Page 33 - Kỷ yếu hội thảo khoa học lần thứ 12 - Công nghệ thông tin và Ứng dụng trong các lĩnh vực (CITA 2023)

Bao Ngoc Vi, Cao Truong Tran, Chi Cong Nguyen 17

(1)

The generator take , and a -dimension noise variable as input and outputs
a vector of imputations :
(2)
where is sampled from a known distribution such as normal distribution, and is
element-wise multiplication.
outputs a value for every component as long as its value is observed. Therefore the
final completed data vector is obtained by replacing missing value in with the cor-
responding value of , that is:
(3)

3.2 Discriminator

The discriminator attempts to distinguish which components of completed vector
are real (observed) or fake (imputed). That is, it try to predicting the mask vector .
In [21], authors showed that if the discriminator is not provided "enough" infor-
mation about , could reproduce several populations that would all be optimal
with respect to . Thus it is necessary to introduce a hint mechanism. A hint mecha-
nism is a random variable and contains some information about M to guarantee that
the generator learns the desired distribution. is defined as below:
(4)

where is defined by first sampling k from uni-
formly at random and then setting:

(5)

and are fed to to predict which components are real or imputed. is denoted
as output of , that is:

(6)
The discriminator is updated after each evolutionary step to further to distinguish which
components of completed vector are real (observed) or fake (imputed), that is:
(7)

3.3 Evolutionary algorithm

Variation Given an individual in the population, the variation operators is utilized
to produce its offspring . Specifically, several copies of each parent

ISBN: 978-604-80-8083-9 CITA 2023