Page 283 - Contributed Paper Session (CPS) - Volume 6

CPS1930 M. Kayanan et al.
we analysed the performance of LEnet with LASSO and Enet estimators in Root
Mean Square Error (RMSE) sense using the real-world examples.

2. Methodology
2.1. Method to obtain LASSO solutions
The solution of LASSO has been obtained using a modified version of the
Least Angle Regression (LARS) algorithm (Efron et al. (2004)), and it is outlined
as below:
Step 1: Centre the response variable that has to mean zero, and standardise
the predictors that has mean zero and unit norm.
Step 2: Start with all estimates of the coefficients to be equal to 0 with the
residual .
Step 3: Find the predictor most correlated with .

; .
Step 3: Move the estimate of from 0 towards the OLSE coefficients until
some other predictor has as large a correlation with the current
residual as does. At this point instead of continuing in the direction
based on , LAR proceeds in the direction of equiangularity between
the two predictors and .
Step 4: A third variable eventually earns its way into the most correlated
(active set), and then LARS proceeds equiangular between , and
. Continue adding variables to the active set in this way moving in
the direction defined by the least angle direction.
On this step, the coefficient estimates are updating using the following
formula:
̂ = ̂(−1) + (7)
where is a value between [0, 1] which represents how far the estimate of
moves in the direction before another variable enters the model and the
direction changes again, and is the equiangular vector.
The direction is calculated using the following formula:
(8)
where is the matrix with column (1 , 2 ,… . , ), and be the standard
ℎ
unit vector in ℝ .

Then, choose as given below:
+ −
= min{ ∈ [0,1]: ( = or = for some such that ̂ (−1) = 0) or (
= for some such that ̂(−1) ≠ 0)}
∗
(9)
where

and

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