M <- computeMoments(optargs$X,optargs$Y)
}
- weights <- optargs$weights
- if (is.null(weights))
- weights <- rep(1, 3)
-
# Build and return optimization algorithm object
methods::new("OptimParams", "li"=link, "M1"=as.double(M[[1]]),
- "M2"=as.double(M[[2]]), "M3"=as.double(M[[3]]),
- "weights"=weights, "K"=as.integer(K))
+ "M2"=as.double(M[[2]]), "M3"=as.double(M[[3]]), "K"=as.integer(K))
}
# Encapsulated optimization for p (proportions), β and b (regression parameters)
# @field M1 Estimated first-order moment
# @field M2 Estimated second-order moment (flattened)
# @field M3 Estimated third-order moment (flattened)
-# @field weights Vector of moments' weights
# @field K Number of populations
# @field d Number of dimensions
#
M1 = "numeric", #order-1 moment (vector size d)
M2 = "numeric", #M2 easier to process as a vector
M3 = "numeric", #M3 easier to process as a vector
- weights = "numeric", #weights on moments
# Dimensions
K = "integer",
- d = "integer"
+ d = "integer",
+ # Weights matrix (generalized least square)
+ W = "matrix"
),
methods = list(
}
d <<- length(M1)
+ W <<- diag(d+d^2+d^3) #initialize at W = Identity
},
expArgs = function(x)
f = function(x)
{
- "Sum of squares (Mi - hat_Mi)^2 where Mi is obtained from formula"
+ "Product t(Mi - hat_Mi) W (Mi - hat_Mi) with Mi(theta)"
P <- expArgs(x)
p <- P$p
β3 <- apply(β, 2, function(col) col %o% col %o% col)
return(
- weights[1] * sum( ( β %*% (p * .G(li,1,λ,b)) - M1 )^2 ) +
- weights[2] * sum( ( β2 %*% (p * .G(li,2,λ,b)) - M2 )^2 ) +
- weights[3] * sum( ( β3 %*% (p * .G(li,3,λ,b)) - M3 )^2 ) )
+ sum( ( β %*% (p * .G(li,1,λ,b)) - M1 )^2 ) +
+ sum( ( β2 %*% (p * .G(li,2,λ,b)) - M2 )^2 ) +
+ sum( ( β3 %*% (p * .G(li,3,λ,b)) - M3 )^2 ) )
},
grad_f = function(x)
km1 = 1:(K-1)
grad <- #gradient on p
- weights[1] * t( sweep(as.matrix(β [,km1]), 2, G1[km1], '*') - G1[K] * β [,K] ) %*% F1 +
- weights[2] * t( sweep(as.matrix(β2[,km1]), 2, G2[km1], '*') - G2[K] * β2[,K] ) %*% F2 +
- weights[3] * t( sweep(as.matrix(β3[,km1]), 2, G3[km1], '*') - G3[K] * β3[,K] ) %*% F3
+ 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
grad_β <- matrix(nrow=d, ncol=K)
for (i in 1:d)
dβ3_right[block,] <- dβ3_right[block,] + β2
dβ3 <- dβ3_left + sweep(dβ3_right, 2, p * G3, '*')
- grad_β[i,] <-
- weights[1] * t(dβ) %*% F1 +
- weights[2] * t(dβ2) %*% F2 +
- weights[3] * t(dβ3) %*% F3
+ grad_β[i,] <- t(dβ) %*% F1 + t(dβ2) %*% F2 + t(dβ3) %*% F3
}
grad <- c(grad, as.double(grad_β))
grad = c(grad, #gradient on b
- weights[1] * t( sweep(β, 2, p * G2, '*') ) %*% F1 +
- weights[2] * t( sweep(β2, 2, p * G3, '*') ) %*% F2 +
- weights[3] * t( sweep(β3, 2, p * G4, '*') ) %*% F3 )
+ t( sweep(β, 2, p * G2, '*') ) %*% F1 +
+ t( sweep(β2, 2, p * G3, '*') ) %*% F2 +
+ t( sweep(β3, 2, p * G4, '*') ) %*% F3 )
grad
},