From Search to Sampling: Generative Models for Robust Algorithmic Recourse
Authors: Prateek Garg
Lokesh Nagalapatti
Sunita Sarawagi
Venue: ICLR 2025 Poster (2025)
Keywords: Algorithmic recourse
explainability
generative modelling
Primary area: alignment, fairness, safety, privacy, and societal considerations
TL;DR: We propose a generative modelling approach for recourse that provides a distribution over likely recourse instances.

Abstract: Algorithmic Recourse provides recommendations to individuals who are adversely impacted by automated model decisions, on how to alter their profiles to achieve a favorable outcome. Effective recourse methods must balance three conflicting goals: proximity to the original profile to minimize cost, plausibility for realistic recourse, and validity to ensure the desired outcome. We show that existing methods train for these objectives separately and then search for recourse through a joint optimization over the recourse goals during inference, leading to poor recourse recommendations. We introduce GenRe, a generative recourse model designed to train the three recourse objectives jointly. Training such generative models is non-trivial due to lack of direct recourse supervision. We propose efficient ways to synthesize such supervision and further show that GenRe's training leads to a consistent estimator. Unlike most prior methods, that employ non-robust gradient descent based search during inference, GenRe simply performs a forward sampling over the generative model to produce minimum cost recourse, leading to superior performance across multiple metrics. We also demonstrate GenRe provides the best trade-off between cost, plausibility and validity, compared to state-of-art baselines. Our code is available at: https://github.com/prateekgargX/genre

Published as a conference paper at ICLR 2025
FROM SEARCH TO SAMPLING: GENERATIVE MODELS FOR ROBUST ALGORITHMIC RECOURSE
Prateek Garg" Lokesh Nagalapatti
Sunita Sarawagi
Indian Institute of Technology Bombay
ABSTRACT
Algorithmic Recourse provides recommendations to individuals who are ad- versely impacted by automated model decisions, on how alter their profiles to achieve a favorable outcome. Effective recourse methods must balance three conflicting goals: proximity to the original profile to minimize cost, plausibil- ity for realistic recourse, and validity to ensure the desired outcome. We show that existing methods train for these objectives separately and then search for recourse through a joint optimization over the recourse goals during inference, leading to poor recourse recommendations. We introduce GenRe, a generative recourse model designed to train the three recourse objectives jointly. Train- ing such generative models is non-trivial due to lack of direct recourse super- vision. We propose efficient ways to synthesize such supervision and further show that GenRe's training leads to a consistent estimator. Unlike most prior methods, that employ non-robust gradient descent based search during inference, GenRe simply performs a forward sampling over the generative model to pro- duce minimum cost recourse, leading to superior performance across multiple metrics. We also demonstrate GenRe provides the best trade-off between cost, plausibility and validity, compared to sfate-of-art baselines. Our code is available at: https::///// / /t/tt/ttttttttt con/ ptat//raaaaeeeeeeeeeaaee eekgargx /eazz..
INTRODUCTION
Machine learning models are increasingly used in high-stakes molsiion-makin areas such as in fi- nance (Josyula et al., 2024), judiciary (Elyounes, 2019). healthcare (Burger, 2020), and hiring (Schu- mann et al., 2020), prompting the need for transparency and fairness in decision-making (Barocas al., 2023). This has driven the development of tools and techniques to provide recourse, redress mechanisms for individuals adversely impacted by these model decisions, a legal requirement in certain jurisdictions (Kaminski, 2019). For example, consider a loan applicant with profile æ who is denied loan. Recourse seeks to answer the question, 'How should x improve their profile to an alternative * to secure a loan in the future?'. A good recourse instance x should be (1) valid, i..., it achieves the desired label, (2) proximal to minimize the effort involved in implementing recourse, and (3) be a plausible member of the desired class. The decision- decision-making model is often proprietary and is kept hidden to safeguard enterprises from strategic gaming (Hardt et al., 2016), model theft (Reith et al., 2019), and other risks. We are given instead examples of individuals who got the desired label (positive instances), and those who did not (negative instances). Our goal is to learn recourse mechanism using just these samples.
The recourse problem has been widely explored under frameworks like algorithmic recourse (Ustun al., 2019). counterfactual explanations (Wachter et al., 2017). and contrastive explanations (Karimi et al., 2022). Most prior work assume direct access to the recourse instance through constrained optimization during inference on objectives which encourage low cost and validity (Karimi et al., 2022; Wachter et al., 2017; Mothilal et al., 2020; Laugel et al., 2017). Others aim for robust recourse by searching for an + that remains valid under small changes to either the model or the proposed x= itself (Pawelezyk et al., 2020b; Rawal al., 2020). The plausibility criterion is often overlooked, and some methods propose to address it by training generative models (Joshi al., 2019; Pawelezyk et al., 2020a; Downs al., 2020). Most recently, Friedhaum et al. (2024) attempts to increase the validity of a by including a separate verifier model that checks whether (x. ax+) belong to different classes after the optimizer generates a candidate t
moiisoioommiingg model, and search for the
One significant limitation of all prior methods is that none of them are trained jointly optimize the three conflicting recourse criteria of validity, proximity, and plausibility. Instead, during inference,
"Correspondence Prateck Garg <prateekg@ wtb..aa..... in>

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they either ignore some recourse objectives rely non-robust gradient-basee search the joint objective to balance the trade-offs between them. We show in Figure that this disconnect between training and inference leads to poor recourse outputs.
In significant departure from the existing paradigms, take generative approach recourse. We train a novel recourse likelihood model Ro [=) that when conditioned on any instance æ seeking recourse, outputs a distribution over likely recourse instances. Using such model during inference, we just forward sample recourse instances, unlike existing methods that perform gradient descent optimization to find one xt However, to train such a model we would need several instance pairs {(z,, x i = 1.... } where zi is good recourse for any 2; with an unfavorable outcome. Such direct supervision is lacking. We show how to leverage standard unpaired classification data to sample a training set of instance pairs. We theoretically show that the sampled pairs are consistent, and the error of the expected recourse instance converges at the rate O(1/N+) where N₂ denotes the number of instances in the positive class.
In terms of empirical validation, we first present a visual demonstration of the pros and cons of various methods using three 2-D datasets. We then evaluate on three large real-life datasets that popularly used in the recourse literature and compare our results with eight existing methods. We show that our method achieves (1) the best score combining validity, proximity and plausibility, (2) is more robust to changes in the cost magnitude compared to SOTA likelihood- basee methods, and (3) more faithfully learns the conditional density of recourse than methods that separately learn unconditional data density.
2 PROBLEM FORMULATION
Let X' C Rd represent the input space and y {0, 1) the output space where the joint distribution between them is P(X,Y) In the recourse task, one label, say is an unfavorable outcome (c.g., loan rejection) and the other label y+ 1 denotes favorable one (e.g., loan approval). We are given a training dataset of n instances D = (( y:) }=) sampled i.i.d. from P(X, Y). We use DI and Do to denote the subset of D with label and 0 respectively. We assume that we have pretrained classifier h X' + [0, 1] trained on the available dataset D, serves as an approximation for P(Y 1|X). Given an instance x ~ P(X), recourse is sought on instances where h(x) 0.5. Our objective is to design a mechanism, & X' + X' that outputs a recourse instance xt such that P(ytlat) > 0.5, while minimizing the cost of shifting x+ measured in terms of a cost function C:X= x X ~ R++ & distance is a popular choice for C. Additionally, the recourse instance a should be representative in the desired class distribution ((X)+t), and not an outlier. In real- life applications, weird unrepresentative profiles may not be achievable, and mislead the purpose of recourse. For instance, in domains such as banking, ensuring high P(x ly+t is important because an user should not be gaming the system to get loan approval.
Y(
D
P
>
0.5
Sperieens well 37)
Genenating Process
Chusiiier
P
high
h
low
y
Recouse Mecharisn
Figure 1: The recourse pipeline starts with any instance z that received unfavorable label h((:)
y The recourse mechanism outputs an alternative x* such that h(x +) = yt. The user is satisfied as long as x+ (1) is valid i.e., achieves the desired label from Ply- la+ (2) is plausible and actionable in real-life, and (3) is proximal to the original æ to incur low cost.
Based on the above considerations an ideal recourse mechanism can be defined follows:
(x) arg min AC x .x) log ((**(y*) s.t. P(y |æ > 0.5
(1)
z
where À is a balance parameter which helps to trade-off cost with plausibility. Additionally, not all features can be altered for x for example, in loan applications, recourse mechanism should not suggest recourse where immutable attributes like race are different. We assume that the cost func- tion models immutability and for any two instances x, x'' where immutable attributes are different,
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C(x,, x²) - For æ, x' where immutable attributes are same, use & distance cost as suggested in Wachter et al. (2017).
3 RELATED WORK
We will illustrate the working of various methods using three 2D binary classification datasets as shown in Figure 2. Training instances are shown in light red (for Dn) and blue color (for Di). Recourse is sought on instances æ marked in dark color and they are connected by an edge the corresponding recourse instance returned by various methods. Experimental details of these figures appear in Section 5.
WACHTER
PROBE
CRUDS
GenRe(Ours)
training data cless 0 training data class
negalive instances
htx > 0.5 valid recourse
recourse instances
hix) 0.5
invalid recourse
Figure 2: Comparison of different classes of recourse methods. Training instances shown in light red and blue colors. Recourse is sought on instances marked in dark red color and they are connected by an edge the recourse instance they were mapped From left right:(1) Wachter, cost minimizing method maps instances to classifier boundaries away from the blue data distribution. (2) PROBE, a robust recourse method, maps instances away from the boundary and from the blue data distribution. (3) CRUDS, likelihood based method suffers mode collapse and for the circles dataset strays away from data distribution. to train (4) GenRe(our method) produces plausible recourse instances by being on the blue cloud while also minimizing cost. Recourse instances are also diverse.
We group prior work into three categories based on how they approach the recourse problem.
Cost Minimizing Methods. This class of methods search for instances that minimize cost under the constraint that classifier h assigns the desired label, that is, h(x) 0.5. The search is performed in various ways: GS (Laugel et al., 2017) uses a random search, whereas Wachter (Wachter et al., 2017) uses gradient search differentiable objective based on cost and classifier h as follows:
* (x) = arg min Clx, x +) log(h(x+)))
(2)

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DICE (Mothilal et al., 2020) extends the above objective to include diversity. As noted by Fokkema et al. (2024), such methods often push recourse instances near the boundary of h, as can be seen in Figure 2 (first column). In particular, these methods suffer because: a.) Recourse instances that lie on boundary of h have equal probability of being assigned either label and therefore are prone to be invalidated. h.) Recourse instances can be away from data manifold and thus unrealistic and unreliable since these methods do not consider data density.
Next we discuss two classes of methods which attempt to improve on these shortcomings.
Robust Recourse Methods. This class of methods trade-off cost in order to generate recourse instances which are more robust by generating recourse instances at some 'margin' away from the boundary of h. ROAR (Upadhyay et al., 2021) attempts output recourse instances which are robust to small changes to the classifier h by optimising for worst case model shift under the assumption that the change in parameters of h is bounded. PROBE (Pawelezyk al., 2023) attempts generate instances which are robust to small perturbations to the recourse instances. These methods also do not consider data density and thus are prone to generate recourse instances which are unrealistic and unreliable as shown in Figure 2 (middle column) and may land in low density regions and/or around spurious decision boundaries. Recently, TAP (Friedbaum et al., 2024) introduces verifier model which checks whether two given instances belong to the same class. This verifier is used to check if a negative-recourse instance pair belong to different class.
Plausibility Seeking Methods. Methods in this class leverage generative models to ensure that they predict plausible recourse by staying close to the training data manifold. REVISE (Joshi et al., 2019), CRUDS (Downs et al., 2020), and CCHVAE (Pawelczyk et al., 2020a) train variants of VAE (Kingma & Welling, 2014) on the training data, and then during inference they either do a gradient search latent space, or perform rejection sampling forward samples generated by the VAE. Suppose Dg Z + X denotes a VAE decoder, their recourse objective during inference is:
((x) = Do ( arg min log(h(Do(=)) + A C(x, (o()))
Gradient Search for z on the above objective fails to keep the generated recourse example within the data distribution and suffers from mode collapse we show in Figure 2 (Third column). Notice that particularly for the circle dataset, the recourse instances are not at all within the data distribution, and collapse single point.
We provide more extensive overview of related work in Appendix A, and present comparisons on real-life data in Section
4
OUR APPROACH
The above discussion highlights that the main challenge in recourse is jointly optimizing three con- flicting objectives. The cost function C(æ,, is minimum near where the density P(æ*lyy)) of the desired positive class is low. The learned classifier h(x+)) could be maximized at regions where positive class density is low, particularly in the presence of spurious boundaries. The regions of high positive density could be far away from æ leading to high costs. Unlike all prior methods that op- timize for these terms during inference, we train a recourse likelihood model (a æ²) that when conditioned on an input negative instance provide a distribution over possible recourse instances a We start by rewriting the ideal recourse objective defined in Equation 1 as
(xx) arg max exp (- (=, x: ()) P(x by (zx*) +
where V(x+)= 8(P x+)) 0.5) denotes the desired validity constraint on a recourse instance. Using the above we define the ideal un an-normalized recourse likelihood as:
R(x: + [æ)) x (-pC x: xz) P(x: Jy (x(+).
(5)
Our goal during training is to learn a model Ra to estimate this ideal recourse density R(x (x). The main challenge here is that we are given only individual labeled instances D Di U Do. whereas what we ideally want is instance- -aann sampled from R(x*(z) In Section 4.1 we present how we construct such samples from D, and then present how use the constructed pairs to architect and train our estimated model R₂ (x (z). In Section 4.2, we describe one convenient model parameterization which allows for sampling.
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C(o,o) ,
21
Mrt
D
D
Q(x (x))
The Recoums
R4
D
Autesgrenna
Training
Indersnce
Figure 3: Overview of GenRe. We define an empirical distribution of instance pairs (æ, x+) using training data D, classifier h, cost function C and balance parameter to train the recourse model Ra. an encoder-decoder model. During inference, the given negative instance is fed to the decoder, and recourse instances sampled from the decoder auto-regressively.
4.1 CREATING TRAINING PAIRS
We define D := {a, Dlu hx.)) - 0.5}. These denote training instances where recourse desired. Similarly define D := fæ, E Dly, y* h(x,) > ) for some chosen ? 0.5. These denote the subset of training examples from the positive class that are also predicted positive by the classifier with confidence 7, For each D we define empirical distribution as follows:
ACle,wt)
if xt E D
Q( x))
Σ lent AClmaat
(6)
otherwise
where denotes the balance parameter as described 1. We show in Section 4.4 that Q( las) consistent estimator of R(x (æz), and the difference in the expected value of the recourse in- stance ||E +xx] |a]| En fz[[==] [=]]] reduces at the rate of 1 N_ where N 'Dit denotes the number of positive instances, when h(x) is the actual conditional distribution P(Y)X). We note that as + 0o, will always return the nearest neighbor of in D In section 5.4, we compare our method GenRe with nearest neighbor search from D
4.2 ARCHITECTURE AND TRAINING OF THE GENERATIVE MODEL
We choose R. be auto-regressive generative model that during inference only need to perform a forward sampling on the model to obtain recourse instances. We next describe the architecture of Rg. We use transformer-ben æ is input to the encoder with learned position embeddings. The decoder defines the output recourse distribution auto-regressively as (= [æ) I Re(x;" [ .... ...,,..,,,,,). The decoder also uses learned position embeddings and performs cross attention on the encoder states and causal self- attention on decoder states. The output conditional distribution for each attribute 2 is modeled as kernel density:
encoder-decoder architecture. The negative instance
Ro(1 12,21 .... x Σ ph. K(((F 11.,k//5..))
Here, PS. 2 O, such that Σ P/ = 1, represents the kernel weights output by the transformer, and is implemented by binning the 7th attribute in D into nj partitions, with Mj as the bin center and wj. as the bin width. We use the RBF Kernel. The loss for paired sample (xx x) Q is computed as,
Softmax layer. The means PijA and width wj,k of the 1.th component are fixed
L(x (x:0) = Σ log
PS.. K((at M5,k)/
j=1
n2
K((x (53x)//U,,n)
<
llo -og +
(8)
Di K((x,t - MMR)/
j=1 R=1
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Here have used Jensen's inequality to express the loss simple cross entropy loss the pf vector output by the last softmax layer with the kernel ratios serving as soft-labels.
The overall training process of the model is shown in Figure and outlined in Algorithm 1. We emphasize that this also be considered. In appendix 5.6, we show results on pre-trained diffusion models with guidance sample from distribution described in 5.
particular choice of parameterisation, with note that other models can
4.3 INFERENCE
Once the rettoreegeesive encoder-decoder is trained, finding recourse on any input negative instance during test time, entails just simple forward sampling step on Rg. We input æ to the encoder, and sample the recourse instance auto-regressively feature-by-feature. The full inference method appears in Algorithm 2. Another advantage of our approach is that a user can sample multiple recourse instances and choose which recourse action to implement.
4.4 THEORETICAL ANALYSIS
Theorem 4.1. Let f(x*, x)) be any function of (x* x). For Q(x x)) defined in Equation 6 and R(x (x) defined in Equation 4, let μ Exlf and jı Eqlf). Then ia is consistent estimate of ja when h(x) > 0.5 and Ply |x) > 0.5 agree.
Proof. Let D2 denote the subset of DD where y, = y² Substituting the definition of Q, is easy to that
- AC V(++)
[ols(([=)]
Σ f(x ExteDt e -CCla,.t)
()EE)
V(x*) = ((P(y+1=) > 0.5) = 8(h(x) > 0.5). The above can seen as a normalized importance weighted estimator for μ En[f] when treat P(**ly+)
proposal distribu- tion for R(w (e) distribution. The proposal distribution is sound since P(*
0 when- ever R(x= + xx) 0 because includes P(*+ I(*+l*** one of its terms. The training data D, is representative sample from P(X]y+). The unnormalized weight of the importance sampling step
vi(=)) AC (v lut) -- V((r+) Substituting these in Eq 9
that Eolf] a self-normalized importance weighted estimate, which is well-known to be a consistent estimator when proposal is non-zero at support point of target.
P(X
Theorem 4.2. The difference the expected value of the counterfactual [Eq[=*[z] Eg(=* [=]]] reduces at the rate of 1 when h(x) is the actual conditional distribution P(Y N.
Proof. Using f(x*, x) x the proof of Theorem 4.1 showed that Eqjæ [|] |=]] is a normaizerd importance sampling estimate of E [x |x]]. The variance of this estimate for given is ap- proximately T Va) [f(X + Var (xx(C(X,))) which reduces at the rate
TD.T (Koller & Friedman (2009), Chapter 12).
EXPERIMENTAL RESULTS
We next present empirical comparisons of our generative recourse model with several prior recourse methods. We already presented a visual comparison on synthetic datasets in Figure 2. In this section we focus on real datasets.
5.1 EXPERIMENTAL. SETUP
Datasets: We experimented with benchmark datasets commonly used to evaluate recourse al- gorithms:
Adult Income (Becker & Kohavi, 1996), FICO HELOC (FICO, 2018), and COM- PAS (Angwin et al., 2016). These datasets contain mix of continuous and categorical features. All continuous attributes encoded. We defer detailed descriptions of these datasets to Appendix C. and present a summary in Table 1. For each dataset, train Random Forest (RF) classifier mimic the latent decision- making model, which assigns the gold labels. No method has access to this classifier during training; instead, they have access to training data D sampled from it. This classifier is used to evaluate the
normalized to the range of [0, 1]. while categorical attributes are one-hot

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validity of recourse output by various methods. We ensure that the RF classifier is calibrated by using the www.brattdlaaasiiiiiiic fierc API from sklearn (Pedregosa et al., 2011) 1).
Baselines: We compare our method with eight prior recourse methods covering each of the three cat- egory of prior methods already described in Section 3: Wachter (Wachter al., 2017), GS (Laugel et al., 2017), DICE (Mothilal et al., 2020), ROAR (Upadhyay et al., 2021), PROBE (Pawelczyk et al., 2023), REVISE (Joshi et al., 2019), CRUDS (Downs et al., 2020), and CCHVAE (Pawelczyk al., 2020a). TAP (Friedbaum et al.. 2024). For standardized comparison, we used their public imple- mentation from CARLA recourse library' (Pawelczyk et al., 2021).
Implementation Details. For the labeled dataset 2, we adopt the features from the real data as is and assign labels sampled from the RF classifier. The classifier h(x) is an Artificial Neural Network (ANN) ReLU-based model with three hidden layers of size 10 each, trained with learning rate of 0.001 for 100 epochs using batch size of 64. The accuracy of h(z) is reported in Table 1.
Dataset
#Feat.
#Cat.
#lmmut.
#Pos
#Neg
#Train
#Test
ANN accuracy
Adult Income
13
8,742
27,877
36624
12208
77.33
COMPAS
7
4
2
3,764
865
4629
1543
69.60
HELOC
21
0
0
3,548
3,855
7403
2468
74.23
Table 1: Data Statistics along with accuracy of ANN classifier
For training Rg. we use Transformer (Vaswani et al., 2017) from PyTorch (Paszke et al., 2019) with learned position embedding, embedding size 32, and 16 layers in each of encoder and decoder, and 8 heads. The number of bins in the last layer is 50. We choose the value of X 5.0 when sampling training pairs. During inference (Algorithm 2), we set the temperature for bin selection 10.00 and a 0.00, generate 10 samples and choose the sample which gets highest probability from the classifier (ar). In Appendix D.2, we provide results over other values of 7 and a. We describe other relevant hyperparameters in Appendix C.2.
Performance Metrics. We evaluate the performance of recourse method on test set { consisting of m negative instances using the following metrics:
1. Cost: We define cost as the & distance between the negative instance a and its corresponding recourse instance x
2. Val: Validity measures if the recourse was successful, that is, the RF classifier assigns yt.
3. LOF: LOF(Breunig et al., 2000) assesses how plausible or representative the recourse instance is.
We report the fraction of recourse instances which were assigned as inliers by this module.
4. Score: To evaluate all methods using a single metric, we define Score as Score = Val + LOF Cost where d is the number of features in the dataset. Note that the maximum possible value of Score is 2.
d'
Dataset
Adult Income
COMPAS
HELOC
Method
Cost | Val
LOF 1 Score t Cost
Val f LOF 1 Score 1 Cost | Val f LOF Score
Wachter
0.31
0.51
0.76
1.24
0.20
0.59
0.23
0.79
0.79
0.35
0.97
1.28
GS
1.82
0.40
0.49
0.75
1.20
0.66
0.48
0.97
0.58
0.32
0.94
1.23
DICE
0.22
0.62
0.73
1.33
0.19
0.57
0.44
0.99
0.49
0.34
0.97
1.29
ROAR
10.17
0.96
0.01
0.19
4.01
0.87
0.01
0.30
9.64
0.47
0.17
0.19
PROBE
33.91
1.00
0.00
-1.61
5.77
0.82
0.00
-0.00
5.37
0.69
0.07
0.49
TAP
1.10
0.99
0.67
1.57
1.46
0.88
0.70
1.37
0.71
0.36
0.53
0.86
CCHVAE
2.11
0.00
1.00
0.84
3.03
1.00
0.07
0.64
3.58
0.04
0.14
0.02
CRUDS
3.17
1.00
0.96
1.72
1.10
0.98
1.00
1.83
4.30
1.00
0.57
1.37
GenRe
0.69 1.00
0.98
1.93
0.51
0.99
0.97
1.89
2.01
1.00
1.00
1.90
Table 2: Comparing different recourse mechanisms on three real-life datasets. For each mechanism. we report cost, validity, LOF, and a combined Score=Wdl+LOF-Covll/ GenRe provides the best score across all datasets, and is close to 2, the maximum achievable score.

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5.2 OVERALL COMPARISON WITH BASELINES
Table presents comparison of our method GenRe with several other baselines on the cost, va- lidity, and LOF metrics, and an overall combined score. From this table we can make number of important observations: (1) First, observe that our method GenRe consistently provides competent performance across all metrics on all three datasets. GenRe's average score across the three datasets is the highest. (2) we compare on cost alone, the first three methods (Wachter, GS and DICE) that ignore plausibility, achieve lower cost than GenRe but they provide poor validity (close to 0.5). This is possibly because they optimize for validity on the learned h(z) which may differ from the gold classifier. (3) The next two methods (ROAR and PROBE) choose more robust instances with a margin, and thus they achieve much higher validity. However, they struggle with choosing good margins, and the recourse instances they return are very far from a seen by the abnormally high costs. Also, these methods mostly yield outliers for recourse as seen in the low LOF scores. TAP, which trains an auxiliary verifier model select highly valid recourse instances during inference, outperforms ROAR and PROBE, achieving good validity scores in Adult and COMPAS. However, it falls short in other recourse metrics, resulting in a consistent subpar overall score. (4) The next two methods CCHVAE and CRUDS incorporate plausibility with VAE, and of these CRUDS provides competitive LOF and validity values but it generally incurs higher cost than our method.
5.3 GENERATING RECOURSE FROM RECOURSE LIKELIHOOD MODEL VS OPTIMIZING JOINTLY DURING INFERENCE.
We present a more in-depth comparison of GenRe, our training- recourse method, with CRUDS that emerged as the second best in the comparisons above. CRUDS includes all three objectives of validity, proximity, and plausibility like in GenRe but combines them during infer- ence. In the CRUDS implementation? inference entails solving an objective like in Equation 3 but with some set fixed. Thus À in this method also allows control the magnitude of cost like in GenRe's s objective (Equation 4). No matter what the X. an actionable recourse method should always generate plausible instances from the data manifold in order to be taken seriously in real-life. The can be used to tradcoff expense Vs guarantee of achieving the target label. From this perspective compare how CRUDS and GenRe respond to changing cost magnitude X. We perform experiments with x E (0.5, 1.0, 2.5, 5.0, 10.0). In the Figure below we plot the value of -costtostaa az. x xt)/d on the X-axis against validity in the first row and against LOF in the second row. Each point denotes a specific From these graphs we can make the following interesting observations:
Adult Income
COMPAS
HELOC
1.0
Soft Volidity
0.8
0.6
0.80
0.05
0.90
0.95
0.75
0.80
0.05
0.50
0.89
0.90
0.91
0.8
0.6
0.80
0.85
0.95
0.75
0.80
0.85
0.90
0.84
0.90
0.91
Cld
Cld
Genta
CRUBS
Figure 4: Comparing GenRe with CRUDS for different values of balance parameter E (0.5, 1.0, 2.0. 10.0). Note that z-axis is on exponential scale. Top: Comparing soft validity. Bottom: Comparing fraction of recourse instances that were inliers. GenRe provides better trade- offss than CRUDS with changing cost: GenRe always returns plausible instances and tradesoff validity gradually with cost. CRUDS shows huge swings in validity and plausibility with changing X.
(1) On all datasets we observe that GenRe consistently provides plausible recourse instances as seen by the high LOF scores across all À values, even while cost increases. In contrast, except for the
Thhe inference method described in the CRUDS paper differs from their implementation in the CARLA library
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HELOC dataset, the LOF scores of CRUDS swings significantly with changing À even though the cost stays the same. (2) The validity values change gradually with changing À whereas in CRUDS on two of the datasets COMPAS and HELOC, observe much greater swings.
5.4 ABLATION: ROLE OF CONDITIONAL LIKELIHOOD
Apart from the joint training of recourse likelihood, another explanation for the superior perfor- mance of GenRe is that our approach involves training the conditional likelihood of recourse stances R(x* (z). The conditioning on input negative instances results in density that is more tractable to learn than the unconditional data density of P(Xly*) that needs to capture the entire data manifold of positive instances. We show this visually on two synthetic datasets from Figure 2. For each dataset, we train two density models: Rg(2 | and P( Both these densities are learned using transformer models. Since P(X does not need encoder, its transformer uses twice the number of layers as the conditional one. We show the contours of these two conditional densities in Figure 5. The large red dot in the plot represents the negative instance which the density is conditioned.
(andi
CondiBonalicickaz
Unconditonal(Croeaa
Figure 5: Visual Comparison between contours of density learned by conditional model (odd posi- tions) and unconditional model (even positions)
We can see vividly that the conditional density of Ro(x+12) is concentrated around an optimal re- gion on the data manifold that meets all three recourse goals. In contrast, the unconditional density of the blue training points from the positive class is subpar. Such density models when combined with cost and validity objectives during inference are less likely to yield recourse on the data mani- fold.
5.5 COMPARISON WITH NEAREST NEIGHBOR SEARCH
As A > x0, Q (as defined in Eq. 6) will always return the nearest neighhor of x: in D as defined in Section 4.1. In this section we establish the advantages of GenRe over nearest neighbor search. We consider three variants: (a) NNR (Nearest Neighbor Recourse) that selects the closest neighbor which has the desired class label. (b) NNR (7 0.7) that selects recourse instances which are assigned confidence of more than 0.7 from classifier h, and finally, (c) NNR (D,,) that returns nearest recourse instance which in addition to having a confidence of y 0.7 by the classifier h,
also enforces that observed label in the training data y We present the results in table 3
Dataset
Adult Income
COMPAS
HELOC
Method
Cost Val f LOF t Score Cost J Val LOF 1 Score f Cost | Val f LOF 1 Score
NNR
0.36 0.48
0.89
1.34
0.17
0.86
0.88
1.71
1.22
0.58
1.00
1.53
NNR (-= 0.7)
0.46 0.72
0.84
1.53
0.43
0.99
0.97
1.90
1.52
0.69
1.00
1.62
NNR (D))
0.47 0.85
0.89
1.71
0.45
0.99
0.97
1.90
1.57
0.96
0.99
1.88
GenRe
0.69 1.00
0.98
1.93
0.51
0.99
0.97
1.89
2.01
1.00
1.00
1.90
Table 3: Comparison of Nearest Neighbor Search with GenRe.
GenRe performs much better in
term of LOF across all the datasets.
We make the following observations: (1) Among the NNR methods, a consistent trend emerges: NNR (y 0.7) consistently outperforms standard NNR, while NNR (Dit) outperforms NNR (Y > 0.7) across all recourse metrics, except cost. This underscores the value of incorporating both constraints when providing recourse and further justifies the pairing approach adopted by GenRe.

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(2) On the Adult Income and HELOC datasets, GenRe outperforms all variations of NNR in terms of the overall score, while achieving comparable performance on the COMPAS dataset. Note that NNR completely ignores the plausibility of instances and therefore succumbs to outliers. as reflected in their low LOF scores. GenRe, on the contrary, trades-off cost to provide instances which are more plausible. In Table 12, we also compare GenRe across range of balance parameter X.
5.6 COMPARISON WITH PRE-TRAINED DIFFUSION MODELS
Recent work on guidance in diffusion models allows for sampling from distribution of the form 5 using pre-trained models. To investigate if GenRe which trains with pairs has any advantage over such methods, we experiment with the current best performing diffusion model for tabular data, TabSyn (Zhang al., 2024) and constrained it with state-of-thes of-t---rrtt--t derivative-fiee guidance method SVDD (Li et al., 2024). To ensure a fair comparison, we train the diffuusin model only on Dí described in section 4.1. We compare with two methods: (I) TabSyn+QQ: We implement semi-ideal, brute-force method in which we sample a dataset D + sym- which is of the same size as original dataset. For a given negative instance x define Q on D agn as described in Eq. 6. This experiments sets a skyline for guidance methods. (2) TabSyn+SVDD: SVDD requires specifying a downstream 'reward' function for conditional generation but does not require this function to be differentiable. we let the reward function negative of cost, we recover the distribution in Eq. 5.
Dataset
Adult Income
COMPAS
HELOC
Method
Cost L Val 1 LOF Score
Cost
Val f LOF Score
Cost
Val f LOF Score
TabSyn+Q
0.86 1.00
0.79
1.72
0.78
0.99
0.81
1.69
2.41
0.99
0.99
1.87
TahSyn=SVDD(A= = 5.0)
3.11 0.99
0.83
1.58
2.18
1.00
0.69
1.37
3.14
0.98
0.97
1.8
TahSyn-SVDD(A 10.0)
3.10 1.00
0.87
1.63
2.20
1.00
0.79
1.48
2.85
0.99
0.99
1.84
GenRe(XX5.0)
0.69
1.00
0.98
1.93
0.51
0.99
0.97
1.89
2.01
1.00
1.90
Table 4: GenRe outperforms pre-trained Diffusion models with guidance
While T performs similarly to GenRe on the HELOC dataset, it performs worse on the Adult Income and COMPAS datasets, particularly struggling with the LOF metric. TahSyn+SVDD performs significantly worse both datasets in terms of cost as well as the LOF metric. Addition- ally, we observed that in many instances, TabSyn+SVDD failed to generate recourse instances that satisfy the immutability constraints.
6 CONCLUSION
In this work, we proposed model GenRe to maximize likelihood of recourse over instances that meet the three recourse goals of validity, proximity, and plausibility. We demonstrated that methods that are not trained jointly with the three recourse goals fail to achieve all of them during inference. We confirmed this empirically on toy 2D datasets and three standard recourse benchmarks across eight state-of-the-art recourse baselines. Another interesting property of GenRe is that it generates recourse just via forward sampling from the trained recourse model, unlike most existing methods that perform expensive and non-robust gradient descent search during inference. The main chal- lenge we addressed in developing GenRe was training the generator given lack of direct recourse supervision. We addressed this by designing a pairing strategy that pairs each negative instance instance seeking recourse with plausible positive recourse instances in the training data. We proved these pairs are consistent, and hence GenRe's method of training on them is consistent with the ideal recourse objective. Our experiments and sensitivity analysis further demonstrate GenRe's ability to optimally balance the three recourse criteria, while remaining robust across a wide range of hyper- parameters.
ACKNOWLEDGEMENTS
We acknowledge the support of the SBI Foundation Hub for Data Science & Analytics, and the Centre for Machine Intelligence and Data Science (C-MInDS) at the Indian Institute of Technology Bombay for providing financial support and infrastructure for conducting the research presented in this paper.
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A DETAILED RELATED WORK
Cost minimizing Methods. Laugel al. (2017) suggests a random search algorithm, which gen- erates samples around the factual input point until a point with corresponding counterfactual class label was found. The random samples are generated around æ using growing hyper spheres. Ustun et al. (2019) formulates a discrete optimization problem on user-specified constraints and uses in- teger programming solvers such as CPLEX or CBC. Karimi et al. (2020a) translates the problem as satisfiability problem which can be solved using off the shelve SMT-solvers. Wachter et al. (2017) formulates a differentiable objective using cost and classifier and generates counterfactual explana- tions by minimizing the objective function using gradient descent Mothilal al. (2020) extends the differentiable objective with a diversity constraint to the objective uses gradient descent to find a solution that trades-off cost and diversity
Robust Methods. Several recent methods acknowledge that deployed models in practice often change with time Rawal et al. (2020), and as a consequence recourse generated using the classifier used during training can be invalidated by the deployed model. This calls for need robust re- course. Upadhyay et al. (2021) finds counterfactual in worst case model shifts under the assumption of bounded change in parameter space. Hamman et al. (2023) challenges this assumption and in- stead defines "natural" model shifts where model prediction do not change drastically in-distribution of training data.
Another line of work considers robustness in the case with respect to small perturbations to the input. As noted by Fokkema et al. (2024) most recourse algorithms map instances to close to the boundary of classifiers If user implementation of recourse is noisy, the recourse can get invali- dated. Pawelczyk al. (2023) address the problem by optimising for expected label after recourse under normal noise. Recourse can also be noisy due to underlying causal model. Karimi et al. (2020b). Dominguez-Olmedo et al. (2022) suggest minmax objective which reduces to outputting a point some 'margin' away from the boundary in the case of linear classifiers. Recent work Fried- baum et al. (2024) trains auxiliary verifier models ensure robustness in recourse validity. Black et al. (2021) also considers recourse validity in case of model shift and ensures that the generated counterfactuals are in smooth regions of classifier
Likely Recourse Methods. Joshi et (2019) use a VAE(Kingma & Welling (2014)) ensure that the generated recourse instances are close to the data-manifold and perform gradient descent latent space to optimise the recourse instance. Pawelczyk et (2020a) perform random search in latent space and filter out the instances which correctly flip the predictions. Downs et al. (2020) extends the method to include a class conditional VAE which can be incorporated in CCHVAE and REVISE.
Schut et al. (2021) asserts that the recourse instances should belong to the region where classification model has high certainty. They estimate the uncertainty using an ensemble of models and include that in their objective. Antorán al. (2020) considers the case of Bayesian Neural Networks and estimate the uncertainty by sampling multiple models from the model distribution.
Others. More recent work includes Kanamori et al. (2024) which attempts to learn decision tree classifiers which facilitate more desirable recourse, as opposed to us where we assume that the classifiers are given to Gao & Lakkaraju (2024) attempts to generate recourse which is invariant across multiple subgroups. Bewley et al. (2024) attempts to generate human readable rules from a suggested recourse instances.
We note that quite few methods (Upadhyay et al., 2021; Pawelczyk al., 2023; Ustun al., 2019; Dominguez-Olmedd et al., 2022) are originally developed for linear models but are extended to non-linear models like neural networks by using local linear approximation using LIME coefficients Ribeiro et al. (2016)
B ALGORITHMS
In this section, we specify the training and inference algorithm for the autoregressive model used in the paper.
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Algorithm Training Recourse model Rs
Require: Training data D, Irn rate 7,, batch size b, epochs sampling parameter K, cost coefficient
A. pair validity 7, classifier
Ensure: Trained model Rs with parameters 0
1: Dí + { E Dly = 0, h(x,) & 0.5): Dj + (a, E Dlus = y" h((x)) > >
2: Ra f- Initialize { RB }
3: Quune( ( = TopK (Q (0/2, ()) K)
> Truncate Q (Eq. 6) to Top K entries for a E D
4: for epoch E [<] do
5: for each minibatch of size from Dj do
6: Sample x (x))) for each æ; E B,
7: [()) = Sum of loss on (æ;, æt)) using Eq. 8; f- GradDescStep((..))
8: end for
9: end for
Algorithm Forward Sampling one Recourse Instance
Require: negative instance æ categorical indices me, recourse model RS perature т, bin means {, bin width {az,}}
{RT Ro J, tem-
Ensure: predicted recourse x² Zgne < R.
b Encode the input neg. instance b Init. x' with d zeros
2: x' (0.0....0)
3: for j E [d] do
4: Pj = SoftMax (T RB (Iencs x x1))-1)
Rg (Zencr x1 1) is the logits over ny bins
5: Sample c (0, 1), k Pj
6: x¹- Hj.k + J,
7: end for
8: x' prrpojeettattepprcclllddd m.)
> project m. indices in æ' to categorical space.
C EXPERIMENTAL DETAILS
C.I DATASETS
We use the preprocessed datasets from CARLA library where all categorical features from original datasets have been converted to binary categorical features, for example, place of native country has been converted to US, Non-US, race into white and non-white etc
The Adult data set Becker & Kohavi (1996) originates from the 1994 Census database, consisting of 13 attributes and 48,832 instances. The classification consists of deciding whether an individual has an income greater than 50,000 USD/year. The train split has 36624 examples and test split has 12208 examples. The features sex and race are set as immutable. Categorical features in this dataset workelass, marital-status, occupation, relationship, race, sex, native-country.
The HELOC dataset (FICO, 2018) contains anonymized information about the Home Equity Line of Credit applications by homeowners in the US with binary response indicating whether or not the applicant has even been more than 90 days delinquent for a payment. The dataset consists of 9871 rows and 21 features. The train split has 7403 examples and test split has 2468 examples. All features in this dataset are continuous and mutable.
The COMPAS data set (Angwin et al., 2016) contains data for criminal defendants in Florida, USA. It is used by the jurisdiction to score defendant's likelihood of reoffending. The classification task consists of classifying an instance into high risk recidivism (score). The dataset consists of 6172 and features. The train split has 4629 examples and test split has 1543 examples. Immutable features for COMPAS are sex and race. Categorical features are two year recid, charge degree, race and
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Dataset
#Features
#Categoricals
#Immutables
#Positives
#Negatives
Adult Income
13
8,742
27,877
COMPAS
2
3,764
865
HELOC
3,548
3,855
Table 5: Training Data Statistics
We normalise each feature in every dataset to range [0, 1].
C.2 HYPERPARAMETERS
C.2.1 TRUE CLASSIFIERS
We train RandsseForesClassiffeer calibrated with CalibrateCCassifiecCY using isotonic calibra- tion. We generate binary labels by sampling from the predictive probabilities for each input. We also provide sample weights to the fit function. The data is split into train and test after getting true classifiers and below we report various metrics this test split. This input and its corresponding generated label will be utilized as training data for the ANN classifiers.
Dataset
Accuracy
ROC AUC
Precision
Recall
F1-Score
Briar Score
Adult Income
94.36
0.9996
0.90
0.96
0.93
0.05
COMPAS
85.74
0.9886
0.78
0.91
0.81
0.10
HELOC
100.00
1.0000
1.00
1.00
1.00
0.02
Table 6: Performance Metries for the trained classifiers. Precision, Recall and Fl-score are macro averaged. Briar Score determines the quality of calibration lower the better.
C.2.2 PREDICTIVE MODELS
We use train fully connected ReLU models with 10,10,10 layers using learning rate=0.001 and number epochs =100, batch size =
Dataset
Accuracy
ROC AUC
Precision
Recall
F1-Score
Adult Income
77.33
0.86
0.76
0.78
0.76
COMPAS
69.60
0.75
0.68
0.69
0.68
HELOC 74.23
0.80
0.74
0.74
0.74
Table 7: Performance Metries for the trained classifiers. Precision, Recall and FI Fi-score are macro averaged
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C.2.3 BASELINES
Method
Hyperparameters
Other Params
Jype: "BCE" binary_cat_featuree True
Wachter
GS
loss type: "BCE"
DICE
binary cat features: True
ROAR
delta: 0.01
loss Jisp:: "BCE" invalidation .arget: 0.05
PROBE
noise_ variance: 0.01
Verifier Params:
layers: [50.50,50,50]
n-iter: 1000 step size: 0.01
TAP
epochs: 2000
Ir: 0.0001
batch_size: 128
VAE Params:
layers: [512, 256,
n_search_samples 100
lambda reg: 0,000001
CCHVAE
step: 0.1 max iter: 1000
epochs: 100
Ir: 0.001
batch_size: 32
VAE Params: layers: [512, 256, 8)
lambda_ param:: 0.001
optimizer: "RMSprop" Ir: 0.008
train: True
CRUDS
epochs: 100
max iter:: 2000
Ir: 0.001 batch size:
Table 8: Hyperparameters used for baseline methods
C.2.4 GENRE
For each feature in the input have learnable position embedding which we then pass into the transformer model. We use the same architecture across all the datasets, below we describe the various parameters.
Parameter
Value
Number of Bins
50
Number of layers Encoder
16
Number of layers in Decoder
16
Embedding Size
32
Feed Forward Dim
32
Table 9: Architecture specifications for the Transformer Layer used.
All datasets uses learning rate le-4 and batch size 16384 for Adult Income dataset else 2048.
C.3
EVALUATION
We entire dataset train+test, with predicted label assigned by the true classifiers and train class conditional LocalOutierFacttor from skleam. We use n. _ww.eigbhbrrsss,. novelty = True. Results shown in 2 averaged over 200 instances from test split.
17

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Published as a conference paper at ICLR 2025
D ADDITIONAL EXPERIMENTS
D.1 COMPARISON WITH BASELINES ALONG WITH STANDARD DEVIATION
Datasel
Adult Income
COMPAS
HELOC
Metric
Cool
Val
LOF
Scure
Cost
Val
LOF
Soore
Cost
Val
LOF
Score
Wachter
0.3120.16
0.5120.50
0.7610.43
1.24
0.20.0.17
0,5910.19
0.2310.42
0.79
0.7910.47
0.3520.48
0.97.0.17
1.28
GS
18221.07
0:4020.99
0.4920.50
0.75
1.2040.73
0.6620.47
0.4840.50
0.97
0.58,0.38
0.3220.47
0.9120225
1.23
DICE
0.22+0.10
0.620.49
0.73+0.45
1.33
0.19.0.16
0,57+0.49
0.44+0.50
0.99
0.4900.31
0.34e0.47
0:97=0.16 16
1.29
ROAR
10.17=2.62
18
0.01
0.19
4.01=2.01
0.8720.34
0.01=0.07
0.30
9.64ah.88
0.47a0.50
0:17:0.38
0.19
TAP
1.10g0.93
0.99.0.10
0.67.0.47
1.57
1,4610.59
0.8810.32
0.70.0.46
1.37
0.71
0.3620.48
0.53,0.50 5050
0.86
PROBE
33.91214.70
1.000.000
0.0010.00
-1.61
5.77L:163
0.8210.38
0.00.0.00
-0.00
5.3745.11
0.6920.16
0.07.0:25
0.19
CCHVAE
2.11
0.00.0.00
1.000.000
0.84
3.03
1.00+0.00
0.0720.26
0.64
3.58
0.0120.21
0.14::035
0.02
CRUDS
3.1711.11
1. 1.000.000
8.9660.10 18
1.72
1,10+0822
0.98+0.12
1 1.00+0.00
1.83
4.30+2.23
1.000.000
0.57=0.50
1.37
GenRe
0.69:0.30
1.0000.00
0.98 12
1.93
0,51
0.99.0.10
0.97,0.17
1.89
2.01.0.59
1.00g0.00
1.00:0.00
1.90
Table 10: Comparison with baselines along with standard deviation
D.2 PERFORMANCE ACROSS DIFFERENT TEMPERATURE 7 AND a SETTINGS
Datasel
Adult Income
COMPAS
HBLOC
T
Cost
Val
LOF
Score
Cost
LOF
Score
Cost
Val
LOF
Score
5.0, 26-07
0.7360.32
0.0500.10
0.9400225
1.87
0.5440.21
0.9940.10
0.8660.34
1.78
2.12H1.62
1,0000.00
1,000.00
1.9
10.0, 2o-07
0.70.0.32
0.9940.07
0.9700.16
1.92
0.50+0.18
1.0000.00
0,96g0.20
1.89
2.00+0.57
1.0000.00
1.0040.00
1.9
15.0, 2o-07
0.68:0.30
0.99.0.07
0.9900.10
1.93
0.50+0.18
1.0000.00
0,9680.20
1.89
1.9540.57
1.00g0.00
1,00+0.00
1.91
5.0, 2o-06
0.72:0.30
0.97.0..16
0.9620 20
1.88
0.5410.19 19
0.9910.10
0.88g0.32
1.79
2.08.01.58
1.0000.00
1.0010.000
1.9
10.0, 2c-06
0.69.0.30
0.9920.07
0.9910. 10
1.93
0,51 18
0.9910.07
0.97.0.16
1.9
2.00.10558
1.0000.00
1.00,0.00
1,9
15.0, 2o-06
0.68-0.29
0.09 10
0.98+0.14 14
1.92
0,50+0.10 18
1.000000
0.96=0.18 18
1.89
1.06+0..5
1.0000.00
1,0000.00
1.91
5.0, 2e-05
0,7320.33
0.9920.10
0.9720.17
1.9
0.5320.20
0.99.0.07
0.89g0.31
1.81
2.0820.61
1.00g0.00
1,00+0.00
1.9
10.0, 2e-05
0.69:0.30
0.98
0.9720.16
1.91
0.51+0.18
0.9920.07
0.96a0.20
1.88
2.00m0.60
1.0000.00
1.00+0.00
1.9
15.0, 26-06
0.6800.30
0.99 10
0.96 14
1.92
0.50a0.18 18
1.0000000
0.97s0.17
1.9
1.95#0.56
1.0000.00
1.00+0.00
1.91
5.0, 26-4
0.73
0.99900.07
0.4400224 24
1.88
0.53+0.19 19
0.99
0.88
1.79
2. 10600.60
1.000.000
1,000.00
1.9
10.0, 2o-4
0.70m0.32
0.99
097
1.92
0.51+0.18 18
1.00+000
0.9640.20
1.89
2. 2.0040.58
1.0000.00
1,0000.00
1.9
15.0, 2o-4
0.68-0.29
1.00+0000
0.9840114 14
1.93
0,50+0 18
1. 1,000000
0.92e0.16 16
1.9
1.9440,35
1.0040.00
1,0040.00
1.91
3.0 2o-3
0,74+0,37
0.9760.17
0.9300.26
1.84
0,54+0.20 20
0.99:0.07
0.8480.36
1.76
2. 2.1240.60
1.00H0.00
1,0000.00
1.9
10.0, 2o-3
0.69:0.30
1.0g0.000
0.9900.10
1.94
0,51s0.15 18
1,00:0.000
0,95.0.21
1.88
1.99s0,556
1.00,0.000
1,00+0.00
1.91
15.0, 2o-3
0.69.0.32
0.9910.10
0.9800.14
1.92
0,50.0 18
1,0000.00
0.95g0.21
1.88
1.94.0,56
1.00,0.00
1,0010.00
1.91
5.0, 2e-2
0.7520.32
0.97.00.16
0.9200.28
1.83
0,5610.11 19
0,9810.12
0.7720.42
1.67
2.26110.62
0.9810.12
1,0010.000
1.8
10.0, 2x-2
0.72:0.29
0.9420.23
0.9340.26
1.82
0.5540.18
0,9810.12
0.79g0.41
1.69
2.2240.559
0,9840.14
1,0010.00
L87
15.0, 2o-2
0,73g0.30
0.9420.23
0.9240.28
1.8
0.5520.18 18
0,9940.07
0.7820.41
1.7
2.1840.60
0.98.0.14
1.0040.00
L.88
Table 11: Performance of GenRe across (5.0, 10.0, 15.0) and a2ee- - 7, 2e - 6,
6,...,
2e
2}
D.3 COMPARISON WITH NEAREST NEIGHBOR SEARCH ALONG WITH STANDARD DEVIATION
Dataset
Adelt Income
COMPAS
HELOC
Metric
Cost
VaL
LOF
Score
Cost
Val.
LOP
Score
Cost
Val.
LOp
Score
0.36+0
0.48-0.50
0.8940.3 32
1.34
0.17H0
0.8600:3
0.85=0.3
1.21
1,22+0.41
0.58+0.49
1.00+0:00
1.53
NNR
0.4640.24
0.7260.45
0.8460 36
1.53
0,4360.10
0.9900100
0,97,0.16
1.5360.50
0.69:0:46
1.000.000
1.62
NNR 077.y-
0.47e01.24
0.550.35
0.8900
0.4560.21
0.9980.10
0,9750116
1.5750.53
0.96a8)
0:9960.07
0.5)
2.28401.86
0.99+0.10
0.9940.10
188
1,95e0069
1,0000000
0.93m027
1.6
2.640.71
1.0000000
1.0+6:000
1.87
GeaRe(A 1.0)
1.66209
0.9200288
0.9920.10
1.78
1.340058
1.0020::00
0.952021
1.76
2.000.68
100010000
1,000:000
188
GeaRelA- 2.5)
0.1181139
0.0900311
L.00500.00
1.53
1.02:0.58
0.9900.12
0.95.0.12
1.82
2.430068
1.00891000
1.000.000
1.88
GoiRo(A 5.0)
0.69H0.30 30
1.000.00
0.9840.12
1.93
0,51=0
0.9900.00
0,97=0.17
1.89
2.01
1.0000.00
1.000.000
1.9
GenReA= 10.0)
0.6640.28
0.08+0.14
0.9940.07
0,48x0.1
0.9400211
0.86x0.35
1.35
1.84+0.55
1.0000.00
1.0+0.000
1.91
Table 12: Best is highlighted in bold and second best is highlighted bold blue
D.4 DETAILS ON EXPERIMENT WITH TABSYN AND SVDD
SVDD requires a reward function to guide diffusion model such as TabSyn towards a required distribution. For a given diffusion model which can sample from P(x), SVDD allows us to sample from a distribution P'(x)) such that,
P'(x) x P(x) exp (A r(x))
(10)
where r(x) is a reward function which models how desirable a generated example is. To sample from 5, we first train diffusion model on the data which satisfies our constraints and then for each
18

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Published as a conference paper at ICLR 2025
define the reward function as,
r(x') = (2 ( x)) 100 1[2] # x;
Z; refers to the subset features which are immutable. We add a penalty of 100 to the usual cost whenever immutability constraints violated.
Metric
Cost
Val
Lor
Val
LOF
Val
LOP
Score
SVDD) 5.0)
3.11&1.44
0.9
0.8320.38
1.58
2.18.0.77
1.050.00
0.6969446
1.37
3.1450.8
0.96a0).14
0.9720:17
1.80
SVDD(A 10.))
3.10g1.39
1.00x0.00
0.5769134
1.63
2.2080.82
1.0g50000
0.79gt041
1.8
2.8500.8
0.99801.10
0.99
1.84
TakSyn+Q
0.9960:07
Geoßee
1,0+0.000
0.5140.18
1,0000000
D.5 PERFORMANCE OF GENRE WITH THE AMOUNT OF DATA
To assess scalability we conducted an experiment in which train the model on various subsets of data, below we report the results on Adults Income dataset largest dataset used in this paper.
Fraction of Data
Time
Cost
Val
LOF
Score
0.1
798.94
1.09+0.66
0.92+0.27
0.85+0.35
1.69
0.2
1454.15
1.23+0.63
1.00+0.00
0.99+0.07
1.90
0.4
2768.06
0.94+0.51
0.97=0.17
0.92+0.27
1.82
0.8
5219.66
0.67+0.28
0.92+0.27
0.98+0.14
1.85
1.0
8464.71
0.6910.30
1.00+0.00
0.98+0.12
1.93
Table 13: Performance metrics for different fractions of data.
19


Reviews:
[{"review_id": "nDn6CxudtT", "reviewer": "Reviewer_92zH", "summary": "In this work, the authors propose a generative model designed for algorithmic recourse, which transforms a negative sample $\\mathbf{x}^-$ into a positive sample $\\mathbf{x}^+$. The resulting positive sample must satisfy the following criteria:\n\n- $\\mathbf{x}^+$ is a high-quality sample that adheres to the underlying data distribution.\n- $\\mathbf{x}^+$ is classified with a high probability as belonging to the positive class by a pre-trained classifier.\n- $\\mathbf{x}^+$ should be close to $\\mathbf{x}^-$ in the feature space.\n\nThe authors demonstrate that training a single model to simultaneously meet these objectives leads to improved overall performance compared to previous approaches.", "questions": "1. What is the purpose of \"TopK\" in Line 290? What does \"Top\" refer to? Is this clarified in the main text? I was unable to find any explanation.  \n2. How does the model determine which dimensions of $\\mathbf{x}^-$ to freeze? Are these dimensions predefined by the dataset? How is the loss function formulated in practice?  \n3. Have you started training the generative model from scratch, or are you using pre-trained weights?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "Some strengths of this work include:\n\n- The development of a single generative model that converts negative examples into positive samples suitable for addressing the algorithmic recourse problem.\n- The model enhances the overall performance of recourse mechanisms.\n- The authors have anonymously open-sourced their codebase, allowing others to reproduce their approach.", "weaknesses": "## Clarity\nThe notation, definitions, and equations should be carefully rechecked. In the current form of the paper, the following points severely reduce the paper's readability, and the reader has to guess what is most likely implied.\n\n- Quantities are not properly defined.\n\n     1. In Eq. (2), the cost function employed in this work is not defined. What is the cost? Did the authors provide clarifications regarding its final form?\n     2. Line 251, $N^+$ is not defined.\n     3. Eq (6) what is $\\lambda$ values? \n     4. Algorithm 1, Line 290: what is $\\mathbf{x}$\n     5. Algorithm 2: Where is the projectCategoricals defined? What is $m_c$?\n     2. Algorithm 2: Line 5, is $k$ sampled? If yes, how?\n\n- Notation Consistency\n     1. Are the bin scales the same as bin widths? If yes, please be consistent.\n     2. Is $D_1$ the same as $N^+$\n     3. Alg. 1: Line 290: $\\mathbf{x}$ is not defined.\n     3. Alg. 2: Step 1: $\\mathbf{x}$ is not defined.\n     4. Eq (7) and (8) seem to have different K.\n     5. I suggest to limit the notation to $\\mathbf{x}^+$ and $\\mathbf{x}^-$ whenever possible.\n\n\n- Are you using a random forest or an MLP for the classifier? If you use both, in which case do you use the first and the second? What is the accuracy of each classifier?\n\n- For the baselines, how are the final checkpoints selected?\n\n- Something is weird; why do you select variance equal to zero (line 376)? This choice makes step 2 of Algorithm 2 redundant.\n\n## Experiments\n\n### Efficiency analysis\n- How does the proposed approach differ from prior work regarding the number of parameters, training time, and GPU/time requirements (during training/inference)?\n\n### Ablations\n- What is the benefit of using an autoregressive model for generation compared to other architectures? Did the author try a different setup? What is the models' performance for different generative architectures (non-autoregressive)?\n\n## Minor\n- Lines 557-560 double entry for the same paper.\n- Steps can be added to Alg. 1 similarly to Alg. 2.\n- Proofs can be moved to the appendix.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KdNloUbe3H", "reviewer": "Reviewer_m8hr", "summary": "The paper introduces GenRe, a generative-based approach to algorithmic recourse that seeks to optimize three core recourse objectives via joint training, including validity, proximity, and plausibility. The authors claim that previous method fail to unify all objectives into the training and instead use a gradient-based inference time searching technique that could lead to unsatisfying performance. GenRe uses an auto-regressive generative model to sample recourse solutions directly, with a hand-craft training objective defined with the cost function and the vanilla data distribution. The authors validate GenRe's performance through comprehensive experiments on synthetic and real-world datasets.", "questions": "No additional question beyond the weaknesses above.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- First of all, the paper is well-written and organized, making it easily followed. The problem definition and motivation are presented clearly, allowing readers to understand the contribution.\n- Undoubtedly, the problem of recourse via AI is an important and open problem. It is also closely related to conditional generation, and consequently, the technical discussion (if useful) can be apply to a wide range of problems beyond.\n- I appreciate that the authors analyze their proposed method on various tasks, helping us to understand the performance of GenRe.", "weaknesses": "I think the major weaknesses are a lack of careful motivation of the proposed method, as well as a more direct comparison with methods beyond the field of algorithmic recourse (but can be directly applied). Specifically,\n\n- From the aspect of this specific problem (algorithmic recourse), if I understand correctly, the major improvement in the training process is the goal of Eq (4), which includes all properties that users care about (as well as the empirical distribution $Q(x^+|x)$ for sampling). However, to me, this task is different from sampling over $P(x|y=1)$ only because the additional cost function, $C(x,x')$ should be imposed. As a result, a very clear derivation is to sample from the distribution of $P(x|y=1)\\exp^{-\\lambda C(x,x')}$. The introduction of $V(x')$ seems to break the probabilistic explanation of the distribution, because $P(y=1|x)$ is naturally contained in $P(x|y=1)$ by the Bayesian law. In addition, the reason for choosing an auto-regressive model for sampling is also left unjustified, as sequential sampling is not a major concern in the problem. More justification (both intuitively and experimentally, and ideally, theoretically) of the technique selection is unavoidable. \n- From a more general sense of conditional generation, the problem of cost-aware sampling is not a novel problem and has been studied both in a general scenario and for specific generative models such as AR models or diffusion models. For instance, a direct method if to train a classifier-free diffusion model that allows sampling from $P(X,Y)$, and use a standard guidance technique (such that the $L_2$ norm like the CLIP score) to guide the diffusion process using $e^{-\\lambda C(X, X')}$. The proposed training technique for unpair data (Sec 4.1) is, in fact, a very standard processing technique that has been widely used, and the choice of AR model seems to be more strange than another generative model such as VAE and diffusion. Therefore, while I admit that joint training is a new approach (in this field, maybe), the author should compare with the above alternatives to see if the proposed method can outperform existing baselines. One paper for reference: [Learning from Invalid Data: On Constraint Satisfaction in Generative Models]. In addition, [Classifier-Free Diffusion Guidance] is a straight-forward go-to method to compare with.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "oNOB0Q4fu8", "reviewer": "Reviewer_sL8f", "summary": "The paper introduces **GenRe**, a generative model that provides actionable, realistic recourse for individuals affected by automated decisions. By jointly optimizing for **proximity** (low cost), **plausibility** (realistic changes), and **validity** (desired outcomes), GenRe outperforms traditional methods that address these goals separately. Rather than using gradient-based search, GenRe generates recommendations through efficient sampling, offering robust, balanced recourse. The model's code is publicly available to support further research and applications.", "questions": "Are there particular large-scale use cases you envision as especially suited for GenRe's capabilities? Can you implement GenRe in a modern generative model, such as a pretrained one?\n\nHow does it handle biased or limited datasets? \n\nAs GenRe integrates multiple complex objectives, how do you ensure interpretability in the generated recommendations?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "GenRe effectively integrates proximity, plausibility, and validity into a single generative model, addressing the core challenges of algorithmic recourse in a unified way. This contrasts with traditional methods that optimize these objectives separately, offering a more balanced solution.\n\nBy using forward sampling instead of gradient-based search, GenRe reduces computational costs during inference. This makes the model more scalable and applicable to real-world scenarios where speed is crucial.\n\nThe paper demonstrates that GenRe achieves better trade-offs between cost, plausibility, and validity compared to existing methods, providing evidence of its effectiveness across multiple datasets and scenarios.\n\nThe authors have made their code available, promoting transparency and enabling other researchers to build on their work, which helps advance the field of algorithmic recourse.", "weaknesses": "While GenRe shows improvements in the tested scenarios, its generalizability to highly diverse datasets or domains with different types of constraints might require additional adjustments or fine-tuning.\n\nThe paper acknowledges the challenge of synthesizing recourse supervision for training, which may introduce assumptions or heuristics that could impact the model's robustness in practice.\n\nThe success of GenRe heavily depends on the quality of the generative model and the training data. If the data is biased or limited, the recourse recommendations might be less effective or skewed.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "qVHIdPHzwL", "reviewer": "Reviewer_SyMJ", "summary": "This paper addresses the problem of algorithmic recourse for individuals adversely impacted by automated model decisions. It proposes a generative model based method to finish recourse task by directly sampling without optimization at inference. The main goal is to balance three objectives: proximity to the original profile to minimize cost, plausibility to ensure realistic changes, and validity to achieve the desired result. Experimental results shows its effectiveness.", "questions": "See weakness.\n\nAlso, after reading the original definition of LOF, it is higher when the data point is more abnormal (out of distribution). Why is there a upper arrow in table2?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* This paper provides a thorough analysis of the limitations in current algorithmic recourse methods, highlighting the challenges of separately optimizing proximity, plausibility, and validity, which often leads to suboptimal results. This establishes a solid foundation and motivation for the proposed method.\n* The GenRe method is intuitive and easy to implement and consistently providing more effective trade-offs among different factors.", "weaknesses": "1. **Advantage beyond Nearest neighbor**: The biggest issue is the neccessity of involving a complicated auto-regressive method. Essentially, this method uses a model to learn a smoothly-mixed version of nearest-neighbor search in positive samples. It lacks detailed analysis and ablation study for its advantage beyond simple KNN. Why should we bother to train a huge transformer instead of just finding the nearest valid sample and imitate it? I believe there are subtleties here because it requires some generalization stuff. But all these aspects are absent in the paper.\n2. **Interpretability Issue**: While GenRe is effective in balancing recourse objectives, the generative approach may lead to less interpretable outputs, especially for stakeholders who require clear, actionable insights. The model could benefit from an analysis of interpretability or user-friendliness of the generated recourse.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)