin H. Wilson
kevin.h. www.....iiitom@rccooooaa.....
RBC Borealis
Reviewed on OpenReview: https: // openreview. net/ forum? id= egiizAG9rOu
Abstract
Machine learning (ML) methods have experienced significant growth the past decade, yet their practical application in high-impact real-world domains has been hindered by their opacity. When ML methods are responsible for making critical decisions, stakeholders often require insights into how to alter these decisions. Counterfactual explanations (CFEs) have emerged as solution, offering interpretations of opaque MT. models and providing pathway to transition from one decision to another. However, most existing CFE methods require access to the model's training dataset, few methods can handle multivariate time- series, and none of model-agnostic CFE methods can handle multivariate time-series without training datasots. These limitations can be formidable in many scenarios. In this paper, we present NTD-CFE, novel model-agnostic CFE method based on reinforcement learning (RL) that generates CFEs when training datasets unavailable. NTD-CFE is suitable for both static and multivariate time-series datasets with contimuous and discrete features. NTD-CFE reduces the CFE search space from multivariate time-serics domain to lower dimensional space and addresses the problem using RL. Users have the flexibility to specify non-actionable, immutable, and preferred features, as well as causal constraints. We demonstrate the performance of NTD-CFE against four basclines on several datasots and find that, despite not having access training dataset, NTD-CFE finds CFEs that make significantly fewer and significantly smaller changes to the input time-series. These properties make CFEs more actionable, the magnitude of change required to alter an outcome is vastly reduced. The code is available in the supplementary material.
1 Introduction
After receiving a negative decision-4 denial of a loan, a poor performance review, or a rejection from a prestigious conference-2 very natural question to ask is "What could have done differently?" When the decision is made by person, that question can be answered directly by the person. Indeed, peer reviews represent the reasons why paper is accepted or rejected from conference and, in the best case, give authors actionable feedback which may lead to an acceptance in the future (assuming the underlying decision algorithm remains unchanged). But when a decision is made or influenced by black-box model, it can be much harder to provide insights. Telling a loan applicant they have a "poor credit score" does not. tell them how they might approach getting approved at a later date.
Counterfactual Explanations (CFEs) Waahter al. 2017) were introduced to fill this gap. Given an input to model, CFE is perturbed version of the input which yields a prescribed output from the model. For

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instance, if Bob's mortgage application is rejected, CFE might suggest that Bob make $20,000 more per year, or alternatively, make $10,000 more per year and purchase a house in different neighborhood.
CFEs also provide a method for examining how "fair" a model is, a concern that has become paramount in many real-world applications (Mehrabi et al. 2021 Angwin et al., 2022 Osoba et al.) 2017). For instance, a CFE that shows Bob's name were Alice his loan application would have been accepted points to potential discrimination on the basis of protected characteristic. Classic models such as logistic regression and
low-depth decision trees often called inherently interpretable (Verma et al., 2024 Murphy 2012 Breiman 2017) the relative influence of imput features can be read off from learned coefficients. But relations between learned parameters and input features are much harder to discern with more complex models. Indeod, even a logistic regression model with pairwise interaction terms can be complicated to reason about: Perhaps a woman who purchases a home in one neighborhood is less likely to have her application accepted than a man, but an additional $1, $1,000 a year in income increases her chance of acceptance significantly more than a man's 's chance.
There exist many CFE methods for static datasets (Mothilal et al. 2020 Samoilescu et al. 2021 Verma et al. 2022). However, CFE methods for multivariate time-series data are less common due to the challenges posed by higher dimensionality (Ates et al.) 2021 Theissler et al.) 2022). Additionally, to the best of our knowledge, all eristing model-agnostic CFE melhods for mullivariate lime-series require access to large collection of samples from the training distribution of the model being explained. This requirement can be infeasible in real-world domains especially due to privacy and other concerns.
In this paper, we introduce No- To-TTranning-atasee reinforeeeent-lammingg based CFE (NTD-CFF), reinforce- ment learning (RL) based CFE method designed for both static and multivariate timo-scries data containing both continuous and discrete altributes. Remarkably, NTD-CFE operates without training dalasets similar data samples and is aggostic so that it is compatible with any (even coo-differentiable) predictive models. NTD-CFE also allows the user to specify which features they prefer to change, as well as how changing a particular feature may affect another feature, thus allowing the user to express both what counterfactuals are feasible for them and any causal relationships ween those features. While NTD-CFE works for both static and time-series data, we focus on the harder setting of multivariate time-series data in this paper. We compare NTD-CFF to four statc-of-tho-art CFE methods nine real-world multivariate time-scries datasels. We find that NTD-CFE yields CFEs with significantly better proximily (the total magnilude of change proposed by the CFE) and sparsity (how many features the CFE proposes to alter) compared to the baselines.
The paper is struct as follows. We discuss related works and preliminaries in Section 2 and Section respectively. Scction describes the proposed algorithm NTD-CFE. Experiments with nine real-world datasets and five predictive models are given in Section 5 Finally, we conclude in Section 6
2 Related Works
Explainable AI (XAI) Counterfactual explanations belong to a much broader category of methods often called Explainable AI. XAI techniques can be broadly classified into two buckets (Verma et al. 2024]: (a) inherently interpretable machine learning techniques and (b) post-hoc explanatory techniques. The first category is primarily a restriction on the types of models that a practitioner can employ to model a phenomenon. However, models often held out as interpretable (e.g., linear regression and low-depth decision trees (Murphy 2012 Breiman 2017)) may not have the capacity to capture complex phenomena. In the latter category, practitioners attempt to "model the model" with subsequent techniques (Sun et al. 2020 Liu et al. 2021 These methods can be further subdivided into global and local methods (Ates et al. 2021 Islam et al. )021). Global methods attempt to simulate the opaque, complex logic of the original model using interpretable methods. On the other hand, local methods aim lo explain the rationale behind a specific prediction made for a specific input. For instance, feature-based based methods such as SHAP (Lundberg & Leck 2017). ; identify features that have the most significant influence on a prediction. On the other hand,
sample- based methods attempt to identify relevant samples to clarify a prediction (Kim al. 2016 Mothilal
et al. 2020 CFFs are an example of a post-hoe, local, sample-based explanation technique.
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Counterfactual Explanations (CFEs) CFEs were introduced by Wachter et al. (2017) to explore optimization--aased technique for differentiable predictive models. Building upon this foundation, DiCE (Mothilal et al.) )020) noted that there were potentially many different CFES proximal to any particular imput and whether one was "better" than another was really a matter for the CFE's user to decide. As such, DiCE returns several diverse CFEs for any given sample. However, the base algorithm of DICE is not guaranteed to return CFEs which satisfy causal constraints, and so DiCE introduced an expensive pruning step to filter methods they require the underlying predictive model to be differentiable
"non-feasible" CFEs, i.e., those that do not satisfy causal constraints. These optimization-baase are, unfortunately, not model-agnostic, and thus exclude popular predictive models such as random forests and k-nearest neighbors. To overcome this limitation, methods such as those of Tsirtsis et al. (2021) leverage dynamic programming to identify an optimal counterfactual policy and subsequently utilize this policy to find CFEs. However, due to the high memory requirements of these methods, this technique is best suited for low-dimensional data with discrete features. Another line of work employs Bayesian optimization (BO) to address the CFE task (Spooner et al.j 2021 Romashov et al.] 2022: Huang et al.] 2024). While these methods do not require training dalasets, due to computational inefficiency of BO, they address static or univariate time-series data rather than multivariate time-series data.
RL-based Methods CFRL (Samoilescu et al. 2021 and FastAR (Verma et al. 2022 take a different. tactic, employing techniques from RL to generate CFEs. CFRL first encodes samples into latent space using autocncoders (Kingma & Welling, 2013), then an RL agent trained to find a CFE in the latent space. Finally, decoder converts the latent CFE back to the input space. Similarly, FastAR converts the CFE problem to Markov decision process (MDP) (Sutton & Barto, 2018) and then uses proximal policy optimization (PPO) (Schulman et al. 2017) to solve the MDP, However, the action candidates in FastAR are discrete and fixed, making it impractical for complex multivariate time-series data. Moreover, both CFRL and Fast. require access to training datasets.
CFEs for Time-sories Data These and several other CFE techniques cater to static data, but methods for handling multivariate time-series data are much less prevalent (Theissler et al.) 2022). For time-series data with k-nearest neighbor random shapelet forest models, Karlsson et al. (220)) introduce one approach. Wang et al. (2021a) focus univariate time-series, seeking CFEs in a latent space before decoding them back to the imput space. Native-Guide (Delaney et al. 2021) finds the nearest unlike neighbor of an original univariate time-series sample, identifies the most influential subsequence of the neighbor, and substitutes it for the corresponding region in the original sample. On the other hand, CoMTE (Ates et al., 2021 can handle multivariate time-series data. First, searches for distractor candidates, which are the original sample's ss neighbors in the training dataset that are predicted as the target class. Then, it identifies the best substitution parts each distractor candidate. Finally, it gives CFE by replacing corrosponding part of the original sample with the best substitution of the best distractor candidate.
Adversarial Learning We also note that, on the surface, generating adversarial examples seems quite similar to generating CFEs: both create proximal samples that yield distinct predictions from the original inputs. However, while adversarial learning considers proximity, essential CFE properties such as actionability, feasibility, and causal constraints are mostly ignored (Wachter et al. 2017 Verma al. 2024 Sulem et al.,
2022
3 Preliminaries
Problem Definition CFEs aim to solve the following task: Given a user input x", a predictive model
I and a target. prediction Y' such that f(x") * Y", the goal is to find a transformation from x" to a new
sample x' (i.c. CFE) such that (Verma et al. 2024 Karimi et al. 2020 Guidotti 2022
valid: f(x') = Y',
actionable: if the user cannot modify feature j, then x;- x/j,
sparse: the CFF a' should differ in few features from xt as possible,
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proximal: the distance between x² and x' should be small in some metric, and
plausible: x' should satisfy all causal constraints on the input.
where 2y denotes the j-th feature of æ.
Reinforcement Learning Our method for finding CFEs will rely on reinforcement learning (RL). In RL, an agent and an environment interact with each other (uuton & Barto 2018). The agent takes an action de on a state Sy at time step t. The environment receives O, and 8t from the agent and returns the next state 8:41 and a reward R to the agent. The goal of the agent to maximize the expected cumulative (discounted) reward. RL can be categorized as model-free RL and model-based RL. In model-free RL (Mnih et al. 2015 Haarnoja et al. 2018), the agent learns a policy from real experience when a model of the enviromment not. available to the agent. In model-based RL (Silver et al. 2017 Ha & Schmidhuber 2018), the agent plans a policy from simulated experience generated by model of the environment. This model of the environment is either learned or given. Furthermore, a policy-based RL algorithm (Williams) 1992 Schulman et al. 2017 2015) typically samples actions from a policy network To paramcterized by neural networks with parameters 0. Given a state, me trained to return the best action that maximizes the expected cumulative reward.
4 The proposed method: NTD-CFE
In this work, we propose No- Training-Dataann CFE as an RL problem. In this setup, the RL enviromment is the CFE predictive model f. The RL state is sequence of CFFs beginning at the original user input x² and ending in final generated CFE O An action taken by the RL agent represents small perturbation on the way from xx to O A reward is a function of the predictive model and other objectives we introduce to maintain the properties discussed in Section (more details below).
manffrrementt-eerming--oeo based CFE (NTD-CFE), formulating
One-hot encoding is applied for categorical features. We assume that the prediction function of f is computationally efficient, which is a common assumption in model-based RL (Sutton & Barto 2018).
NTD-CFE pseudocode is given in Algorithm 1 Let x" E RRKD denote user input sample, where K and D denote the total number of time steps and features, respectively. To provide for plausibility, the D features can optionally be categorized into actionable features Dact, which the user can directly change; non-actionable features Dmon-act, which may change due to causal constraints but which the user cannot directly change (Sun & Schulte 2023): and immutable fcatures Dimmu, which may be used by the prodictive model but which cannot change. x² is static if K = or temporal if K 1. The time complexity of the algorithun is O(ME Mr).
Action (Line 11 of Algorithm NTD-CFE reduces the CFE search space from a multivariate time- scries domain to a lower dimensional action space. Let To represent an RL policy network parameterized by neural networks with parameters O. Each action a sampled from Fo is 3-dimensional a = {Orime Qteat dstre), where Otime denotes the time step of the intervention, afeat denotes which feature to intervene on, and astre corresponds to the strength of the intervention. To be more specific, let DC and DD denote the numbers of actionable continuous and discrete features, respectively, where DC + DD Dacil and |aael denotes the total number of actionable features. Given an æ, the neural network parameterized by 0 produces parameters to define four distributions {ptimes Pieat, MDC (DC, dDC, PNa.. } == f(x),, such that Peime R Piict E R P PDC E DC DDC DC and PNa R Nai, where Náis ΣDD Nais,; and each p vector contains negateee probabilities that sum to 1. The parameters Ptime and Pleat define two categorical distributions from which Otime and Ofeat are sampled, c.g. Qtime Cat(ptime) and Ofeat ~ Cat(picat). When Qjeat is a inntis feature, the corresponding mean and standard deviation parameters JDCC, and DDC. define a normal distribution from which we sample how strong the intervention is for this continuous feature, e.g. Ostre (HHDC, o...an.)) When afeat is a discrete fcature, the corresponding parameters P define a categorical distribution from which we sample what the interventional value is for this discrete feature, e.g. Ostre Cat aaa
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Algorithm 1 NTD-CFE. Best viewed in color. Typical RL code is colored in gray.
Input: the original user imput æ", predictive model target class Y', reward function R, state transition function Fp, proximity measure D pamtt a proximity weight Apamet feature feasibility weights Wfath, maximum number of episodes Mg, maximum number of interventions per episode Mr, discrete feature indicators Dais, numbers of possible values of the discrete features {Nais,ald E Dais
2: Optional Input: non-actionable feature indicators D nou--cct: immutable feature indicators Dimmus causal constraints Cenasal: feature range constraints C Crange; in-distribution detector Fin dist, a discount factor 7 a learning rate a, regularization weight XwD
Output: CFE O
O [0}
5: E :=0
6: while << ME do
7:
{0)
# Keep a record of (state, action, reward) pairs
t:=0
3t := x²'
10: while < Mr do
11:
(2)) # Sample action from the RL policy network 21+1 = FT as) # State transition from the current to the next x (Optionally, Fe+1 = (Crange((ee11) (euusa((De+11) D Dimmu(
12:
13:
14:
TH+1 == R(f(2t+1)) D', Dpamataa" (2=" #t+1, Wssit), ((ssit,>paaue >pxmmt # Compute the reward T :: T UU Tt-1) # Add the pair to the record
15:
16:
if f( Y and x++1 & O then # If new valid CFE is found
17:
0: O U Je++1 (Optionally, if also Fin dist (I++1) True)
18:
t: ++1+1
19:
Break end if
20:
21:
t==t+1
22:
end while
23:
T
24:
for t- = 0, 1..... ....,, T do # Update network parameters
= Et L1tt11 7x -t---1 TV
25:
26:
0 = + a. 7 G. G.IInoo(aauu
27:
end for
28:
-==++1 end while
29:
30:
0 = min; D parmss (x" Oi, W wwa)) # Return the valid CFE with the lowest prozimity
State Transition (Line 12 of Algorithm
The state transition function Fp can be any appropriate function for an application domain. In Section we define Fy a; = {atimer Afeat (stre)) as:
(k,d) xt
+ astre
for 2 atime and Afeat (when feature d is continuous)
F441
(k.d)
Ostre (k.d)
for 1: 2 atime and Afeat (when feature d is discrete)
otherwise
(k,d) denotes the d-th feature of the t-th at the time step k. where 2r(
Constraints (Line 13 of Algorithm 1 Constraints (i.e., Grange and Coensat) can be applied straightfor- wardly as sets of rules. For instance, a Crange constraint can be rule that enforces that Feature 1 must remain within range 1]. If an action allempts to change the value of Feature 1 to 2, the state transition can either be discarded or adjusted to cap the feature value at 1. Similarly, a Ceansal constraint such that Feature an interventional function of Feature 2, can be incorporated into the state transition function, ensuring that any action on Feature updates Feature accordingly. This dynamic is reflected in the reward function, which in turn influences the policy network, allowing the RL-based method to adapt accordingly.
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Reward and Proximity (Line 14 of Algorithm 1
We define the reward function R. as:
Apzmt Dpame Wistti if f())= = Y
r: ":=R(f(z),Y D pamaa x, Wssib), Apama)
0
otherwise
It combines prediction reward (1 0) and weighted proximity loss D pamtt D Dpams is 0 when f(x) + Y'. Otherwise, in difficult settings where f(x)= * Y' dominates over f(z) Y', the RL agent would learn to produce CFEs that are too close to the original user input, which results in invalid CFEs. Apzmt ensures that the reward is posilive when f(x)= -Y.
The proximity measure prmt can be any suitable measures for the application domain. In Section we define Dammt as the In-norm for continuous features and as the Lo-norm for discrete features, weighted by faihi
Dyamss ( add fsitt)
K Ekml (otlird) x |. W jsib
(if feature d is continuous)
(1)
===1 Tarlhid) & xlhht)) W fuib (if feature d is discrete)
W faib denotes the feasibility to change the d-th feature, which encodes the user's preference on altering this feature. xd denotes the d-th feature of æ, and z(kd4) denotes the d-th feature of at the time step k. NTD-CFF prefers to generate CFFs by altering features associated with small Wist- If user does not. specify preference features, Wisb is 1 for all features.
Classification and Regression (Line 16 of Algorithm Algorithm describes NTD-CFE for a classification model f. As a model-agnostic method, NTD-CFE supports not only classification but also regression models. To work with a regression predictive model f, one can replace the first condition of Line [6 by Viower S fx1+11) < Yuppers where Yooer and upper represent the lower and upper bounds for the target regression value, respectively.
On Line 17 if a valid CFE is reached and is not already in the set O, then added to O. Optionally, an additional condition can be imposed such that a valid CFE is added to O only if it is also plausible. Finally, Line 30 NTD-CFE returns the CFE with the lowest proximity from the set O.
Output (Lines 17 and 30 of Algorithm 1
Operating Without Training Datasets The input x" in Algorithm 1 is a testing sample X i.e., the user sample to be explained or for which CFFs are generated. To clarify, the baseline methods require a training datasct Derain to generate CFEs for Xust, whereas the proposed method operates directly on Xtest without the need for Derain. More details about how the baselines use Dtrain is discussed in Section
Motivation of Using RL A search algorithm required to solve the modcl-agnostic CFE problem without training dataset. For multivariate time-series data, the CFE search space (K x D) is large. BO-based CFE methods primarily focus on static or univariate time-series data (Spooner et al. 2021 Romashov al. 2022 Huang et al. 2024) and do not scale well to multivariate time series. Optimization--asse approaches, such as DiCE, are not model-agnostic since they require differentiable predictive models. Instead, we formulate the search problem as a continuous control task using reinforcement. learning (RI.), reducing it to a lower dimensional action space for improved scalability. Additionally, causal constraints are crucial for CFE methods |Veraa et al. 2024). While BO-based methods can impose simple value constraints (e.g., bounding ranges), they struggle with complex causal constraints. Our RL approach encodes causal constraints more naturally.
4.1 Limitation
Features on different scales can impact the performance of models like neural networks. Without training datasots, standardizing the features becomes impractical. One approach is to leverage jas to mitigate the impact of continuous features on different scales. Assuming domain knowledge about the ranges of feature values (which is often available in practice), one assign smaller Wist to continuous features on
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larger scales and larger Wistt to continuous features smaller scales. In evaluation, we assume that the continuous features have mean of 0 and a variance of 1. We leave the evaluation of this approach or more sophisticated approach for future work.
The performance of the proposed model is unaffected by the size of the predictive model. Instead, its performance depends on the frequency with which the predictive model returns the desired prediction. We assume that the desired prediction returned by the predictive model is not sparse. This a realistic assumption in many real-world domains. For example, numerous applicants with diverse personal characteristics applying for credit cards receive approval from the decision model of bank. This assumption ensures that the RL agent receives enough reward signals to improve its performance. Without both training datasets and reward signals, it would be extremely challenging for ML methods to solve meaningful tasks.
5 Evaluation
In this section, we provide qualitative examples and quantitative experiment results to demonstrate the eflectiveness of NTD-CFE for multivariate data-series data. The details about datasets and hyperparameters are provided in Appendix A and Appendix [ respectively.
5.1 Qualitative Examples
We illustrate qualitative examples generated by NTD-CFE with two interpretable rule-based predictive models and an interpretable Life Expectancy dataset. Please refer to Appendix [.1 for the definitions of the interpretable rulc-based models. All examples in this section are generated using the first sample, which represents the country Albania, in the Life Expectancy dataset.
5.1.1 Equal feature feasibility weights Wfib
all features have equal feasibility weights (Wjs0 jab 1.0) as no user preferences are set. In Figure la following the definition of rule-based model 1 (Appendix B.1 Albania's prediction is 0 (i.e. undesired), because
In Figure 1
and srrutth--cpendituree in the last 5 years are below O. Accordingly, NTD-CFE generates a CFE by increasing these values above O. In Figure 1b if at least one of " "GDP-per-capitaa or hhealth- "eaillh-eppeddluree is above 0 in the last 5 years, then rule-based model 2 predicts 1 (i.e. desired). NTD-CFE generates a valid CFE for based model 2 by raising "OPP-per-capita" above O.
5.1.2 Different feature feasibility weights Weib
However, changing "GDP-per "IDP--er-capita" for Albania may be impractical. An alternative way make rule-based model 2 predict 1 is to increase "health- coppeniturrp above O. NTD-CFE can achieve this in three different ways: (1) marking
non-actionable; (2) assigning small feasibility weight to "health- expenditure;" or (3) assigning a large feasibility weight to " "GDP-per-capine
H.DP-per-capite
(1) is straightforward with NTD-FFE. Hence, we only present the results for (2) and (3). In Appendix Figure 2a the feasibility weight Wiss for "health-ense "eralth-erpendituree is set to 0.1, ten times smaller than that "GDP pprr-caacppiaa " which remains unchanged as 1. With the reduced feasibility weight for " ereendh--epennditurr" " NTD-CFF generates a valid CFE by modifying thealth--zpenddinn
" In Appendix Figure 2b the fcasibility weight for " (GDD-per-captle is set to 10, ten times greater than other features. With the high feasibility weight for # "DD--per-caplla" NTD-CFE preserves " (GDD-per-cappe capita" and looks for other features to achieve the desired prediction. As result, NTD-CFE learns to alter "health-erpenddturr""
Next, we show that setting small leasibility weights on irrelevant ures does not affect the CFEs generated by NTD-CFE, In Appendix Figure 2c] although the feasibility weights for irrelevant features " *CO2-emissions; a wwtpworrooossuptioonnoooomom and "forest-area" are set be ten times smaller than others, NTD-CFF still alters the relevant feature " "GDP-per CGD--per-capita". Additional results for different feasibility weights are provided in Appendix Figure 3
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Orginnal User
Generated CFE
Feotures Changed (Origine))
Pestures Changed (CFE)
2.0
2.0
Iepuattrn (1.00
EU2 emssiitt (1.0)
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Fealth ecce iccendituue intervennt)
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(1.0)
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0.5
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0,5
Indivduels
intemmett
Milkary exponelture (1.)
People practconggnn ppen derecat (1.9)
Houpic dir diriking wate servics (1.0)
-0.5
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Obeaity among eduts (1.00
Beer cons .mptro _ee__apite (1.0)
Continet (1.))
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Loaal Develoged (2.0)
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Time Stop
Step
Time Step
Stop
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Elstri, puwar coneumpttion (1.0)
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Forest area 1:
GDP per capka Intervened) 1.0)
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Miltary eww.ecteeueeeee (1.6)
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(b) Rule-based model
Figure 1: Qualitative examples with rule-based models and equal feature feasibility weights Waa-- "Original User Input" shows the original input with the original feature values. "Generated CFE" shows the generated CFE with the modified features. The other two plots, "Features Changed (Original)" and "Features Changed (CFE)", omit most features and only show the modified features.
5.2 Quantitative Experiments
In this section, we compare NTD-CFE to four baseline methods in 45 experiments, which correspond to nine real-world datasets each evaluated with five predictive models. Additional experiments are provided and analyzod the appendix.
Datasets Nine real-world multivariate time-series datasets are used for evaluation (Appendix for details).
We benchmark NTD- CFE against four model-agnostic bascline methods: CoMTE (Ates et al. 2021). Native-Guide (Delaney al. 2021), CFRL (Samoilescu et al. 2021 and FastAR [eerma
Bascline Methods
et al. 2022 Optimization-based methods (Mothiaal al. 2020 Sulem al. 2022 Hsich et al. 2021 are excluded from the comparison, because our predictive models are not restricted to differentiable models. For Native-Guide, we follow the approach of Bahri et al. (022) by concatenating multivariate time-series samples into univariate time-series samples. Unlike the proposed NTD-CFF, the baselines require training datasets, i.c. either (X trains Yirain) or (Xras)). We omit comparisons with other methods and use these popular methods as the representative baselines.
Five predictive models are employed per dataset: a long short-term memory (LSTM) neural network, a k-nearest neighbor (KNN), random forest and two interpretable rule models; see Appendix B for details. Given nine datasets, there is total of 45 predictive models.
Predictive Models
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Table 1: Quantitative results with the eRing dataset for different predictive models and methods. Our proposed method NTD-CFE consistently achieves significantly better proximity and sparsity.
Predictive
Nine
Methods
Success
Validity
Plausibility Rate (%)
Proximity
Sparsity
Model
Rate (%)
Rate (%)
COMTE
100
100
100
346.746 316.502
260.0
Native-Guide
100
100
100
260.0
LSTM
14
CFRL
0
FastAR
NTD-CFE
100
100
100
54.682
31.214
CoMTE
100
100
100
338.141 148
260.0
Nativo-Guide
100
100
93.75
3.789 x 10
229.938
KNN
16
CFRL
100
100
100
321.046
260.0
FastAR
NTD-CFE
100
100
100
144.937
86.688
CoMTE
100
100
100
340.338
260.0
Native-Guic
100
100
93.333
3.275 x 10
246.467
Random
15
CFRL
Forest
FastAR
NTD-CFE
100
100
100
68.882
46.733
CoMTE
Rule
Native-Guide
100
100
44.828
9.928 x 10
256.552
Based 1
29
CFRL
FastAR
0
NTD-CFE
100
100
100
103.953
63.345
COMTE
100
100
100
347.295
260.0
Rule Based 2
Native-Guide
100
100
88.0
5.075 x 10
245.4
25
CFRL
FastAR
NTD-CFE
100 100
100
31.301
14.76
5.2.1 Results
The methods are evaluated using five metrics. Tel New denote the total number of invalid samples, i.e., those classified as the undesired class by predictive model, Niw eat denote the number of invalid samples for which a CFE method generates valid CFEs, Neat denote the number of valid CFEs generated by CFE method, NCFE denote the number of CFEs generated by CFE method, and Npiau val denote the number of plausible and valid CFFs generated by CFE method. We set feature feasibility weights W faib = 1 for all the features d E D.
Table D shows the results with the eRing dataset as an example. The proposed NTD-CFE consistently has the lowest proximity and sparsity. The results for all other datasets are given in Appendix Tables 3 to 10 this section, we analyze and compare the complete results, including these in the appondix.
Results dimmed in gray in the tables are skipped from analysis and comparison. For Plausibility Rate, Proximity and Sparsity, we only compare the methods under 100% success rates. The reason is that if a method always generates CFEs that are close to the original invalid user input x", even though these CFEs may often be invalid due to their closeness to x", the plausibility rate, proximity and sparsity will always superior. the extreme case, method always returns the original but invalid x", would achieve a perfect plausibility rate, proximity and sparsity, but at the same time fail completely as a CFE method in terms of success rate.
There are scenarios for a CFE method to fail: 1) no valid CFEs are generated; 2) no CFFs (either valid or invalid) are generated. For RI-based baselines, CFRL and FastAR fail with 0%
Success Rate: New
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success rate in 30/45 and 34/40 cases (excluding the 5 cases where FastAR crashes due to memory usage Table 4 respectively. NTD-CFF outperforms CFRL in 31 31/45 cases, and is on par with CFRL in 10/45 cases. In contrast, NTD-CFE underperforms CFRL in 4/45 cases, NTD-CFE outperforms FastAR in all 40/40 cases. Compared to the other basclines, Mative-Guide CoMTE and NTD-CFE fail with a 0% success rate in 0/40 (excluding the 5 cases where Native-Guide crashes due to memory usage on Table 4. 3/45 and 1/45 cases, respectively. NTD-CFE outperforms Native-Guide in 8/40 cases, and is on par with it in 25/40 cases. NTD-CFE underperforms Waiive-Guide in 7/40 cases. However, the minimum success rate of Native-Guide is 30.855% which is better than that of NTD-CFE (0.68%). NTD-CFE underperforms CoMTE in success rate. NTD-CFE produces lower success rates than CoMTE in 15/45 cases, achieves the same success rates in 27/ /5 cases, and outperforms it in only 3/45 cases. More comparison with CoMTE is provided at the end of this subsection.
It is important to note that: 1) We provide training datasets to the baselines (because they require training datasets to operate), but not to NTD-CFE. This additional information provided only to the basclines gives them an advantage over NTD-CFE. Without training datasets, the methods stop working except NTD-CFE. 2) In Appendix Table 19 show that the success rate of NTD-CFE can be further improved, e.g. from 0.68% to 76.87%
Validity Rate: Neal
Nore Both NTD-CFE and COMTE ensure perfect validity rates by design (i.c. 100%); they either produce a valid CFE or do not produce a CFE at all. In contrast, the other three baselines may return invalid CFEs; therefore, their validity rates can be lower than 100%. Therefore, NTD-CFE and CoMTE outperform other basclines in terms of validity rate.
The comparisons to CFRL. and FastAR are skipped because more than half of the experiments yield 0% success rates, and therefore, undofined plausibility rates. NTD-CFE outperforms and is on par with Native-Guide in 14/24 and 1/24 cases, respectively. NTD-CFE underperforms Native-Guide in 9/24 cases. NTD-CFE is on par with COMTE in 8/27 cases and underperforms it in 19/27 cases. In summary, in terms of plausibility rate, COMTE outperforms the proposed NTD-CFE, and NTD-CFE outperforms Aulive-Guide, Again, the baselines have the advantage by utilizing additional training information that is not provided to NTD-CFF.
Plausibility Rate: Naiun Noat
Additionally, one can enforce plausibility in NTD-CFE (Linc 17 of Algorithm D.. NTD-CFE achieves 100% plausibility rates at the cost of lower success rates and higher proximity and sparsity. Please see Appendix D for details.
Proximity and Sparsity Proximity and Sparsity are defined as the L1- or Lo-norm, respectively, of the difference between a CFE and the original x² (Verma et al., 2022: Samoilescu et al., 2021 Due to the aforementioned reason, proximity and sparsity are computed only with valid CFEs. Therefore, comparison with FastAR is skipped. NTD-CFE oulperforms all baselines in procinily und sparsily in all cases. Il also surpasses the baselines by large margin. For example, there are 4, 8 or 15 cases where the proximity of NTD-CFE is at least 20 times, 10 times or times lower than that of all the basclines, respectively (c.g., 16.183 vs. 220.552 in Appendix Table 7 Similarly, there are 3, 5 or 21 cases where the sparsity of NTD-CFE is at least 50 times, 20 times or 10 times lower than that of all the baselines, respectively (e.g., 20.587 vs. 1224.0 in Appendix Table 5)
Comparison with RL-based methods. NTD-CFF oulperforms the two RL-based baselines, CFRL and FastAR, in all the metrics. CFRL and FastAR often fail to generate valid CFEs for complex multivariate time-series data. Please note that this is not a criticism of CFRL or FastAR, because they are not designed for multivariate time-series data.
Comparison with COMTE Although CoMTE outperforms NTD-CFE in success rate and in plausibility rate, it is important to highlight that: 1) CoMTE requires a training dataset, while NTD-CFE does not. The better performance of CoMTE over NTD-CFF comes at the cost of needing more information and reducod versatility in practical applications. 2) COMTE relies on finding distractors correctly classified as the target class. Tables 1 and g for rule-based model 1 show that when the predictive models classify all training
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samples the undesired class, CoMTE fails completely with 0% success rate. In contrast, NTD-CFF is more versatile and can operate in such difficult situations. 3) Appendix Table 19 shows that the success rates of NTD-CFE can be improved by increasing the maximum number of episodes Mg or the maximum number of interventions per episode Mr, which correspond to more exhaustive RL search.
6 Conclusion
In this paper, we introduce NTD-CFE, a model-agnostic RL-based method that generales CFEs for static and multivariate time-series data. NTD-CFE operates without requiring a training dataset, is compatible with both classification and regression predictive models, handles continuous and discrete features, and offers functionalities such as feature feasibility (i.e. user preference), feature actionability and causal constraints. We illustrate the effectiveness of NTD-CFF, through qualitative examples and benchmark it against. four tate-offthheart methods using nine real-world multivariate time-series datasets. Our results consistently show that NTD-CFE produces CFEs with significantly better proximity and sparsity. Future research includes extending the work to large language models, examining more advanced RL algorithms to potentially improve performance, using Wist for features on different scales, and exploring alternation solutions other than RL for multivariate time-series data without training datasets.
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A
Datasets
Nine real-world multivariate time-scries datascts used for evaluation in Section 5.2
Life Expectancy Each sample has 16 time steps (from 2000 to 2015) and 17 features per time step. All the features are interpretable. Please see Table 2 for feature names and types. We remove " "Country Nome" and " "Yerr" from the list. of input features and use " *Life Expectancy" in 2015 as the label. Therefore, the dataset has K 16 and D 14 in notation. We set Y = if " Life Expectancy" in 2015 is greater equal to 75 as the target class and otherwise Y 0 as the undesired class.
NATOPS The NATOPS dataset contains sensory data on hands, elbows, wrists and thumbs to classify movement types. K 51 and D 24. All the features in this dataset are continuous. There are classes of different movements. We set class 4 to 6 as the target class.
PEMS-SF K 144 and D 963. The dataset contains transportation data from California. All the features are continuous. There are seven classes and we use the last four classes the target class.
Heartbeat 405 and D 61. All the features in this datasot are continuous. There are two classes: normal heartbeat (Larget class) and abnormal heartbeat. (undesired class).
eRing = 65 and = 4. All the features in this dataset are continuous. There are six classes and we use the last three classes as the target class.
Racket Sports == 30 and D = 6. All the features in this dataset are continuous. There are four classes: "Badminton Smash", " Badminton Clear", "Squash Forehand Boast" and " "Squash Backhand Boast". We use the last two classes as the larget class.
Basic Motions K 100 and D 6. All the features in this dataset are continuous. There are four classes: "Badminton", RRnniing, " "Standing" and "Wllking.. We use "Standing" as the target class.
Japanese Vowels K = 29 and D = 12. All the features in this dataset are continuous. There are nine classes and we use the last five classes as the target class.
Libras = 45 and D 2. All the features in this dataset are continuous. There are 15 classes and we use the last cight classes as the target class.
All categorical features are one-hot encoded. All continuous features are standardized to have mean 0 and variance
B Predictive Models Used in Section 5.2
Since NTD-CEF DID-CFE is model-agnostic, we expect it work for predictive models with arbitrary hyperparameter values and architectures. In Section 5.2 evaluate the methods using five predictive models: two interpretable rule- based models, long short-term memory (LSTM) neural network, a K-nearest neighbor (KNNs), and a random forest.
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Matiitooons
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B.1 Rule- predictive models
Two interpretable rule-based predictive models are implemented for each dataset.
Rule-based models for the Life Expectancy dataset
We employed two interpretable rule-based predictive models for the Life Expectancy dataset in Section 5.1 and Section 5.2 Let d1, d2: d3, d4, ds denote the features "least-develope" *GDP-per-capita" "health- expenditure", "people-using tesinn-at-least mulss-basic-eee respectively. We define the first rulc based model as:
water-services" and prople-practicnng-oe---ddee deffeettnnnnninon
Y
if (x:d)) A x (R,d2) AΛ (Nrda) > ( > >0ll)>>>>>a ( <0 K
f(x)
Y
otherwise
and the second rule-based model as:
f(x) Y
if (k.d)) = A (xtk.22) > 0 x > 0) A arthidet 0 xtkidd3 <0 for K - k SK K
otherwise
where Y' is the target class and Y is the undesired class.
Rule-based models for the PEMS-SF dataset
Let d, denote the i-th feature. We define the first rule-based model as:
( Y if z(kdd > 0 (k,d1000) 0 A (idddooo) 0 for K 50 s k $ K
[(x) y
otherwise
and the sccond rulc-based model as:
Y if if > V (k,d100)) > OV [k.doo > 0 for K - 50 < k < K
((x)
Y otherwisc
where Y' is the target class and Y is the undesired class.
Rule-based models for the NATOPS dataset
Let and d2 denote the features HHand tip left, coordinate" and " Honnd tip right, X coordinate", respectively. We define the first based model as:
Y if a(k.d))) > 0 a(tidd)) > 0 for K
f(x)
Y
otherwise
and the second mnle-based model as:
f(x) Y
if (h.d.)) > 0 (kid)) > 0 for K - 9 5 K
Y otherwise
where Y" is one of the target classes and Y is one of the undesired classes.
based models for the Heartbeat dataset
Let de denote the i-th feature. We define the first rule-based model
Y' if (kkdi AA (kkdd)) > A (kidat > 0 for - 45kSK
f(x)
otherwise
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Generated CFE
Feotures Changed (Origine))
Pestures Changed (CFE)
2.0
2.0
Neguatton (1.00
CU2 emsssiote (1.00
1.5
1.5
1.5
1.5
Feshh ndlium intervenes
(1.0)
1.0
0.5
Value
0.5
0,5
0.5
Indivduels intemeet
Miltary, exponelture (1.)
People pww.ttttttnng... ppen derecatiion (1.9)
Houplc dir wate: Servics (2.0)
-0.5
-0.5
-0.5
-0.5
Obeaity among eduts (1.80
Beer sons .mpoooottoo... _ee__pppte (1.0)
Continet
-1.0
-1.0
Loaal, Develoged (2.0)
10
10
15
10
10
15
Time Stop
Step
Time Step
Stop
(a) Rule-based model 2 Weight health 0.1
Original User imput
Generated CFE
Features Changed (Original)
Features Changed [CFE)
2.0
1.5
1.5
Intervened 11.0
Easii puwae coneummption (1.0)
1.0
1.0
1.0
1.0
Forest area (1:0)
GDP per sapka 10.00
Volue
0.5
Velue
0.5
Indirduan joiig the Internn (1.0)
Miltary eapenctuuee 11.0)
0.0
0.0
0.0
0.0
Peopre practiong spen de 11.0)
(1.0
Obesity boesttyomong.asve
-0.5
-0.5
per_cepla
-10
1.0
-1.0
-1.0
Least Developed
10
15
10
15
Time Stop
Time Step
Time Steo
Time Stop
(b) Rule-based model 2 Weight GDP 10
Original irput
Changed (Originet)
Changed
2.0
2.0
2.0
2.0
Popu ater (1.00
CO2 emsssier 0.
1.5
1.5
Muali, secsenatione (.0)
Elecrit powerr imptio 5.11
1.0
1.0
1.0
1.0
Forest area [0.3
C2PP capta (Itercored) (.5)
Value
Velue
0.5
0.5
0.5
0.0
0.0
peepie_neetiing wwwpe//_ppooeeeeeeeeeeeeee
hoopie drinking Service
0.5
0.5
0.5
0.5
Disedlyy aemang adula (1.0)
Beer_cons watpsstppptteeeeeeceoo per_pppps (1.0)
Continent (1.0)
-1.0
Loast Devcloped (1.0)
Time Step
Time
(c) Rule-based model 2 Weight CO2 Elec Forest 0.1
Figure 2: Qualitative examples with rule-based model and different feature feasibility weights Wj
and the second mule-based model as:
Y Y
if (k.d) > 0v ((hdds)) > ov > for K - 4 otherwise
f(x)
where y" is the target class and Y the undesired class.
Rule-based models for the Racket Sports dataset
Let d, denote the i-th feature. We define the first rule-based model
Y
if (kdd) > 0 A (k;ds)) > for K - -5kkS K
f(x)
Y otherwise
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Urgi
Generated CFE
Feotures Changed (Originel)
Pestures Changed (CFE)
2.0
Ngu aber (1.0)
CU2 emsssiot (1.00
1.5
1.5
1.5
1.5
hesht, nnttuur (1.0)
Eectri_pooer www.:/ooossmmiiinnnoomoo (1.0)
0.5
value
0.5
0,5
0,5
Indiviuves:
Milkary, exponelture
People pww.tttttnnnn... ppen derecae on
Houpre dir diriking wate: servics (1.0)
-0.5
-0.5
-0.5
-0.5
Obeaity among eduts (1.8)
Beer sons imptron _ee__apite (1.00
Continett (1.0)
-1.0
-1.0
Loaal Developed (2.0)
10
10
15
10
10
15
Time Step
Time Stap
Stop
(a) Rule-based model 2 Weight GDP 0.1
Original User imput
Generated CFE
Features Changed (Original)
Features Changed [CFE)
1.5
1.5
Heltnneugenduur
Elstri, puwar coneumptionn (3.0)
1.0
1.0
1.0
1.0
Forest area 1:
GDP per rapka Intervened) 1.0)
Volue
Velue
Indirtuon joing the Inteennt (1.0)
Millary ewp.ecttuuee 11.6)
0.0
0.0
0.0
0.0
Pespre practiong spen derecat 11.0)
(1.0
Obesity
-0.5
-0.5
per_cepla
-10
-10
-1.0
-1.0
Least Develoged
10
15
Time Stop
Time Step
Time Steo
Time Stop
(b) Rule-based model 2 Weight health 10
Figure 3: Qualitative examples with rule-based model and different feature feasibility weights WMaB- Among relevant features to the predictive model prediction, NTD-CFE prefers the features with smaller Wfssb-
and the second rulc-basod model as:
Y Y otherwise
if ((hdd:) > 0 (hidds > 0 for K - 4 S K
f(x)
where Y' the target class and Y the undesired class.
Rule-based models for the Basic Motions dataset Let de denote the i-th feature. We define the first rule-based model as:
Y' if (k.di) > A (dbdd)) > 0 stkddat > 0 for - K
f(x) otherwise
and the second rule-based model as:
f(x) Y' if (k.dit > 0V ((kdds) > OV otkdda > for K - k otherwise
where y" the target class "Standing", and Y is the undesired class.
Rule-based models for the eRing dataset
Let d, denote the i-th feature. We define the first rule-based model as:
Y
if (kkd)) > 0 x (h.da) > for K - - k K
f(x) = Y otherwise
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Published in Transactions on Machine Learning Research (06/2025)
and the second rule-based model as: Y Y otherwise
if (R.d2)) > 0 V [(Hida)) > 0 for K - 9 ks K
f(x)=
where Y' is the target class and Y is the undesired class.
Rule-based models for the Japanese Vowels dataset
Let de denote the i-th feature. We define the first rule-based model as:
f(x)) = Y Y
if if 0 0 mikkdd) oA > for - k
otherwise
and the second based model as:
Y
if if > OV x(kddc) (V > 0 for K 19 s K otherwise
f(z) Y
where Y is the target class and Y is the undesired class.
Ruse- models for the Libras dataset
Let di denote the i-th feature. We define the first rule-based model as:
Y y
((k,d)) > A w(kddg) > 0 for K - 19 k
f(x)=
otherwise
and the second based model as:
Y (k.dd)) > 0 x(hdd2) > for K 19 S k s K
f(z) = Y otherwise
where y" the target class and Y the undesired class.
B.2 Other Predictive Models
Besides the rule-based models, each the following predictive models is also used for each datasct.
long short-term memory (LSTM). The first layer of the neural network LSTM layer with 30 hidden states, followed by two linear layers. The first linear layer takes input of dimension of 30 and produces an outpul of dimension 60, then passes the output to ReLU activation function. The second linear layer takes input of dimension of 60 and produces output, then passes the output to sigmoid activation function. We train the LSTM with learning rate 0.001 and weight decay 0.001 for 5000 epochs.
K-nearest neighbor (KNN). The number of neighbors to use for prediction vN, where N denotes the number of samples the datasct.
Random Forest. The number of trees is 100. The minimum number of samples required split an internal node 2. The minimum number of samples required to be leaf node 1.
C Hyperparameters used in Section 5
We use unique set of hyperparameter values for NTD-CFE throughout the paper, unless otherwise stated, without fine-tuning them:
19

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proximity weight Apamt 0.001
maximum number of interventions per episode Mr 100
maximum number of episodes Me = 100
discount factor 7 0.99
learning rate 0.0001
regularization weight ÄwD 0.0
The RL policy network contains two hidden linear layers with 1000 and 100 neurons, respectively. Adam (Kingma & Ba 2014) is used as the optimizer.
It important to note that NTD-CFB is not supervised learning algorithm. As reinforcement learning method, NTD-CFE does not rely training datasets. Instead, it interacts with the environment (i.e., the predictive model f) for optimization. We select the set of hyperparameter values that works best for the Life Expectancy dataset from ten candidate sets of hyperparameter values. Although more exhaustive hyperparameter search could potentially find anot set of hyperparameters that produces better results, we leave this for future work. For the baseline methods, we use the hyperparameter values and architectures that are provided as default in their code All the experiments are conducted on CPU and with 32GB of RAM.
Quantitative Experiments: NTD-CFE Versus NTD-CFEin dist
In this section, we compare NTD-CFE, which does not enforce plausibility, with NTD-CFE,, dist which enforces plausibility. For NTD-CFF,, _iit, Fi dist dist (a:) = True applied (Tine) 17 of Algorithm 1 while any _iit
other hyperparameter values remain unchanged. We employ local outlier factor (LOF) (Breunig et al.) 2000)
as the (optional) oracular in-distribution detector Fm dist LOF is common method for assessing plausibility
in CFF literature [Kanamori et al. 2020 Delaney et al.
2021 Wang et al. 2021b Romashov et al. 2022 Tt.
employs KNNs to measure the degree to which a data point is unusual compared to others.
As shown in Tables to 18 NTD-CFEn, dist achieves plausibility rates of 100%. However, its success rates are lower than those of NTD-CFE in 22/39 cases. We further compare their proximity and sparsity under the same success rates. Although NTD-CFE,, dist gets higher proximity in 8/17 cases and higher sparsity in 7/17 cases, the changes in the values small.
10e code publicly available at:
CoMTE: http://tttthb.ooocc//oe/ec
Nativo-Guides http:p/s//gituub.ooo/ee/o
/tl////ttttnnsseeeeeee Basedd CFE TSC
CFRL: http://ddoos.eedoo..o//pgegeee/p htt.a/aieeeeetoo/CC/C.....
Fast AR: http:///hhhaoooommmm///a/aaaaaaa
20

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Table 2: Features in the Life Expectancy dataset.
Features
Type
Country Name
Categorical
Year
Categorical
Continent
Categorical
Least Developed
Categorical
Population
Continuous
CO2 Emissions
Continuous
Health Papendibure
Continuous
Electric Power Consumption
Contimuous
Forest Area
Continuous
GDP per Capita Individuuls Using the Internet
Contimuous
Continuous
Military Eapenditure
Continuous
People Practicing Open Defecation
Continuous
People Using at Least Basic Drinking Water Services Obesity Among Adults
Continuous
Continuous
Beer Consumplion per Capila
Continuous
Label: Life Expectancy
Categorical
21

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Published in Transactions on Machine Learning Research (06/2025)
Table 3: Quantitative results with the Life Expectancy dataset.
Predictive Model
inv
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
COMTE
100
100
37.475
201.54
Native-Guide
100
100
85.714
30.674
190.238
LSTM
63
CFRL
0
FastAR
1.587
1.587
100
0.45
1.0
NTD-CFE
98.413
100
80.645
10.893
64.065
CoMTE
100
100
100
46.366
204.176
Native-Guide
100
100
48.529
1.452 x 10
200.574
KNN
68
CFRL
100
100
100
44.264
206.824
FastAR
0
NTD-CFE
85.294
100
58.621
19.756
82.879
CoMTE
100
100
100
33.752
199.468
Nativo-Guide
100
100
79.032
2.834 x 1013
200.548
Random
62
CFRL
100
100
100
44.684
207.484
Forest.
FastAR
0
NTD-CFE
100
100
96.774
8.724
49.661
COMTE
100
100
100
47.542
203.747
Rule-
Nativo-Guide
65.517
65.517
66.667
8.580
1013
193.526
Based
87
CFRL
0
FastAR
0
NTD-CFE
82.759
100
88.889
10.566
49.25
COMTE
100
100
100
47.108
203.327
Rule- Based 2
Native-Guie Guide
72.727
72.727
60.0
7.749 x 1013
183.025
55
CFRL
0
FastAR
0
NTD-CFE
81.818
100
86.667
11.238
52.667
22

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Published in Transactions on Machine Learning Research (06/2025)
Table Quantitative results with the PEMS-SF dataset. Both FastAR and Native-Guide fail to run on this dataset, crashing due to memory issues, even after their memory allocation was increased eight times that of the other methods.
Predictive Model
Nie
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
COMTE
100
100
81.25
139133.019
138672.0
Nativo-Guide
LSTM
64
CFRL
100
100
139107.344
138672.0
FastAR
NTD-CFE
40.625
100
80.769
1511.488
961.654
CoMTE
100
100
74.118
139101.786
138672.0
Native-Guide
KNN
96
CFRL
100
100
139100.448
138672.0
FastAR
NTD-CFE
5.208
100
60.0
1657.268
1267.8
CoMTE
100
100
80.328
139134.122
138672.0
Random Forest
Native-Guide
81
CFRL
100
100
139105.953
138672.0
FastAR
NTD-CFE
CoMTE
100
100
92.806
139122.140
138671.986
Rule Based
Native-Guide
139
CFRL
FastAR
NTD-CFE
96.403
100
73.881
3695.285
3520.687
CoMTE
100
100
87.5
139067.896
138672.0
Rule
Native-Guie Guide
Based
24
CFRL
FastAR
NTD-CFE
100
100
58.333
2586.61
2357.750
23

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Published in Transactions on Machine Learning Research (06/2025)
Table 5: Quantitative results with the NATOPS dataset.
Predictive Model
ine
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
COMTE
100
100
1285.262
1224.0
Native-Guide
100
100
63.333
1.270 1013
1158.133
LSTM
90
CFRL
0
FastAR
0
NTD-CFE
100
100
28.889
227.184
135.1
CoMTE
100
100
100
1284.259
1224.0
Native-Guide
100
100
55.914
6.332 x 1013
1213.172
KNN
93
CFRL
FastAR
0
NTD-CFE
6.452
100
50.0
588.817
496.333
CoMTE
100
100
100
1285.888
1224.0
Nativo-Guide
100
100
28.889
3.193 x 10
927.722
Random
90
CFRL
100
100
1277.502
1224.0
Forest.
FastAR
0
NTD-CFE
100
100
45.556
228.323
157.733
COMTE
0
Rule- Based 1
Native-Guide
66.854
66.854
17.647
1.349 10
1207.563
178
CFRL
0
FastAR
0
NTD-CFE
96.629
100
86.047
188.263
144.105
CoMTE
100
100
100
1294.181
1224.0
Rule- Based 2
Native-Guii
93.651
93.651
72.881
1.445 x 10
1208.458
126
CFRL
0
FastAR
0
NTD-CFE
100
100
100
33.756
20.587
24

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Published in Transactions on Machine Learning Research (06/2025)
Table 6: Quantitative results with the Heartbeat dataset.
Predictive Model
Niw
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
CoMTE
100
100
100
621.692
609.926
Native-Guide
100
100
77.206
1.075 10"
591.346
LSTM
136
CFRL
2.941
2.941
100
627.946
610.0
FastAR
0
NTD-CFE
97.794
100
88.722
16.825
12.12
CoMTE
100
100
100
626.788
609.948
Native-Gute
97.396
97.396
60.963
4.749 x 10
600.824
KNN
192
CFRL
0
FastAR
NTD-CFE
72.396
100
30.935
145.611
132.288
CoMTE
100
100
100
622.636
609.864
Random Forest
Native-Guide
65.986
65.986
79.381
1.877 10
600.68
147
CFRL
0
FastAR
0
NTD-CFE
0.68
100
57.664
48.0
CoMTE
100
100
100
624.442
609.883
Rule Based
Native-Guide
99.415
99.415
78.235
5.192 x 1012
571.535
171
CFRL
0
FastAR
0
NTD-CFE
70.175
100
43.333
173.931
162.692
COMTE
100
100
100
619.454
609.917
Rule
Nalive-Guide
100
100
82.5
2.236 x 10
589.658
Based
120
CFRL
0
FastAR
NTD-CFE
100
100
90.833
13.842
9.008
25

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Published in Transactions on Machine Learning Research (06/2025)
Table 7: Quantitative results with the Racket Sports dataset.
Predictive Model
inv
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
COMTE
100
100
214.707 202.626
180.0
Native-Guide
100
100
75.641
161.59
LSTM
78
CFRL
0
FastAR
14.103
14.103
100
1.786
1.091
NTD-CFE
100
100
98.718
16.734
8.295
CoMTE
100
100
100
217.73
180.0
Native-Guide
100
100
76.786
5.320 x 10
172.723
KNN
112
CFRL
FastAR
0
NTD-CFE
100
100
66.964
54.974
29.366
CoMTE
100
100
100
214.105
180.0
Random Forest
Native-Guide
98.78
98.78
77.778
3.529 x 10
167.222
82
CFRL
0
FastAR
0
NTD-CFE
100
100
90.244
43.695
26.232
COMTE
100
100
100
222.762
180.0
Rule
Native-Guide
94.595
94.595
67.619
1.170 10
172.486
Based
111
CFRL
0
FastAR
0
NTD-CFE
98.198
100
93.578
24.46
13.385
CoMTE
100
100
100
220.552
180.0
Rule
Native-Guide
100
100
75.0
228.065
170.125
Based
16
CFRL
FastAR
0
NTD-CFE
100
100
100
16.183
9.438
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Published in Transactions on Machine Learning Research (06/2025)
Table 8: Quantitative results with the Basic Motions dataset.
Predictive Model
N 'ne
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
CoMTE
100
100
100
782.188
600.0
Native-Guide Guide
100
100
85.714
699.261
527.429
LSTM
14
CFRL
100
100
100
802.065
600.0
FastAR
7.143
7.143
100
2.85
1.0
NTD-CFE
100
100
100
87.828
38.429
CoMTE
100
100
100
761.556
600.0
Native-Guide
100
100
78.947
706.719
562.526
KNN
19
CFRL
100
100
100
795.277
600.0
FastAR
0
NTD-CFE
100
100
94.737
206.984
121.421
CoMTE
100
100
100
751.741
600.0
Random
Native-Guide
100
100
80.0
721.01
574.9
Forest
20
CFRL
100
100
100
773.104
600.0
FastAR
0
NTD-CFE
100
100
50.0
305.677
182.25
CoMTE
100
100
100
896.874
600.0
Rule
Native-Guide
97.143
97.143
88.235
804.033
584.971
Based
35
CFRL
0
FastAR
0
NTD-CFE
97.143
100
73.529
133.66
80.559
CoMTE
100
100
100
703.79
600.0
Rule Based
Native-Guide
100
100
75.0
687.975
562.0
CFRL
FastAR
0
NTD-CFE
100
100
100
44.01
19.25
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Published in Transactions on Machine Learning Research (06/2025)
Table 9: Quantitative results with the Japanese Vowels dataset.
Predictive Model
N
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
CoMTE
100
100
100
330.771
300.0
Native-Guide
100
100
88.43
3.725 10
281.05
LSTM
121
CFRL
100
100
100
335.712
300.0
FastAR
0
NTD-CFE
100
100
99.174
35.3
19.413
CoMTE
100
100
100
331.845
300.0
Native-Guse
100
100
85.484
3.574 x 10
283.419
KNN
124
CFRL
100
100
100
334.799
300.0
FastAR
1.613
1.613
100
1.6
1.0
NTD-CFE
100
100
71.774
104.147
62.073
CoMTE
100
100
100
331.467
300.0
Random Forest
Mative-Guide
100
100
89.167
9.824 10
290.233
120
CFRL
100
100
100
334.707
300.0
FastAR
0
NTD-CFE
100
100
90.0
83.856
52.55
CoMTE
Rule Based
Native-Guide
30.855
30.855
78.313
3.032 1013
300.0
269
CFRL
0
FastAR
0
NTD-CFE
53.903
100
57.241
166.07
123.869
COMTE
100
100
100
330.597
300.0
Rule
Nalive-Guide
67.114
67.114
77.0
6.965 x 1012
289.92
Based
149
CFRL
0
FastAR
NTD-CFE
100
100
97.987
38.206
18.436
28

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Published in Transactions on Machine Learning Research (06/2025)
Table 10: Quantitative results with the Tibras dataset.
Predictive Model
N 'ne
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
CoMTE
100
100
100
120.329 111.969
89.494
Native-Guide Guide
100
100
64.045
88,382
LSTM
89
CFRL
0
FastAR
59.551
59.551
64.151
2.037
1.094
NTD-CFE
100
100
32.584
21.421
12.73
CoMTE
100
100
100
118.379
88.989
Native-Guide
100
100
51.685
126.318
89.213
KNN
89
CFRL
100
100
100
139.54
90.0
FastAR
1.124
1.124
0
4.4
3.0
NTD-CFE
100
100
14.607
45.306
24.112
CoMTE
100
100
100
108.074
88.393
Random Forest
Native-Guide
100
100
75.0
111.086
87.143
84
CFRL
0
FastAR
0
NTD-CFE
100
100
13.095
50.151
27.024
CoMTE
100
100
100
144.053
88.836
Rule
Native-Guide
100
100
87.069
135.861
88.836
Based
116
CFRL
0
FastAR
0
NTD-CFE
100
100
6.034
74.67
39.647
CoMTE
100
100
100
131.461
90.0
Rule
Native-Guide
100
100
98.113
135.119
90.0
Based
53
CFRL
FastAR
0
NTD-CFE
100
100
20.755
45.037
23.962
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Published in Transactions on Machine Learning Research (06/2025)
Table 11: Compare NTD-CFE and NTD-CFEj, dist with the Life Expectancy dataset.
Predictive Model
Ni
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
WTD-CFE
98.413
100
80.645 100
10.893
64.065
LSTM
63
NTD-CFE. Enn dist
93.651
100
12.546
57.695
WTD-CFE
85.294
100
58.621
19.756
82.879
KNN
68
NTD-CFE, dist
79.412
100
100
25.653
82.241
Random
NTD-CFE
100
100
96.774
8.724
49.661
62
Forest
NTD-CFE;, dist
100
100
100
8.984
49.242
Rule
NTD-CFE
82.759 79.31
100
88.889
10.566
49.25
87
Based
NTD-CFE; dist
100
100
10.063
46.014
Rule
NTD-CFE 81.818 76.364
100
86.667
11.238
52.667
55
Based
NTD-CFE, dist.
100
100
9.329
46.69
Table 12: Compare NTD-CFE and NTD-CFF, dist with the NATOPS dataset.
Predictive Model
Niw
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
NTD-CFE NTD-CFE; dist
100
100
28.889 100
227.184
135.1
LSTM
90
40.0
100
192.739
125.5
NTD-CFE
6.452
100
50.0
588.817
496.333
KNN
93
NTD-CFE, dist
3.226
100
100
109.59
67.0
Random
NTD-CFF
100
100
45.556
228.323
157.733
90
Forest
NTD-CFE,., dist
63.333
100
100
212.14
156.333
Rule
NTD-CFF
96.629
100
86.047
188.263
144.105
178
Based
NTD-CFE, dist
90.449
100
100
133.034
95.646
Rule Based 2
NTD-CHF CFFE
100
100
100
33.756
20.587
126
NTD-CFE, Ej
100
100
100
33.756
20.587
30

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Published in Transactions on Machine Learning Research (06/2025)
Table 13: Compare NTD-CFE and NTD-CFEmn_dse with the Heartbeat dataset.
Predictive Model
Niw
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
NTD-CFE
97.794
100
88.722 100
16.825 19.104
12.12
LSTM
136
NTD-CFE, Ein dist.
97.794
100
14.714
NTD-CFE
72.396
100
30.935
145.611
132.288
KNN
192
NTD-CFE, dist.
25.521
100
100
87.665
77.245
Random Forest
NTD-CFE 0.68
100
0
57.664
48.0
147
NTD-CFE,, dist
0
Rule
NTD-CFE
70.175 30.994
100
43.333
173.931
162.692
171
Based 1
NTD-CFE, Ein dist
100
100
83.472
75.906
Rule
WTD-CFE
100
100
90.833
13.842
9.008
120
Based 2
NTD-CFE,, dist
99.167
100
100
14.205
9.613
Table Compare NTD-CFE and NTD-CFF,, dist with the Racket Sports dataset.
Predictive Model
Nive
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
NTD-CFE
100
100
98.718 100
16.734
8.295
LSTM
78
NTD-CFF, dist.
100
100
16.961
8.423
NTD-CFF
100
100
66.964
54.974
29.366
KNN
112
NTD-CFF, dist
100
100
100
64.028
36.42
Random
NTD-CFE
100
100
90.244
43.695
26.232
82
Forest
NTD-CFF, dist
100
100
100
44.611
27.768
Rule
NTD-CFE
98.198
100
93.578
24.46
13.385
111
Based
NTD-CFE, dist
98.198
100
100
25.226
13.633
Rule
NTD-CFE
100
100
100
16.183
9.438
16
Based
NTD-CFE, dist
100
100
100
16.183
9.438
31

---

Published in Transactions on Machine Learning Research (06/2025)
Table 15: Compare NTD-CFE and NTD-CFEin_dae dist with the Basic Motions dataset.
Predictive Model
Nine
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
NTD-CFE
100
100
100
87.828 87.828
38.429
LSTM
NTD-CFE, Ein dist.
100
100
100
38.429
NTD-CFE
100
100
94.737
206.984
121.421
KNN
19
NTD-CFE, dist.
100
100
100
223.681
128.368
Random
NTD-CFE
100
100
50.0
305.677
182.25
20
Forest
NTD-CFE,, dist
95.0
100
100
321.474
199.895
Rule
NTD-CFE
97.143
100
73.529
133.66
80.559
35
Based
NTD-CFE, Ein dist
97.143
100
100
157.419
104.824
Rule
WTD-CFE
100
100
100
44.01
19.25
8
Based
NTD-CFE,, dist
100
100
100
44.01
19.25
Table 16: Compare NTD-CFE and NTD-CFF,, -in_FFen_ddis dist with the eRing dataset.
dist
Predictive
N Nine
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
Model
NTD-CFE
100
100
100
54.682 54.682
31.214
LSTM
NTD-CFF dist.
100
100
100
31.214
NTD-CFF
100
100
100
144.937
86.688
KNN
16
NTD-CFF, dist
100
100
100
144.937
86.688
Random
NTD-CFE
100
100
100
68.882
46.733
15
Forest
NTD-CFF, dist
100
100
100
68.882
46.733
Rule
NTD-CFE
100
100
100
103.953
63.345
29
Based
NTD-CFES dist
100
100
100
103.953
63.345
Rule
NTD-CFE
100
100
100
31.301
14.76
25
Based
NTD-CFES dist
100
100
100
31.301
14.76
32

---

Published in Transactions on Machine Learning Research (06/2025)
Table 17: Compare NTD-CFE and NTD-CFE,, dist with the Japanese Vowels dataset.
Predictive Model
Niw
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
NTD-CFE
100
100
99.174 100
35.3
19.413
LSTM
121
NTD-CFE, dist
99.174
100
35.753
19.833
NTD-CFF
100
100
71.774
104.147
62.073
KNN
124
NTD-CFF, Fi dist
94.355
100
100
114.437
74.667
Random
NTD-CFE
100
100
90.0
83.856
52.55
120
Forest
NTD-CFF,, dist
98.333
100
100
85.103
54.314
Rule
NTD-CFE
53.903
100
57.241
166.07
123.869
269
Based
NTD-CFF. Fin dist
34.201
100
100
135.475
98.674
Rule
NTD-CFE
100
100
97.987
38.206
18.436
149
Based
NTD-CFF dist
99.329
100
100
38.038
18.926
Table 18: Compare NTD-CFE and NTD-CFEJ, dist with the Libras dataset.
Predictive
N
Methods
Success Rate (%)
Validity Rate (%)
Plausibility Rate (%)
Proximity
Sparsity
Model
NTD-CFE
100
100
32.584 100
21.421
12.73
LSTM
89
NTD-CFF dist
93.258
100
39.937
23.831
NTD-CFF
100
14.607
45.306
24.112
KNN
89
NTD-CFE, dist
88.764
100
100
63.915
37.215
Random
NTD-CFE
100
100
13.095
50.151
27.024
84
Forest
NTD-CFE, dist
88.095
100
100
61.098
40.635
Rule
NTD-CFE
100
100
6.034
74.67
39.647
116
Based
NTD-CFE, Em dist
50.862
100
100
87.461
50.695
Rule
NTD-CFE 100
100
20.755
45,037
23.962
53
Based
NTD-CFE,. dist
84.906
100
100
75.344
38.289
33

---

Published in Transactions on Machine Learning Research (06/2025)
Table 19: This table shows that success rates are improved with increased maximum number of episodes ME and maximum number of interventions per episode My, which correspond to more exhaustive RL search. We only test against the cases from Tables and below 50%.
10 in which the default hyperparameters give success rates
NTD-CFE Hyperparameters
Success Rate (%)
Validity Rate (%)
Plausibility
Rate (%)
Proximity
Sparsity
ME 100, My 100
0.68
100
57.664
48.0
ME 1000, MT 100
10.204
100
20.0
267.045
253.2
ME 1000, Mr 1000
76.87
100
4.425
444.993
417.336
(a) Dataset: Heartbeat. Predictive model: random forest.
NTD-CFE Hyperparameters
Success Rate (%)
Validity Rate (%)
Plausibility
Rate (%)
Proximity
Sparsity
ME 100, Mr 100
6.452
100
50.0
588.817
496.333
ME 1000, Mr 100
12.903
100
33.333
711.761
595,583
ME 10000, My 100
26.882
100
16.0
782.599
627.96
(b) Dataset: NATOPS. Predictive model: KNN.
34


Reviews:
[{"review_id": "0kqAdcfPdt", "reviewer": "Reviewer_9A2J", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n- The idea of leveraging RL and counterfactual explanation is interesting.\n- The proposed method is intuitive and can be applied to many data types.\n\nWeaknesses\n- The current writing needs to improve. Specifically, the paper only aims to present the technical specification the method, but lacks of providing their motivations and further analysis.\n- The related works lack the discussions and references to other important works in explainable AI solving the same problem as this paper, typically [1], [2], [3]. It is encouraging to compare the proposed method and these methods.\n- Some notions used in this paper are not good, leading to confusion, for example, the ones in Reward and Proximity. The notions need to be revised and this section needs to be rewritten to make it clearer. \n\n\n[1] Ramaravind K Mothilal, Amit Sharma, and Chenhao Tan. 2020. Explaining machine learning classifiers through diverse counterfactual explanations. In Proceedings of the 2020 conference on fairness, accountability, and transparency.\n\n[2] Annabelle Redelmeier, Martin Jullum, Kjersti Aas, and Anders Løland. 2021. MCCE: Monte Carlo sampling of realistic counterfactual explanations. arXiv preprint arXiv:2111.09790 (2021)\n\n[3] Vo, V., Le, T., Nguyen, V., Zhao, H., Bonilla, E. V., Haffari, G., & Phung, D. (2023, August). Feature-based learning for diverse and privacy-preserving counterfactual explanations. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (pp. 2211-2222).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes No-Training-Dataset Counterfactual Explanation (NTD-CFE), a reinforcement learning (RL)-based method for generating counterfactual explanations (CFE) in both static and multivariate time-series data with continuous and discrete attributes. Notably, NTD-CFE operates without requiring a training dataset or similar data samples and is model-agnostic, making it compatible with any predictive model, including non-differentiable ones. Additionally, it allows users to specify which features can be modified and define dependencies between features, enabling the incorporation of feasibility constraints and causal relationships into the counterfactual generation process.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- Provide the motivations and further analysis for technical terms and specification.\n\n- Supplement the related works as mentioned. If possible, empirically compare to the aforementioned approaches.\n\n- Make the notions in reward and proximity more concise and easier to read. Rewrite the Reward and Proximity section.", "broader_impact_concerns": "There is no broader impact concern.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "BCUtvwT6vC", "reviewer": "Reviewer_AiGr", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n    1. This study tackles an important problem—counterfactual explanations—and the integration of RL for feature selection is a promising approach.\n    2. The method is validated on multiple real-world datasets, highlighting its practical applicability.\n\n\nWeakness:\n1. Novelty:\n    Several RL-based counterfactual methods already exist. A key claimed contribution is that the proposed method does not require training data from the model being explained. However, this claim remains unclear, as the paper does not specify how the RL model is trained.\n\n2. Presentation & Readability:\n    1)\tThe motivation and core ideas of the proposed method should be introduced and summarized more clearly.\n    2)\tAlgorithm 1 outlines the explanation generation process, but its description is too high-level and lacks essential details. For example:\n        a. How is the RL model trained?\n        b. How are constraints incorporated in line 13?\n        c. Providing more details on these aspects would improve clarity.\n3. Soundness:\n    1) The paper does not explain how the learnable parameters of the RL model are obtained.\n    2) The action space and feature selection process need further clarification:\n        a. Are candidate features selected one-by-one or in batches?\n        b. How is the policy model updated? Given the high-dimensional feature space, is the approach computationally scalable?\n\n4. The reliability of the results is unclear:\n    a. How are the counterfactuals estimated, how does the method interact with the model being explained, and what ground-truth knowledge is available for validation?\n    b. The success rate varies drastically between 100% and 0% (Table 1 and the appendix), raising concerns about the reliability and consistency of the results.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work introduces a model-agnostic counterfactual explanation method for multivariate time-series data, leveraging reinforcement learning (RL) to identify key features for generating counterfactuals.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "Refer to the weaknesses section.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "9o6wNbxe9M", "reviewer": "Reviewer_U7fP", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n\n1. Overall, the manuscript is well-written and easy to follow. \n\n2. The proposed algorithm is simple and straight-forward. In general, the manuscript should be accessible to a broad audience.\n\n3. Many experiments on real-world data sets are conducted.\n\n**Weaknesses**\n\nGenerally, I believe there is still a lot of work to do until this manuscript meets the acceptance criteria.\n\n1. It is not clear at all what the relevance of reinforcement learning is to the proposed method. The authors rightfully criticize that most counterfactual explanation methods require differentiability of the used predictor, which can be restrictive. However, there exist many zero-order optimization methods like Bayesian optimization that seem more straightforward to me and do not require gradients either. The fundamental components to reinforcement learning are 1) state transition dynamics, 2) a stochastic environment, and 3) an expected cumulative reward. All of these components seem to be missing here. The soundness of using reinforcement learning for the purpose of generating counterfactual explanations needs to be greatly and critically discussed.\n\n2. While I appreciate the comparison to many other RL based methods, the most relevant baselines are missing, in my opinion. This point is strongly related to weakness 1 and I believe it would be very important to demonstrate at least one more straight-forward approach to solving the problem, in comparison. Specifically, I recommend comparing to methods based on Bayesian optimization such as the one proposed by [1].\n\n3. The proposed algorithm seems quite naive and I am convinced that this problem can be solved both more efficiently and effectively. For instance, I am highly sceptical about the choice of reward function which simply puts zero reward on infeasible solutions. There are many more effective ways of dealing with constraints in optimization that don't require the user to ``hope'' for valid counterfactuals, but ensure validity of counterfactuals by design of the optimization procedure (https://en.wikipedia.org/wiki/Constrained_optimization). I believe that such methods for taking into accounts should be greatly discussed as well.\n\n[1] Spooner, Thomas, et al. \"Counterfactual explanations for arbitrary regression models.\" arXiv preprint arXiv:2106.15212 (2021).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors propose *NTD-CFE*, a model-agnostic counterfactual explanation method for low-dimensional time series data. *NTD-CFE* is based on reinforcement learning and does not require training data (except for rescaling features), in constrast to similar existing methods. The method is experimentally demonstrated on multiple real-world data sets and compared against other counterfactual explanation methods that are based on reinforcement learning.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "I will proceed to list requested changes one-by-one. Points that are critical for meeting the acceptance criteria are highlighted by *(critical)*.\n\n**Abstract**\n\n- *When ML methods are responsible for making critical decisions, stakeholders often\nrequire insights into how to alter these decisions* I am not sure if this is a good way of putting it. How about *When ML methods are responsible for making critical decisions, stakeholders often\nrequire and understanding of how this decision came about*?\n\n- *most existing CFE methods require access to the model’s training dataset, few methods can handle multivariate time-series, and none of model-agnostic CFE methods can handle multivariate time-series without training datasets*. First of all, I believe italics should be used a bit more sparingly. Also, I disagree that training data is required for computing CFE. From what I understand, the only thing that is required is a machine learning model that has been trained and a factual example. Please clarify.\n\n**Introduction**\n\n- *Counterfactual Explanations (CFEs) (Wachter et al., 2017) were introduced to fill this gap* I would disagree with this statement. A counterfactual explanation only tells what must have been different for a different prediction to be made. Actionability in counterfactual explanations has been critized and discussed by many authors [1, 2, 3]. Please clarify.\n\n- *For instance, a CFE that shows if Bob’s name were Alice* This is actually a perfect example regarding my previous point. Changing one's name is not actionable and vanilla counterfactual explanations generate such outputs.\n\n- *(critical)* *Additionally, to the best of our knowledge, all existing model-agnostic CFE methods for multivariate time-series require access to large collection of samples from the training distribution of the model being explained. This requirement can be infeasible in real-world domains especially due to privacy and other concerns.* Given that not requiring training data seems to lie at the core of the manuscript, I am surprised to find no information about how and why these existing methods require a training set. I believe there should be a major section that discusses this aspect.\n\n- *high dimensionality* I cannot find experiments with high-dimensional data in the experiments. Please remove the claim or demonstrate experiments on high-dimensional data sets for time series such as [4].\n\n**4 The proposed method: NTD-CFE**\n\n- *from $\\mathbf{x}^*$ to $\\mathbf{O}^*$*. I find this notation a bit strange. Why not simply call the factual point $\\mathbf{x}$ and the counterfactual $\\mathbf{x}'$ or similar? Please consider changing this, unless there is a good reason to have the original.\n\n- *We assume that the prediction function of f computes quickly* Please consider replacing by something like *We assume that the prediction function of f is computationally efficient*.\n\n- *can optionally be divided into actionable features $\\mathbf{D}_{\\text{act}}$, which...* I would assume that these sets can be overlapping (?). If yes, then the word *divided* does not seem correct. If they cannot be overlapping, why not? Please clarify.\n\n- *(critical)* **State Transition** I am greatly struggling to understand the relevance of this state transition component, which is also related to weakness 1. What would happen if one were to remove this component and instead have the policy directly output the next state $x_{t+1}$? It would be important to showcase an ablation that highlights the relevance of this component. Additional explanation in the main text would also be relevant.\n\n- *Reward and Proximity* This choice of reward function seems quite inefficient, because the agent needs to learn the space of feasible solutions itself. In addition, It cannot be that this reward function effectively leads to solutions that are valid. I guess the authors consider some sort of epsilon radius around the counterfactual value to be valid. I believe that it would be much more effective to address this circumstance with constrained optimization methods such as the augmented Lagrangian method, which should also be applicable to zero-order optimization. Please discuss.\n\n**Algorithm 1**\n\n- I appreciate that the authors make use of different colors. However, the type of gray used seems a bit too light for my taste. Would it be possible to choose a slightly darker color for this?\n\n- line 16: I find this line in the algorithm quite sketchy. Does that mean one needs to run the algorithm and hope that at some point a valid counterfactual is guessed? This sounds very inefficient, considering that there exist methods for constrained optimization that are guaranteed to yield valid solutions on the first try, like aforementioned augmented Lagrangian method (see weakness 3).\n\n**5.2.1 Results**\n\n*Comparison with CoMTE* The authors write that CoMTE requires training data. It would be very important to know how this method uses training data. It seems also not totally correct that the proposed method does not require any training data, as mentioned in *4.1 Limitations*. To evaluate the contribution, it would be important to know more about what these baselines do.\n\n**Figure 1** \n\n*(critical)* I do not understand this figure at all. For instance, why would the original user input change over time? And why does such a prominent figure showcase what rule-based models do, without even a comparison to the proposed algorithm? And what is even the counterfactual value in these plots? I believe this figure needs to be greatly revised or omitted.\n\n[1] Karimi, Amir-Hossein, Bernhard Schölkopf, and Isabel Valera. \"Algorithmic recourse: from counterfactual explanations to interventions.\" Proceedings of the 2021 ACM conference on fairness, accountability, and transparency. 2021.\n\n[2] Karimi, Amir-Hossein, et al. \"Algorithmic recourse under imperfect causal knowledge: a probabilistic approach.\" Advances in neural information processing systems 33 (2020): 265-277.\n\n[3] Kladny, Klaus-Rudolf, et al. \"Deep backtracking counterfactuals for causally compliant explanations.\" Transactions on Machine Learning Research (2024).\n\n[4] Requena-Mesa, Christian, et al. \"EarthNet2021: A large-scale dataset and challenge for Earth surface forecasting as a guided video prediction task.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2021.", "broader_impact_concerns": "None.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: Using RL for counterfactual explanation is a straightforward and reasonable direction. The proposed method has been specifically designed the method in the scenario of time-series data. 

The claim is supported by its clear design and analysis. All major issues have been resolved in the conversation between authors and reviewers. 

The paper's contents are relevant to the TMLR audience's interest.
Decision: Accept (poster)