+#' optimParams
+#'
#' Wrapper function for OptimParams class
#'
-#' @param K Number of populations.
-#' @param link The link type, 'logit' or 'probit'.
+#' @name optimParams
+#'
#' @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")
-#' μ = computeMu(io$X, io$Y, list(K=2))
+#' 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"))
+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))
+ {
+ # Precompute empirical moments
+ Mtmp <- computeMoments(X, Y)
+ M1 <- as.double(Mtmp[[1]])
+ M2 <- as.double(Mtmp[[2]])
+ M3 <- as.double(Mtmp[[3]])
+ M <- c(M1, M2, M3)
+ }
+ else
+ M <- c(M[[1]], M[[2]], M[[3]])
# Build and return optimization algorithm object
methods::new("OptimParams", "li"=link, "X"=X,
- "Y"=as.integer(Y), "K"=as.integer(K))
+ "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"
),
"Check args and initialize K, d, W"
callSuper(...)
- if (!hasArg("X") || !hasArg("Y") || !hasArg("K") || !hasArg("li"))
+ if (!hasArg("X") || !hasArg("Y") || !hasArg("K")
+ || !hasArg("li") || !hasArg("Mhat") || !hasArg("nc"))
+ {
stop("Missing arguments")
-
- # Precompute empirical moments
- M <- computeMoments(X, Y)
- M1 <- as.double(M[[1]])
- M2 <- as.double(M[[2]])
- M3 <- as.double(M[[3]])
- Mhat <<- c(M1, M2, M3)
+ }
n <<- nrow(X)
- d <<- length(M1)
- W <<- diag(d+d^2+d^3) #initialize at W = Identity
+ d <<- ncol(X)
+ # W will be initialized when calling run()
},
expArgs = function(v)
list(
# p: dimension K-1, need to be completed
"p" = c(v[1:(K-1)], 1-sum(v[1:(K-1)])),
- "β" = matrix(v[K:(K+d*K-1)], ncol=K),
+ "β" = t(matrix(v[K:(K+d*K-1)], ncol=d)),
"b" = v[(K+d*K):(K+(d+1)*K-1)])
},
{
"Linearize vectors+matrices from list L into a vector"
- c(L$p[1:(K-1)], as.double(L$β), L$b)
+ # β linearized row by row, to match derivatives order
+ c(L$p[1:(K-1)], as.double(t(L$β)), L$b)
},
+ # TODO: relocate computeW in utils.R
computeW = function(θ)
{
- #require(MASS)
+ "Compute the weights matrix from a parameters list"
+
+ require(MASS)
dd <- d + d^2 + d^3
- W <<- MASS::ginv( matrix( .C("Compute_Omega",
- X=as.double(X), Y=Y, M=Moments(θ), pn=as.integer(n), pd=as.integer(d),
- W=as.double(W), PACKAGE="morpheus")$W, nrow=dd, ncol=dd ) )
- NULL #avoid returning W
+ M <- Moments(θ)
+ Omega <- matrix( .C("Compute_Omega",
+ X=as.double(X), Y=as.integer(Y), M=as.double(M),
+ pnc=as.integer(nc), pn=as.integer(n), pd=as.integer(d),
+ W=as.double(W), PACKAGE="morpheus")$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)))
+ -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: list")
if (is.null(θ0$β))
stop("At least θ0$β must be provided")
- if (!is.matrix(θ0$β) || any(is.na(θ0$β)) || ncol(θ0$β) != K)
- stop("θ0$β: matrix, no NA, ncol == K")
+ if (!is.matrix(θ0$β) || any(is.na(θ0$β))
+ || nrow(θ0$β) != d || ncol(θ0$β) != K)
+ {
+ stop("θ0$β: matrix, no NA, nrow = d, ncol = K")
+ }
if (is.null(θ0$p))
θ0$p = rep(1/K, K-1)
- else if (length(θ0$p) != K-1 || sum(θ0$p) > 1)
- stop("θ0$p should contain positive integers and sum to < 1")
- # Next test = heuristic to detect missing b (when matrix is called "beta")
- if (is.null(θ0$b) || all(θ0$b == θ0$β))
+ else if (!is.numeric(θ0$p) || length(θ0$p) != K-1
+ || any(is.na(θ0$p)) || sum(θ0$p) > 1)
+ {
+ stop("θ0$p: length K-1, no NA, positive integers, sum to <= 1")
+ }
+ # NOTE: [["b"]] instead of $b because $b would match $beta (in pkg-cran)
+ if (is.null(θ0[["b"]]))
θ0$b = rep(0, K)
- else if (any(is.na(θ0$b)))
- stop("θ0$b cannot have missing values")
+ else if (!is.numeric(θ0$b) || length(θ0$b) != K || any(is.na(θ0$b)))
+ stop("θ0$b: length K, no NA")
- # TODO: stopping condition? N iterations? Delta <= epsilon ?
- for (loop in 1:10)
+ # (Re)Set W to identity, to allow several run from the same object
+ W <<- if (is.null(userW)) diag(d+d^2+d^3) else userW
+
+ # 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( 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)) )
-
- computeW(expArgs(op_res$par))
- # debug:
- #print(W)
- print(op_res$value)
- print(expArgs(op_res$par))
+ if (loop < loopMax) #avoid computing an extra W
+ W <<- computeW(expArgs(op_res$par))
+ #x_init <- op_res$par #degrades performances (TODO: why?)
}
expArgs(op_res$par)
projects / morpheus.git / blobdiff