update EMGLLF.c following changes in EMGLLF.R
[valse.git] / pkg / R / EMGLLF.R
1 #' EMGLLF
2 #'
3 #' Description de EMGLLF
4 #'
5 #' @param phiInit an initialization for phi
6 #' @param rhoInit an initialization for rho
7 #' @param piInit an initialization for pi
8 #' @param gamInit initialization for the a posteriori probabilities
9 #' @param mini integer, minimum number of iterations in the EM algorithm, by default = 10
10 #' @param maxi integer, maximum number of iterations in the EM algorithm, by default = 100
11 #' @param gamma integer for the power in the penaly, by default = 1
12 #' @param lambda regularization parameter in the Lasso estimation
13 #' @param X matrix of covariates (of size n*p)
14 #' @param Y matrix of responses (of size n*m)
15 #' @param eps real, threshold to say the EM algorithm converges, by default = 1e-4
16 #'
17 #' @return A list ... phi,rho,pi,LLF,S,affec:
18 #' phi : parametre de moyenne renormalisé, calculé par l'EM
19 #' rho : parametre de variance renormalisé, calculé par l'EM
20 #' pi : parametre des proportions renormalisé, calculé par l'EM
21 #' LLF : log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
22 #' S : ...
23 #' affec : ...
24 #'
25 #' @export
26 EMGLLF <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
27 X, Y, eps, fast)
28 {
29 if (!fast)
30 {
31 # Function in R
32 return(.EMGLLF_R(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
33 X, Y, eps))
34 }
35
36 # Function in C
37 n <- nrow(X) #nombre d'echantillons
38 p <- ncol(X) #nombre de covariables
39 m <- ncol(Y) #taille de Y (multivarié)
40 k <- length(piInit) #nombre de composantes dans le mélange
41 .Call("EMGLLF", phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
42 X, Y, eps, phi = double(p * m * k), rho = double(m * m * k), pi = double(k),
43 LLF = double(maxi), S = double(p * m * k), affec = integer(n), n, p, m, k,
44 PACKAGE = "valse")
45 list(phi = phi, rho = rho, pi = pi, llh = llh, S = S, affec=affec)
46 }
47
48 # R version - slow but easy to read
49 .EMGLLF_R <- function(phiInit, rhoInit, piInit, gamInit, mini, maxi, gamma, lambda,
50 X, Y, eps)
51 {
52 # Matrix dimensions
53 n <- nrow(X)
54 p <- ncol(X)
55 m <- ncol(Y)
56 k <- length(piInit)
57
58 # Adjustments required when p==1 or m==1 (var.sel. or output dim 1)
59 if (p==1 || m==1)
60 phiInit <- array(phiInit, dim=c(p,m,k))
61 if (m==1)
62 rhoInit <- array(rhoInit, dim=c(m,m,k))
63
64 # Outputs
65 phi <- phiInit
66 rho <- rhoInit
67 pi <- piInit
68 llh <- -Inf
69 S <- array(0, dim = c(p, m, k))
70
71 # Algorithm variables
72 gam <- gamInit
73 Gram2 <- array(0, dim = c(p, p, k))
74 ps2 <- array(0, dim = c(p, m, k))
75 X2 <- array(0, dim = c(n, p, k))
76 Y2 <- array(0, dim = c(n, m, k))
77
78 for (ite in 1:maxi)
79 {
80 # Remember last pi,rho,phi values for exit condition in the end of loop
81 Phi <- phi
82 Rho <- rho
83 Pi <- pi
84
85 # Computations associated to X and Y
86 for (r in 1:k)
87 {
88 for (mm in 1:m)
89 Y2[, mm, r] <- sqrt(gam[, r]) * Y[, mm]
90 for (i in 1:n)
91 X2[i, , r] <- sqrt(gam[i, r]) * X[i, ]
92 for (mm in 1:m)
93 ps2[, mm, r] <- crossprod(X2[, , r], Y2[, mm, r])
94 for (j in 1:p)
95 {
96 for (s in 1:p)
97 Gram2[j, s, r] <- crossprod(X2[, j, r], X2[, s, r])
98 }
99 }
100
101 ## M step
102
103 # For pi
104 b <- sapply(1:k, function(r) sum(abs(phi[, , r])))
105 gam2 <- colSums(gam)
106 a <- sum(gam %*% log(pi))
107
108 # While the proportions are nonpositive
109 kk <- 0
110 pi2AllPositive <- FALSE
111 while (!pi2AllPositive)
112 {
113 pi2 <- pi + 0.1^kk * ((1/n) * gam2 - pi)
114 pi2AllPositive <- all(pi2 >= 0)
115 kk <- kk + 1
116 }
117
118 # t(m) is the largest value in the grid O.1^k such that it is nonincreasing
119 while (kk < 1000 && -a/n + lambda * sum(pi^gamma * b) <
120 # na.rm=TRUE to handle 0*log(0)
121 -sum(gam2 * log(pi2), na.rm=TRUE)/n + lambda * sum(pi2^gamma * b))
122 {
123 pi2 <- pi + 0.1^kk * (1/n * gam2 - pi)
124 kk <- kk + 1
125 }
126 t <- 0.1^kk
127 pi <- (pi + t * (pi2 - pi))/sum(pi + t * (pi2 - pi))
128
129 # For phi and rho
130 for (r in 1:k)
131 {
132 for (mm in 1:m)
133 {
134 ps <- 0
135 for (i in 1:n)
136 ps <- ps + Y2[i, mm, r] * sum(X2[i, , r] * phi[, mm, r])
137 nY2 <- sum(Y2[, mm, r]^2)
138 rho[mm, mm, r] <- (ps + sqrt(ps^2 + 4 * nY2 * gam2[r]))/(2 * nY2)
139 }
140 }
141
142 for (r in 1:k)
143 {
144 for (j in 1:p)
145 {
146 for (mm in 1:m)
147 {
148 S[j, mm, r] <- -rho[mm, mm, r] * ps2[j, mm, r] +
149 sum(phi[-j, mm, r] * Gram2[j, -j, r])
150 if (abs(S[j, mm, r]) <= n * lambda * (pi[r]^gamma)) {
151 phi[j, mm, r] <- 0
152 } else if (S[j, mm, r] > n * lambda * (pi[r]^gamma)) {
153 phi[j, mm, r] <- (n * lambda * (pi[r]^gamma) - S[j, mm, r])/Gram2[j, j, r]
154 } else {
155 phi[j, mm, r] <- -(n * lambda * (pi[r]^gamma) + S[j, mm, r])/Gram2[j, j, r]
156 }
157 }
158 }
159 }
160
161 ## E step
162
163 # Precompute det(rho[,,r]) for r in 1...k
164 detRho <- sapply(1:k, function(r) gdet(rho[, , r]))
165 sumLogLLH <- 0
166 for (i in 1:n)
167 {
168 # Update gam[,]; use log to avoid numerical problems
169 logGam <- sapply(1:k, function(r) {
170 log(pi[r]) + log(detRho[r]) - 0.5 *
171 sum((Y[i, ] %*% rho[, , r] - X[i, ] %*% phi[, , r])^2)
172 })
173
174 logGam <- logGam - max(logGam) #adjust without changing proportions
175 gam[i, ] <- exp(logGam)
176 norm_fact <- sum(gam[i, ])
177 gam[i, ] <- gam[i, ] / norm_fact
178 sumLogLLH <- sumLogLLH + log(norm_fact) - log((2 * base::pi)^(m/2))
179 }
180
181 sumPen <- sum(pi^gamma * b)
182 last_llh <- llh
183 llh <- -sumLogLLH/n #+ lambda * sumPen
184 dist <- ifelse(ite == 1, llh, (llh - last_llh)/(1 + abs(llh)))
185 Dist1 <- max((abs(phi - Phi))/(1 + abs(phi)))
186 Dist2 <- max((abs(rho - Rho))/(1 + abs(rho)))
187 Dist3 <- max((abs(pi - Pi))/(1 + abs(Pi)))
188 dist2 <- max(Dist1, Dist2, Dist3)
189
190 if (ite >= mini && (dist >= eps || dist2 >= sqrt(eps)))
191 break
192 }
193
194 affec = apply(gam, 1, which.max)
195 list(phi = phi, rho = rho, pi = pi, llh = llh, S = S, affec=affec)
196 }