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Shapley value in convolutional neural networks
(CNNs): A Comparative Study
Seyedamir Shobeiri
Department of Computer Science, Islamic Azad University of Zanjan, Zanjan, Iran.
seyedamir.shobeiri@iauz.ac.ir
Mojtaba Aajami
Department of Computer Science, Islamic Azad University of Zanjan, Zanjan, Iran.
aajami@iauz.ac.ir
Abstract—Deep learning models are in dire need of
training data. This need can be addressed by
encouraging data holders to contribute their data
for training purpose. Data valuation is a mechanism
that assigns a value reflecting a number to each data
instances. The SHAP Value is a method for assigning
payouts to players of coalition game depending on
their contribution to the total payout that entails
many criteria for the notion of data value. In this
paper, the value of the SHAP parameter is calculated
in different convolutional neural network for
varieties of image datasets. Calculated SHAP value
for each data instance shows whether data is high
value or low value and it is different in each model.
In other words, if you have an image in the VGG
model and it is high value, necessarily, it is not high
value in ResNet model. The results show that the
value of data varies in each dataset and model.
Keywords— Deep learning, SHAP Value.
I. INTRODUCTION
A computer program is said to learn from
experience E with respect to some class of tasks
T and performance measure P, if its
performance at tasks in T, as measured by P,
improves with experience E. The machine
learning can be split into different classes of
problems, Supervised learning and
Unsupervised learning.In supervised learning,
these algorithms, also called classifiers, receive
data that has already been labeled. In fact, the
data sent to the classification algorithms tells
these algorithms which category each data
should be placed in.
We do not tell the algorithm which category
each data should fit into. In fact, we have no
presumption about what category or group the
existing data falls into, and the algorithm
automatically detects the data classification.
This is why these types of algorithms are called
unsupervised learning algorithms.
The third type of algorithm, which can
perhaps be classified as unsupervised
algorithms, is a group called reinforced learning.
In this type of algorithm, a machine (actually its
controller program) is trained to make a specific
decision, and the machine is based on its
current position (set of available variables) and
permissible actions (e.g. moving forward,
moving Back and forth…) makes a decision that
for the first time, this decision can be completely
random and for each action or behavior that
occurs, the system gives him a points from this
feedback , The machine realizes whether it has
made the right decision or not to repeat the
same action the next time in that situation or try
another action and behavior.
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Fig. 1 Machine learning overview.
Deep Learning refers to a machine learning
technique that establish artificial neural networks
(ANNs) to imitate the structure and function of
the human brain. Indeed, an artificial neural
network, or neural network (NN), is a collection
of connected computational units or nodes
called neurons arranged in multiple
computational layers that map a data input into a
desired output. Each neuron applies a linear
function to its inputs that sums up the products
of weights and inputs. Subsequently, the output
of this function is passed through an activation
function. NN generates the desired output via
feed-forward data flow and then updates the
weights of each neuron by backpropagation of
errors during the training phase.
Fig. 2 Neural Network Overview.
In general, according to the employed
NN architecture supervised deep learning can
be categorized to the Recurrent neural networks
(RNN) and Convolutional neural networks
(CNN). RNN is a type of artificial neural network
commonly used in speech recognition and
natural language processing. Recurrent neural
networks recognize data's sequential
characteristics and use patterns to predict the
next likely scenario. CNN is a type of artificial
neural network used in image recognition and
processing that is specifically designed to
process pixel data.
A Recurrent Neural Network is a type of
neural network that contains loops, allowing
information to be stored within the network. In
short, Recurrent Neural Networks use their
reasoning from previous experiences to inform
the upcoming events. Recurrent models are
valuable in their ability to sequence vectors,
which opens up the API to performing more
complicated tasks.
Convolutional neural network, is a deep
learning neural network designed for processing
structured arrays of data such as images.
Convolutional neural networks are widely used
in computer vision and have become the state of
the art for many visual applications such as
image classification, and have also found
success in natural language processing for text
classification.CNNs are very good at picking up
on patterns in the input image, such as lines,
gradients, circles, or even eyes and faces. It is
this property that makes convolutional neural
networks so powerful for computer vision. Unlike
earlier computer vision algorithms, convolutional
neural networks can operate directly on a raw
image and do not need any preprocessing.A
convolutional neural network is a feed-forward
neural network, often with up to 20 or 30 layers.
The power of a convolutional neural network
comes from a special kind of layer called the
convolutional layer.Convolutional neural
networks contain many convolutional layers
stacked on top of each other, each one capable
of recognizing more sophisticated shapes. With
three or four convolutional layers it is possible to
recognize handwritten digits and with 25 layers it
is possible to distinguish human faces.The
usage of convolutional layers in a convolutional
neural network mirrors the structure of the
human visual cortex, where a series of layers
process an incoming image and identify
progressively more complex features.The
architecture of a convolutional neural network is
a multi-layered feed-forward neural network,
made by stacking many hidden layers on top of
each other in sequence. It is this sequential
design that allows convolutional neural networks
to learn hierarchical features. The hidden layers
are typically convolutional layers followed by
activation layers, some of them followed by
pooling layers.A simple convolutional neural
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network that aids understanding of the core
design principles is the early convolutional
neural network LeNet-5, published by Yann
LeCun in 1998. LeNet is capable of recognizing
handwritten characters.
Fig. 3 Convolutional neural networks (CNN)Overview.
Machine learning models in general and
deep learning in particular need to be trained
with a wide variety of data in order to have
acceptable performance. Hence there is a high
demand from developers of machine learning
models for training data. On the other hand, this
data is owned by sectors that often do not
voluntarily provide their data to model
developers. In addition, we are interested in
using data to training a model that will improve
the efficiency of the model. Given this, there is a
need for a mechanism that can evaluate the
data needed and used to training the model. By
using this method to provide incentives to data
owners to share their data or to evaluate the
data that is available for free before using it for
training in terms of quality. In the seminal work,
a mechanism for data valuation is provided.
Inspired by Shapley Value method, this
mechanism has presented a formula that can be
used to numerically express the value of a
specific data in improving the performance of a
specific model. In this article, we have selected
several famous CNN models that are widely
used in various image recognition applications.
we have calculated Shapley Value for two
datasets, ImageNet and 10 Monkey Species, in
each of these models. The rest of paper is
organized as follows. Section II describes the
architecture of several well-known CNNs.
Fig. 4 NN architecture supervised deep learning Overview.
II. prolific CNN architectures
This paper seeks to empirically establish a
correspondence between the shapely value and
the components of a CNN based learning
systems including model, training data set. For
this purpose, we selected some CNNs as the
representatives of the models that are widely
used in practice.
Fig. 5 vgg16 architecture.
Fixed size 224 x 224 RGB image is input of
cov1 layer. The image through a
convolutional.3*3 layers, which is the smallest
size to capture the notion of left/right, up/down,
center. it also utilizes 1×1 convolution filters,
which as a linear transformation of the input
channels. The convolution stride is fixed to 1
pixel; the spatial padding of convolution layer
input is such that the spatial resolution is
preserved after convolution, i.e., the padding is
1-pixel for 3×3 convolution layers. Spatial
pooling is carried out by five max-pooling layers,
which follow some of the convolution. Max-
pooling is performed over a 2×2-pixel window,
with stride 2. Three Fully-Connected (FC) layers
follow a stack of convolutional layers (which has
a different depth in different architectures): the
first two have 4096 channels each, the third
performs 1000-way ILSVRC classification and
thus contains 1000 channels .The final layer is
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the soft-max layer. The configuration of the fully
connected layers is the same in all networks.
Fig. 6 ResNet50 architecture.
A convolution with a kernel size of 7 * 7 and
64 different kernels all with a stride of size 2
giving us 1 layer. Then we observe max pooling
with a stride size of 2.In the next convolution
there is a 1 * 1,64 kernel following this a 3 * 3,64
kernel and at last a 1 * 1,256 kernel, These
three layers are repeated in total 3 time so
giving us 9 layers in this step.Next step,we
observe kernel of 1 * 1,128 after that a kernel of
3 * 3,128 and at last a kernel of 1 * 1,512 this
step was repeated 4 time so giving us 12 layers
in this step.so there is a kernal of 1 * 1,256 and
2 more kernels with 3 * 3,256 and 1 * 1,1024
and this is repeated 6 time giving us a total of 18
layers.again a 1 * 1,512 kernel with two more of
3 * 3,512 and 1 * 1,2048 and this was repeated
3 times giving us a total of 9 layers. Finally, we
do an average pool and end it with a fully
connected layer consist of 1000 nodes and at
the end a Softmax function so this gives us 1
layer.Actually, we ignore activation functions and
the max/ average pooling layers.as a result, it
gives us a 1 + 9 + 12 + 18 + 9 + 1 = 50 layers
Deep CNN.
Fig. 7 MobileNetV2 architecture.
MobileNet-V2 is one of the efficient models
from the MobileNet group. Two types of blocks
are in the MobileNet-V2.one of them is residual
block with stride of 1. Other one is block with
stride of 2 for downsizing. There are three layers
for two types of blocks.1*1 Convolution with
ReLU6 is the first layer. Depthwise convolution
is second layer. 1*1 convolution but without any
non-linearity is third layer. t is expansion factor
and t=6 for all main experiments. internal output
would get 64×t=64×6=384 channels if the input
got 64 channels.
Fig. 8 MobileNet architecture.
MobileNet is a simple architecture. it
uses depthwise divisible convolutions to build
lightweight deep CNNs and provides a model for
embedded vision applications and mobile.As
shown in Figure 8 ,MobileNet structure is
depthwise divisible filters. Depthwise divisible
convolution filters are composed of depthwise
convolution filters and point convolution filters.
The depthwise convolution filter performs a
single convolution on each input channel, and
the point convolution filter combines the output
of depthwise convolution linearly with 1 ∗ 1
convolutions.
Fig. 9 InceptionV3 architecture.
Inception-v3 is a CNN with 48 layers for help
in image, and start as a module of GoogleNet.
The third edition of Google's Inception CNN is
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Inception-V3, at first, it introduced for the
ImageNet Recognition Challenge. Inception
assists classification of objects in the computer
vision.
Fig. 10 EfficientNet B0 architecture.
EfficientNet-b0 is a CNN that is trained on
more than a million images from the ImageNet
database. The model can classify images into
1000 object categories, such as camera, boat,
bird. So, the network learned rich features. The
input of network is 224*224.EfficientNet-B0 the
developed by AutoML MNAS.
Fig. 11 DenseNet169 architecture.
III. Shapley Value
Fig. 12 Shapley Value example.
Shap Value performs the equitable data
valuation in supervised machine learning. For a
given set of training data points D and a
performance metric, the “Shap Value” value
of a data point xi ∈ D is defined as:
Where V(S)is the performance of the
model trained on subset S of the data. V(S)is the
prediction accuracy on the validation set.
Intuitively, the Shapley value of a data point is a
weighted average of its marginal contribution to
subsets of the rest of the dataset. As a result, it
can be used as a measure of data quality: a
data point with a high Shapley value is one that
improves the model’s performance if we add it to
most subsets of the data, while a data point with
a negative value on average hurts the
performance of the model. Exact computation of
Eq. requires an exponential number of
computations in the size of the dataset, which is
infeasible in most realistic settings. In fact, High
value indicate high quality of image and correct
label while low value represents low quality of
image and incorrect label.
Finally, SHAP Value has three outputs,
which are value, growth rate, and main data,
respectively. Value: An array that each cell
represents a pixel, each cell of the array
contains another array that contains three cells
and represents the RGB effect as shown: Value
= [ [ R, G, B], [ R, G, B], [ R, G, B], …] and the
growth rate, which is a base number, and our
main data, which is the original values of our
image. How to calculate the value of an image is
as follows:
According to the above formula i = 0 because
the array cells start from zero and N is the
number of pixels, R represents the effect of red,
G represents the effect of green, B represents
the effect of blue, which indicates each of these
pixel colors. How effective the image has been
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in our model is that the sum of the effects of red,
green, and blue with the base, which represents
the growth rate, reflects the value of image.
next, two datasets are tested that whether the
value of an image is always the same or
depends on another factor.
IV. Evolution and results
Due to the large volume of images, we
randomly selected 50 images from each dataset
and created two datasets smaller than ImageNet
and 10Moneky Species. Images in the datasets
are numbered from 0 to 49, and to refer to each
image, Refer to the relevant number. In this
article, we use the first formula, we obtained the
value of each color of each pixel (RGB), and
then use the second formula, we obtained the
value of each image on different Convolutional
neural networks, include VGG16, ResNet50,
DenseNet169, MobileNet, EfficientNetB0,
MobileNetV2. The table below has two rows that
represent high quality and low-quality images
and six columns that represent different
architectures. The numbers you see in the
tables indicate the number of images in each
dataset. The numbers in the first row indicate
the high-quality data of datasets in the
architecture and the second row indicates low
quality data in the same architecture.
Table 1: ImageNet Datasets
VGG16
ResNet50
DenseNet169
MobileNet
EfficientNetB0
MobileNetV2
High
Value
3
3
3
3
11
31
Low
Value
34
25
18
32
25
18
Table 2: 10 Monkey Species Datasets
VGG16
ResNet50
DenseNet169
MobileNet
EfficientNetB0
MobileNetV2
High
Value
34
30
19
25
32
31
Low
Value
46
43
36
38
46
37
V. Conclusions
Training data is used for training deep
learning models. This need can be addressed by
encouraging data holders to contribute their data
for training purpose. We need a method for
numerical evaluation of data that the Data
valuation method is very efficient
. The Shap
Value is a way to evaluate each data relative to
its contribution to deep learning models.
According to the above experiments, we realized
that the value of each image is very different
from the network architecture and the value of
each image is directly related to the architecture
of that network.
REFERENCES
Ghorbani, A., & Zou, J. (2019, May). Data
shapley: Equitable valuation of data for
machine learning. In International Conference
on Machine Learning (pp. 2242-2251). PMLR.
Lundberg, S. (2018). SHAP documentation.
SHAP. https://shap.readthedocs.io/en/latest/i
ndex.html
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