Update vignette + optim code

[morpheus.git] / pkg / R / computeMu.R

#' Compute μ
#'
#' Estimate the normalized columns μ of the β matrix parameter in a mixture of
#' logistic regressions models, with a spectral method described in the package vignette.
#'
#' @param X Matrix of input data (size nxd)
#' @param Y Vector of binary outputs (size n)
#' @param optargs List of optional argument:
#'   \itemize{
#'     \item 'jd_method', joint diagonalization method from the package jointDiag:
#'       'uwedge' (default) or 'jedi'.
#'     \item 'jd_nvects', number of random vectors for joint-diagonalization
#'       (or 0 for p=d, canonical basis by default)
#'     \item 'M', moments of order 1,2,3: will be computed if not provided.
#'     \item 'K', number of populations (estimated with rank of M2 if not given)
#'   }
#'
#' @return The estimated normalized parameters as columns of a matrix μ of size dxK
#'
#' @seealso \code{multiRun} to estimate statistics based on μ,
#'   and \code{generateSampleIO} for I/O random generation.
#'
#' @examples
#' io = generateSampleIO(10000, 1/2, matrix(c(1,0,0,1),ncol=2), c(0,0), "probit")
#' μ = computeMu(io$X, io$Y, list(K=2)) #or just X and Y for estimated K
#' @export
computeMu = function(X, Y, optargs=list())
{
	if (!is.matrix(X) || !is.numeric(X) || any(is.na(X)))
		stop("X: real matrix, no NA")
	n = nrow(X)
	d = ncol(X)
	if (!is.numeric(Y) || length(Y)!=n || any(Y!=0 & Y!=1))
		stop("Y: vector of 0 and 1, size nrow(X), no NA")
	if (!is.list(optargs))
		stop("optargs: list")

	# Step 0: Obtain the empirically estimated moments tensor, estimate also K
	M = if (is.null(optargs$M)) computeMoments(X,Y) else optargs$M
	K = optargs$K
	if (is.null(K))
	{
		# TODO: improve this basic heuristic
		Σ = svd(M[[2]])$d
		large_ratio <- ( abs(Σ[-d] / Σ[-1]) > 3 )
		K <- if (any(large_ratio)) max(2, which.min(large_ratio)) else d
	}

	# Step 1: generate a family of d matrices to joint-diagonalize to increase robustness
	d = ncol(X)
	fixed_design = FALSE
	jd_nvects = ifelse(!is.null(optargs$jd_nvects), optargs$jd_nvects, 0)
	if (jd_nvects == 0)
	{
		jd_nvects = d
		fixed_design = TRUE
	}
	M2_t = array(dim=c(d,d,jd_nvects))
	for (i in seq_len(jd_nvects))
	{
		rho = if (fixed_design) c(rep(0,i-1),1,rep(0,d-i)) else normalize( rnorm(d) )
		M2_t[,,i] = .T_I_I_w(M[[3]],rho)
	}

	# Step 2: obtain factors u_i (and their inverse) from the joint diagonalisation of M2_t
	jd_method = ifelse(!is.null(optargs$jd_method), optargs$jd_method, "uwedge")
	V =
		if (jd_nvects > 1) {
			#NOTE: increasing itermax does not help to converge, thus we suppress warnings
			suppressWarnings({jd = jointDiag::ajd(M2_t, method=jd_method)})
#			if (jd_method=="uwedge") jd$B else solve(jd$A)
			if (jd_method=="uwedge") jd$B else MASS::ginv(jd$A)
		}
		else
			eigen(M2_t[,,1])$vectors

	# Step 3: obtain final factors from joint diagonalisation of T(I,I,u_i)
	M2_t = array(dim=c(d,d,K))
	for (i in seq_len(K))
		M2_t[,,i] = .T_I_I_w(M[[3]],V[,i])
	suppressWarnings({jd = jointDiag::ajd(M2_t, method=jd_method)})
#	U = if (jd_method=="uwedge") solve(jd$B) else jd$A
	U = if (jd_method=="uwedge") MASS::ginv(jd$B) else jd$A
	μ = normalize(U[,1:K])

	# M1 also writes M1 = sum_k coeff_k * μ_k, where coeff_k >= 0
	# ==> search decomposition of vector M1 onto the (truncated) basis μ (of size dxK)
	# This is a linear system μ %*% C = M1 with C of size K ==> C = psinv(μ) %*% M1
	C = MASS::ginv(μ) %*% M[[1]]
	μ[,C < 0] = - μ[,C < 0]
	μ
}