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### tests for stochastic gradient ascent
###
### do not run unless 'NOT_CRAN' explicitly defined
### (Suggested by Sebastian Meyer and others)
if(!identical(Sys.getenv("NOT_CRAN"), "true")) {
message("We are on CRAN: skipping slow optimizer tests")
q("no")
}
if(!requireNamespace("tinytest", quietly = TRUE)) {
message("These tests require 'tinytest' package\n")
q("no")
}
library(maxLik)
### Test the following things:
###
### 1. basic 2-D SGA
### SGA without function, only gradient
### SGA neither function nor gradient
### SGA in 1-D case
### 2. SGA w/momentum
### 3. SGA full batch
### 4. SGA, no gradient supplied
### SGA, return numeric hessian, gradient provided
### SGA, return numeric hessian, no gradient provided
### SGA, printlevel 1, storeValues
### SGA, NA as iterlim: should give informative error
### SGA, storeValues but no fn (should fail)
###
### using highly unequally scaled data
### SGA without gradient clipping (fails)
### SGA with gradient clipping (works, although does not converge)
## ---------- OLS
## log-likelihood function(s):
## return log-likelihood on validation data
loglik <- function(beta, index) {
e <- yValid - XValid %*% beta
-crossprod(e)/length(y)
}
## gradlik: work on training data
gradlik <- function(beta, index) {
e <- yTrain[index] - XTrain[index,,drop=FALSE] %*% beta
g <- t(-2*t(XTrain[index,,drop=FALSE]) %*% e)
-g/length(index)
}
### create random data
set.seed(1)
N <- 1000
x <- rnorm(N)
X <- cbind(1, x)
y <- 100 + 100*x + rnorm(N)
## training-validation
iTrain <- sample(N, 0.8*N)
XTrain <- X[iTrain,,drop=FALSE]
XValid <- X[-iTrain,,drop=FALSE]
yTrain <- y[iTrain]
yValid <- y[-iTrain]
## Analytic solution (training data):
start <- c(const=10, x=10)
b0 <- drop(solve(crossprod(XTrain)) %*% crossprod(XTrain, yTrain))
names(b0) <- names(start)
tol <- 1e-3 # coefficient tolerance
## ---------- 1. working example
res <- maxSGA(loglik, gradlik, start=start,
control=list(printLevel=0, iterlim=200,
SG_batchSize=100, SG_learningRate=0.1,
storeValues=TRUE),
nObs=length(yTrain))
expect_equal(coef(res), b0, tolerance=tol)
# SGA usually ends with gradient not equal to 0 so we don't test that
## ---------- store parameters
res <- maxSGA(loglik, gradlik, start=start,
control=list(printLevel=0, iterlim=20,
SG_batchSize=100, SG_learningRate=0.1,
storeParameters=TRUE),
nObs=length(yTrain))
expect_equal(dim(storedParameters(res)), c(1 + nIter(res), 2))
## ---------- no function, only gradient
expect_silent(
res <- maxSGA(grad=gradlik, start=start,
control=list(printLevel=0, iterlim=10, SG_batchSize=100),
nObs=length(yTrain))
)
## ---------- neither function nor gradient
expect_error(
res <- maxSGA(start=start,
control=list(printLevel=0, iterlim=10, SG_batchSize=100),
nObs=length(yTrain))
)
## ---------- 1D case
N1 <- 1000
t <- rexp(N1, 2)
loglik1 <- function(theta, index) sum(log(theta) - theta*t[index])
gradlik1 <- function(theta, index) sum(1/theta - t[index])
expect_silent(
res <- maxSGA(loglik1, gradlik1, start=1,
control=list(iterlim=300, SG_batchSize=20), nObs=length(t))
)
expect_equal(coef(res), 1/mean(t), tolerance=0.2)
expect_null(hessian(res))
## ---------- 2. SGA with momentum
expect_silent(
res <- maxSGA(loglik, gradlik, start=start,
control=list(printLevel=0, iterlim=200,
SG_batchSize=100, SG_learningRate=0.1, SGA_momentum=0.9),
nObs=length(yTrain))
)
expect_equal(coef(res), b0, tolerance=tol)
## ---------- 3. full batch
expect_silent(
res <- maxSGA(loglik, gradlik, start=start,
control=list(printLevel=0, iterlim=200,
SG_batchSize=NULL, SG_learningRate=0.1),
nObs=length(yTrain))
)
expect_equal(coef(res), b0, tolerance=tol)
## ---------- 4. no gradient
expect_silent(
res <- maxSGA(loglik, start=start,
control=list(iterlim=1000, SG_learningRate=0.02), nObs=length(yTrain))
)
expect_equal(coef(res), b0, tolerance=tol)
## ---------- return Hessian, gradient provided
expect_silent(
res <- maxSGA(loglik, gradlik, start=start,
control=list(iterlim=1000, SG_learningRate=0.02),
nObs=length(yTrain),
finalHessian=TRUE)
)
expect_equal(coef(res), b0, tolerance=tol)
expect_equal(dim(hessian(res)), c(2,2))
## ---------- return Hessian, no gradient
expect_silent(
res <- maxSGA(loglik, start=start,
control=list(iterlim=1000, SG_learningRate=0.02),
nObs=length(yTrain),
finalHessian=TRUE)
)
expect_equal(coef(res), b0, tolerance=tol)
expect_equal(dim(hessian(res)), c(2,2))
### ---------- SGA, printlevel 1, storeValues ----------
### it should just work
expect_silent(
res <- maxSGA(loglik, gradlik, start=start,
control=list(iterlim=2, storeValues=TRUE, printLevel=1),
nObs=length(yTrain),
finalHessian=TRUE)
)
### ---------- SGA, NA as iterlim ----------
### should give informative error
expect_error(
res <- maxSGA(loglik, gradlik, start=start,
control=list(iterlim=NA),
nObs=length(yTrain),
finalHessian=TRUE),
pattern = "invalid class \"MaxControl\" object: NA in 'iterlim'"
)
### ---------- SGA, fn missing but storeValues=TRUE
### should give informative error
expect_error(
res <- maxSGA(grad=gradlik, start=start,
control=list(iterlim=10, storeValues=TRUE),
nObs=length(yTrain)),
pattern = "Cannot compute the objective function value: no objective function supplied"
)
## ---------- gradient by observations
gradlikO <- function(beta, index) {
e <- yTrain[index] - XTrain[index,,drop=FALSE] %*% beta
g <- -2*drop(e)*XTrain[index,,drop=FALSE]
-g/length(index)
}
expect_silent(
res <- maxSGA(grad=gradlikO, start=start,
control=list(printLevel=0, iterlim=100,
SG_batchSize=100),
nObs=length(yTrain))
)
expect_equal(coef(res), b0, tolerance=tol)
## ---------- 0 iterations
expect_silent(
res <- maxSGA(grad=gradlik, start=start,
control=list(iterlim=0),
nObs=length(yTrain))
)
expect_equal(coef(res), start)
# should return start values exactly
### -------------------- create unequally scaled data
set.seed(1)
N <- 1000
x <- rnorm(N, sd=100)
XTrain <- cbind(1, x)
yTrain <- 1 + x + rnorm(N)
start <- c(const=10, x=10)
## ---------- no gradient clipping:
## should fail with informative "NA/Inf in gradient" message
expect_error(
res <- maxSGA(loglik, gradlik, start=start,
control=list(iterlim=100, SG_learningRate=0.5),
nObs=length(yTrain)),
pattern = "NA/Inf in gradient"
)
## ---------- gradient clipping: should not fail
expect_silent(
res <- maxSGA(loglik, gradlik, start=start,
control=list(iterlim=100, SG_learningRate=0.5,
SG_clip=1e6),
nObs=length(yTrain)
)
)
|
