FEAMOE Fair Explainable and Adaptive Mixture of Experts Shubham Sharma

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FEAMOE: Fair, Explainable and Adaptive Mixture

of Experts

Shubham Sharma

University of Texas at Austin

shubham_sharma@utexas.edu

Jette Henderson

CognitiveScale

jhenderson@cognitivescale.com

Joydeep Ghosh

University of Texas at Austin

jghosh@utexas.edu

Abstract

Three key properties that are desired of trustworthy machine learning models

deployed in high-stakes environments are fairness, explainability, and an ability to

account for various kinds of "drift". While drifts in model accuracy, for example

due to covariate shift, have been widely investigated, drifts in fairness metrics

over time remain largely unexplored. In this paper, we propose FEAMOE, a

novel "mixture-of-experts" inspired framework aimed at learning fairer, more

explainable/interpretable models that can also rapidly adjust to drifts in both the

accuracy and the fairness of a classiﬁer. We illustrate our framework for three

popular fairness measures and demonstrate how drift can be handled with respect

to these fairness constraints. Experiments on multiple datasets show that our

framework as applied to a mixture of linear experts is able to perform comparably

to neural networks in terms of accuracy while producing fairer models. We then

use the large-scale HMDA dataset and show that while various models trained on

HMDA demonstrate drift with respect to both accuracy and fairness, FEAMOE

can ably handle these drifts with respect to all the considered fairness measures

and maintain model accuracy as well. We also prove that the proposed framework

allows for producing fast Shapley value explanations, which makes computationally

efﬁcient feature attribution based explanations of model decisions readily available

via FEAMOE.

1 Introduction

The ﬁeld of responsible artiﬁcial intelligence has several desiderata that are motivated by regulations

such as the General Data Protected Regulation [

]. These include: ensuring that an AI model is

non-discriminatory and transparent; individuals subject to model decisions should have access to

explanations that point a path towards recourse; and models should adapt to any changes in the

characteristics of the data post-deployment so as to maintain their quality and trustworthiness.

Most approaches towards the mitigation of any form of bias assume a static classiﬁer. A practitioner

decides on some deﬁnition of fairness, trains a model that attempts to enforce this notion of fairness

and then deploys the model. Many of the fairness deﬁnitions are based on model outcomes or

on error rates (the gap between true and/or false positive rates) that are associated with different

subgroups speciﬁed by a protected attribute. The goal is to reduce the difference between these error

rates across relevant subgroups. For example, average odds difference [

] is a measure signifying

equalized odds and is given by the sum of the differences in both true positive and false positive rates

between two groups, scaled by a factor of 0.5. Equality of opportunity and demographic parity [

]

Preprint. Under review.

arXiv:2210.04995v1 [cs.LG] 10 Oct 2022

are also popular deﬁnitions of fairness. Recently, fairness in terms of a gap of recourse has been

proposed, where recourse is deﬁned as the ability to obtain a positive outcome from the model [

While the suitability of a fairness measure is application dependent [

], demographic parity and

equalized odds remain the most popularly used, and the need for recourse gap-based fairness is being

increasingly recognized [18].

However, static models can encounter drift once deployed, as the statistical properties of real data

often change over time. This can lead to deteriorating performance. Model drift can occur when the

properties of the target variable change (concept drift) or when the input data distribution changes, or

both. The performance of models has largely been measured through accuracy-based metrics such

as misclassiﬁcation rates, F-score or AUC. [

]. However, a model trained in the past and found

to be fair at training time may act unfairly for data in the present. Addressing drift with respect to

fairness in addition to accuracy has remained largely unexplored though it is an important aspect of

trustworthy AI in practice.

Explainability of individual model outcomes is another principal concern for trustworthy ML. Among

many methods of explanations in terms of feature attribution, [

], the SHAP approach based on Shap-

ley values is particularly popular as it enjoys several axiomatic guarantees [21]. While computation

of SHAP values is fast for linear and tree-based models, it can be very slow for neural networks

and several other model types, especially when the data has a large numbers of features or when a

large number of explanations are required [

]. This poses a barrier to deployments that demand fast

explanations in real-time, production settings.

In this paper, we address these fairness, data/model drift, and explainability concerns by proposing

FEAMOE: Fair, Explainable and Adaptive Mixture of Experts, an incrementally grown mixture of

experts (MOE) with fairness constraints. In the standard mixture of experts setup, each expert is

a machine learning model, and so is the gating network. The gating network learns to assign an

input-dependent weight

gu(x)

to the

uth

expert for input

, and the ﬁnal output of the model is a

weighted combination of the outputs of each expert. Hence, each expert contributes differently for

every data point towards the ﬁnal outcome, which is a key difference from standard ensembles.

Many types of MOE’s exist in the literature [

] - the architecture is not standard. For FEAMOE, we

chose this family, with some novel modiﬁcations described later, for three main reasons: 1) Suitable

regularization penalties that promote fairness can be readily incorporated into the loss function. 2)

Online learning is possible, so changes in the data can be tracked. Crucially, since localized changes

in data distribution post-deployment may impact only one or a few experts, the other experts may not

need to be adjusted, making the experts localized and only loosely coupled. This allows for handling

drift and avoiding catastrophic forgetting, which is a prime concern in widely used neural network

models [

]. 3) Simpler models can be used to ﬁt a more complex problem in the mixture of experts,

as each model needs to ﬁt well in only a limited part of the input space. In particular, even linear

models, which provide very fast SHAP explanations, can be used. The overall mixture of experts,

even with such simple base models (the "experts") often has predictive power that is comparable to a

single complex model such as a neural network, as shown by our experiments as well as in many

previous studies [40].

A motivating toy example of why FEAMOE is needed and how it works is shown in Figure 1.

Consider a linear binary classiﬁer (1a) that has perfect accuracy. The colors represent the ground

truth labels, and green is the positive (desired) class label. The circles are the privileged group and

diamonds are the underprivileged group. As can be seen in the ﬁgure, more diamonds receive a

negative outcome and more circles receive a positive outcome. Consider new data that arrives for

predictions. This classiﬁer (1b) not only misclassiﬁes individuals but also gives more underprivileged

individuals that were actually in the positive class a negative outcome, hence inducing bias with

respect to equalized odds. There is drift with respect to accuracy and fairness. A more complex

model (1c) such as a neural network, if retrained, may handle some of these concerns but would be

less explainable.

FEAMOE can address these imperative concerns, as shown in 1d. Trained in an online manner, a

new linear model is added (i.e., an expert) once the new data arrives. The gating network dictates

which region each expert operates in (shown by the blue and pink colors), and FEAMOE is able

to adapt automatically with respect to accuracy and fairness. This dynamic framework enables the

overall model to be fairer, adjust to drift, maintain accuracy, while also remaining explainable since

the decision boundary is locally linear.

(a) (b) (c) (d)

Figure 1: A toy example demonstrating the need and use of FEAMOE. The color of every datapoint

corresponds to the original class label. Diamonds represent the underprivileged group and circles

represent the privileged group. (a) Represents a perfectly accurate linear classiﬁer, (b) represents the

same classiﬁer mis-classifying new data points and inducing bias (drift), (c) represents an alternate

non-linear model that corrects for drift but has a complex decision boundary and (d) represents

FEAMOE where the blue and pink regions show the regions of operation for each of the two experts,

separated by the gating network

We show how three fairness constraints–demographic parity, equalized odds, and burden-based

fairness–can be incorporated into the mixture of experts training procedure in order to encourage

ﬁtting fairer models (according to these measures). We use these three popular fairness measures as

illustrative examples to demonstrate the effectiveness of FEAMOE, but our method can be adapted to

incorporate other fairness constraints as well. We then describe a new algorithm for training to account

for drift, where the drift in question can be due to accuracy or fairness. We show experimentally that

by using a set of logistic regression experts, the accuracy of the mixture is comparable to using a

complex model like a neural network. Additionally, we show we can efﬁciently compute Shapley

value explanations when explanations for every individual expert can be computed quickly. To the

best of our knowledge, this is the ﬁrst work that addresses the problem of drift with respect to fairness

in a large-scale real world dataset. We then introduce a framework that can ﬂexibly adapt to drifts in

both fairness and accuracy with the added beneﬁt of delivering explanations quickly, while comparing

to the less explainable neural network model class trained in online mode.

The key contributions of this work are: a mixture of experts framework that can incorporate multiple

fairness constraints, a method to handle drift, where drift can be with respect to accuracy or fairness,

empirical evidence of the presence of drift with respect to fairness in a real-world, large-scale dataset,

a theoretical proof that FEAMOE leads to the generation of fast explanations given a suitable choice

of experts, and extensive experimentation on three datasets to show that our method has predictive

performance similar to neural networks while being fairer, handling different types of drift, and

generating faster explanations.

2 Related Work

The mixture of experts (MOE) [

] represent a class of co-operative ensemble models; detailed

surveys on their design and use can be found in [

] and [

]. Very recently, the deep learning

community has started recognizing and leveraging several advantageous properties that MOE’s have

for efﬁcient design of complex, multi-purpose learners [

]. This paper contributes to this expanding

literature by proposing a new algorithm to train this model class to account for both fairness and drift,

and by also adding an explainability module.

Fairness in machine learning is a growing ﬁeld of research [

]. Mitigating biases in models can

be done through pre-processing, in-processing, or post-processing techniques. A description of

these techniques can be found in [

]. In-processing techniques for fairness have been gaining

traction [

]. However, there is limited work on investigating the usefulness of ensemble

models in dealing with biases. [

] show that an ensemble of fair classiﬁers is guaranteed to be

fair for several different measures of fairness, an ensemble of unfair classiﬁers can still achieve

fair outcomes, and an ensemble of classiﬁers can achieve better accuracy-fairness trade-offs than a

single classiﬁer. However, they neither provide experimental evidence nor discuss speciﬁc methods

to incorporate fairness into ensemble learning. [

] develop a method to learn to defer in the case

of unfair predictions. [

] use an AdaBoost framework to build a fairer model. [

] use adaptive

random forest classiﬁers to account for fairness in online learning, only considering the statistical

parity deﬁnition of fairness.

Accounting for drift is a widely explored problem, and is now appearing in commercial products

as well (e.g. model monitoring is a key part of MLOPs) as ML solutions get deployed in business

environments. Details on many such approaches can be found in [

]. Among these approaches,

the one that comes closest to ours is [

] which uses a committee of decision trees to account for drift.

However, ensuring fairness in the presence of drift remains an open problem. [

] is a very recent

work on achieving a fairer model by building a set of classiﬁers in the presence of prior distribution

shifts. The method is built for a shift between the training and test distributions, and not for online

learning.

There are many ways to explain a machine learning model [

]. In this paper, we focus on Shapley

values-based explanations, which are widely used in practical applications [

]. [

] propose the

computation of Shapley values for tree ensembles, which is a faster way to get Shapley values than

through the more broadly applicable method, KernelShap [

]. We show that in FEAMOE, the Shap

values for the overall model are just a data-dependent linear combination of the values from individual

experts. Thus the mixture approach does not add any signiﬁcant complexity to the computation of

feature attribution scores.

3 Theory

We ﬁrst summarize the original mixture of experts framework and then describe the addition of

fairness constraints. Then, we introduce the algorithm to detect and mitigate data drift when the data

input is sequential (online learning). Thereafter, we show how using the proposed mixture of experts

architecture leads to computing faster Shapley value explanations for the overall non-linear model.

Mixture of Experts (MoE) [

] is a technique where multiple experts (learners) can be used to

softly divide the problem space into regions. A gating network decides which expert to weigh most

heavily for each input region. Learning thus consists of the following: 1) learning the parameters of

individual learners and 2) learning the parameters of the gating network. Both the gating network

and every expert have access to the input

. The gating network has one output

for every expert

. The output vector is the weighted (by the gating network outputs) mean of the expert outputs:

y(x) = Pm

i=1 gi(x)yi(x)

. Consistent with [

], the error associated with training the mixture of

experts for case

for an accurate prediction is given by:

acc =−log Pigj

−1

2||dj−yj

i||2

,where

is the output vector of expert

on case

is the proportional contribution of expert

to the

combined output vector, and djis the desired output vector.

3.1 Fairness Constraints

In this paper, we incorporate three diverse fairness deﬁnitions into the mixture of experts framework:

demographic parity only depends on the model outcome, equalized odds is conditioned on the

ground-truth label, and burden-based fairness depends on the distance of the input to the boundary.

These three popular deﬁnitions have been chosen as illustrative metrics; our approach can be readily

extended to several other fairness metrics as well.

For simplicity, we consider a binary classiﬁcation setting with a binary protected attribute (our

approach readily extends to multi-class and multi-protected attribute problems, where a protected

attribute is a feature such as race or gender). Let

i= 1

be the positive outcome. Let

A= 0

and

A= 1

represent the underprivileged and privileged protected attribute groups, respectively. For a

given dataset

, let

Dad

represent all individuals that belong to the protected attribute group

and

original class label d.

Statistical parity difference (SPD), which is a measure of demographic parity, measures the difference

between the probability of getting a positive outcome between protected attribute groups [

Let

be the set of individuals in the underprivileged group and

be the set of individuals in

the privileged group. Inspired by [

], the associated penalty for demographic parity for case

is:

SP D = [j∈D0](1 −Pigiyj

i) + [j∈D1](Pigiyj

i).

The idea behind this term is that

individuals belonging to the underprivileged group predicted as getting a negative outcome are

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FEAMOE:Fair,ExplainableandAdaptiveMixtureofExpertsShubhamSharmaUniversityofTexasatAustinshubham_sharma@utexas.eduJetteHendersonCognitiveScalejhenderson@cognitivescale.comJoydeepGhoshUniversityofTexasatAustinjghosh@utexas.eduAbstractThreekeypropertiesthataredesiredoftrustworthymachinelearningmodelsde...

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