910 DMSs was the main contributor to each of 1,250 DEGs.

ds, it was aimed to investigate whether the top-ranked DMS in a

n model for a DEG was a local or a remote methylation site in the

Based on the information, a statistical analysis was carried out to

te the trend of the methylation-to-expression interplay pattern,

g the local or remote interplay.

ose ܠ௚ was used to represent a differential expression vector of

EG, which was the target (dependent) variable of a regression

n such a model, 910 DMSs were treated as the regressors or the

ent variables. Moreover, w was used to represent a vector of

n coefficients or model parameters for 910 regressors and M was

epresent a matrix of the differential methylation ratios of 910

The M matrix has 114 rows and 910 columns. The regression

r the g^th DEG was defined as below,

ܠ௚ൌ݂ሺۻ, ܟሻ



n such a regression model, f was designed as a regression function,

as either linear or nonlinear. In a constrained (such as RLR) linear

n model, the above equation was simplified as below,

ܠ௚ൌۻܟ൅ߣܟ^௧ܟ



were 1,250 such regression models for 1,250 DEGs. These

were designed to investigate how DMSs, which were from either

emote methylation sites, contributed to the differential expression

attern) of the g^th DEG. Only the top-ranked DMSs were used for

ct analysis in this chapter. If a remote DMS was ranked at the top,

nce between this remote DMS and the g^th DEG was then

ted. The Lasso, RLR, SVM and random forest were used to

e relationship between the variables (between the g^th DEG and all

Ss) and rank variables. Figure 4.29 shows the R-square

ments for four models. It can be seen that four models all fitted to

well.