In Artificial Intelligence, one of the most important issue concerns the necessity to understand why a particular prediction is chosen by a model from the considered input data. In this work, we propose a model, named Global Prediction Architecture, based on three layers (MultiLayerPerceptron, Closest Classes and Elements, and a third layer to combine them), where first layer produces both a partial prediction and features extraction useful for the second layer. We are interested in analyzing the behavior of the model both for accuracy and for explainability in terms of input data. We apply our study in the healthcare context of diabetes. Diabetes (diabetes mellitus) is a disease present when a person has a high blood sugar level for a long period. One import issue is related to the possibility to do prevention of the disease. We analyze the possibility to determine the diabetes risk in respect to daily lifestyle and health parameters, such as Body Mass Index, age, waist circumference, use of blood pressure medication, history of high blood glucose, physical activity, consumption of vegetables/fruits/berries, and family history of diabetes. We produce datasets randomly generated according to the rule named Finnish Diabetes Risk Score. This work aim to produce random and anonymized diabetes risk datasets, to test a model in terms of improving accuracy for the prediction of diabetes risk, and, most of all, to propose and test a method for explainability in the context of diabetes prediction, using an approach initially derived from Layer-Wise Relevance Propagation and Deep Taylor Decomposition.
ogy section reports the step followed in the research for level of the NN by a conservation rule:
ttpehrsiinstcowiuporarlskot.oluTotolisooalnsn. daDneadntavesinreovt nidrmoefinneinmttiosennutssseedscettciootiniomnopurlteelmipnoeernsttsthatnehde = ∑︁ ∑︀ (
In this section, we first briefly cite three chosen works n equals to the number of neurons in the lower level of about prediction in the context of diabetes. Then, we N; + = ||. Defining as the final output of the NN present some concepts about explainability, in particular for a particular input data, we have that [[ ] ] correfor LRP and DTD. sponds to the quantity of distributed from one node j
In [15], they use Pima Indian Diabetes (PID) dataset to one node i, where i is an input node for node j. [ ] and they test seven Machine Learning (ML) algorithms corresponds to the quantity of distributed on node i: for predictions related to diabetes, using WEKA tool too.
They obtain the best results by using Logistic Regression 1
(LR) and Support Vector Machine (SVM) for diabetes pre- [ ] = ∑︁ [[ ] ] (
In the general context of explainability, as basis for our 1 equals to the number of nodes in the higher level studying we are interested on LRP and DTD. In this sec- of node i, and n is the number of neurons in the lower tion, we review some of the concepts described in [5], [7], level of j (the same level of i). At the beginning, we have [18], [19], and [20]. In LRP, prediction back propagate [ ] = and = 1. By induction, there is a in the NN. Each propagation redistributes in the lower product structure with a backward propagation rule and the conservation of the output (redistribution on input nodes).
1 1 1 [ ] = ∑︁ [[ ] ] = ∑︁ [ ] = ∑︁ [ ] =
=1 =1
diabetes risk predictions and explainability for LRP and DTD. We selected a rule (FINDRISC) to produce random datasets. We defined our prediction model, named GPA, with three layers: MLP for partial prediction and features extraction, Closest Classes and Elements (CCE) for partial prediction, Weighted Sum (WS) for final prediction. CCE evaluates similarity between one unlabeled node and all labelled nodes, using extracted features. WS sums the two partial predictions, adequately weighted, to define the final prediction by argmax. We analyzed the best hyper-parameters, using GridSearchCV of scikit-learn tool too. We analyzed the test predictions comparing GPA accuracies against MLP accuracies and some WEKA algorithms accuracies. We defined explainability solution based on a forward DTD derived component for ifrst and implicitly third layer, and on weight (standard deviation) of extracted features (related to the training data) for second and implicitly third layer. We tested the explainability using a simplified MLP.
Four datasets are for prediction experiments (2500
elements for testing; 1000, 1500, and 2000 for training),
and other four are for explainability experiments (1750
elements for testing; 1000, 1250, and 1500 for training).
The rule identifies risk individuals, without laboratory
tests. It considers five risk levels in respect to score: very
low (
considered the dataset with 2000 elements and we analyzed in details both their data distribution and accuracy results, by using WEKA tool [2]. In Table 2 we can see accuracy results for the considered algorithms: J48, KStar, MLP, Naïve Bayes (NB), RandomTree (RT). We used 10fold cross-validation for the analysis.
MLP, second layer is CCE (it uses features extracted from
MLP), and third layer combines predictions of both MLP
and CCE. MLP have the following elements: dense, batch
normalization, activation–ReLU, dropout, dense, batch
normalization, activation–ReLU, dropout, dense, batch
normalization, activation–ReLU, dropout, dense,
activation–Softmax. CCE uses the features extracted from third
dense layer; for each testing node we implement this
algorithm:
• Calculate Euclidean distance between the
considered testing node and all training nodes
• Normalize these distances to [0,1]
• Using normalized distances, calculate Gaussian
kernel similarity between the considered testing
node and all training nodes:
, = − (,)2
2 2
(
The second definition uses the similarities between labels, because risk levels are orderable. In particular: np is the number of unlabeled nodes, is the right label for i node, () is the value of probability distribution for unlabeled node i considering label j, and m is the number of possible labels (classes, risk levels).
nary tests. Initially, for MLP component we considered GridSearchCV for a first analysis. We produced a random dataset of 1000 nodes using mlpClassifier with 200 max iterations and the following parameter space: hiddenLayerSizes with (128,256,32), (256,512,32), (512,1024,32); learningRateInit with 0.01, 0.1; validationFraction with 0.1, 0.2; batchSize with 50, 100. For this analysis, we obtained this results as best: batchSize=100, hiddenLay =
∑︀=1 (∈{1,...,} () = , 1, 0) 1 = ∑︀=1 (1 − |∈{1,...,} ()− | )
− 1
erSizes=(128, 256, 32), learningRateInit=0.01, validationFraction=0.1. After other empirical tests, we chose the hyper-parameters described in Table 3.
to calculate the relevance of the single input parameter
7.3. Prediction results against the single feature extracted from MLP first layer.
We consider the weights of the edges for the trained
In Table 4, we present accuracy results for both only MLP MLP. We do not consider biases. Moreover, we manage
component and all model GPA. In Figure 2, we outline the possible weight of the features for the Gaussian
kerthe diferences between accuracy of GPA and MLP. As we nel distances in the CCE layer. The potential weight is
can see, we have a slightly better performance with GPA. calculated according to labelled nodes, corresponding
Moreover, the results are better than the results obtained to training data. We weight the standard deviation of
with the algorithms tested with WEKA tool. Of course, a feature. In fact, features with a high variation give a
we must remember that we are reasoning with restricted high contribute to the substantial distances and so they
random datasets and so our conclusions are useful only have a significant contribute for prediction classification
from a testing point of view and not for healthcare formal (we could also analyze better the possibility to normalize
deductions. In Table 5, we present execution times for training features values). We first obtain a formula for
prediction tests. explainability which does not depend from the particular
input data and prediction. Then, we apply the formula
to a single input data by multiplication, so to calculate
the percentage of relevance for that parameter in the
considered prediction. Here, we use a forward definition
for explainability, maintaining the conservation of total
relevance. Formally, if we have a normalized unlabeled
node represented by the input data (1, . . . , ), with
∀ ∈ {1, . . . , } ∈ [0, 1], we can establish the
relevance of input i in the prediction as , ddefined in the
equations (
MLP (layer 0 is the input data) • LF is the layer of MLP for features extraction;
for a particular f, this layer has only one neuron , = ∑︀
=1 [,0 ] ∑︀=1 ∑︀
=1 [,0 ] ∑︀=1 )2 − ∈{1,...}
√︂ = √︂ ∑︀=1 ( −
√︂ ∈{1,...} ∑︀=1 ( − ∑︀=1 )2 − ∈{1,...} ∑︀=1 ( − ∑︀=1
)2 ∑︀=1 ( − √︂ ∑︀=1
)2 +1 ,+1 + , = ∑=︁1 ∑︀= 1 ++1+1 1, = 1 As we can see, is the only element related to the particular input data. All the other elements expressed in the formulas depends only on fixed hyper-parameters and on original training dataset. Moreover, in our tests, we calculate the constant components of , only once, so to optimize the tests computation.
8.2. Explainability results predict diabetes risk. We have tested our model using random defined datasets produced according to a healthcare In Figure 3, we present the results of explainability tests. rule named FINDRISC. We chose to define random data to In particular, we can see the average relevancies for all have the possibility to evaluate our model in a controlled input data in respect to all testing predictions. E.g., we manner (input data are suficiently distributed and risk can see particular relevancies for parameter 1 (age), 2 predictions are equally distributed) and to overcome any (BMI), 3 (waist circumference), 8 (family history) and privacy problem. We defined our model, named GPA, usless relevancies for parameter 2 (gender). Of course, we ing three layers. First layer considers a MLP module and must remember that we are reasoning with restricted it is used both to produce a first partial mixed prediction random datasets and so our conclusions are useful only and to extract features for the second layer. This layer, from a testing point of view and not for healthcare formal named CCE, produces a partial mixed prediction considdeductions. In Table 7, we present execution times for ering the similarity between a single unlabeled node in explainability tests. respect to all labelled nodes, managing class distances too. In this layer, a node is represented by the features extracted from first layer. Third layer, named WS, considers the sum of the partial mixed prediction of the first and second layer (in a weighted manner) to obtain the final prediction by argmax. Experimentally, we noticed that accuracy improves using the all GPA model in respect to using only MLP layer. Moreover, we noticed that accuracy results are better than considering accuracy results produced using some algorithms of WEKA tool. The most contribute of our research is the explainability of our model in terms of input parameters, useful for a MD (medical doctor) understanding, also considering more predictions together. Generally, we must remember that now our conclusions are useful only from a testing point of view and not for real deductions.