logistic_GAGA {GAGAs}

Fit a logistic model via the Global Adaptive Generative Adjustment algorithm

Description

Fit a logistic model via the Global Adaptive Generative Adjustment algorithm

Usage

logistic_GAGA(
  X,
  y,
  alpha = 1,
  itrNum = 30,
  thresh = 0.001,
  flag = TRUE,
  lamda_0 = 0.001,
  fdiag = TRUE,
  subItrNum = 20
)

Arguments

X

Input matrix, of dimension nobs*nvars; each row is an observation. If the intercept term needs to be considered in the estimation process, then the first column of X must be all 1s.

y

should be either a factor with two levels.

alpha

Hyperparameter. The suggested value for alpha is 1 or 2. When the collinearity of the load matrix is serious, the hyperparameters can be selected larger, such as 5.

itrNum

The number of iteration steps. In general, 20 steps are enough. If the condition number of X is large, it is recommended to greatly increase the number of iteration steps.

thresh

Convergence threshold for beta Change, if max(abs(beta-beta_old))<threshold, return.

flag

It identifies whether to make model selection. The default is TRUE.

lamda_0

The initial value of the regularization parameter for ridge regression. The running result of the algorithm is not sensitive to this value.

fdiag

It identifies whether to use diag Approximation to speed up the algorithm.

subItrNum

Maximum number of steps for subprocess iterations.

Value

Coefficient vector.

Examples

# binomial
set.seed(2022)
cat("\n")
cat("Test binomial GAGA\n")
p_size = 30
sample_size=600
test_size=1000
R1 = 1
R2 = 3
ratio = 0.5 #The ratio of zeroes in coefficients
#Set the true coefficients
zeroNum = round(ratio*p_size)
ind = sample(1:p_size,zeroNum)
beta_true = runif(p_size,R2*0.2,R2)
beta_true[ind] = 0
X = R1*matrix(rnorm(sample_size * p_size), ncol = p_size)
X[1:sample_size,1]=1
t = 1/(1+exp(-X%*%beta_true))
tmp = runif(sample_size,0,1)
y = rep(0,sample_size)
y[t>tmp] = 1
fit = GAGAs(X,y,family = "binomial", alpha = 1)
Eb = fit$beta
#Generate test samples
X_t = R1*matrix(rnorm(test_size * p_size), ncol = p_size)
X_t[1:test_size,1]=1
t = 1/(1+exp(-X_t%*%beta_true))
tmp = runif(test_size,0,1)
y_t = rep(0,test_size)
y_t[t>tmp] = 1
#Prediction
Ey = predict(fit,newx = X_t)
cat("\n--------------------")
cat("\n err:", norm(Eb-beta_true,type="2")/norm(beta_true,type="2"))
cat("\n acc:", cal.w.acc(as.character(Eb!=0),as.character(beta_true!=0)))
cat("\n pacc:", cal.w.acc(as.character(Ey),as.character(y_t)))
cat("\n")