#' 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)
+#' @param nc Number of cores (default: 0 to use all)
#'
-#' @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)
+optimParams <- function(X, Y, K, link=c("logit","probit"), M=NULL, nc=0)
{
# Check arguments
if (!is.matrix(X) || any(is.na(X)))
if (!is.numeric(Y) || any(is.na(Y)) || any(Y!=0 & Y!=1))
stop("Y: binary vector with 0 and 1 only")
link <- match.arg(link)
- if (!is.numeric(K) || K!=floor(K) || K < 2)
- stop("K: integer >= 2")
+ if (!is.numeric(K) || K!=floor(K) || K < 2 || K > ncol(X))
+ stop("K: integer >= 2, <= d")
if (is.null(M))
{
# Build and return optimization algorithm object
methods::new("OptimParams", "li"=link, "X"=X,
- "Y"=as.integer(Y), "K"=as.integer(K), "Mhat"=as.double(M))
+ "Y"=as.integer(Y), "K"=as.integer(K), "Mhat"=as.double(M), "nc"=as.integer(nc))
}
-#' 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 nc Number of cores (OpenMP //)
+# @field W Weights matrix (initialized at identity)
+#
setRefClass(
Class = "OptimParams",
K = "integer",
n = "integer",
d = "integer",
+ nc = "integer",
# Weights matrix (generalized least square)
W = "matrix"
),
callSuper(...)
if (!hasArg("X") || !hasArg("Y") || !hasArg("K")
- || !hasArg("li") || !hasArg("Mhat"))
+ || !hasArg("li") || !hasArg("Mhat") || !hasArg("nc"))
{
stop("Missing arguments")
}
c(L$p[1:(K-1)], as.double(t(L$β)), L$b)
},
+ # TODO: relocate computeW in utils.R
computeW = function(θ)
{
+ "Compute the weights matrix from a parameters list"
+
require(MASS)
dd <- d + d^2 + d^3
M <- Moments(θ)
Omega <- matrix( .C("Compute_Omega",
X=as.double(X), Y=as.integer(Y), M=as.double(M),
- pn=as.integer(n), pd=as.integer(d),
+ pnc=as.integer(nc), pn=as.integer(n), pd=as.integer(d),
W=as.double(W), PACKAGE="morpheus")$W, nrow=dd, ncol=dd )
MASS::ginv(Omega)
},
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
res
},
- run = function(θ0)
+ # userW allows to bypass the W optimization by giving a W matrix
+ run = function(θ0, userW=NULL)
{
"Run optimization from θ0 with solver..."
stop("θ0$b: length K, no NA")
# (Re)Set W to identity, to allow several run from the same object
- W <<- diag(d+d^2+d^3)
+ W <<- if (is.null(userW)) diag(d+d^2+d^3) else userW
- loopMax <- 2 #TODO: loopMax = 3 ? Seems not improving...
+ #NOTE: loopMax = 3 seems to not improve the final results.
+ loopMax <- ifelse(is.null(userW), 2, 1)
x_init <- linArgs(θ0)
for (loop in 1:loopMax)
{
- op_res = constrOptim( x_init, .self$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) ),