Feasible and Desirable Counterfactual Generation by Preserving Human Deﬁned Constraints Homayun Afrabandpey

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Feasible and Desirable Counterfactual Generation by

Preserving Human Deﬁned Constraints

Homayun Afrabandpey

Nokia Technologies

Finland

homayun.afrabandpey@nokia.com

Michael Spranger

Sony AI

Japan

michael.spranger@sony.com

Abstract

We present a human-in-the-loop approach to generate counterfactual (CF) expla-

nations that preserve global and local feasibility constraints. Global feasibility

constraints refer to the causal constraints that are necessary for generating ac-

tionable CF explanation. Assuming a domain expert with knowledge on unary

and binary causal constraints, our approach efﬁciently employs this knowledge to

generate CF explanation by rejecting gradient steps that violate these constraints.

Local feasibility constraints encode end-user’s constraints for generating desirable

CF explanation. We extract these constraints from the end-user of the model and

exploit them during CF generation via user-deﬁned distance metric. Through user

studies, we demonstrate that incorporating causal constraints during CF generation

results in signiﬁcantly better explanations in terms of feasibility and desirability

for participants. Adopting local and global feasibility constraints simultaneously,

although improves user satisfaction, does not signiﬁcantly improve desirability of

the participants compared to only incorporating global constraints.

1 Introduction

Complex Machine Learning (ML) models have been adopted in many real-world decision-making

tasks either to support humans or even substitute them. Despite their superior performance, the black-

box nature of these models necessitates need for interpretability methods to explain their automated

decisions for individuals who are subject to these decisions. Among the large body of literature on

interpretable ML [

], Counterfactual (CF) explanations have shown promise for practitioners.

A CF explanation contains one or more CF instances. A CF instance is a perturbed version of the

original instance that ﬂips the black–box model’s prediction. By comparing a CF instance with the

original instance, a human user receives hints on what changes to the current situation would have

resulted in an alternative decision, i.e., “If

was

, the outcome would have been

rather than

.”

Generating CF explanations that are useful in real-world is still challenging. First, CF explanations

generated by many existing works do not take into account causal relationships among features. This

results in CF instances that are not actionable in the real-world. Take a loan application as example,

a CF explanation approach that does not adopt causal relationships among features could suggests

to change the present employment type from “newbie”

to “senior”

while the age is unchanged.

Second, CF explanations are subjective and should be personalized, while existing works do not take

into account constraints from the end-users of the ML models. Back to the loan application example,

a user might ﬁnd it feasible to change the housing type, while another might instead prefer changing,

e.g., number of installments (duration in month).

In German credit dataset, this qualitative value is deﬁned as a person who has less than

year experience in

his/her current job.

2Between 4to 7years of experience according to German credit dataset.

Preprint. Under review.

arXiv:2210.05993v1 [cs.LG] 12 Oct 2022

To bridge these gaps, we propose a new approach to generate CF explanations for any differentiable

classiﬁer via feasible perturbations. For this, we extend [

] by formulating an objective function for

generating CF instances that takes into account two types of feasibility constraints:

•Global feasibilities

: unary and binary monotonic causal constraints extracted from a domain

expert,

•Local feasibilities

: constraints in the form of feature perturbation difﬁculty values, given

by the end-users.

The objective function is optimized using gradient descent and feasibility constraints are satisﬁed

during the optimization by rejecting gradient steps that do not satisfy them. It is important to note

that, here we differentiate between end-user and domain expert. An end-user is the individual who is

subject to the decision of the ML model, e.g. a bank customer whose loan application is rejected. A

domain expert, on the other hand, knows the data and the application. We believe domain experts are

naturally able to give feedback on causal relationship among (at least) some features, without being

constrained to know the exact functional relationship.

The same feasibility constraints were also considered in [

] for CF generation. They propose a

generative model based on an encoder-decoder framework, where the encoder projects features into a

latent space and the decoder generates CF instances from the latent space. Their approach, however,

requires complete information about the structural causal model including the causal graph and the

structural equations. This assumption is highly restrictive for applicability of the method in real-world

applications. To cope with this issue, [

] proposed a data driven approach to approximate unary and

binary monotonic causal constraints and adopt the approximated relationships in the CF generation.

For local feasibility constraints, they considered implicit user preferences, i.e., given a pair of original

instance and CF instance,

(x,x0)

, the user outputs

if CF instance is locally feasible and

otherwise.

However, since there is no access to the

(x,x0)

query pairs apriori, they approximate the user by

ﬁrst asking user preferences on some

(x,q)

, where

are sample CF instances generated by a CF

generator without considering user preferences, and then learn a model that generates scores for each

pair that mimics user preferences.

Our approach is different from [7] in several aspects:

•

in [

], for approximating each binary constraint, the model learns

extra parameters. This

hinders the scalability of the method. Furthermore, these approximated binary constraints

could be imprecise as they are learned from the data, while in our approach we rely on

domain experts to provide such constraints which is more reliable,

•

local feasibility constraints are incorporated via implicit feedbacks that are approximated

using a function. These feedbacks are not directly related to the ﬁnal CF instances to be

generated. This could result in undesirable CF instances that do not satisfy user’s constraints.

On the other hand, we adopt explicit user feedbacks directly into the optimization function,

•

the type of the user feedback considered in [

] for local feasibility is difﬁcult to provide

and restrictive. It is difﬁcult to provide since the user must compare the CF instance with

the original instance to ﬁnd out if perturbations are locally feasible or not. It is restrictive

because the approach provides no tool for the user to state the level of local infeasibilty. As

an example, assume a CF instance is generated by perturbing more than one feature of the

original instance where all but one perturbation satisfy user’s feasibility constraints. In our

approach, user feedbacks are "feature level" and they are not restricted to {0,1},

•

last but not least, [

] did not test they approach in a real user study and it is not evident from

the paper how a real user could be adopted in-the-loop to obtain desirable CF explanation.

To explore the effectiveness of our explanations, we design user studies where users are asked to rank

CF instances generated under different conditions. Through these studies, we found that users tend to

give signiﬁcantly better ranks to CF instances generated by considering global feasibility constraints

compared to the case where such constraints are not considered. Furthermore, CF instances generated

by adopting both local and global feasibility constraints are better than those generated by only

considering global feasibility constraints. However, their difference is not statistically signiﬁcant.

In summary, we make the following contributions:

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FeasibleandDesirableCounterfactualGenerationbyPreservingHumanDenedConstraintsHomayunAfrabandpeyNokiaTechnologiesFinlandhomayun.afrabandpey@nokia.comMichaelSprangerSonyAIJapanmichael.spranger@sony.comAbstractWepresentahuman-in-the-loopapproachtogeneratecounterfactual(CF)expla-nationsthatpreserveglob...

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Feasible and Desirable Counterfactual Generation by Preserving Human Deﬁned Constraints Homayun Afrabandpey

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