pkg/R/computeMu.R

   1 #' Compute μ
   2 #'
   3 #' Estimate the normalized columns μ of the β matrix parameter in a mixture of
   4 #' logistic regressions models, with a spectral method described in the package vignette.
   5 #'
   6 #' @param X Matrix of input data (size nxd)
   7 #' @param Y Vector of binary outputs (size n)
   8 #' @param optargs List of optional argument:
   9 #'   \itemize{
  10 #'     \item 'jd_method', joint diagonalization method from the package jointDiag:
  11 #'       'uwedge' (default) or 'jedi'.
  12 #'     \item 'jd_nvects', number of random vectors for joint-diagonalization
  13 #'       (or 0 for p=d, canonical basis by default)
  14 #'     \item 'M', moments of order 1,2,3: will be computed if not provided.
  15 #'     \item 'K', number of populations (estimated with rank of M2 if not given)
  16 #'   }
  17 #'
  18 #' @return The estimated normalized parameters as columns of a matrix μ of size dxK
  19 #'
  20 #' @seealso \code{multiRun} to estimate statistics based on μ,
  21 #'   and \code{generateSampleIO} for I/O random generation.
  22 #'
  23 #' @examples
  24 #' io = generateSampleIO(10000, 1/2, matrix(c(1,0,0,1),ncol=2), c(0,0), "probit")
  25 #' μ = computeMu(io$X, io$Y, list(K=2)) #or just X and Y for estimated K
  26 #'
  27 #' @export
  28 computeMu = function(X, Y, optargs=list())
  29 {
  30   if (!is.matrix(X) || !is.numeric(X) || any(is.na(X)))
  31     stop("X: real matrix, no NA")
  32   n = nrow(X)
  33   d = ncol(X)
  34   if (!is.numeric(Y) || length(Y)!=n || any(Y!=0 & Y!=1))
  35     stop("Y: vector of 0 and 1, size nrow(X), no NA")
  36   if (!is.list(optargs))
  37     stop("optargs: list")
  38
  39   # Step 0: Obtain the empirically estimated moments tensor, estimate also K
  40   M = if (is.null(optargs$M)) computeMoments(X,Y) else optargs$M
  41   K = optargs$K
  42   if (is.null(K))
  43   {
  44     # TODO: improve this basic heuristic
  45     Σ = svd(M[[2]])$d
  46     large_ratio <- ( abs(Σ[-d] / Σ[-1]) > 3 )
  47     K <- if (any(large_ratio)) max(2, which.min(large_ratio)) else d
  48   }
  49
  50   # Step 1: generate a family of d matrices to joint-diagonalize to increase robustness
  51   d = ncol(X)
  52   fixed_design = FALSE
  53   jd_nvects = ifelse(!is.null(optargs$jd_nvects), optargs$jd_nvects, 0)
  54   if (jd_nvects == 0)
  55   {
  56     jd_nvects = d
  57     fixed_design = TRUE
  58   }
  59   M2_t = array(dim=c(d,d,jd_nvects))
  60   for (i in seq_len(jd_nvects))
  61   {
  62     rho = if (fixed_design) c(rep(0,i-1),1,rep(0,d-i)) else normalize( rnorm(d) )
  63     M2_t[,,i] = .T_I_I_w(M[[3]],rho)
  64   }
  65
  66   # Step 2: obtain factors u_i (and their inverse) from the joint diagonalisation of M2_t
  67   jd_method = ifelse(!is.null(optargs$jd_method), optargs$jd_method, "uwedge")
  68   V =
  69     if (jd_nvects > 1) {
  70       # NOTE: increasing itermax does not help to converge, thus we suppress warnings
  71       suppressWarnings({jd = jointDiag::ajd(M2_t, method=jd_method)})
  72       if (jd_method=="uwedge") jd$B else MASS::ginv(jd$A)
  73     }
  74     else
  75       eigen(M2_t[,,1])$vectors
  76
  77   # Step 3: obtain final factors from joint diagonalisation of T(I,I,u_i)
  78   M2_t = array(dim=c(d,d,K))
  79   for (i in seq_len(K))
  80     M2_t[,,i] = .T_I_I_w(M[[3]],V[,i])
  81   suppressWarnings({jd = jointDiag::ajd(M2_t, method=jd_method)})
  82   U = if (jd_method=="uwedge") MASS::ginv(jd$B) else jd$A
  83   μ = normalize(U[,1:K])
  84
  85   # M1 also writes M1 = sum_k coeff_k * μ_k, where coeff_k >= 0
  86   # ==> search decomposition of vector M1 onto the (truncated) basis μ (of size dxK)
  87   # This is a linear system μ %*% C = M1 with C of size K ==> C = psinv(μ) %*% M1
  88   C = MASS::ginv(μ) %*% M[[1]]
  89   μ[,C < 0] = - μ[,C < 0]
  90   μ
  91 }