Project

This is a review of my previous work of master capstone project.

Two algorithm

• regression
• smoothed l0 norm

Five methods of power comparison

• top n
• type 1 error
• permutation (5% lagest beta)
• permutation (largest beta)
• permutation (mean square error)

Calculation

• type one error

1. reg

##        [,1]   [,2]  [,3]   [,4]   [,5]
## [1,] 0.3400 0.6400 0.800 0.9000 0.8600
## [2,] 0.3800 0.5000 0.580 0.5800 0.7000
## [3,] 0.2933 0.3467 0.480 0.5333 0.4467
## [4,] 0.3000 0.3550 0.475 0.4600 0.4250
## [5,] 0.2720 0.3960 0.388 0.3640 0.3680

2. smo

##        [,1]  [,2]   [,3]   [,4]   [,5]
## [1,] 0.2800 0.540 0.8600 0.9400 1.0000
## [2,] 0.2300 0.390 0.6800 0.7300 0.8700
## [3,] 0.2733 0.380 0.5133 0.4933 0.6067
## [4,] 0.2150 0.305 0.4500 0.4650 0.5200
## [5,] 0.2200 0.276 0.3400 0.3480 0.3120

3. difference

##        [,1]     [,2]     [,3]   [,4]   [,5]
## [1,] -0.060 -0.10000  0.06000  0.040  0.140
## [2,] -0.150 -0.11000  0.10000  0.150  0.170
## [3,] -0.020  0.03333  0.03333 -0.040  0.160
## [4,] -0.085 -0.05000 -0.02500  0.005  0.095
## [5,] -0.052 -0.12000 -0.04800 -0.016 -0.056

• permutation (5% lagest beta)

1. reg

##        [,1]   [,2]   [,3]   [,4]   [,5]
## [1,] 0.4040 0.6440 0.8160 0.8120 0.8760
## [2,] 0.3600 0.4760 0.5340 0.6240 0.6360
## [3,] 0.3053 0.4320 0.4533 0.4867 0.5120
## [4,] 0.2820 0.3610 0.3710 0.3810 0.4480
## [5,] 0.2632 0.3112 0.3480 0.3512 0.3376

2. smo

##        [,1]   [,2]   [,3]   [,4]   [,5]
## [1,] 0.2280 0.4480 0.6200 0.8080 0.9360
## [2,] 0.1820 0.2640 0.3420 0.3860 0.4760
## [3,] 0.1467 0.1840 0.1667 0.1933 0.1653
## [4,] 0.1290 0.1190 0.1180 0.1360 0.1360
## [5,] 0.0992 0.0896 0.0872 0.0792 0.0912

3. difference

##         [,1]    [,2]    [,3]    [,4]    [,5]
## [1,] -0.1760 -0.1960 -0.1960 -0.0040  0.0600
## [2,] -0.1780 -0.2120 -0.1920 -0.2380 -0.1600
## [3,] -0.1587 -0.2480 -0.2867 -0.2933 -0.3467
## [4,] -0.1530 -0.2420 -0.2530 -0.2450 -0.3120
## [5,] -0.1640 -0.2216 -0.2608 -0.2720 -0.2464

Result interpretation

• when will smo better than reg
  • the strength of signals larger than 0.2
  • the num is small
  • the size is large

## [1] "y with noise:"

##        V1        
##  Min.   :0.0572  
##  1st Qu.:0.5814  
##  Median :0.8660  
##  Mean   :0.8876  
##  3rd Qu.:1.1655  
##  Max.   :1.6986

## [1] "y without noise:"

##        V1       
##  Min.   :0.400  
##  1st Qu.:0.700  
##  Median :0.800  
##  Mean   :0.833  
##  3rd Qu.:1.000  
##  Max.   :1.200

## [1] "noise"

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -0.8350 -0.1350  0.0651  0.0127  0.2520  0.6700

• factors that may affect result: str, num, size, epsilon.

Question

• The power of smo is different under controlling type one error and permutation, while the power of reg is same.

• Power is reducing with the increasing of significant signal number.