Dynamic and locally-faithful explanation of machine learning models for precision medicine
A method of explaining a machine learning model, including: receiving a plurality of disease states for a patient over time from a database, wherein the disease states have a plurality of features; generating a plurality of locally faithful explanation models for the patient for each disease state based upon the machine learning model; calculating an explanation with respect to one feature of the plurality of features over time using the locally faithful explanation models; and calculating the importance of the one feature of the plurality of features over time based upon the plurality of locally faithful explanation models.
1. A method of explaining a machine learning model, comprising:
receiving, by a processor, a plurality of disease states for a patient over time from a database, wherein the disease states have a plurality of features;
generating, by the processor, a plurality of locally faithful explanation models for the patient for each disease state;
calculating, by the processor, an explanation with respect to one selected feature of the plurality of features over time using the locally faithful explanation models, wherein the locally faithful explanation models are a linear model y=βx, where y is the value of the machine learning model, x is a feature vector, and β is a vector of linear coefficients that are explanations for each feature in the vector x;
calculating, by the processor, the importance of the one selected feature of the plurality of features over time based upon the plurality of locally faithful explanation models; and
providing, by the processor, the importance of the one selected feature of the plurality of features over time for evaluating the plurality of disease states of the patient.
2. The method of claim 1 , further comprising presenting on a graphical user interface a plot of the explanation and importance of the one selected feature of the plurality of features over time.
3. The method of claim 1 , wherein the explanation of a feature x k at time t is:
β
k
t
=
Δ
y
Δ
x
k
❘
"\[RightBracketingBar]"
t
.
4. The method of claim 3 , wherein the importance of feature x k at time t is:
I
k
t
=
β
k
Σ
β
❘
"\[RightBracketingBar]"
t
*
100.
5. The method of claim 1 , wherein generating a plurality of locally faithful explanation models for the patient for each disease state includes optimizing
ξ
(
x
)
=
min
g
ϵ
G
L
(
f
,
g
,
∏
x
)
+
Ω
(
g
)
,
where ξ(x) is the optimal model explanation that minimizes the sum of loss L and complexity measure, g is a locally faithful explanation model, f is the machine leaning model being explained, L(f, g, Πx) is the measure of how unfaithful g is in approximating f in the locality defined by Πx, and Ω(g) is the complexity of g based upon the number of parameters of g.
6. The method of claim 5 , wherein Ω(g) is the number of non-zero coefficients when g is a linear model.
7. The method of claim 5 , wherein Ω(g) is the depth of a decision three when g is a decision tree.
8. A method of explaining machine learning models, comprising:
receiving, by a processor, a plurality of disease states for a patient over time from a database, wherein the disease states have a plurality of features;
generating, by the processor, a plurality of locally faithful explanation models for the patient for each disease state;
calculating, by the processor, an explanation with respect to one selected feature of the plurality of features over time using the locally faithful explanation models, wherein the locally faithful explanation models are a linear model y=βx, where y is the value of the machine learning model, x is a feature vector, and β is a vector of linear coefficients that are explanations for each feature in the vector x;
calculating, by the processor, the average explanation of the one selected feature of the plurality of features over a specific time period based upon the plurality of locally faithful explanation models; and
providing, by the processor, the average explanation of the one selected feature of the plurality of features over the specific time period for evaluating the plurality of disease states of the patient.
9. The method of claim 8 , further comprising presenting on a graphical user interface a plot of the average explanation of the one selected feature of the plurality of features over the specific time period.
10. The method of claim 8 , wherein the explanation of a feature x k at time t is:
β
k
t
=
Δ
y
Δ
x
k
❘
"\[RightBracketingBar]"
t
.
11. The method of claim 10 , wherein the average importance of feature x k over time t 1 , to t 2 , is
β
t
1
,
t
2
=
1
t
2
-
t
1
1
Σ
θ
∑
t
=
t
1
t
2
θ
t
β
t
,
where θ t is the model confidence.
12. The method of claim 8 , wherein generating a plurality of locally faithful explanation models for the patient for each disease state includes optimizing
ξ
(
x
)
=
min
g
ϵ
G
L
(
f
,
g
,
∏
x
)
+
Ω
(
g
)
,
where ξ(x) is the optimal model explanation that minimizes the sum of loss L and complexity measure, g is a locally faithful explanation model, f is the machine leaning model being explained, L(f, g, Πx) is the measure of how unfaithful g is in approximating f in the locality defined by Πx, and Ω(g) is the complexity of g based upon the number of parameters of g.
13. The method of claim 12 , wherein Ω(g) is the number of non-zero coefficients when g is a linear model.
14. The method of claim 12 , wherein Ω(g) is the depth of a decision three when g is a decision tree.
15. A method of producing a model to predict the explanation of a machine learning models, comprising:
receiving, by a processor, a plurality of disease states for a patient over time from a database, wherein the disease states have a plurality of features;
generating, by the processor, a plurality of locally faithful explanation models for the patient for each disease state;
calculating, by the processor, an explanation vector based on the plurality of features over time using the locally faithful explanation models, wherein the locally faithful explanation models are a linear model y=βx, where y is the value of the machine learning model, x is a feature vector, and β is a vector of linear coefficients that are explanations for each feature in the vector x;
training, by the processor, a prediction model to predict the explanation of the machine learning model based upon the explanation vector; and
providing, by the processor, the explanation of the machine learning model for evaluating the plurality of disease states of the patient.
16. The method of claim 15 , further comprising presenting on a graphical user interface a plot of a prediction of the explanation of the machine learning model over time.
17. The method of claim 15 , wherein the explanation of a feature x k at time t is
β
k
t
=
Δ
y
Δ
x
k
❘
"\[RightBracketingBar]"
t
.
18. The method of claim 15 , wherein generating a plurality of locally faithful explanation models for the patient for each disease state includes optimizing
ξ
(
x
)
=
min
g
ϵ
G
L
(
f
,
g
,
∏
x
)
+
Ω
(
g
)
,
where ξ(x) is the optimal model explanation that minimizes the sum of loss L and complexity measure, g is a locally faithful explanation model, f is the machine leaning model being explained, L(f, g, Πx) is the measure of how unfaithful g is in approximating f in the locality defined by fix, and Ω(g) is the complexity of g based upon the number of parameters of g.
19. The method of claim 18 , wherein Ω(g) is the number of non-zero coefficients when g is a linear model.
20. The method of claim 18 , wherein, Ω(g) is the depth of a decision three when g is a decision tree.