ARD: Automatic Relevance Determination

In ChubingZeng/ARD: Automatic Relevance Determination

Description

ARD returns the estimated coefficients, estimated hyper-parameters, number of iterations and likelihood scores by Automated Relevance Determination (ARD).

Usage

ARD(X, Y, sigma.square = estimateVariance(X, Y),
  sigma.square.init = as.numeric(var(Y)), gamma.init = rep(1, ncol(X)),
  eta.init = rep(1, ncol(X)), threshold_eta = 10000, maxstep = 1000,
  margin = 0.001, verbosity = 1, compute.likelihood = TRUE,
  method = "FixedPoint")

Arguments

X	predictor matrix of dimension n*q.
Y	continuous outcome vector of dimension p.
sigma.square	variance of noise, used for method 'Reweighted l1'. Default value is estimated by estimateVariance(X,Y)
sigma.square.init	variance of noise, used for method 'FixedPoint' and 'EM'. Default value is var(Y) initial_val initial value for α. Default value is a vector of 0s.
gamma.init	initial value for hyper parameter, only for method 'Reweighted l1'
eta.init	initial value for hyper parameter, only for method 'EM' and 'FixedPoint'
threshold_eta	cut off point for very large eta
maxstep	max number of iterations
margin	iteration stoping creteria
verbosity	print current iteraction number
compute.likelihood	whether compute likelihood in each step

Details

ARD based on three optimization algorithms – EM algorithm, Fixed Point update rule and Reweighted-l1 algorithm. If use method 'reweighted-l1', please provide sigma.square otherwise an external function was called to estimate sigma square if you have prefered initial value for gamma, set gamma.init, otherwise gamma.init was initialized to be rep(1,ncol(X)) If use method: EM or Fixed Point update,sigma.square.init was used,the default initial value is variance of Y,if you have prefered initial value for eta, set eta.init, otherwise eta.init was initialized to be rep(1,ncol(X))

Value

returns the estimated coefficients, estimated hyper-parameters, number of iterations and likelihood scores by Automated Relevance Determination (ARD).

Examples

set.seed(99)
n = 100
p = 200
x <- matrix(rnorm(2*n*p,0,1),nrow=2*n,ncol=p)
betas=rnorm(n = p, s = 1/exp(z_design%*%alpha))
y <- x%*%betas + rnorm(2*n,0,1)
x_train = x[1:n,]
y_train = y[1:n]
x_test = x[(n+1):(2*n),]
y_test = y[(n+1):(2*n)]
ARD.fit = ARD(x_train,y_train)
1-get_mse(x_test%*%ARD_fit$coef,y_test)/var(y_test)

ChubingZeng/ARD documentation built on May 9, 2019, 3:22 a.m.