#' Wrapper function for OptimParams class
#'
-#' @param K Number of populations.
-#' @param link The link type, 'logit' or 'probit'.
#' @param X Data matrix of covariables
#' @param Y Output as a binary vector
+#' @param K Number of populations.
+#' @param link The link type, 'logit' or 'probit'.
+#' @param M the empirical cross-moments between X and Y (optional)
#'
-#' @return An object 'op' of class OptimParams, initialized so that \code{op$run(x0)}
-#' outputs the list of optimized parameters
+#' @return An object 'op' of class OptimParams, initialized so that
+#' \code{op$run(θ0)} outputs the list of optimized parameters
#' \itemize{
#' \item p: proportions, size K
#' \item β: regression matrix, size dxK
#' \item b: intercepts, size K
#' }
-#' θ0 is a vector containing respectively the K-1 first elements of p, then β by
-#' columns, and finally b: \code{θ0 = c(p[1:(K-1)],as.double(β),b)}.
+#' θ0 is a list containing the initial parameters. Only β is required
+#' (p would be set to (1/K,...,1/K) and b to (0,...0)).
#'
#' @seealso \code{multiRun} to estimate statistics based on β, and
#' \code{generateSampleIO} for I/O random generation.
#'
#' @examples
#' # Optimize parameters from estimated μ
-#' io = generateSampleIO(10000, 1/2, matrix(c(1,-2,3,1),ncol=2), c(0,0), "logit")
+#' io <- generateSampleIO(100,
+#' 1/2, matrix(c(1,-2,3,1),ncol=2), c(0,0), "logit")
#' μ = computeMu(io$X, io$Y, list(K=2))
#' o <- optimParams(io$X, io$Y, 2, "logit")
+#' \donttest{
#' θ0 <- list(p=1/2, β=μ, b=c(0,0))
#' par0 <- o$run(θ0)
#' # Compare with another starting point
#' θ1 <- list(p=1/2, β=2*μ, b=c(0,0))
#' par1 <- o$run(θ1)
+#' # Look at the function values at par0 and par1:
#' o$f( o$linArgs(par0) )
-#' o$f( o$linArgs(par1) )
+#' o$f( o$linArgs(par1) )}
+#'
#' @export
optimParams <- function(X, Y, K, link=c("logit","probit"), M=NULL)
{
"Y"=as.integer(Y), "K"=as.integer(K), "Mhat"=as.double(M))
}
-#' Encapsulated optimization for p (proportions), β and b (regression parameters)
-#'
-#' Optimize the parameters of a mixture of logistic regressions model, possibly using
-#' \code{mu <- computeMu(...)} as a partial starting point.
-#'
-#' @field li Link function, 'logit' or 'probit'
-#' @field X Data matrix of covariables
-#' @field Y Output as a binary vector
-#' @field K Number of populations
-#' @field d Number of dimensions
-#' @field W Weights matrix (iteratively refined)
-#'
+# Encapsulated optimization for p (proportions), β and b (regression parameters)
+#
+# Optimize the parameters of a mixture of logistic regressions model, possibly using
+# \code{mu <- computeMu(...)} as a partial starting point.
+#
+# @field li Link function, 'logit' or 'probit'
+# @field X Data matrix of covariables
+# @field Y Output as a binary vector
+# @field Mhat Vector of empirical moments
+# @field K Number of populations
+# @field n Number of sample points
+# @field d Number of dimensions
+# @field W Weights matrix (initialized at identity)
+#
setRefClass(
Class = "OptimParams",
c(L$p[1:(K-1)], as.double(t(L$β)), L$b)
},
+ # TODO: relocate computeW in utils.R
computeW = function(θ)
{
+ "Compute the weights matrix from a parameters list"
+
require(MASS)
dd <- d + d^2 + d^3
M <- Moments(θ)
Moments = function(θ)
{
- "Vector of moments, of size d+d^2+d^3"
+ "Compute the vector of theoretical moments (size d+d^2+d^3)"
p <- θ$p
β <- θ$β
f = function(θ)
{
- "Product t(hat_Mi - Mi) W (hat_Mi - Mi) with Mi(theta)"
+ "Function to minimize: t(hat_Mi - Mi(θ)) . W . (hat_Mi - Mi(θ))"
L <- expArgs(θ)
A <- as.matrix(Mhat - Moments(L))
grad_f = function(θ)
{
- "Gradient of f, dimension (K-1) + d*K + K = (d+2)*K - 1"
+ "Gradient of f: vector of size (K-1) + d*K + K = (d+2)*K - 1"
L <- expArgs(θ)
-2 * t(grad_M(L)) %*% W %*% as.matrix(Mhat - Moments(L))
grad_M = function(θ)
{
- "Gradient of the vector of moments, size (dim=)d+d^2+d^3 x K-1+K+d*K"
+ "Gradient of the moments vector: matrix of size d+d^2+d^3 x K-1+K+d*K"
p <- θ$p
β <- θ$β
W <<- diag(d+d^2+d^3)
loopMax <- 2 #TODO: loopMax = 3 ? Seems not improving...
+ x_init <- linArgs(θ0)
for (loop in 1:loopMax)
{
- op_res = constrOptim( linArgs(θ0), .self$f, .self$grad_f,
+ op_res = constrOptim( x_init, .self$f, .self$grad_f,
ui=cbind(
rbind( rep(-1,K-1), diag(K-1) ),
matrix(0, nrow=K, ncol=(d+1)*K) ),
ci=c(-1,rep(0,K-1)) )
if (loop < loopMax) #avoid computing an extra W
W <<- computeW(expArgs(op_res$par))
- #print(op_res$value) #debug
- #print(expArgs(op_res$par)) #debug
+ #x_init <- op_res$par #degrades performances (TODO: why?)
}
expArgs(op_res$par)
projects / morpheus.git / blobdiff