Package v.1.0 ready to be sent to CRAN
[morpheus.git] / pkg / R / computeMu.R
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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.
d294ece1 15#' \item 'K', number of populations (estimated with rank of M2 if not given)
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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
2b3a6af5 26#'
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27#' @export
28computeMu = function(X, Y, optargs=list())
29{
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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")
cbd88fe5 38
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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 }
cbd88fe5 49
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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 }
cbd88fe5 65
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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) {
0f5fbd13 70 # NOTE: increasing itermax does not help to converge, thus we suppress warnings
6dd5c2ac 71 suppressWarnings({jd = jointDiag::ajd(M2_t, method=jd_method)})
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72 if (jd_method=="uwedge") jd$B else MASS::ginv(jd$A)
73 }
74 else
75 eigen(M2_t[,,1])$vectors
cbd88fe5 76
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77 # Step 3: obtain final factors from joint diagonalisation of T(I,I,u_i)
78 M2_t = array(dim=c(d,d,K))
79 for (i in seq_len(K))
80 M2_t[,,i] = .T_I_I_w(M[[3]],V[,i])
81 suppressWarnings({jd = jointDiag::ajd(M2_t, method=jd_method)})
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82 U = if (jd_method=="uwedge") MASS::ginv(jd$B) else jd$A
83 μ = normalize(U[,1:K])
cbd88fe5 84
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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
cbd88fe5 91}