Learning Recourse on Instance Environment to Enhance Prediction Accuracy
Authors: Lokesh Nagalapatti
Guntakanti Sai Koushik
Abir De
Sunita Sarawagi
Venue: NeurIPS 2022 Accept (2022)
Keywords: Algorithmic Recourse
Intervention design

Abstract: Machine Learning models are often susceptible to poor performance on instances sampled from bad environments. For example, an image classifier could provide low accuracy on images captured under low lighting conditions. In high stake ML applications, such as AI-driven medical diagnostics, a better option could be to provide recourse in the form of  alternative environment settings in which to recapture the instance for more reliable diagnostics. In this paper, we propose a model called {\em RecourseNet} that learns to apply recourse on the space of environments so that the recoursed instances are amenable to better predictions by the classifier.   Learning to output optimal recourse is challenging because we do not assume access to the underlying physical process that generates the recoursed instances. Also, the optimal setting could be instance-dependent --- for example the best camera angle for object recognition could be a function of the object's shape. We propose a novel three-level training method that (a) Learns a classifier that is optimized for high performance under recourse, (b) Learns a recourse predictor when the training data may contain only limited instances under good environment settings, and (c) Triggers recourse selectively only when recourse is likely to improve classifier confidence.

Learning Recourse on Instance Environment to Enhance Prediction Accuracy
Lokesh Nagalapatti Guntakanti Sai Koushik
Abir De Sunita Sarawagi
Department of Computer Science and Engineering ITT Bombay
Abstract
Machine Learning models are often susceptible to poor performance on instances sampled from bad environments. For example, image classifier could provide low accuracy on images captured under low lighting conditions. In high stake MI. applications, such as Al-driven medical diagnostics, better option could be to provide recourse in the form of alternative environment settings in which to recapture the instance for more reliable diagnostics. In this paper, we propose a model called RECOURSENET that learns to apply recourse on the space of environments that the recoursed instances are amenable better predictions by the classifier. Learning to output optimal recourse is challenging because we do not assume access the underlying physical process that generates the recoursed instances. Also, the optimal setting could be mustance-dependee the best camera angle for object recognition could be function of the object's s shape. We propose a novel three-level training method that (a) Learns classifier that is optimized for high performance under recourse, (b) Learns a recourse predictor when the training data may contain only limited instances under good environment settings, and (c) Triggers recourse selectively only when recourse is likely to improve classifier confidence. We experiment with synthetic and real world datasets show the efficacy of our proposed approach.
- for example
Introduction
The performance of any supervised learning model depends strongly on the quality of input instances. However, in practice, instances may be of suboptimal quality when generated in adverse environment settings. For example, even an expressive image classification model may misclassify an image shot extreme close-up such unfavorable instances can deteriorate model performance which can have serious consequences in high stake scenarios like Al guided crop monitoring (21), automatic disease diagnosis from images (22], and AI driven accessibility enhancement for the hearing impaired.
wrong angle under poor lighting [13] 28 Despite large training sizes,
Mitigating the effect of such unfavorable instances entails the design of recourse mechanism to recommend alternative environment settings that yield instances revealing the target class. For example, in low cost smartphone based medical diagnosis [22] where imaging is performed by non-experts, such recourse mechanisms can interactively recommend camera settings that yield images optimal for the downstream diagnosis model. Recourse could be particularly useful for healtheare on the edge where users can be prompted to adjust their edge-device settings in real-tine time deploy the diagnosis model with higher accuracy. The optimal camera settings however could be label dependent. For example, the best camera angle for recognizing an aeroplane could be different from the angle for recognizing poles.
More formally, the problem that this paper seeks to address is as follows. We have an object a in the physical space (e.g. crop) with an unknown true label (e.g. type of disease). Let ( E B be
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36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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the environment setting under which we capture a digital representation x of 2 to diagnose the label from a downstream classifier fx). Our goal during recourse is to recommend an alternative setting 3' (if any) to the user for getting different representation x' of Z where fo(x') is more likely to be correct than (x).. The above problem an instance of algorithmic recourse, on which there has been much recent work [30 29
8 32 III These methods recommend recourse actions on the instance space x, which is difficult to realize on raw data for objects such as images and speech. Instead we propose intervene at the level of the environment which generates the instance via an unknown physical process. We view our contribution under three facets as explained below:
23
(i) Novel framework for recourse mechanism. We propose RECOURSENET, trainable recourse mechanism which recommends modified actions to the end user so that, if acted upon the environment, it can generate instances with improved accuracy. RECOURSENET consists of three components: (1) a classifier fe. (2) recourse trigger т (3) recourse recommender network 9é. Given an instance (x, 3). the recourse trigger ı first decides whether to recommend recourse for x. If so, the recourse recommender I6 suggests an alternative environment 33.. Using these, the user generates new instance x', on which fo would give the correct label with potentially higher confidence.
(ii) Three level training proposal. The main challenge of RECOURSENET is that we do not assume access to the latent physical process Z that generates an x' given a 3' during training. Instead we train with a fixed labeled dataset containing (latent) objects z; rendered as instances {x,₃} under a small but variable set B; of observed settings {Br }- We show that direct end-to-end training of combined likelihood training settles easy local minima, and fails to provide good recourse. Training them stage wise also is challenging; we list some of these. For fe, training on the entire dataset may be suboptimal since instances in poor settings, where recourse will be asked, may mislead decisions on good instances. For Já- we have no direct supervision of good ,3 for a given (x:j. P.y)) For ग, simple heuristics like choosing to recourse examples where so has low confidence does not guarantee improved accuracy. Our training strategy employs careful scheduling and decoupling of the training of the three modules via proxy functions. This achieves substantial gains over simple end-to-end training and existing methods of training classifiers with data selection based purely on noise 20 5
(iii) Characterization of recourse conditions. We provide theoretical characterizations to identify the circumstances under which recourse will enhance prediction accuracy. Specifically, we show that given an instance if the recourse recommender suggests modified environment that is close to at least one of the training environments resulting in an improved accuracy, then the recourse is beneficial. Moreover, if there exists some environment which improves the accuracy by substantial margin, then even a modestly calibrated recourse recommender can lead to improved accuracy.
2
Related work
Our work is closely related to (i) Algorithmic recourse, (ii) Learning with triage and (iii) Machine learning with environment perturbation.
Algorithmic recourse: In recent years, there is an increasing interest in designing recourse on the
instance space (30 29 23
25 9 for a wide variety of applications. For example 30 29 aim to train the models so that the predicted output is preserved under strategic perturbation of the instance space. Another line of work called strategic classification deals with applying causal interventions to instances. However, these work Iearn the
& 32
aim to improve fairness; 15
15 [0] recourse action on the instance space, whereas, goal is to design recourse action on the observed environment. An additional challenge in our setting is that the impact of the environment on the instance is latent and we do not assume presence of enough labeled data to learn a generative model for complex real-world instances under different environments.
Learning with triage: A recent line of work 22
31 aims to learn when to outsource a subset of instances to human and assign the rest of the examples to machine so that machine and human together achieve superior performance than what they would have achieved independently. However, in our problem, humans do not participate prediction task but they only generate new instances under the recommended environments.
2 5 12
14 17
24

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9
Chiir
The image
lnoks great g
No
Classifter Module
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This might need recousse
Trigger nix, d)
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Recsume Module 3/(+)x,
Gould you captiree the object under nocmal white light?
Human gensrratex new image under
Figure I: Architecture of Proposed Approach. The chair image on the top does need recourse but the bottom image obtains the correct label only after recourse.
Machine learning under environment perturbations: Machine learning models are sensitive to environments under which data is generated [3] [28]. . For example [13], show that simple parametric perturbations on the Shapenet dataset can flip class labels. In another related work [T8] suggests interventions on the environment using policy gradients to train recourse model. However, they assume the availability basis. We make no such assumptions and train with fixed labeled dataset.
human through out the training loop to generate data an on-demand
3 Proposed approach
In this section, we first formally present our problem. present our training methodology, and then theoretically characterize the settings under which recourse is possible.
Problem formulation Let Z denote a space of objects, B denote space of environment settings which could be real-valued or discrete mixed, and denote a space of instances obtained via latent physical process Z : Z x B + X. Given a latent object E Z and an environment setting E B, we get an instance x E
Rd i.e., x [zz 33.. Each object 2 has label y E y with [y] = K. We are interested in inferring the object's label using a trained classifier fo. During training, for each of the latent set of objects {E, we are given a true label yi and for a small set of settings
B, B, we are given instance {x1; j. Thus, we view the training data as a set of examples T T= (Xij (.y) JeB, IED We use V to index all the examples, i.e., V UsE {{} x B,). As stated earlier, goal is to design recourse mechanism that given representation x obtained of latent object under given settings 3 will recommend an alternative 3' the resultant x' [(z, 33) expected to yield more accurate prediction under fa. Note that Z is not accessible to during training and we assume this work that difficult to learn Z or infer 2 from the available labeled data T. Our goal instead is to use T learn both fo and the recourse mechanism.
3.1 Training RECOURSENET
RECOURSENET consists of three components:
1. A classifier fo : X' x y + [0, 1] which aims to capture the likelihood of the label given an instance x, fely x) approximates Pr(y x).
recourse recommender network Is x, 338 such that if the user (via Z) were to regenerate a new instance x' using 3 the classifier is likely to provide higher accuracy.
B - [0, 1]. that suggests a modified environment
B ( (
{0, 1} which is binary decision function. Here, ग (x, B3 = indicates that we decide to perform recourse on the environment and the 3 suggested by 96 should be used regenerate the instance.
A recourse trigger network
X'
Training objective. Given set of examples with {wr, (x... we aim to find 0, o and ı by solving the following optimization problem:
max 8,0.5
(1 (1-a8 (Xij, Bsz)) log fo (ya xx,)
JEB
LED
+ π *x Biz) log fa ((2,, argmax (B) Xij, B(y)i)
(1)
subject to,
Σ iED.JEB
T(xi, Big) s b, and π (x,;, B.y) E (0
(2)
3

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Algorithm 1: GREEDYALGORITIM
Algorithm 2: TroinRECOURSENET
for training fe
Require: Train data T = (v., (xij, Bug JER:; J.b. b.
Require: Data T = {vi, {x.,, Bhg b.b
1: 0 <- GREEDDYAL.GRRTTIM([
1: V == Uken {1) x B
2: o, f + RRECRECOMMENER(( 8, 0) 11 Eq 7
2: R < (0) < [FAIN(F( 0))
3: Return 0, 8
3: for E [b] do
4: for (i.3) E V.R do
Algorithm 3: RECOURSENET Inference
5:
(((,,)) )= =
(RU ((, RU ((i,)))
Require: Test instance (z, x. (3). Z (human), 0. a. lCP
6:
((")5") 6 arginax
(L.)ev) (.jee ((i.3)
I: Ω + RecTRIGGER(x, B3 0. á. ((F) // Eq
7:
R- RO-RRUU (((,)))}
2: ý f argmax, y [[L fxx fg (y) x) +
8:
gk+ < TRAIN(F((, R))
argmax *(x, (ol aragaxx 9 (/' |x, 3)1)]
9:
Return (R)
3: Return 5
Here, indicates the maximum number of examples which can undergo recourse. The first term (1 i( log accounts for examples that do not need recourse and accounts for those that need recourse. End to end training of the second term ग. ( log fo is challenging since do not have analytical form of Z and the optimization problem I
in the objective ①
training such a process will be difficult. We propose to train the three components fo. Id. π in a carefully designed shree-stage process that we describe next.
Training the classifier fe- Training Le on the entire training data may be sub-optimal because instances in poor settings would be subject to recourse, and the classifier should instead focus on instances after recourse as the above training objective suggests. For training fo first we es- chew the involvement of Z and 9 from the training objective (T) by noting that π (Xij. B.y) = 1 only if fo(us Z (2z, argmax (3 Xij. Bi,))) 2 folui X:y)- Therefore, we replace the term (z,, argmax 9 (B) x.j B.,)) with some instance (Xir, Bir) for some E B, of the same object 2, such that the predicted classification accuracy on X better than the original instance X,y by a certain margin A. Specifically, given (x,, B:y), we first define Rec (6, Xij: Vs) as the set of environments which would improve the log-likelihood of the gold label by at least a margin A ie.,
Roca (8, X,j. 9i) = (33 E B&l log fo (ys (Z (3)) > log fo (yx Xsz)) + +A}
(3)
and then we pose the following training problem to learn 6.
max 0,77
(1
T (Xig, Bit)) log (y x.y) + ग (x.3, Bin)
max
log fo (ybi xir)
ERec (f...
DED
JEB;
subject to,
Σ
T(xi S 6, and (X.... B.y) E 1).
(4)
IEDJEB;
Since our budget is limited, one needs to spend it on only those instances which not only suffer from poor accuracy, but can also lead to new instances that promote fo to predict the correct label. The presence of non-zero margin A ensures such a condition. In Section 3.2 we provide the conditions under which such a recourse set will exist.
Given (Xij, Biy)) E {0, 1}.
we first define the set A = (i.,)) (T))) (X1,, Big) = 1}. Then, we can
write the objective (4p as
max Sb
F(0, R) =
Σ
log Jo Xxi))= -
Σ
max
log So(ys Xxr)
(5)
(KJ)R B.r E Ro (0.))).)))
(3S)
which gives us the problem of subset selection in conjunction with parameter estimation. Note that the involvement of R as an optimization variable renders the above problem challenging even
log fo(y/) x) is concave in 0. Thus, resort optimization problem (summarized in Algorithm| D]. It is an iterative routine, which picks up an instance (xij- (,jj, 3t) at every iteration which will maximize the training objective. Given update R step l: < b, it chooses candidate instance j) which maximizes F(O* (RU((I,)) RU((i,)))) where (S)) = max; F(B,5 S). We would like to highlight that, by definition of the set Reca, inclusion of (i, in R either improves the log- likelihoodd or keeps it at the same value obtained in the previous iteration. Formally, we can say that F(0 (RU ((. R ())))) 2 F(O* R).
greedy algorithm [19 5 [6] 33) to solve this

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Learning IG. Objective is non -on-differentiable in ø because of the argmax, 96 (+) input to fo and the unknown Z. We first get rid of the argmax term via the following surrogate:
argmax
logfe(ye (21, argmax, (3 Xiy, 9k))))
JEDJEB, xxxy)=1
argmax
Σ
max
log [fo ((z,, ( Xzj. Biy]]
(6)
B
JEDJEB. x(xg)=1
Next we account for the unknown by partitioning all examples in into two groups the set Dg which contains groups with at least one instance where good B3 are available (ie.maxx fa (yv xxr) > 1 8), and the remaining objects D D& where no good instances are available. For the in- stances in D - D& we need to find a good B to train J4. For this we first estimate function ( (Milx:,, 3) that estimates the confidence
That is, it approximates So when By is replaced by /3 for the i-th object. We estimate this quantity as the average classifier ac- curacy on objects with similar labels and under settings B. In general, for continuous ß this can be fit as regression problem. For discrete y. B. simple fractional estimates were found ad- equate in our experiments. We compute these estimates by defining the following counterfactual Σ Upg.=y.B. 9 falu<=lxx))
X:y.
(2,
as (CF(y x, (3)
(LJEEV
where T[ is an indicator function and 0 the
(NJDEV
With these two terms, we maximize the following objective: output of Algorithm] 1 max
max log (Vo xx+) 2 (Brr Xiy, rEB,
logge (argmax f (yr Xiy, B) Xijs Bis)
tEDs JEB,
DE JEB.
Computation of m. Our training objective 11 suggests that π (Xij, G.y) = 1 only if fo(ys Xiy) < folyi X,j = Z(z,, P(y)) where B.g = argmax, 93 (3 x:j, B.y)). Since the recourse budget is limited, we cannot obtain Xly for all instances to compute स. Therefore, in practice, we use (e Bly) proxy for fo X1y = Z(zi, P(y)). Specifically, we set
Big) I (ymax Xija B'y)) fa(mmax Xiz)] where ymax argmax fa(v] xx))
(8)
We call our overall training method as RECOURSENET, which is summarized in Algorithm 3
3.2 Theoretical Analysis
In this section we present the conditions on 0 d. i under which RECOURSENET will be successful in providing recourse. The proofs of the propositions are given in Appendix A
Proposition 1 Assume that Z is Lg-Lipschitz with respect to B, the model log foly xx) is L Lipschitz with respect to x. Given E D and j E B,, if the set Rec (0, x.j. M&) is non-empty and the recourse network 94 gives modified fl,, such that [| Bl S efor some B E Reca (9, X:jy V:).
then, for >> tT. Lgge with t > 1 we have:
log fo(ys Z B(y)) > log So(w: xx;)) + (1 - 1/1)
The above proposition suggests that as long as go X.j, B,g) is close to some 3 E Reca (0, Xij y:). then the accuracy provided by the classifier fe improves. One of the key assumption of this proposition is the non-emptiness of Reca (0, Xij. Ms). In the following proposition, we find the requirements for such conditions in terms of the true classifier fo..
Proposition 2 Let us assume that the true conditional distribution of y given x is so-, log Soly (x) is Lpp-iischhizz w.r.f O and ||0 0- < ō. Moreover, we define the following quantities: (6,5) = maxre [log fo- (y- Xxr) - log fo- (ysl xx5)]. A = (ii.)) E ( > 0}, and
Ao min(r,)EE Ai.j. Then, we have the following results:
1. For (i. E A. Recs. (0*, V1) is non-empty.
2. Given (i,j) E V, if we have 8 < An. 2h.'
then Reca (0, xij.y:) is non-emply for A <
Ao 2
5

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3. If the recourse network 96 gives us modified Big such that ||3:; -131 I c for some
B E Reca (0, X1,, Ub) with A < Do - 2L,o, then, for < (Ao - -2T (tL.3TT)) with
> we have:
so(ual Xiy) < log So Bi)) (11-))))-AAA -2.00)))))))
(10)
Experiments
In this section, we experiment with several datasets to show that RECOURSENET'S 's training strategy outperforms existing methods or simpler alternatives. Our experiments are designed to answer the following research questions through empirical evaluations:
1. In the training of fo- what is the impact of subsetting the training set when compared with default alternatives like training on all available labeled data.
2. In deciding when to trigger recourse, how effective is our method, in contrast to just asking recourse on low confidence examples?
3. In training the recourse recommender, how important was it distinguish between objects with and without good Gss? During inference, how important is it to make instance specific recourse recommendations instead of single ideal beta?
We could not find any existing benchmark that records different environment settings under which objects are rendered. Thus we generate datasets that admit causal relationship across x, B, and y as follows: we first sample a class label from the class prior y ~ Pr(*) and then we choose B, settings by sampling Bs drawn from Pr(B3) y). Finally we generate under the B, chosen environments. We generate 4 datasets of varying complexities as shown in the Table 2
Shapenet-Large Shapenet consists of three dimensional models of many kinds of objects that can be mapped into two dimensional pixel maps under various environments [. Each environment 3 represents the camera settings provided by (view, zoom level, light color). We select | = 10 classes and draw 250 objects from each class to obtain a total of D = 2500 objects. For each object, we draw B; = 4 different 33 from set of [B] = 99 possible camera settings and render them under these settings. Among the four environments, we ensure that each z; contains a B that renders it properly with a probability 0.8. To make the task challenging, we corrupt the rendered xay using various kinds of noise from the image corruptions library" [ In particular, we corrupt X1) if (.. is not a good choice for 2 so as to make learning of such settings difficult for fa.
Shapenet-Small. This dataset differs from Shapenet-Large in the number of environments under which each object is rendered. Among the two environments, each 2, contains good /3 with probability 0.6. This dataset is more challenging than Shapenet-Large because of scarcity in the number of objects that contain atleast one X,y that produces good accuracy. This makes the objective (6) difficult to learn. Here also we add noise to X:j in a manner similar to Shapenet-Larg' The test set for both Shapenet-L.at Large and Shapenet-Small is same, and contains 80 objects per class; each of them rendered under all 9 camera settings f thus contributing to 7200 images.
Speech Commands Dataset. This dataset consists of textual commands that can be converted to speech under different environments 33 defined by (pitch, speed, noise) sampled from B with [B] 60. We select | 20 commonly used Alexa commands and render them speech signals with frame width of 0.5 seconds using Google text to speech library These speech signals are then processed into 2D mel spectrograms [27] In particular, the training dataset consists of 2000 rendered under [B| = 5 environments each thereby contributing to 10000 samples. The test set contains 200 2,5 rendered under all 60 (Ss thereby containing 12000 speech samples.
Skin-Lesion Dataset This dataset consists of images of skin captured using smartphone and the task
is to classify among seven different skin conditions ([)) = 7). The dataset is taken from Kaggle and we synthetically generate 9 different environments (B) 9) where each environment is defined by (zoom, illumination, contrast). The training dataset contains 1400 objects z; rendered
www.:////ooo//ooeeeee Learnii skiniinng-iiiiiiie skin lesion caa.on-cllassiicaiiooooooo
notebook

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MTrain objects ( (122)
#Renderings
Environment
IlCassses D
#Test
Dataset
(8)
objects
Synthetic
1200
8
6 dimensional bit-mask
4
200
Chapenet-Large
2500
4
(view, zoom level, light color) (view, zoom level, light color)
10
800
Shapenct-Small
2500
2
10
800
Speech Commands
2000
5
(pitch, speed, noise) (zoom, illumination, contrast)
20
60
Skin Lesion
1400
4
Table 2: Summary of datasets used. The columns #Train and #Test denote the number of (latent) objects available in train, test dataset respectively. #RRenderings denotes the number of environment settings under which each object 2; is rendered. Environment denotes the different parameters that control the generation of x from 2.
Training Data
Shapenet-Large
Shapenct-Smal
Crecch-Commands
Skin-Lesion
Full-data (Baseline)
71.93 + 0.63
62.97 + 0.80
51.85 + 1.08
56.42 + 0.80
One-shot subsetting
72.63 + 0.54
65.55 + 1.11
54.66 + 1.2
60.89 = 1.11
Iterative greedy (Ours)
77.14 + 0.63
74.13 + 1.10
65.76 + 1.44
68.62 + 0.90
Table Comparing classification accuracy under different strategies for subsetting data for training fe 100% recourse. The table shows mean = one std. deviation of accuracies obtained over 5 seeds.
under |B| = 4 environments each and the test dataset contains 70 objects rendered under all 9 environments.
Further details about dataset preparation and results on synthetic datasets are provided in Appendix B
Models and Hyperparameters. We use the same model architecture and hyper-paramen parameters across datasets. We used Adam optimizer with default learning rate of 10 3 to optimize all our objectives. The architecture for fe is Resnet18 88 model trained from scratch. We use budget b 1000 but to avoid training the model iteratively times, we select 10 instances into R at line 5 of algorithm] per iteration. For 9e too train Resnet18 model from scratch. We obtain 512-dimensional embedding for f as an average of embeddings of its individual components which are trained end-to-end. We concatenate the embeddings of B with last layer embeddings of from Resnet obtain the input embedding which is then fed to a 3-layered neural network that predicts the recourse 3. We learn do using the objective 7 where the D3 is computed by sorting the minimum group loss (min,Cl(is ji), and then selecting the first few groups that produce least min loss into the set Dg. The first few are chosen that the average confidence fo (y) Xig. B.g) of examples in Dj has the maximum gap with corresponding average in D DD-
RQ1: Impact of subsetting the training data in learning So We compare our iterative greedy proposal to train so with two other baselines as follows:
1. Full data: Here we train Se over the entire training dataset.
One-shot subsetting: Here we subset all b examples at once unlike our iterative algorithm [ Lee. compute j(i,j) for all samples given (0) and choose the that incur top-b values into R and then maximize F(e, R) to obtain 0.
the recourse accuracy of Sa at 100% recourse when learned under these three different training strategies. For all three methods recourse recommendations. We observe that our iterative greedy algorithm to train fe consistently outperforms the model trained with the entire data. This establishes the importance of training classifiers differently when recourse is an option. A classifier that is trained only on instances with 'good' environment settings is more suitable for classification under recourse, even in data hungry deep learning models. Simply subsetting by removing the worst b instances is significantly worse than our iterative algorithm.
use Ys trained using our objective (7) obtain
RQ2: Evaluating our method of triggering recourse We compare our proposal for fo and m with four other baselines and the first two adapted from the work of 24).
Score based recourse trigger: Here, we train fa on entire training data. Then during inference, given a budget b, we seek recourse on the least b confident predictions of so-
2.
Full automation based recourse trigger: Here also, we train fo on entire training data. Then for recourse trigger, we learn an error predictor trained on the loss incurred by the classifier on training examples. During inference, for a budget b, seek recourse those examples that
7

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Score based Recourse Recommender
RecourseNet (T)
Random-gresd
Full Automation based Recourse Recommender
Random
Recourse Accuracy
0.6
0.7
0.6
0.4
0.6
0.0 0.2 0.4 0.6 0.8 1.0 Fraction of Recourse (b/[U])
0.0 0.2 0.4 0.6 0.8 1.0 Fraction of Recourse [b/V)
0.0 0.2 0.4 0.6 0.8 1.0 Fraction of Recourse (b/V))
0.0 0.2 0.4 0.6 0.8 1.0
Fraction of Recourse (b/l))
(a) Shapenet-Large
(b) Shapenet-Sman
(c) Speech Commands
(d) Skin-Lesion
Figure 4: Variation of classification accuracy after recourse against the budget 6, i.e., the maximum number instances selected for recourse.
Only &
Constant
IRM
RecourseNet without jCP
RecourseNet do
Recourse Accuracy
0.8
0.7
0.7
0.6
0.7
0.6
0.6
0.4
0.3
0.5
0.0
Fraction of Recourse (b/lV)
Fraction of Recourse (b/lV)
Fraction Recourse (b/IV))
Fraction of Recourse (6/lV)
(a) Shapenet-L.arg
(b) Shapenet-Small.
(c) Speech Commands.
(d) Skin-Lesion.
Figure 5: Variation of classification accuracy after recourse against the budget b, i.e., the maximum number of instances selected for recourse. The figures show mean recourse accuracy + one std. deviation obtained over five seeds.
incur the b highest predicted losses. Details about the neural architecture of the error predictor is provided in Appendix C
Random trigger:
We train fo on entire dataset and apply recourse on instances selected
randomly.
4. Random-greedy trigger: Here we train fo using our greedy algorithm I and then apply recourse on instances selected randomly.
summarrzss the comparison recourse trigger æ against the baselines. Unlike our greedy algorithm, methods that propose full training for Sa are inferior 0% recourse. The steepness in the recourse accuracy for our proposed æ is more in comparison to other baselines because prioritizes recourse not just the instances that suffer from poor accuracy for recourse but also the ones that respond better to recourse by means of modelling the expected recourse accuracy. Our method suggests recourse only when the expected gains that we calculate using fcF is positive, and performs much better than methods based purely on current classifier confidence or an estimate of the confidence. We see that both the random baselines perform much worse and follows the expected linear trend of recourse accuracy as we increase the recourse budget. These results establish the impact of our method triggering response.
RQ3: Evaluating training methods of recourse recommendation 96 four other methods as follows.
We compare our Js against
1. Only ot This model takes a form similar to and learns to recourse the instances (i,j) that incur top 50% losses in the training data By where is obtained from argmax, fo(y Xir).
RECOURSENET without fO;; This model trains 9e using the objective
Constant: This method emits a constant 3 recommendation independent of the features (x, (
We select constant & the one that achieves the best training accuracy.

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Ouly ø
RecourseNet S, without for
Constant
RecourseNet So
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(a) Shapenet-Large
(b) Shapenet-Small
(c) Speech Commands
Figure 6: Accuracy of different recourse recommenders for different classes.
4. IRM: In this baseline, instead of we learn networks that estimate accuracy of an input X,j on counterfactual setting /3 using ideas from Invariant Risk Minimization literature. We extract representations of input (x) by fine tuning Resnet 18 model with pre-trained Imagenet weights. This forms the network of IRMv1 objective in []] The representations are multiplied with scalar w = 1 and then concatenated with representation of the counterfactual environment / for which we want estimate the accuracy. We use a linear layer embed the environments (B)). The concatenated representations are then fed to fully connected network that aims to predict the classifier's 's confidence (fo (y x)) on the examples. For Triage, since these methods directly model the counterfactual accuracy ( B) V3, we use these predicted values in place of our prior fcF term Eq. (). The classifier trained on full data.
The first three baselines are designed to perform an ablation study of our proposal, including assessing the importance of finding the objects that have no good and thereby including them in the set D - D3 in the 96 objective (7). The results presented in Figure 5 shows the following observations. (1) Only á model performs poorly on Shapenet-Large and performs on par with Constant method on other datasets. Because many groups do not have B that produce good accuracy, Only é receives noisy supervision during training. (2) RECOURSENET without fcP achieves decent on Shapenet- and Specch datasets but fails miserably on the Shapenet- Small dataset. Because Shapenet- -mall has [, 2, we can see that 50% examples force the recourse recommender to predict the input / as is under the joint objective (6). This renders identity function strong local maxima which the model struggles to avoid during training. This brittleness of RECOURSENET without JCF to objects with good (3 motivates the need for our current objective 7
(3) The supervision provided by the 7 guides instances in the set D Dy and thus achieves better recourse accuracy. (4) The IRM method is difficult to train as seen by the large variance, and performs poorly. This method does not sufficiently exploit the fact that the training data includes multiple views the same object. Also, it suffers because the classifier is trained on full data. (5) One good competitor to our Is across the datasets is constant prediction which brings us to the other half of RQ3 Is an instance independent constant /3 recourse recommendation always advisable?
fCF term in our 96 objective
We try to answer this question by probing the average error incurred by these methods for each class. Figure 6 summarizes the results for 5 classes which shows that unlike baselines, our Jø garners modest to best accuracy across classes consistently. The performance of constant method in the Shapanet datasets can be attributed to the fact that many objects in it admit unique good B. However, this is not the case in the speech dataset because we found no one 3 to dominate in performance across classes. As a result, the recourse accuracy suffers in the speech dataset with constant B prediction. Thus we conclude by saying that it is always good to make instance specific recourse recommendations.
5 Stability of our proposals in solving the overall objective
In Figure a] we plot the value of the overall objective through the different stages of the So training algorithm and in Figure 7bb) we plot for the second ds training phase. In both cases we observe that the value of the overall objective increases even though the two stages are not directly solving for Equation This provides empirical evidence about the stability of our method.

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Shapenet-Small
Shapenet-Large
Skin-Lesion
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(a) Stability fo
(b) Stability go
Figure 7: Stability of our proposals in solving
Predicted Recourse B
Predicted Recourse f
600
(ace,
400
(sice nemal wans)
400
(tsp, zoom-in in grean) (fron, zoom in yallow) (fron, nermal whits! Phopéfront, normal whits Dhopiftont, acom-out, green] Dipploree, zcam-cut, vello]] Dippleace,, zoamooue pink]
nomnal
ItopSfront
200
Dropdsido, out, pink]
Aeropiane Bench
Bus
Cabinet
Chair
Display
Knife
Lamp
Speaker
Gun
Aeroplane Bench
Bus
Cabinet
Chair
Display
Knife
Lamp
Speaker Gun
(a) Shapenet-Large
(b) Shapenet-Sman
Figure 8: This figure shows the histogram of the counts of different Bs predicted against each class for Shapenet-Large and Shapenet-Smal datasets.
Now, discuss about the details how we evaluated the overall objective in these two stages. For the fe training phase we evaluate the objective using and Rec (0" Xtj, y:) as proxies for ı and as which have not yet been trained. For the Is training since æ is not available, assume full recourse and focus on the impact of (Ss predicted by gø on recourse objective.
Predicted Environments by 94
In this experiment, we plot the counts of different Bs predicted by our Je model against each class for Shapenet-Large and Shapenet-Smal datasets. For Shapenet-Large we see that the recourse recommender never predicted 4 out of 93s for any class and thus those bars are excluded from figure ( aa). However, this is not the case for Shapenet-Small and hence all 93s are included.
7 Conclusions
In this paper, we proposed RECOURSENET that aims to make recourse recommendations to instances that are sampled from poor environments. RECOURSENET has three components: (1) classifier fe. (2) Recourse recommender
and (3) Recourse trigger æ. We learn these components using a novel three level training objective without having model the latent physical generator Z. Moreover, theoretical results assure that under mild conditions, recourse is beneficial. These results effect, press the need for recourse in order to obtain quality predictions from model. The experiments on synthetic and real-world datasets show that our method outperforms several baselines.
Our work opens up many areas of future work. It would be interesting to extend RECOURSENET to regimes where the space of environment variable 3s can be continuous. Also, multiple views of test object collected during recourse could be exploited improve future decisions.
8 Acknowledgements
Lokesh is supported by the Prime Minister Research Fellowship, Government of India.
10

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References
[1] Martin Arjovsky, Léon Bottou, Ishaan Guirajani, and David Lopez-Paz. Invariant risk mini- mization. arXiv preprint arviv: 10X:::997000293 2019.
[2] Gagan Bansal, Besmira Nushi, Ece Kamar, Eric Horvitz, and Daniel S. Weld. Optimizing Al for Teamwork, In AAAI, 2021.
[3] Angel X. Chang, Thomas Funkhouser, Leonidas Guibas, Pat Hanrahan, Qixing Huang, Zimo Li, Silvio Savarese, Manolis Savva, Shuran Song, Hao Su, Jianxiong Xiao, Li Yi, and Fisher Yu. Shapenet: An information-rich 3d model repository, 2015.
[4] Zachary Charles and Dimitris Papailiopoulos. Stability and generalization of learning algorithms that converge to global optima. In International conference on machine learning, pages 745-754 PMLR, 2018.
[5] Abir De, Paramita Koley, Niloy Ganguly, and Manuel Gomez-Rodrigure Regression under human assistance. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34, pages 2611 1-2620, 2020.
[6] Yaroslav Ganin, Evgeniya Ustinova, Hama Ajakan, Pascal Germain, Hugo Larochelle, François Laviolette, Mario Marchand, and Victor Lempitsky. Domain-adverssrial training of neural networks. The journal of machine learning research, 17(1):2096-2330, 2016.
[7] Moritz Hardt, Nimrod Megiddo. Christos Papadimitriou, and Mary Wootters. Strategic classi- fication. Proceedings of the 2016 ACM conference on innovations in theoretical computer science, pages 111-122, 2016.
[8] Moritz Hardt, Eric Price, and Nati Srebro. Equality of opportunity in supervised learning. In Advances in neural information processing systems, pages 3315-3323, 2016.
[9] Amir-Hossein Karimi, Gilles Barthe, Bernhard Schölkopf, and Isabel Valera. A survey of algorithmic recourse: definitions, formulations, solutions, and prospects, 2021.
[10] Sagi Levanon and Nir Rosenfeld. Strategic classification made practical. arXiv preprint a:Xiv:2103.0/826, 2021.
[11] Arnaud Van Looveren and Janis Klaise. Interpretable counterfactual explanations guided by prototypes, 2019.
[12] Brian Lubars and Chenhao Tan. Ask not what ai can do, but what should do: Towards framework of task delegability. Advances in Neural Information Processing Systems, 32, 2019.
[13] Spandan Madan, Tomotake Sasaki, Tzu-Mao Li, Xavier Boix, and Hanspeter Pfister. Small in-distribution changes in 3d perspective and lighting fool both cnns and transformers. arXiv preprint arXiv:2106.16198, 2021.
[14] David Madras, Toni Pitassi, and Richard Zemel. Predict responsibly: improving fairness and accuracy by learning to defer. Advances in Neural Information Processing Systems, 31, 2018.
[15] John Miller, Smitha Milli, and Moritz Hardt. Strategic adaptation to classifiers: A causal perspective. CoRR, abs/1910.10362, 2019.
[16] Baharan Mirzasoleiman, Ashwinkumar Badanidiyuru, Amin Karbasi, Jan Vondrák, and Andreas Krause. Lazier than lazy greedy. arXiv preprint 10Xiv:1409.7938, 2014.
[17] Hussein Mozannar and David Sontag, Consistent estimators for learning to defer to an expert. In International Conference on Machine Learning, pages 7076-7087. PMLR, 2020.
[18] Siddharth Nayak and Balaraman Ravindran. Reinforcement learning for improving object detection. In European Conference on Computer Vision, pages 149-161. Springer, 2020.
[19] George I. Nemhauser, Laurence A Wolsey, and Marshall Fisher. An analysis of approximations for maximizing submodular set functions-i. Mathematical programming, 1978.

---

[20] Nastaran Okati, Abir De, and Manuel GomezzRodriguez, Differentiable learning under triage, 2021.
[21] Godliver Owomugisha and Ernest Mwebaze. Machine learning for plant disease incidence and severity measurements from leaf images. In 2016 15th IEEE International Conference on Machine Learning and Applications (ICMLA), pages 158-163, 2016.
[22] Chunjong Park, Hung Ngo, Libby Rose Lavitt, Vincent Karuri, Shiven Bhatt, Peter Lubell- Doughtie, Anuraj H. Shankar, Leonard Ndwiga, Victor Osoti, Juliana K. Wambua, Philip Bejon, Lynette Isabella Ochola-Oyier, Monique Chilver, Nigel Stocks, Victoria Lyon, Barry R. Lutz, Matthew Thompson, Alex Mariakakis, and Shwetak Patel. The design and evaluation of mobile system for rapid diagnostic test interpretation. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., 5(1), mar 2021.
[23] Rafael Poyiadzi, Kacper Sokol, Raul Santos-Rodriguez Tijl De Bie, and Peter Flach. Face: Fea- sible and actionable counterfactual explanations. In Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, AIES '20, page 344-354 350, New York, NY, USA, 2020. Association for Computing Machinery.
[24] Maithra Raghu, Katy Blumer, Greg Corrado, Jon Kleinberg, Ziad Obermeyer, and Sendhil Mullainathan. The algorithmic automation problem: Prediction, triage, and human effort. arXiv preprint arXiv: 12220, 2019.
[25] Alexis Ross, Himabindu Lakkaraju, and Osbert Bastani. Learning models for actionable recourse. In A. Beygelzimer, Y. Dauphin, P. Liang, and J. Wortman Vaughan, editors, Advances in Neural Information Processing Systems, 2021.
[26] Shai Shalev-Shwariz and Shai Ben-Dan David. Understanding machine learning: From theory to algorithms. Cambridge university press, 2014.
[27] Jonathan Shen, Ruoming Pang, Ron Weiss, Mike Schuster, Navdeep Jaitly, Zongheng Yang. Zhifeng Chen, Yu Zhang, Yuxuan Wang. Rj Skerrv-Ryan, et al. Natural tts synthesis by conditioning wavenet on mel spectrogram predictions. In 2018 IEEE international conference on acoustics, speech and signal processing (ICASSP), pages 1777-777777 IEEE, 2018.
[28] Rohan Taori, Achal Dave, Vaishaal Shankar, Nicholas Carlini, Benjamin Recht, and Ludwig Schmidt. Measuring robustness to natural distribution shifts image classification, 2020.
[29] Berk Ustun, Alexander Spangher, and Yang Liu. Actionable recourse in linear classification. In Proceedings of the Conference on Fairness, Accountability, and Transparency, pages 10-19, 2019.
[30] Wachter, Brent D. Mittelstadt, and Chris Russell. Counterfactual explanations without open- ing the black box: Automated decisions and the gdpr. European Economics: Microeconomics & Industrial Organization eJournal, 2017.
[31] Bryan Wilder, Eric Horvitz, and Ece Kamar. Learning to complement humans. IJCAI, 2020.
[32] Jiaming Zeng, Berk Ustun, and Cynthia Interpretable classification models for recidivism prediction. Journal of the Royal Statistical Society: Series A (Statistics in Society), 3(180):689- 722, 2017.
[33] Ping Zhang, Rishabh Iyer, Ashish Tendulkar, Gaurav Aggarwal, and Abir De. Learning to select exogenous events for marked temporal point process. Advances in Neural Information Processing Systems, 34, 2021.
Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? [Yes] See Section 3.2
(b) Did you describe the limitations of your work? [Yes] See Section
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(c) Did you discuss any potential negative societal impacts of your work? [N/A]
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes]
2. If you are including theoretical results...
(a) Did you state the full of assumptions of all theoretical results? [Yes] See Section [3.2]
(b) Did you include complete proofs of all theoretical results? [Yes] Included in the Appendix.
3. If you ran experiments..
(a) Did you include the code, data, and instructions needed to reproduce the main ex- perimental results (either in the supplemental material or as URL)? [Yes] Code is included in the Supplementary Material and datasets are provided an anonymized
URL.
(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] See Section 4 and Appendix
(c) Did you report error bars (e.g.. with respect to the random seed after running experi- ments multiple times)? [Yes] See Section 4
(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, cloud provider)? [Yes] See Appendix
4. If you using existing assets (e.g., code, data, models) or curating/releasing new assets...
(a) If your work uses existing assets, did you cite the creators? [Yes]
(b) Did you mention the license of the assets? [N/A]
(c) Did you include any assets either in the supplemental material URL? [Yes] Datasets are included in an anonymized URL
(d) Did you discuss whether and how consent was obtained from people whose data you're 're
using/curating? [Yes]
(e) Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
5. If you used crowdsourcing conducted research with human subjects...
(a) Did you include the full text of instructions given to participants and screenshots, applicable? [N/A]
(b) Did you describe any potential participant risks, with links Institutional Review Board (IRB) approvals, if applicable? [N/A]
(c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
13


Reviews:
[{"review_id": "mEGQlK-SxX3", "reviewer": "Reviewer_nfUe", "summary": "**Summary**: The paper tries to improve the prediction accuracy through a different perspective: recourse on instance environment. Firstly, it points out the fact that a classifier’s performance is also dependent on the data quality, that is, a good classifier is also likely to misclassify an image taken in very bad environment setting. To address this problem, the author proposes the RECOURSENET to first identify whether the data is good for classification or needed to taken from another environment setting, such as another angle. If the image is not qualified for a good classification, the recoursenet will recommend the user an appropriate environment setting. Then the recoursenet will trains a classifier to classify the image of good quality or the images generated by the user. \n\n**Contribution**: This paper proposes a novel three-level framework for the recourse mechanism without human involvement in the training. ", "questions": "- It would be better if the author can add a more detailed discussion about the theoretical analysis part, e.g., how does these two propositions benefit the design of the mechanism. It seems the assumption of $||\\beta_{i,j}^{\\prime} - \\beta|| \\le \\epsilon$ is quite strong.", "limitations": "The paper's limitations are not discussed by the author.", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**: \n- The paper provides a novel perspective for enhancing prediction accuracy. Instead of focusing on the classification model for improving robustness, it focuses on the input data quality and introduces a recourse mechanism for improving the data quality and consequently improving the prediction accuracy. This is promising in medical applications. For example, the algorithm can be deployed on some online diagnosis platform and provides hints/tips to the user about how to take a clear image that can make the diagnosis more accurate.\n- The proposed method is intuitive and relatively clearly explained.\n- The experiment is thorough in terms of the ablation study, namely how every component is beneficial.\n\n**Weaknesses**:\n- The experiments are limited to small datasets. \n- There is some inconsistency in terms of notation and writing. For example, the environment setting appears as $B$ or $\\mathcal{B}$. And in line 88: it is inconsistent with the algorithm when saying that humans do not participate in (the) prediction task but they only generate new instances under the recommended environments. \n- How these two propositions benefit seems to be unclear to me. ", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "K9MRrEzfjU", "reviewer": "Reviewer_86ep", "summary": "The authors propose using a recourse mechanism that allows a model to recommend to its human users how they could improve the predictions of the model by capturing another sample of the current instance with somewhat different view hyper-parameters (less zoom, more brightness etc). The model is made of three stages, one for prediction of a target class, one for predicting whether resampling could be useful, and another recommending how the resampling should be made. \n\nThe method requires that the model has access to different views of various instances and a corresponding real value that describes somewhat the transform variation over those views. \n\nThe authors state that this could be useful in settings such as the medical setting. \n\nThey then evaluate their model on a variety of synthetic and non synthetic datasets and show that their method can improve performance successfully on those.", "questions": "1. The authors state that this could be useful in medical settings. But is it really? It can be expensive to get additional MRI/CT etc images for the patient and the hospital, and, more than that, for the model to work it would need to be trained on lots of variations of the same instances with certain imaging parameters annotated. Furthermore, it would need to somehow be able to generalize on different humans and hospital machines and how they interpret the recommended changes for the resampling. It simply seems too expensive for what appears to be highly uncertain and unverifiable (at in-the-wild application) predictive improvements. \n2. Have you evaluated the model on randomly recoursed instances? That could help evaluate whether a. the recourse predictor is useful and b. whether the recourse recommender makes useful recommendations.\n3. Since samples are being resampled, have you considered comparing your method with existing few-shot learning models? ProtoNets and Matching Nets could be an initial baseline to compare to. As sample size increases, the predictions of those models improves as well. ", "limitations": "The technical limitations I stated earlier stand, but in terms of negative societal impact, I don't see any obvious problems (other than potentially increased hospital spending from patients and the government alike if implemented poorly).", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "One of my main concerns is around the idea of recourse/resampling. The authors state that this could be useful in medical settings. But is it really? It can be expensive to get additional MRI/CT etc images for the patient and the hospital, and, more than that, for the model to work it would need to be trained on lots of variations of the same instances with certain imaging parameters annotated. Furthermore, it would need to somehow be able to generalize on different humans and hospital machines and how they interpret the recommended changes for the resampling. It simply seems too expensive for what appears to be highly uncertain and unverifiable (at in-the-wild application) predictive improvements. \n\nOriginality:\n\nThe work attempts to do something novel and potentially useful. I consider it's novelty at acceptable levels. \n\nQuality:\nThe paper is written well, and presented well, however the experimental quality is lacking as the model is only evaluated on datasets that are very precise in how a particular instance is viewed in terms of the view parameters given. In medical settings, for example, this would not be very possible with current datasets. The authors also do not evaluate on a more real world dataset of the types that they mentioned their method could be useful in (such as medical settings).\n\nThe authors also do not compare with randomly recoursed/resampled instances to evaluate the effectiveness of their recommender model.\n\nClarity:\n\nThe paper is overall quite clear, and the methods clearly described. \n\nThe paper is also lacking optimizer settings, data augmentations and regularization details for the models that were trained.\n\nSignificance:\n\nAssuming the work could be reframed in a way that it requires a more realistic data source with more noisy imaging parameters, the idea of recourse could be a useful one. As it currently stands however, it does not seem to offer real world significance, but does offer fair research novelty and significance", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ["I don’t know"]}, "extra_text": {}}, {"review_id": "K7otgbBetl_", "reviewer": "Reviewer_ERbB", "summary": "This paper proposes a RecourseNet, which learns to instance-dependently recourse to environments so that the learner gets better samples at training time and the predictor is well informed which instance to recourse with which environments. Towards this goal, they propose a novel learning objective to optimize trigger, and the parameters of predictor and recourse recommender. Due to its non-differentiability, they resort to simple heuristics to approximate the learning objective and develop an efficient learning framework. The experimental results demonstrate the efficacy of RecourseNet over simple baselines, achieving superior recourse accuracy versus fraction of recourse. The results also show that instance-wise recourse is important as well.", "questions": "# Questions\n- How did you choose the hyperparameters $b$, $\\Delta$ and $\\delta$?\n- In Figure 4, how did you select the 5 classes?\n- In L154, I think $F(\\theta^{k+1}(R\\cup \\{(i,j)\\})) \\geq F(\\theta^{k}(R\\cup \\{(i,j)\\}))$ is wrong (also, $F$ should take two arguments as an input) because we cannot guarantee the predictor performance at the next iteration for many reasons (e.g. non-convexity). What we can guarantee is $F(\\theta^k, R\\cup \\{(i,j)\\}) \\geq F(\\theta^k, R)$. Am I understanding correctly?\n\n# Typo\n- In Eq.(2), $\\pi(x_{ij})$ should be $\\pi(x_{ij},\\beta_{ij})$\n- L124, 125: $(1-\\pi(\\cdot,\\cdot)f_\\theta(\\cdot,\\cdot))$ should be $(1-\\pi(\\cdot,\\cdot) \\log f_\\theta(\\cdot,\\cdot))$\n- In Eq.(6), in the first line there should be $\\log$ before $f_\\theta$ (in Appendix A, the authors say that the second line of Eq.(6) should be argmax, but it sounds weird because argmax returns $\\beta$ which is not something that we maximize)\n- I wonder whether the second line of Eq.(8) is correct? \n", "limitations": "The authors did not particularly mention the limitations of this work.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "# Strengths\n- Paper is generally well written\n- The motivation is very clear, and the problem setup is very interesting, novel, and practical, which I think of as the biggest contribution of this paper. The assumption that the underlying true process $Z$ is unavailable such that we need to instance-wisely recommend alternative $\\beta$ sounds very reasonable.\n- The learning objective (1) and (2) seems novel and looks interesting.\n- The experimental results demonstrate that the proposed RecourseNet clearly outperforms the baselines (although no confidence intervals are provided and those baselines seem rather weak)\n- The authors made a good effort in developing novel datasets, which can be used by other papers.\n\n# Weaknesses\n\n- Doubt about the original learning objective (1) and (2). I understand what (1) and (2) are meant to do, but in my understanding they can have a trivial solution: for instance, with sufficient network capacity and enough training time, the learner may simply find a trivial solution $\\pi(x,\\beta)=0 \\forall (x,\\beta)$ and simply maximize $\\log f_\\theta (y|x)$ as much as it can. I understand that during training and with limited computational capacity of $f_\\theta$, sometimes $\\pi(\\cdot,\\cdot)$ will become $1$ because \"bad\" $x$'s will have high prediction errors, but it is only in terms of training process, not encoded by the learning objective itself. In other words, the learning objective itself cannot distinguish between bad local optima (trivial solutions) and good local optima (meaningful solutions) if those minima can achieve the same loss value. So I guess we need more discussion about whether (1) and (2) are well-posed in the first place. \n\n- Crude approximation of the learning objective. I understand the difficulty of dealing with the original learning objective (1) and (2) and crude approximations are inevitable. Then, what we need to empirically show is that the proposed approximations are indeed maximizing the original objective (1) and (2) in a stable manner. I would appreciate if the authors could show this in the rebuttal phase.\n\n- Typos spread in the text, especially in the mathematical notations. (See questions and typos below)\n\n- Limited baselines. I understand that there may not exist suitable baselines to compare because the problem setup is novel, but I felt they are too few. As an example, in Figure 2 the authors could have added more baselines that train $f_\\theta$ selectively, in order to truly show the validity of the \"steepness\" of the red curves. (i.e. the different steepnesses may come from the superiority of $f_\\theta$?) Honestly I'm not an expert in this area, so I will have discussions about the possible baselines with other reviewers.\n\n- In Figure 4, it would be more informative if the authors could actually show the different $\\beta$ realized for each class (either qualitatively or quantitatively), instead of the actual recourse accuracies.\n\n- The experimental results do not provide confidence intervals, so the authors cannot argue statistical significancy.\n\n# Summary\nIn summary, I found that the problem setup is very meaningful, interesting, novel, and practical. But the overall quality of the paper is a bit low and more experiments seem to be needed. If the authors can address my concerns, I can increase my score.", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "0OoxO2U9SZj", "reviewer": "Reviewer_7yCh", "summary": "The paper proposes a mechanism, termed RecourseNet,  to identify and modify input instances so as to achieve a better classification outcome from a classifier. These modifications are performed in the latent space of environment-settings.\nRecourseNet consists of three components – a classifier, a recourse-trigger (which selects instances that require modification), and a recourse-recommender (that makes modifications).  A mechanism for training the three components is detailed. Conditions under which the recourse-recommendation leads to improved accuracy are studied. Experiments are performed on ShapeNet, Speech Commands dataset, and a synthetic dataset.\n", "questions": "* L21: During training, aren’t such adverse examples (if labeled correctly) important for generalization? It would be concerning if all training instances were from a fixed set of views/environments\n* It is not clear to me what is meant by an ‘upstream’ classifier? In Fig 1, the classifier seems to be downstream. \n* L110: D is used to index the set of objects. Maybe better to use different notation for training dataset.\n* In Eq 1 (training objective), what happens if training data does not contain some objects? How is the summation over i handled?\n* L126 typo: is it analytical form of Z?\n* In Algorithm 1, does the TRAIN() function solve for \\theta using Eq 5? If that is the case, how is Rec constructed? How is x_ir computed?\n* L157: It is not clear why this is an approximation. \n* L169: What is the significance of computing \\pi? Doesn’t Algorithm 1 already compute \\pi? \n", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "STRENGTHS\n==========\n+ Offering recourse in the form of alternative environments is interesting, especially for images.\n+ The proposed optimization problem is original, and various tricks are proposed to solve it.\n+ Various ablations of RecourseNet are studied and the design choices are justified through experimental results.\n\nWEAKNESSES\n===========\n- It is not clear what the problem RecourseNet actually solves. Is it trying to perform classification when training-data is noisy? \n- L21: During training, aren’t such adverse examples (if labeled correctly) important for generalization? It would be concerning if all training instances were from a fixed set of views/environments. Finding alternative environments makes sense during test time, because the classifier might not have seen such examples during training.  \n- Misuse of the concept of offering recourse: In various places (L5,7,37) the problem is defined as “finding an alternative environment setting so that the classifier is more likely to get a correct prediction”. In traditional recourse, a fixed  classifier is assumed, and actionable changes are suggested to a user (input instance) that has been negatively classified. I am not convinced that performing pre-classification data modifications can be termed as recourse. The usage of the concept of recourse needs justification. \n- Lack of a suitable baseline: In experiments, the questions studied are for different settings of the proposed algorithm. For instance, Section 4.1 is an ablation study that measures how important their iterative greedy proposal is for solving eq (5). It would be interesting to see how RecourseNet performs when compared to other methods that solve the same problem.  (Because the underlying problem it solves is not clear to me, it becomes difficult for me to recommend baselines at this time, but I suppose baselines like Invariant Risk Minimization or other methods that attempt to find domain-invariant representations could be baselines.)\n", "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": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}]

Author rebuttal:

Decision: Accept