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 #' @export
  27 computeMu = function(X, Y, optargs=list())
  28 {
  29     if (!is.matrix(X) || !is.numeric(X) || any(is.na(X)))
  30         stop("X: real matrix, no NA")
  31     n = nrow(X)
  32     d = ncol(X)
  33     if (!is.numeric(Y) || length(Y)!=n || any(Y!=0 & Y!=1))
  34         stop("Y: vector of 0 and 1, size nrow(X), no NA")
  35     if (!is.list(optargs))
  36         stop("optargs: list")
  37
  38     # Step 0: Obtain the empirically estimated moments tensor, estimate also K
  39     M = if (is.null(optargs$M)) computeMoments(X,Y) else optargs$M
  40     K = optargs$K
  41     if (is.null(K))
  42     {
  43         # TODO: improve this basic heuristic
  44         Σ = svd(M[[2]])$d
  45         large_ratio <- ( abs(Σ[-d] / Σ[-1]) > 3 )
  46         K <- if (any(large_ratio)) max(2, which.min(large_ratio)) else d
  47     }
  48
  49     # Step 1: generate a family of d matrices to joint-diagonalize to increase robustness
  50     d = ncol(X)
  51     fixed_design = FALSE
  52     jd_nvects = ifelse(!is.null(optargs$jd_nvects), optargs$jd_nvects, 0)
  53     if (jd_nvects == 0)
  54     {
  55         jd_nvects = d
  56         fixed_design = TRUE
  57     }
  58     M2_t = array(dim=c(d,d,jd_nvects))
  59     for (i in seq_len(jd_nvects))
  60     {
  61         rho = if (fixed_design) c(rep(0,i-1),1,rep(0,d-i)) else normalize( rnorm(d) )
  62         M2_t[,,i] = .T_I_I_w(M[[3]],rho)
  63     }
  64
  65     # Step 2: obtain factors u_i (and their inverse) from the joint diagonalisation of M2_t
  66     jd_method = ifelse(!is.null(optargs$jd_method), optargs$jd_method, "uwedge")
  67     V =
  68         if (jd_nvects > 1) {
  69             #NOTE: increasing itermax does not help to converge, thus we suppress warnings
  70             suppressWarnings({jd = jointDiag::ajd(M2_t, method=jd_method)})
  71 #           if (jd_method=="uwedge") jd$B else solve(jd$A)
  72             if (jd_method=="uwedge") jd$B else MASS::ginv(jd$A)
  73         }
  74         else
  75             eigen(M2_t[,,1])$vectors
  76
  77     # Step 3: obtain final factors from joint diagonalisation of T(I,I,u_i)
  78     M2_t = array(dim=c(d,d,K))
  79     for (i in seq_len(K))
  80         M2_t[,,i] = .T_I_I_w(M[[3]],V[,i])
  81     suppressWarnings({jd = jointDiag::ajd(M2_t, method=jd_method)})
  82 #   U = if (jd_method=="uwedge") solve(jd$B) else jd$A
  83     U = if (jd_method=="uwedge") MASS::ginv(jd$B) else jd$A
  84     μ = normalize(U[,1:K])
  85
  86     # M1 also writes M1 = sum_k coeff_k * μ_k, where coeff_k >= 0
  87     # ==> search decomposition of vector M1 onto the (truncated) basis μ (of size dxK)
  88     # This is a linear system μ %*% C = M1 with C of size K ==> C = psinv(μ) %*% M1
  89     C = MASS::ginv(μ) %*% M[[1]]
  90     μ[,C < 0] = - μ[,C < 0]
  91     μ
  92 }