#' \item β: regression matrix, size dxK
#' \item b: intercepts, size K
#' }
-#' x0 is a vector containing respectively the K-1 first elements of p, then β by
-#' columns, and finally b: \code{x0 = c(p[1:(K-1)],as.double(β),b)}.
+#' 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)}.
#'
#' @seealso \code{multiRun} to estimate statistics based on β, and
#' \code{generateSampleIO} for I/O random generation.
#' 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))
#' o <- optimParams(io$X, io$Y, 2, "logit")
-#' x0 <- list(p=1/2, β=μ, b=c(0,0))
-#' par0 <- o$run(x0)
+#' θ0 <- list(p=1/2, β=μ, b=c(0,0))
+#' par0 <- o$run(θ0)
#' # Compare with another starting point
-#' x1 <- list(p=1/2, β=2*μ, b=c(0,0))
-#' par1 <- o$run(x1)
+#' θ1 <- list(p=1/2, β=2*μ, b=c(0,0))
+#' par1 <- o$run(θ1)
#' o$f( o$linArgs(par0) )
#' o$f( o$linArgs(par1) )
#' @export
-optimParams = function(X, Y, K, link=c("logit","probit"))
+optimParams <- function(X, Y, K, link=c("logit","probit"))
{
# Check arguments
if (!is.matrix(X) || any(is.na(X)))
stop("X: numeric matrix, no NAs")
- if (!is.numeric(Y) || any(is.na(Y)) || any(Y!=0 | Y!=1))
+ 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)
li = "character", #link function
X = "matrix",
Y = "numeric",
- M1 = "numeric",
- M2 = "numeric", #M2 easier to process as a vector
- M3 = "numeric", #same for M3
+ Mhat = "numeric", #vector of empirical moments
# Dimensions
K = "integer",
n = "integer",
stop("Missing arguments")
# Precompute empirical moments
- M <- computeMoments(optargs$X,optargs$Y)
- M1 <<- as.double(M[[1]])
- M2 <<- as.double(M[[2]])
- M3 <<- as.double(M[[3]])
+ 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
},
- expArgs = function(x)
+ expArgs = function(v)
{
- "Expand individual arguments from vector x"
+ "Expand individual arguments from vector v into a list"
list(
# p: dimension K-1, need to be completed
- "p" = c(x[1:(K-1)], 1-sum(x[1:(K-1)])),
- "β" = matrix(x[K:(K+d*K-1)], ncol=K),
- "b" = x[(K+d*K):(K+(d+1)*K-1)])
+ "p" = c(v[1:(K-1)], 1-sum(v[1:(K-1)])),
+ "β" = matrix(v[K:(K+d*K-1)], ncol=K),
+ "b" = v[(K+d*K):(K+(d+1)*K-1)])
},
- linArgs = function(o)
+ linArgs = function(L)
{
- " Linearize vectors+matrices into a vector x"
+ "Linearize vectors+matrices from list L into a vector"
- c(o$p[1:(K-1)], as.double(o$β), o$b)
+ c(L$p[1:(K-1)], as.double(L$β), L$b)
},
- getOmega = function(theta)
+ computeW = function(θ)
{
- dim <- d + d^2 + d^3
- matrix( .C("Compute_Omega",
- X=as.double(X), Y=as.double(Y), pn=as.integer(n), pd=as.integer(d),
- p=as.double(theta$p), β=as.double(theta$β), b=as.double(theta$b),
- W=as.double(W), PACKAGE="morpheus")$W, nrow=dim, ncol=dim)
+ #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")$W, nrow=dd, ncol=dd ) )
+ NULL #avoid returning W
},
- f = function(theta)
+ Moments = function(θ)
{
- "Product t(Mi - hat_Mi) W (Mi - hat_Mi) with Mi(theta)"
+ "Vector of moments, of size d+d^2+d^3"
- p <- theta$p
- β <- theta$β
+ p <- θ$p
+ β <- θ$β
λ <- sqrt(colSums(β^2))
- b <- theta$b
+ b <- θ$b
# Tensorial products β^2 = β2 and β^3 = β3 must be computed from current β1
β2 <- apply(β, 2, function(col) col %o% col)
β3 <- apply(β, 2, function(col) col %o% col %o% col)
- A <- matrix(c(
- β %*% (p * .G(li,1,λ,b)) - M1,
- β2 %*% (p * .G(li,2,λ,b)) - M2,
- β3 %*% (p * .G(li,3,λ,b)) - M3), ncol=1)
+ c(
+ β %*% (p * .G(li,1,λ,b)),
+ β2 %*% (p * .G(li,2,λ,b)),
+ β3 %*% (p * .G(li,3,λ,b)))
+ },
+
+ f = function(θ)
+ {
+ "Product t(hat_Mi - Mi) W (hat_Mi - Mi) with Mi(theta)"
+
+ L <- expArgs(θ)
+ A <- as.matrix(Mhat - Moments(L))
t(A) %*% W %*% A
},
- grad_f = function(x)
+ grad_f = function(θ)
{
"Gradient of f, dimension (K-1) + d*K + K = (d+2)*K - 1"
- # TODO: formula -2 t(grad M(theta)) . W . (Mhat - M(theta))
- }
+ L <- expArgs(θ)
+ -2 * t(grad_M(L)) %*% W %*% as.matrix((Mhat - Moments(L)))
+ },
- grad_M = function(theta)
+ grad_M = function(θ)
{
- # TODO: adapt code below for grad of d+d^2+d^3 vector of moments,
- # instead of grad (sum(Mhat-M(theta)^2)) --> should be easier
+ "Gradient of the vector of moments, size (dim=)d+d^2+d^3 x K-1+K+d*K"
- P <- expArgs(x)
- p <- P$p
- β <- P$β
+ p <- θ$p
+ β <- θ$β
λ <- sqrt(colSums(β^2))
μ <- sweep(β, 2, λ, '/')
- b <- P$b
+ b <- θ$b
+
+ res <- matrix(nrow=nrow(W), ncol=0)
# Tensorial products β^2 = β2 and β^3 = β3 must be computed from current β1
β2 <- apply(β, 2, function(col) col %o% col)
G4 = .G(li,4,λ,b)
G5 = .G(li,5,λ,b)
- # (Mi - hat_Mi)^2 ' == (Mi - hat_Mi)' 2(Mi - hat_Mi) = Mi' Fi
- F1 = as.double( 2 * ( β %*% (p * G1) - M1 ) )
- F2 = as.double( 2 * ( β2 %*% (p * G2) - M2 ) )
- F3 = as.double( 2 * ( β3 %*% (p * G3) - M3 ) )
-
+ # Gradient on p: K-1 columns, dim rows
km1 = 1:(K-1)
- grad <- #gradient on p
- t( sweep(as.matrix(β [,km1]), 2, G1[km1], '*') - G1[K] * β [,K] ) %*% F1 +
- t( sweep(as.matrix(β2[,km1]), 2, G2[km1], '*') - G2[K] * β2[,K] ) %*% F2 +
- t( sweep(as.matrix(β3[,km1]), 2, G3[km1], '*') - G3[K] * β3[,K] ) %*% F3
+ res <- cbind(res, rbind(
+ sweep(as.matrix(β [,km1]), 2, G1[km1], '*') - G1[K] * β [,K],
+ sweep(as.matrix(β2[,km1]), 2, G2[km1], '*') - G2[K] * β2[,K],
+ sweep(as.matrix(β3[,km1]), 2, G3[km1], '*') - G3[K] * β3[,K] ))
- grad_β <- matrix(nrow=d, ncol=K)
for (i in 1:d)
{
# i determines the derivated matrix dβ[2,3]
dβ3_right[block,] <- dβ3_right[block,] + β2
dβ3 <- dβ3_left + sweep(dβ3_right, 2, p * G3, '*')
- grad_β[i,] <- t(dβ) %*% F1 + t(dβ2) %*% F2 + t(dβ3) %*% F3
+ res <- cbind(res, rbind(dβ, dβ2, dβ3))
}
- grad <- c(grad, as.double(grad_β))
- grad = c(grad, #gradient on b
- t( sweep(β, 2, p * G2, '*') ) %*% F1 +
- t( sweep(β2, 2, p * G3, '*') ) %*% F2 +
- t( sweep(β3, 2, p * G4, '*') ) %*% F3 )
+ # Gradient on b
+ res <- cbind(res, rbind(
+ sweep(β, 2, p * G2, '*'),
+ sweep(β2, 2, p * G3, '*'),
+ sweep(β3, 2, p * G4, '*') ))
- grad
+ res
},
- # TODO: rename x(0) into theta(0) --> θ
- run = function(x0)
+ run = function(θ0)
{
- "Run optimization from x0 with solver..."
-
- if (!is.list(x0))
- stop("x0: list")
- if (is.null(x0$β))
- stop("At least x0$β must be provided")
- if (!is.matrix(x0$β) || any(is.na(x0$β)) || ncol(x0$β) != K)
- stop("x0$β: matrix, no NA, ncol == K")
- if (is.null(x0$p))
- x0$p = rep(1/K, K-1)
- else if (length(x0$p) != K-1 || sum(x0$p) > 1)
- stop("x0$p should contain positive integers and sum to < 1")
+ "Run optimization from θ0 with solver..."
+
+ if (!is.list(θ0))
+ 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.null(θ0$p))
+ θ0$p = rep(1/K, K-1)
+ else if (length(θ0$p) != K-1 || sum(θ0$p) > 1)
+ stop("θ0$p should contain positive integers and sum to < 1")
# Next test = heuristic to detect missing b (when matrix is called "beta")
- if (is.null(x0$b) || all(x0$b == x0$β))
- x0$b = rep(0, K)
- else if (any(is.na(x0$b)))
- stop("x0$b cannot have missing values")
-
- op_res = constrOptim( linArgs(x0), .self$f, .self$grad_f,
- ui=cbind(
- rbind( rep(-1,K-1), diag(K-1) ),
- matrix(0, nrow=K, ncol=(d+1)*K) ),
- ci=c(-1,rep(0,K-1)) )
-
- # We get a first non-trivial estimation of W: getOmega(theta)^{-1}
- # TODO: loop, this redefine f, so that we can call constrOptim again...
- # Stopping condition? N iterations? Delta <= ε ?
+ if (is.null(θ0$b) || all(θ0$b == θ0$β))
+ θ0$b = rep(0, K)
+ else if (any(is.na(θ0$b)))
+ stop("θ0$b cannot have missing values")
+
+ # TODO: stopping condition? N iterations? Delta <= epsilon ?
+ for (loop in 1:10)
+ {
+ op_res = constrOptim( linArgs(θ0), .self$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))
+ }
expArgs(op_res$par)
}
projects / morpheus.git / blobdiff