Nothing
## ----echo=F--------------------------------------------------------------
### get knitr just the way we like it
knitr::opts_chunk$set(
message = FALSE,
warning = FALSE,
error = FALSE,
tidy = FALSE,
cache = FALSE
)
## ------------------------------------------------------------------------
library(stats4)
set.seed(17822)
y <- rpois(n = 40, lambda=10)
# Easy one-dimensional MLE:
nLL <- function(lambda) -sum(stats::dpois(y, lambda, log = TRUE))
fit0 <- mle(nLL, start = list(lambda = 5), nobs = NROW(y))
## ------------------------------------------------------------------------
summary(fit0)
## ------------------------------------------------------------------------
logLik(fit0)
## ------------------------------------------------------------------------
y1 <- y[1:20]
y2 <- y[21:27]
y3 <- y[28:40]
## ------------------------------------------------------------------------
library(gmp)
library(homomorpheR)
Site <- R6::R6Class("Site",
private = list(
## name of the site
name = NA,
## only master has this, NA for workers
privkey = NA,
## local data
data = NA,
## The next site in the communication: NA for master
nextSite = NA,
## is this the master site?
iAmMaster = FALSE,
## intermediate result variable
intermediateResult = NA
),
public = list(
## Common denominator for approximate real arithmetic
den = NA,
## The public key; everyone has this
pubkey = NA,
initialize = function(name, data, den) {
private$name <- name
private$data <- data
self$den <- den
},
setPublicKey = function(pubkey) {
self$pubkey <- pubkey
},
setPrivateKey = function(privkey) {
private$privkey <- privkey
},
## Make me master
makeMeMaster = function() {
private$iAmMaster <- TRUE
},
## add neg log lik and forward to next site
addNLLAndForward = function(lambda, enc.offset) {
if (private$iAmMaster) {
## We are master, so don't forward
## Just store intermediate result and return
private$intermediateResult <- enc.offset
} else {
## We are workers, so add and forward
## add negative log likelihood and forward result to next site
## Note that offset is encrypted
nllValue <- self$nLL(lambda)
result.int <- floor(nllValue)
result.frac <- nllValue - result.int
result.fracnum <- as.bigq(numerator(as.bigq(result.frac) * self$den))
pubkey <- self$pubkey
enc.result.int <- pubkey$encrypt(result.int)
enc.result.fracnum <- pubkey$encrypt(result.fracnum)
result <- list(int = pubkey$add(enc.result.int, enc.offset$int),
frac = pubkey$add(enc.result.fracnum, enc.offset$frac))
private$nextSite$addNLLAndForward(lambda, enc.offset = result)
}
## Return a TRUE result for now.
TRUE
},
## Set the next site in the communication graph
setNextSite = function(nextSite) {
private$nextSite <- nextSite
},
## The negative log likelihood
nLL = function(lambda) {
if (private$iAmMaster) {
## We're master, so need to get result from sites
## 1. Generate a random offset and encrypt it
pubkey <- self$pubkey
offset <- list(int = random.bigz(nBits = 256),
frac = random.bigz(nBits = 256))
enc.offset <- list(int = pubkey$encrypt(offset$int),
frac = pubkey$encrypt(offset$frac))
## 2. Send off to next site
throwaway <- private$nextSite$addNLLAndForward(lambda, enc.offset)
## 3. When the call returns, the result will be in
## the field intermediateResult, so decrypt that.
sum <- private$intermediateResult
privkey <- private$privkey
intResult <- as.double(privkey$decrypt(sum$int) - offset$int)
fracResult <- as.double(as.bigq(privkey$decrypt(sum$frac) - offset$frac) / den)
intResult + fracResult
} else {
## We're worker, so compute local nLL
-sum(stats::dpois(private$data, lambda, log = TRUE))
}
})
)
## ------------------------------------------------------------------------
keys <- PaillierKeyPair$new(1024) ## Generate new public and private key.
den <- gmp::as.bigq(2)^256 #Our denominator for rational approximations
## ------------------------------------------------------------------------
site1 <- Site$new(name = "Site 1", data = y1, den = den)
site2 <- Site$new(name = "Site 2", data = y2, den = den)
site3 <- Site$new(name = "Site 3", data = y3, den = den)
## ------------------------------------------------------------------------
## Master has no data!
master <- Site$new(name = "Master", data = c(), den = den)
master$makeMeMaster()
## ------------------------------------------------------------------------
site1$setPublicKey(keys$pubkey)
site2$setPublicKey(keys$pubkey)
site3$setPublicKey(keys$pubkey)
master$setPublicKey(keys$pubkey)
## ------------------------------------------------------------------------
master$setPrivateKey(keys$getPrivateKey())
## ------------------------------------------------------------------------
master$setNextSite(site1)
site1$setNextSite(site2)
site2$setNextSite(site3)
site3$setNextSite(master)
## ------------------------------------------------------------------------
fit1 <- mle(master$nLL, start = list(lambda = 5))
## ------------------------------------------------------------------------
summary(fit1)
## ------------------------------------------------------------------------
logLik(fit1)
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