Fix typos and mistakes
[morpheus.git] / pkg / R / optimParams.R
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4263503b 1#' Wrapper function for OptimParams class
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2#'
3#' @param K Number of populations.
4#' @param link The link type, 'logit' or 'probit'.
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5#' @param X Data matrix of covariables
6#' @param Y Output as a binary vector
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7#'
8#' @return An object 'op' of class OptimParams, initialized so that \code{op$run(x0)}
9#' outputs the list of optimized parameters
10#' \itemize{
11#' \item p: proportions, size K
12#' \item β: regression matrix, size dxK
13#' \item b: intercepts, size K
14#' }
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15#' θ0 is a vector containing respectively the K-1 first elements of p, then β by
16#' columns, and finally b: \code{θ0 = c(p[1:(K-1)],as.double(β),b)}.
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17#'
18#' @seealso \code{multiRun} to estimate statistics based on β, and
19#' \code{generateSampleIO} for I/O random generation.
20#'
21#' @examples
22#' # Optimize parameters from estimated μ
23#' io = generateSampleIO(10000, 1/2, matrix(c(1,-2,3,1),ncol=2), c(0,0), "logit")
24#' μ = computeMu(io$X, io$Y, list(K=2))
4263503b 25#' o <- optimParams(io$X, io$Y, 2, "logit")
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26#' θ0 <- list(p=1/2, β=μ, b=c(0,0))
27#' par0 <- o$run(θ0)
cbd88fe5 28#' # Compare with another starting point
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29#' θ1 <- list(p=1/2, β=2*μ, b=c(0,0))
30#' par1 <- o$run(θ1)
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31#' o$f( o$linArgs(par0) )
32#' o$f( o$linArgs(par1) )
33#' @export
b389a46a 34optimParams <- function(X, Y, K, link=c("logit","probit"))
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35{
36 # Check arguments
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37 if (!is.matrix(X) || any(is.na(X)))
38 stop("X: numeric matrix, no NAs")
39 if (!is.numeric(Y) || any(is.na(Y)) || any(Y!=0 | Y!=1))
40 stop("Y: binary vector with 0 and 1 only")
cbd88fe5 41 link <- match.arg(link)
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42 if (!is.numeric(K) || K!=floor(K) || K < 2)
43 stop("K: integer >= 2")
cbd88fe5 44
cbd88fe5 45 # Build and return optimization algorithm object
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46 methods::new("OptimParams", "li"=link, "X"=X,
47 "Y"=as.integer(Y), "K"=as.integer(K))
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48}
49
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50#' Encapsulated optimization for p (proportions), β and b (regression parameters)
51#'
52#' Optimize the parameters of a mixture of logistic regressions model, possibly using
53#' \code{mu <- computeMu(...)} as a partial starting point.
54#'
55#' @field li Link function, 'logit' or 'probit'
56#' @field X Data matrix of covariables
57#' @field Y Output as a binary vector
58#' @field K Number of populations
59#' @field d Number of dimensions
60#' @field W Weights matrix (iteratively refined)
61#'
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62setRefClass(
63 Class = "OptimParams",
64
65 fields = list(
66 # Inputs
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67 li = "character", #link function
68 X = "matrix",
69 Y = "numeric",
7737c2fa 70 Mhat = "numeric", #vector of empirical moments
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71 # Dimensions
72 K = "integer",
4263503b 73 n = "integer",
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74 d = "integer",
75 # Weights matrix (generalized least square)
76 W = "matrix"
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77 ),
78
79 methods = list(
80 initialize = function(...)
81 {
4263503b 82 "Check args and initialize K, d, W"
cbd88fe5 83
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84 callSuper(...)
85 if (!hasArg("X") || !hasArg("Y") || !hasArg("K") || !hasArg("li"))
cbd88fe5 86 stop("Missing arguments")
cbd88fe5 87
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88 # Precompute empirical moments
89 M <- computeMoments(optargs$X,optargs$Y)
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90 M1 <- as.double(M[[1]])
91 M2 <- as.double(M[[2]])
92 M3 <- as.double(M[[3]])
93 Mhat <<- matrix(c(M1,M2,M3), ncol=1)
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94
95 n <<- nrow(X)
cbd88fe5 96 d <<- length(M1)
e92d9d9d 97 W <<- diag(d+d^2+d^3) #initialize at W = Identity
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98 },
99
7737c2fa 100 expArgs = function(v)
cbd88fe5 101 {
7737c2fa 102 "Expand individual arguments from vector v into a list"
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103
104 list(
105 # p: dimension K-1, need to be completed
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106 "p" = c(v[1:(K-1)], 1-sum(v[1:(K-1)])),
107 "β" = matrix(v[K:(K+d*K-1)], ncol=K),
108 "b" = v[(K+d*K):(K+(d+1)*K-1)])
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109 },
110
7737c2fa 111 linArgs = function(L)
cbd88fe5 112 {
7737c2fa 113 "Linearize vectors+matrices from list L into a vector"
cbd88fe5 114
7737c2fa 115 c(L$p[1:(K-1)], as.double(L$β), L$b)
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116 },
117
7737c2fa 118 computeW = function(θ)
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119 {
120 dim <- d + d^2 + d^3
7737c2fa 121 W <<- solve( matrix( .C("Compute_Omega",
b389a46a 122 X=as.double(X), Y=as.double(Y), M=as.double(Moments(θ)),
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123 pn=as.integer(n), pd=as.integer(d),
124 W=as.double(W), PACKAGE="morpheus")$W, nrow=dim, ncol=dim) )
125 NULL #avoid returning W
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126 },
127
b389a46a 128 Moments = function(θ)
4263503b 129 {
7737c2fa 130 "Vector of moments, of size d+d^2+d^3"
cbd88fe5 131
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132 p <- θ$p
133 β <- θ$β
cbd88fe5 134 λ <- sqrt(colSums(β^2))
7737c2fa 135 b <- θ$b
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136
137 # Tensorial products β^2 = β2 and β^3 = β3 must be computed from current β1
138 β2 <- apply(β, 2, function(col) col %o% col)
139 β3 <- apply(β, 2, function(col) col %o% col %o% col)
140
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141 matrix(c(
142 β %*% (p * .G(li,1,λ,b)),
143 β2 %*% (p * .G(li,2,λ,b)),
144 β3 %*% (p * .G(li,3,λ,b))), ncol=1)
145 },
146
147 f = function(θ)
148 {
149 "Product t(Mi - hat_Mi) W (Mi - hat_Mi) with Mi(theta)"
150
b389a46a 151 A <- Moments(θ) - Mhat
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152 t(A) %*% W %*% A
153 },
cbd88fe5 154
7737c2fa 155 grad_f = function(θ)
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156 {
157 "Gradient of f, dimension (K-1) + d*K + K = (d+2)*K - 1"
158
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159 -2 * t(grad_M(θ)) %*% W %*% (Mhat - Moments(θ))
160 },
4263503b 161
7737c2fa 162 grad_M = function(θ)
4263503b 163 {
7737c2fa 164 "Gradient of the vector of moments, size (dim=)d+d^2+d^3 x K-1+K+d*K"
4263503b 165
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166 L <- expArgs(θ)
167 p <- L$p
168 β <- L$β
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169 λ <- sqrt(colSums(β^2))
170 μ <- sweep(β, 2, λ, '/')
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171 b <- L$b
172
173 res <- matrix(nrow=nrow(W), ncol=0)
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174
175 # Tensorial products β^2 = β2 and β^3 = β3 must be computed from current β1
176 β2 <- apply(β, 2, function(col) col %o% col)
177 β3 <- apply(β, 2, function(col) col %o% col %o% col)
178
179 # Some precomputations
180 G1 = .G(li,1,λ,b)
181 G2 = .G(li,2,λ,b)
182 G3 = .G(li,3,λ,b)
183 G4 = .G(li,4,λ,b)
184 G5 = .G(li,5,λ,b)
185
7737c2fa 186 # Gradient on p: K-1 columns, dim rows
cbd88fe5 187 km1 = 1:(K-1)
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188 res <- cbind(res, rbind(
189 t( sweep(as.matrix(β [,km1]), 2, G1[km1], '*') - G1[K] * β [,K] ),
190 t( sweep(as.matrix(β2[,km1]), 2, G2[km1], '*') - G2[K] * β2[,K] ),
191 t( sweep(as.matrix(β3[,km1]), 2, G3[km1], '*') - G3[K] * β3[,K] )))
cbd88fe5 192
d08fef42 193 # TODO: understand derivatives order and match the one in optim init param
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194 for (i in 1:d)
195 {
196 # i determines the derivated matrix dβ[2,3]
197
198 dβ_left <- sweep(β, 2, p * G3 * β[i,], '*')
199 dβ_right <- matrix(0, nrow=d, ncol=K)
200 block <- i
201 dβ_right[block,] <- dβ_right[block,] + 1
202 dβ <- dβ_left + sweep(dβ_right, 2, p * G1, '*')
203
204 dβ2_left <- sweep(β2, 2, p * G4 * β[i,], '*')
205 dβ2_right <- do.call( rbind, lapply(1:d, function(j) {
206 sweep(dβ_right, 2, β[j,], '*')
207 }) )
208 block <- ((i-1)*d+1):(i*d)
209 dβ2_right[block,] <- dβ2_right[block,] + β
210 dβ2 <- dβ2_left + sweep(dβ2_right, 2, p * G2, '*')
211
212 dβ3_left <- sweep(β3, 2, p * G5 * β[i,], '*')
213 dβ3_right <- do.call( rbind, lapply(1:d, function(j) {
214 sweep(dβ2_right, 2, β[j,], '*')
215 }) )
216 block <- ((i-1)*d*d+1):(i*d*d)
217 dβ3_right[block,] <- dβ3_right[block,] + β2
218 dβ3 <- dβ3_left + sweep(dβ3_right, 2, p * G3, '*')
219
7737c2fa 220 res <- cbind(res, rbind(t(dβ), t(dβ2), t(dβ3)))
cbd88fe5 221 }
cbd88fe5 222
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223 # Gradient on b
224 res <- cbind(res, rbind(
225 t( sweep(β, 2, p * G2, '*') ),
226 t( sweep(β2, 2, p * G3, '*') ),
227 t( sweep(β3, 2, p * G4, '*') )))
cbd88fe5 228
7737c2fa 229 res
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230 },
231
7737c2fa 232 run = function(θ0)
cbd88fe5 233 {
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234 "Run optimization from θ0 with solver..."
235
236 if (!is.list(θ0))
237 stop("θ0: list")
238 if (is.null(θ0$β))
239 stop("At least θ0$β must be provided")
240 if (!is.matrix(θ0$β) || any(is.na(θ0$β)) || ncol(θ0$β) != K)
241 stop("θ0$β: matrix, no NA, ncol == K")
242 if (is.null(θ0$p))
243 θ0$p = rep(1/K, K-1)
244 else if (length(θ0$p) != K-1 || sum(θ0$p) > 1)
245 stop("θ0$p should contain positive integers and sum to < 1")
d294ece1 246 # Next test = heuristic to detect missing b (when matrix is called "beta")
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247 if (is.null(θ0$b) || all(θ0$b == θ0$β))
248 θ0$b = rep(0, K)
249 else if (any(is.na(θ0$b)))
250 stop("θ0$b cannot have missing values")
d294ece1 251
7737c2fa 252 op_res = constrOptim( linArgs(θ0), .self$f, .self$grad_f,
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253 ui=cbind(
254 rbind( rep(-1,K-1), diag(K-1) ),
255 matrix(0, nrow=K, ncol=(d+1)*K) ),
256 ci=c(-1,rep(0,K-1)) )
257
7737c2fa 258 # debug:
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259 #computeW(expArgs(op_res$par))
260 #print(W)
7737c2fa 261 # We get a first non-trivial estimation of W
4263503b 262 # TODO: loop, this redefine f, so that we can call constrOptim again...
b389a46a 263 # Stopping condition? N iterations? Delta <= epsilon ?
4263503b 264
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265 expArgs(op_res$par)
266 }
267 )
268)
269
270# Compute vectorial E[g^{(order)}(<β,x> + b)] with x~N(0,Id) (integral in R^d)
271# = E[g^{(order)}(z)] with z~N(b,diag(λ))
4263503b 272# by numerically evaluating the integral.
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273#
274# @param link Link, 'logit' or 'probit'
275# @param order Order of derivative
276# @param λ Norm of columns of β
277# @param b Intercept
278#
279.G <- function(link, order, λ, b)
280{
281 # NOTE: weird "integral divergent" error on inputs:
282 # link="probit"; order=2; λ=c(531.8099,586.8893,523.5816); b=c(-118.512674,-3.488020,2.109969)
283 # Switch to pracma package for that (but it seems slow...)
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284 sapply( seq_along(λ), function(k) {
285 res <- NULL
286 tryCatch({
287 # Fast code, may fail:
288 res <- stats::integrate(
289 function(z) .deriv[[link]][[order]](λ[k]*z+b[k]) * exp(-z^2/2) / sqrt(2*pi),
290 lower=-Inf, upper=Inf )$value
291 }, error = function(e) {
292 # Robust slow code, no fails observed:
293 sink("/dev/null") #pracma package has some useless printed outputs...
294 res <- pracma::integral(
295 function(z) .deriv[[link]][[order]](λ[k]*z+b[k]) * exp(-z^2/2) / sqrt(2*pi),
296 xmin=-Inf, xmax=Inf, method="Kronrod")
297 sink()
298 })
299 res
300 })
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301}
302
303# Derivatives list: g^(k)(x) for links 'logit' and 'probit'
304#
305.deriv <- list(
306 "probit"=list(
307 # 'probit' derivatives list;
4263503b 308 # NOTE: exact values for the integral E[g^(k)(λz+b)] could be computed
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309 function(x) exp(-x^2/2)/(sqrt(2*pi)), #g'
310 function(x) exp(-x^2/2)/(sqrt(2*pi)) * -x, #g''
311 function(x) exp(-x^2/2)/(sqrt(2*pi)) * ( x^2 - 1), #g^(3)
312 function(x) exp(-x^2/2)/(sqrt(2*pi)) * (-x^3 + 3*x), #g^(4)
313 function(x) exp(-x^2/2)/(sqrt(2*pi)) * ( x^4 - 6*x^2 + 3) #g^(5)
314 ),
315 "logit"=list(
316 # Sigmoid derivatives list, obtained with http://www.derivative-calculator.net/
317 # @seealso http://www.ece.uc.edu/~aminai/papers/minai_sigmoids_NN93.pdf
318 function(x) {e=exp(x); .zin(e /(e+1)^2)}, #g'
319 function(x) {e=exp(x); .zin(e*(-e + 1) /(e+1)^3)}, #g''
320 function(x) {e=exp(x); .zin(e*( e^2 - 4*e + 1) /(e+1)^4)}, #g^(3)
321 function(x) {e=exp(x); .zin(e*(-e^3 + 11*e^2 - 11*e + 1) /(e+1)^5)}, #g^(4)
322 function(x) {e=exp(x); .zin(e*( e^4 - 26*e^3 + 66*e^2 - 26*e + 1)/(e+1)^6)} #g^(5)
323 )
324)
325
326# Utility for integration: "[return] zero if [argument is] NaN" (Inf / Inf divs)
327#
328# @param x Ratio of polynoms of exponentials, as in .S[[i]]
329#
330.zin <- function(x)
331{
332 x[is.nan(x)] <- 0.
333 x
334}