arXiv:1705.07874v2 [] 25 Nov 2017

A Unified Approach to Interpreting Model
Predictions
Scott M. Lundberg
Paul G. Allen School of Computer Science
University of Washington
Seattle, WA 98105
slund1@cs.washington.edu

Su-In Lee
Paul G. Allen School of Computer Science
Department of Genome Sciences
University of Washington
Seattle, WA 98105
suinlee@cs.washington.edu

Abstract
Understanding why a model makes a certain prediction can be as crucial as the
prediction’s accuracy in many applications. However, the highest accuracy for large
modern datasets is often achieved by complex models that even experts struggle to
interpret, such as ensemble or deep learning models, creating a tension between
accuracy and interpretability. In response, various methods have recently been
proposed to help users interpret the predictions of complex models, but it is often
unclear how these methods are related and when one method is preferable over
another. To address this problem, we present a unified framework for interpreting
predictions, SHAP (SHapley Additive exPlanations). SHAP assigns each feature
an importance value for a particular prediction. Its novel components include: (1)
the identification of a new class of additive feature importance measures, and (2)
theoretical results showing there is a unique solution in this class with a set of
desirable properties. The new class unifies six existing methods, notable because
several recent methods in the class lack the proposed desirable properties. Based
on insights from this unification, we present new methods that show improved
computational performance and/or better consistency with human intuition than
previous approaches.

1

Introduction

The ability to correctly interpret a prediction model’s output is extremely important. It engenders
appropriate user trust, provides insight into how a model may be improved, and supports understanding
of the process being modeled. In some applications, simple models (e.g., linear models) are often
preferred for their ease of interpretation, even if they may be less accurate than complex ones.
However, the growing availability of big data has increased the benefits of using complex models, so
bringing to the forefront the trade-off between accuracy and interpretability of a model’s output. A
wide variety of different methods have been recently proposed to address this issue [5, 8, 9, 3, 4, 1].
But an understanding of how these methods relate and when one method is preferable to another is
still lacking.
Here, we present a novel unified approach to interpreting model predictions.1 Our approach leads to
three potentially surprising results that bring clarity to the growing space of methods:
1. We introduce the perspective of viewing any explanation of a model’s prediction as a model itself,
which we term the explanation model. This lets us define the class of additive feature attribution
methods (Section 2), which unifies six current methods.
1

https://github.com/slundberg/shap

31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA.

2. We then show that game theory results guaranteeing a unique solution apply to the entire class of
additive feature attribution methods (Section 3) and propose SHAP values as a unified measure of
feature importance that various methods approximate (Section 4).
3. We propose new SHAP value estimation methods and demonstrate that they are better aligned
with human intuition as measured by user studies and more effectually discriminate among model
output classes than several existing methods (Section 5).

2

Additive Feature Attribution Methods

The best explanation of a simple model is the model itself; it perfectly represents itself and is easy to
understand. For complex models, such as ensemble methods or deep networks, we cannot use the
original model as its own best explanation because it is not easy to understand. Instead, we must use a
simpler explanation model, which we define as any interpretable approximation of the original model.
We show below that six current explanation methods from the literature all use the same explanation
model. This previously unappreciated unity has interesting implications, which we describe in later
sections.
Let f be the original prediction model to be explained and g the explanation model. Here, we focus
on local methods designed to explain a prediction f (x) based on a single input x, as proposed in
LIME [5]. Explanation models often use simplified inputs x0 that map to the original inputs through a
mapping function x = hx (x0 ). Local methods try to ensure g(z 0 ) ≈ f (hx (z 0 )) whenever z 0 ≈ x0 .
(Note that hx (x0 ) = x even though x0 may contain less information than x because hx is specific to
the current input x.)
Definition 1 Additive feature attribution methods have an explanation model that is a linear
function of binary variables:
g(z 0 ) = φ0 +

M
X

φi zi0 ,

(1)

i=1

where z 0 ∈ {0, 1}M , M is the number of simplified input features, and φi ∈ R.
Methods with explanation models matching Definition 1 attribute an effect φi to each feature, and
summing the effects of all feature attributions approximates the output f (x) of the original model.
Many current methods match Definition 1, several of which are discussed below.
2.1

LIME

The LIME method interprets individual model predictions based on locally approximating the model
around a given prediction [5]. The local linear explanation model that LIME uses adheres to Equation
1 exactly and is thus an additive feature attribution method. LIME refers to simplified inputs x0 as
“interpretable inputs,” and the mapping x = hx (x0 ) converts a binary vector of interpretable inputs
into the original input space. Different types of hx mappings are used for different input spaces. For
bag of words text features, hx converts a vector of 1’s or 0’s (present or not) into the original word
count if the simplified input is one, or zero if the simplified input is zero. For images, hx treats the
image as a set of super pixels; it then maps 1 to leaving the super pixel as its original value and 0
to replacing the super pixel with an average of neighboring pixels (this is meant to represent being
missing).
To find φ, LIME minimizes the following objective function:
ξ = arg min L(f, g, πx0 ) + Ω(g).

(2)

g∈G

Faithfulness of the explanation model g(z 0 ) to the original model f (hx (z 0 )) is enforced through
the loss L over a set of samples in the simplified input space weighted by the local kernel πx0 . Ω
penalizes the complexity of g. Since in LIME g follows Equation 1 and L is a squared loss, Equation
2 can be solved using penalized linear regression.
2

2.2

DeepLIFT

DeepLIFT was recently proposed as a recursive prediction explanation method for deep learning
[8, 7]. It attributes to each input xi a value C∆xi ∆y that represents the effect of that input being set
to a reference value as opposed to its original value. This means that for DeepLIFT, the mapping
x = hx (x0 ) converts binary values into the original inputs, where 1 indicates that an input takes its
original value, and 0 indicates that it takes the reference value. The reference value, though chosen
by the user, represents a typical uninformative background value for the feature.
DeepLIFT uses a "summation-to-delta" property that states:
n
X

C∆xi ∆o = ∆o,

(3)

i=1

where o = f (x) is the model output, ∆o = f (x) − f (r), ∆xi = xi − ri , and r is the reference input.
If we let φi = C∆xi ∆o and φ0 = f (r), then DeepLIFT’s explanation model matches Equation 1 and
is thus another additive feature attribution method.
2.3

Layer-Wise Relevance Propagation

The layer-wise relevance propagation method interprets the predictions of deep networks [1]. As
noted by Shrikumar et al., this menthod is equivalent to DeepLIFT with the reference activations of all
neurons fixed to zero. Thus, x = hx (x0 ) converts binary values into the original input space, where
1 means that an input takes its original value, and 0 means an input takes the 0 value. Layer-wise
relevance propagation’s explanation model, like DeepLIFT’s, matches Equation 1.
2.4

Classic Shapley Value Estimation

Three previous methods use classic equations from cooperative game theory to compute explanations
of model predictions: Shapley regression values [4], Shapley sampling values [9], and Quantitative
Input Influence [3].
Shapley regression values are feature importances for linear models in the presence of multicollinearity.
This method requires retraining the model on all feature subsets S ⊆ F , where F is the set of all
features. It assigns an importance value to each feature that represents the effect on the model
prediction of including that feature. To compute this effect, a model fS∪{i} is trained with that feature
present, and another model fS is trained with the feature withheld. Then, predictions from the two
models are compared on the current input fS∪{i} (xS∪{i} ) − fS (xS ), where xS represents the values
of the input features in the set S. Since the effect of withholding a feature depends on other features
in the model, the preceding differences are computed for all possible subsets S ⊆ F \ {i}. The
Shapley values are then computed and used as feature attributions. They are a weighted average of all
possible differences:
φi =

X
S⊆F \{i}


|S|!(|F | − |S| − 1)! 
fS∪{i} (xS∪{i} ) − fS (xS ) .
|F |!

(4)

For Shapley regression values, hx maps 1 or 0 to the original input space, where 1 indicates the input
is included in the model, and 0 indicates exclusion from the model. If we let φ0 = f∅ (∅), then the
Shapley regression values match Equation 1 and are hence an additive feature attribution method.
Shapley sampling values are meant to explain any model by: (1) applying sampling approximations
to Equation 4, and (2) approximating the effect of removing a variable from the model by integrating
over samples from the training dataset. This eliminates the need to retrain the model and allows fewer
than 2|F | differences to be computed. Since the explanation model form of Shapley sampling values
is the same as that for Shapley regression values, it is also an additive feature attribution method.
Quantitative input influence is a broader framework that addresses more than feature attributions.
However, as part of its method it independently proposes a sampling approximation to Shapley values
that is nearly identical to Shapley sampling values. It is thus another additive feature attribution
method.
3

3

Simple Properties Uniquely Determine Additive Feature Attributions

A surprising attribute of the class of additive feature attribution methods is the presence of a single
unique solution in this class with three desirable properties (described below). While these properties
are familiar to the classical Shapley value estimation methods, they were previously unknown for
other additive feature attribution methods.
The first desirable property is local accuracy. When approximating the original model f for a specific
input x, local accuracy requires the explanation model to at least match the output of f for the
simplified input x0 (which corresponds to the original input x).
Property 1 (Local accuracy)
f (x) = g(x0 ) = φ0 +

M
X

φi x0i

(5)

i=1

The explanation model g(x0 ) matches the original model f (x) when x = hx (x0 ).
The second property is missingness. If the simplified inputs represent feature presence, then missingness requires features missing in the original input to have no impact. All of the methods described in
Section 2 obey the missingness property.
Property 2 (Missingness)

x0i = 0 =⇒ φi = 0

Missingness constrains features where

x0i

(6)

= 0 to have no attributed impact.

The third property is consistency. Consistency states that if a model changes so that some simplified
input’s contribution increases or stays the same regardless of the other inputs, that input’s attribution
should not decrease.
Property 3 (Consistency) Let fx (z 0 ) = f (hx (z 0 )) and z 0 \ i denote setting zi0 = 0. For any two
models f and f 0 , if
fx0 (z 0 ) − fx0 (z 0 \ i) ≥ fx (z 0 ) − fx (z 0 \ i)
(7)
for all inputs z 0 ∈ {0, 1}M , then φi (f 0 , x) ≥ φi (f, x).
Theorem 1 Only one possible explanation model g follows Definition 1 and satisfies Properties 1, 2,
and 3:
X |z 0 |!(M − |z 0 | − 1)!
φi (f, x) =
[fx (z 0 ) − fx (z 0 \ i)]
(8)
M
!
0
0
z ⊆x

0

where |z | is the number of non-zero entries in z 0 , and z 0 ⊆ x0 represents all z 0 vectors where the
non-zero entries are a subset of the non-zero entries in x0 .
Theorem 1 follows from combined cooperative game theory results, where the values φi are known
as Shapley values [6]. Young (1985) demonstrated that Shapley values are the only set of values
that satisfy three axioms similar to Property 1, Property 3, and a final property that we show to be
redundant in this setting (see Supplementary Material). Property 2 is required to adapt the Shapley
proofs to the class of additive feature attribution methods.
Under Properties 1-3, for a given simplified input mapping hx , Theorem 1 shows that there is only one
possible additive feature attribution method. This result implies that methods not based on Shapley
values violate local accuracy and/or consistency (methods in Section 2 already respect missingness).
The following section proposes a unified approach that improves previous methods, preventing them
from unintentionally violating Properties 1 and 3.

4

SHAP (SHapley Additive exPlanation) Values

We propose SHAP values as a unified measure of feature importance. These are the Shapley values
of a conditional expectation function of the original model; thus, they are the solution to Equation
4

Figure 1: SHAP (SHapley Additive exPlanation) values attribute to each feature the change in the
expected model prediction when conditioning on that feature. They explain how to get from the
base value E[f (z)] that would be predicted if we did not know any features to the current output
f (x). This diagram shows a single ordering. When the model is non-linear or the input features are
not independent, however, the order in which features are added to the expectation matters, and the
SHAP values arise from averaging the φi values across all possible orderings.
8, where fx (z 0 ) = f (hx (z 0 )) = E[f (z) | zS ], and S is the set of non-zero indexes in z 0 (Figure 1).
Based on Sections 2 and 3, SHAP values provide the unique additive feature importance measure that
adheres to Properties 1-3 and uses conditional expectations to define simplified inputs. Implicit in this
definition of SHAP values is a simplified input mapping, hx (z 0 ) = zS , where zS has missing values
for features not in the set S. Since most models cannot handle arbitrary patterns of missing input
values, we approximate f (zS ) with E[f (z) | zS ]. This definition of SHAP values is designed to
closely align with the Shapley regression, Shapley sampling, and quantitative input influence feature
attributions, while also allowing for connections with LIME, DeepLIFT, and layer-wise relevance
propagation.
The exact computation of SHAP values is challenging. However, by combining insights from current
additive feature attribution methods, we can approximate them. We describe two model-agnostic
approximation methods, one that is already known (Shapley sampling values) and another that is
novel (Kernel SHAP). We also describe four model-type-specific approximation methods, two of
which are novel (Max SHAP, Deep SHAP). When using these methods, feature independence and
model linearity are two optional assumptions simplifying the computation of the expected values
(note that S̄ is the set of features not in S):
f (hx (z 0 )) = E[f (z) | zS ]
= EzS̄ |zS [f (z)]

SHAP explanation model simplified input mapping
expectation over zS̄ | zS

(9)
(10)

assume feature independence (as in [9, 5, 7, 3])
assume model linearity

(11)
(12)

≈ EzS̄ [f (z)]
≈ f ([zS , E[zS̄ ]]).
4.1

Model-Agnostic Approximations

If we assume feature independence when approximating conditional expectations (Equation 11), as
in [9, 5, 7, 3], then SHAP values can be estimated directly using the Shapley sampling values method
[9] or equivalently the Quantitative Input Influence method [3]. These methods use a sampling
approximation of a permutation version of the classic Shapley value equations (Equation 8). Separate
sampling estimates are performed for each feature attribution. While reasonable to compute for a
small number of inputs, the Kernel SHAP method described next requires fewer evaluations of the
original model to obtain similar approximation accuracy (Section 5).
Kernel SHAP (Linear LIME + Shapley values)
Linear LIME uses a linear explanation model to locally approximate f , where local is measured in the
simplified binary input space. At first glance, the regression formulation of LIME in Equation 2 seems
very different from the classical Shapley value formulation of Equation 8. However, since linear
LIME is an additive feature attribution method, we know the Shapley values are the only possible
solution to Equation 2 that satisfies Properties 1-3 – local accuracy, missingness and consistency. A
natural question to pose is whether the solution to Equation 2 recovers these values. The answer
depends on the choice of loss function L, weighting kernel πx0 and regularization term Ω. The LIME
choices for these parameters are made heuristically; using these choices, Equation 2 does not recover
the Shapley values. One consequence is that local accuracy and/or consistency are violated, which in
turn leads to unintuitive behavior in certain circumstances (see Section 5).
5

Below we show how to avoid heuristically choosing the parameters in Equation 2 and how to find the
loss function L, weighting kernel πx0 , and regularization term Ω that recover the Shapley values.
Theorem 2 (Shapley kernel) Under Definition 1, the specific forms of πx0 , L, and Ω that make
solutions of Equation 2 consistent with Properties 1 through 3 are:
Ω(g) = 0,
(M − 1)
,
(M choose |z 0 |)|z 0 |(M − |z 0 |)
X

0
0 2
0
L(f, g, πx0 ) =
f (h−1
x (z )) − g(z ) πx0 (z ),
πx0 (z 0 ) =

z 0 ∈Z

where |z 0 | is the number of non-zero elements in z 0 .
The proof of Theorem 2 is shown in the Supplementary Material.
It is important to note that πx0 (z 0 ) = ∞ when |z 0 | ∈ {0, M }, which enforces φ0 = fx (∅) and f (x) =
PM
i=0 φi . In practice, these infinite weights can be avoided during optimization by analytically
eliminating two variables using these constraints.
Since g(z 0 ) in Theorem 2 is assumed to follow a linear form, and L is a squared loss, Equation 2
can still be solved using linear regression. As a consequence, the Shapley values from game theory
can be computed using weighted linear regression.2 Since LIME uses a simplified input mapping
that is equivalent to the approximation of the SHAP mapping given in Equation 12, this enables
regression-based, model-agnostic estimation of SHAP values. Jointly estimating all SHAP values
using regression provides better sample efficiency than the direct use of classical Shapley equations
(see Section 5).
The intuitive connection between linear regression and Shapley values is that Equation 8 is a difference
of means. Since the mean is also the best least squares point estimate for a set of data points, it is
natural to search for a weighting kernel that causes linear least squares regression to recapitulate
the Shapley values. This leads to a kernel that distinctly differs from previous heuristically chosen
kernels (Figure 2A).
4.2

Model-Specific Approximations

While Kernel SHAP improves the sample efficiency of model-agnostic estimations of SHAP values, by
restricting our attention to specific model types, we can develop faster model-specific approximation
methods.
Linear SHAP
For linear models, if we assume input feature independence (Equation 11), SHAP values can be
approximated directly from the model’s weight coefficients.
Corollary 1 (Linear SHAP) Given a linear model f (x) =

PM

j=1

wj xj + b: φ0 (f, x) = b and

φi (f, x) = wj (xj − E[xj ])
This follows from Theorem 2 and Equation 11, and it has been previously noted by Štrumbelj and
Kononenko [9].
Low-Order SHAP
Since linear regression using Theorem 2 has complexity O(2M + M 3 ), it is efficient for small values
of M if we choose an approximation of the conditional expectations (Equation 11 or 12).
2

During the preparation of this manuscript we discovered this parallels an equivalent constrained quadratic
minimization formulation of Shapley values proposed in econometrics [2].

6

(A)

(B)
hapley

f3

f1

f3

f2

f1

f2

Figure 2: (A) The Shapley kernel weighting is symmetric when all possible z 0 vectors are ordered
by cardinality there are 215 vectors in this example. This is distinctly different from previous
heuristically chosen kernels. (B) Compositional models such as deep neural networks are comprised
of many simple components. Given analytic solutions for the Shapley values of the components, fast
approximations for the full model can be made using DeepLIFT’s style of back-propagation.

Max SHAP
Using a permutation formulation of Shapley values, we can calculate the probability that each input
will increase the maximum value over every other input. Doing this on a sorted order of input values
lets us compute the Shapley values of a max function with M inputs in O(M 2 ) time instead of
O(M 2M ). See Supplementary Material for the full algorithm.
Deep SHAP (DeepLIFT + Shapley values)
While Kernel SHAP can be used on any model, including deep models, it is natural to ask whether
there is a way to leverage extra knowledge about the compositional nature of deep networks to improve
computational performance. We find an answer to this question through a previously unappreciated
connection between Shapley values and DeepLIFT [8]. If we interpret the reference value in Equation
3 as representing E[x] in Equation 12, then DeepLIFT approximates SHAP values assuming that
the input features are independent of one another and the deep model is linear. DeepLIFT uses a
linear composition rule, which is equivalent to linearizing the non-linear components of a neural
network. Its back-propagation rules defining how each component is linearized are intuitive but were
heuristically chosen. Since DeepLIFT is an additive feature attribution method that satisfies local
accuracy and missingness, we know that Shapley values represent the only attribution values that
satisfy consistency. This motivates our adapting DeepLIFT to become a compositional approximation
of SHAP values, leading to Deep SHAP.
Deep SHAP combines SHAP values computed for smaller components of the network into SHAP
values for the whole network. It does so by recursively passing DeepLIFT’s multipliers, now defined
in terms of SHAP values, backwards through the network as in Figure 2B:
φi (f3 , x)
xj − E[xj ]
φi (fj , y)
=
yi − E[yi ]

mxj f3 =
∀j∈{1,2} myi fj

myi f3 =

2
X

(13)
(14)

myi fj mxj f3

chain rule

(15)

linear approximation

(16)

j=1

φi (f3 , y) ≈ myi f3 (yi − E[yi ])

Since the SHAP values for the simple network components can be efficiently solved analytically
if they are linear, max pooling, or an activation function with just one input, this composition
rule enables a fast approximation of values for the whole model. Deep SHAP avoids the need to
heuristically choose ways to linearize components. Instead, it derives an effective linearization from
the SHAP values computed for each component. The max function offers one example where this
leads to improved attributions (see Section 5).
7

(A)

Feature importance

SHAP

Shapley sampling

LIME

True Shapley value

(B)

Dense original model

Sparse original model

Figure 3: Comparison of three additive feature attribution methods: Kernel SHAP (using a debiased
lasso), Shapley sampling values, and LIME (using the open source implementation). Feature
importance estimates are shown for one feature in two models as the number of evaluations of the
original model function increases. The 10th and 90th percentiles are shown for 200 replicate estimates
at each sample size. (A) A decision tree model using all 10 input features is explained for a single
input. (B) A decision tree using only 3 of 100 input features is explained for a single input.

5

Computational and User Study Experiments

We evaluated the benefits of SHAP values using the Kernel SHAP and Deep SHAP approximation
methods. First, we compared the computational efficiency and accuracy of Kernel SHAP vs. LIME
and Shapley sampling values. Second, we designed user studies to compare SHAP values with
alternative feature importance allocations represented by DeepLIFT and LIME. As might be expected,
SHAP values prove more consistent with human intuition than other methods that fail to meet
Properties 1-3 (Section 2). Finally, we use MNIST digit image classification to compare SHAP with
DeepLIFT and LIME.
5.1

Computational Efficiency

Theorem 2 connects Shapley values from game theory with weighted linear regression. Kernal SHAP
uses this connection to compute feature importance. This leads to more accurate estimates with fewer
evaluations of the original model than previous sampling-based estimates of Equation 8, particularly
when regularization is added to the linear model (Figure 3). Comparing Shapley sampling, SHAP, and
LIME on both dense and sparse decision tree models illustrates both the improved sample efficiency
of Kernel SHAP and that values from LIME can differ significantly from SHAP values that satisfy
local accuracy and consistency.
5.2

Consistency with Human Intuition

Theorem 1 provides a strong incentive for all additive feature attribution methods to use SHAP
values. Both LIME and DeepLIFT, as originally demonstrated, compute different feature importance
values. To validate the importance of Theorem 1, we compared explanations from LIME, DeepLIFT,
and SHAP with user explanations of simple models (using Amazon Mechanical Turk). Our testing
assumes that good model explanations should be consistent with explanations from humans who
understand that model.
We compared LIME, DeepLIFT, and SHAP with human explanations for two settings. The first
setting used a sickness score that was higher when only one of two symptoms was present (Figure 4A).
The second used a max allocation problem to which DeepLIFT can be applied. Participants were told
a short story about how three men made money based on the maximum score any of them achieved
(Figure 4B). In both cases, participants were asked to assign credit for the output (the sickness score
or money won) among the inputs (i.e., symptoms or players). We found a much stronger agreement
between human explanations and SHAP than with other methods. SHAP’s improved performance for
max functions addresses the open problem of max pooling functions in DeepLIFT [7].
5.3

Explaining Class Differences

As discussed in Section 4.2, DeepLIFT’s compositional approach suggests a compositional approximation of SHAP values (Deep SHAP). These insights, in turn, improve DeepLIFT, and a new version
8

(A)

(B)
Human
SHAP
LIME
Orig. DeepLIFT

Human
SHAP
LIME

Figure 4: Human feature impact estimates are shown as the most common explanation given among
30 (A) and 52 (B) random individuals, respectively. (A) Feature attributions for a model output value
(sickness score) of 2. The model output is 2 when fever and cough are both present, 5 when only
one of fever or cough is present, and 0 otherwise. (B) Attributions of profit among three men, given
according to the maximum number of questions any man got right. The first man got 5 questions
right, the second 4 questions, and the third got none right, so the profit is $5.

Orig. DeepLift

New DeepLift

SHAP

LIME

Explain 8 Explain 3

Masked

(B)
60
Change in log-odds

Input

(A)

50
40
30
20
Orig. DeepLift

New DeepLift

SHAP

LIME

Figure 5: Explaining the output of a convolutional network trained on the MNIST digit dataset. Orig.
DeepLIFT has no explicit Shapley approximations, while New DeepLIFT seeks to better approximate
Shapley values. (A) Red areas increase the probability of that class, and blue areas decrease the
probability. Masked removes pixels in order to go from 8 to 3. (B) The change in log odds when
masking over 20 random images supports the use of better estimates of SHAP values.
includes updates to better match Shapley values [7]. Figure 5 extends DeepLIFT’s convolutional
network example to highlight the increased performance of estimates that are closer to SHAP values.
The pre-trained model and Figure 5 example are the same as those used in [7], with inputs normalized
between 0 and 1. Two convolution layers and 2 dense layers are followed by a 10-way softmax
output layer. Both DeepLIFT versions explain a normalized version of the linear layer, while SHAP
(computed using Kernel SHAP) and LIME explain the model’s output. SHAP and LIME were both
run with 50k samples (Supplementary Figure 1); to improve performance, LIME was modified to use
single pixel segmentation over the digit pixels. To match [7], we masked 20% of the pixels chosen to
switch the predicted class from 8 to 3 according to the feature attribution given by each method.

6

Conclusion

The growing tension between the accuracy and interpretability of model predictions has motivated
the development of methods that help users interpret predictions. The SHAP framework identifies
the class of additive feature importance methods (which includes six previous methods) and shows
there is a unique solution in this class that adheres to desirable properties. The thread of unity that
SHAP weaves through the literature is an encouraging sign that common principles about model
interpretation can inform the development of future methods.
We presented several different estimation methods for SHAP values, along with proofs and experiments showing that these values are desirable. Promising next steps involve developing faster
model-type-specific estimation methods that make fewer assumptions, integrating work on estimating
interaction effects from game theory, and defining new explanation model classes.
9

Acknowledgements
This work was supported by a National Science Foundation (NSF) DBI-135589, NSF CAREER
DBI-155230, American Cancer Society 127332-RSG-15-097-01-TBG, National Institute of Health
(NIH) AG049196, and NSF Graduate Research Fellowship. We would like to thank Marco Ribeiro,
Erik Štrumbelj, Avanti Shrikumar, Yair Zick, the Lee Lab, and the NIPS reviewers for feedback that
has significantly improved this work.

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