poisson_GAGA {GAGAs}

Fit a Poisson model via the GAGA algorithm

Description

Fit a Poisson model the Global Adaptive Generative Adjustment algorithm

Usage

poisson_GAGA(
  X,
  y,
  alpha = 1,
  itrNum = 30,
  thresh = 0.001,
  flag = TRUE,
  lamda_0 = 0.5,
  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. In order to run the program stably, it is recommended that the value of X should not be too large. It is recommended to preprocess all the items in X except the intercept item by means of preprocessing, so that the mean value of each column is 0 and the standard deviation is 1/ colnum(X).

y

Non-negative count response vector.

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

# Poisson
set.seed(2022)
p_size = 30
sample_size=300
R1 = 1/sqrt(p_size)
R2 = 5
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,0,R2)
beta_true[ind] = 0
X = R1*matrix(rnorm(sample_size * p_size), ncol = p_size)
X[1:sample_size,1]=1
y = rpois(sample_size,lambda = as.vector(exp(X%*%beta_true)))
y = as.vector(y)
# Estimate
fit = GAGAs(X,y,alpha = 2,family="poisson")
Eb = fit$beta
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)))