achieve the purpose of selecting variables. ^
b
0
j represents least squares estimation of b j
and compression will happen once t\
P p
j¼1
^
b
0
j
, with some coefficients changing
toward 0.
3 Prediction Model Based on Lasso
In order to build the model, the original data is normalized at first, and then, the
collinearity between properties is judged. If collinearity exists, Lasso is used for
dimensionality reduction. Otherwise, multiple regression analysis is performed. Whole
process is shown in Fig. 1.
1. Normalization of data.
When using Lasso regression, in order to eliminate the influence of dimensions of
different indexes, it is necessary to standardize and normalize the observation data.
2. Feature selection by Lasso.
After calculation through Lasso, when the parameter regression result corresponding to
influencing factor is “0”, the feature is discarded. Otherwise, the feature is included in
the candidate feature set. Thereby, a sparse solution is obtained for dimensionality
reduction.
3. Generation of model family.
After obtaining a subset of low-redundancy features, the model family is created by
using feature subsets to obtain regression coefficients corresponding to different alpha
values.
4. Model optimization.
This article uses the 10-fold tutorial verification method to select the model, and
specific steps are as follows: ① Disturb the order of the training set randomly. ②
Divide the disturbed training set into 10 parts. ③ Start with the first parameter in the
parameter set and select one parameter each time without repeating. ④ From the first
copy, take one copy each time as a test set, and the rest as a training set. ⑤ Use training
sets and selected parameters for model training. ⑥ Forecast test sets with trained
Raw
data
Norma
lizatio
n
Collinear
ity?
Colline
arity
diagno
sis
Lasso
Feature
selection
Low
redund
ancy
feature
subset
Model
family
Choose the
best model
(10 fold
cross
validation)
multiple regression
analysis
Satisfies
the
condition?
Predict
ion
Yes
Yes
NO
Fig. 1. Modeling process of Lasso penalty regression algorithm
Research on Prediction Model of Gas Emission Based on Lasso …
167
b
0
j represents least squares estimation of b j
and compression will happen once t\
P p
j¼1
^
b
0
j
, with some coefficients changing
toward 0.
3 Prediction Model Based on Lasso
In order to build the model, the original data is normalized at first, and then, the
collinearity between properties is judged. If collinearity exists, Lasso is used for
dimensionality reduction. Otherwise, multiple regression analysis is performed. Whole
process is shown in Fig. 1.
1. Normalization of data.
When using Lasso regression, in order to eliminate the influence of dimensions of
different indexes, it is necessary to standardize and normalize the observation data.
2. Feature selection by Lasso.
After calculation through Lasso, when the parameter regression result corresponding to
influencing factor is “0”, the feature is discarded. Otherwise, the feature is included in
the candidate feature set. Thereby, a sparse solution is obtained for dimensionality
reduction.
3. Generation of model family.
After obtaining a subset of low-redundancy features, the model family is created by
using feature subsets to obtain regression coefficients corresponding to different alpha
values.
4. Model optimization.
This article uses the 10-fold tutorial verification method to select the model, and
specific steps are as follows: ① Disturb the order of the training set randomly. ②
Divide the disturbed training set into 10 parts. ③ Start with the first parameter in the
parameter set and select one parameter each time without repeating. ④ From the first
copy, take one copy each time as a test set, and the rest as a training set. ⑤ Use training
sets and selected parameters for model training. ⑥ Forecast test sets with trained
Raw
data
Norma
lizatio
n
Collinear
ity?
Colline
arity
diagno
sis
Lasso
Feature
selection
Low
redund
ancy
feature
subset
Model
family
Choose the
best model
(10 fold
cross
validation)
multiple regression
analysis
Satisfies
the
condition?
Predict
ion
Yes
Yes
NO
Fig. 1. Modeling process of Lasso penalty regression algorithm
Research on Prediction Model of Gas Emission Based on Lasso …
167