CODEWITHSUNDEEP
rglmnetr-caret
stmax
stmax

Reputation: 6595

glmnet refuses to predict

I have a glm model that works. Since I'd like to add (ridge) regularization I thought I'd switch to glmnet. For some reason I cannot get glmnet to work. It seems to always predict the first class, never the second, which results in low accuracy and kappa = 0.

Below is some code to reproduce the problem. What am I doing wrong?

The test data it generates looks like this:

Data

Since the data cannot be linearly separated two polynomial terms A^2 and B^2 are added.

A glm model predicts the data correctly (with accuracy = 1 and kappa = 1). Here is its prediction boundary:

GLM

While a glmnet model always has kappa = 0, no matter what lambda it tries:

  lambda  Accuracy  Kappa  Accuracy SD  Kappa SD
  0       0.746     0      0.0295       0       
  1e-04   0.746     0      0.0295       0       
  0.01    0.746     0      0.0295       0       
  0.1     0.746     0      0.0295       0       
  1       0.746     0      0.0295       0       
  10      0.746     0      0.0295       0

Code to reproduce the problem:

library(caret)

# generate test data
set.seed(42)
n <- 500; m <- 100
data <- data.frame(A=runif(n, 98, 102), B=runif(n, 98, 102), Type="foo")
data <- subset(data, sqrt((A-100)^2 + (B-100)^2) > 1.5)
data <- rbind(data, data.frame(A=rnorm(m, 100, 0.25), B=rnorm(m, 100, 0.25), Type="bar"))

# add a few polynomial features to match ellipses
polymap <- function(data) cbind(data, A2=data$A^2, B2=data$B^2)
data <- polymap(data)

plot(x=data$A, y=data$B, pch=21, bg=data$Type, xlab="A", ylab="B")

# train a binomial glm model
model.glm <- train(Type ~ ., data=data, method="glm", family="binomial",
                   preProcess=c("center", "scale"))

# train a binomial glmnet model with ridge regularization (alpha = 0)
model.glmnet <- train(Type ~ ., data=data, method="glmnet", family="binomial",
                      preProcess=c("center", "scale"),
                      tuneGrid=expand.grid(alpha=0, lambda=c(0, 0.0001, 0.01, 0.1, 1, 10)))

print(model.glm)    # <- Accuracy = 1,   Kappa = 1 - good!
print(model.glmnet) # <- Accuracy = low, Kappa = 0 - bad!

Calling glmnet directly (without caret) results in the same problem:

x <- as.matrix(subset(data, select=-c(Type)))
y <- data$Type
model.glmnet2 <- cv.glmnet(x=x, y=y, family="binomial", type.measure="class")
preds <- predict(model.glmnet2, x, type="class", s="lambda.min")
# all predictions are class 1...

EDIT: Plot of the scaled data and the decision boundary found by glm:

decision boundary as found by glm

Model: -37 + 6317*A + 6059*B - 6316*A2 - 6059*B2

Upvotes: 3

Views: 1556

Answers (1)

topepo
topepo

Reputation: 14316

You should center and scale data prior to making polynomial versions of the predictor. Numerically, things work better that way:

set.seed(42)
n <- 500; m <- 100
data <- data.frame(A=runif(n, 98, 102), B=runif(n, 98, 102), Type="foo")
data <- subset(data, sqrt((A-100)^2 + (B-100)^2) > 1.5)
data <- rbind(data, data.frame(A=rnorm(m, 100, 0.25), B=rnorm(m, 100, 0.25), Type="bar"))
data2 <- data
data2$A <- scale(data2$A, scale = TRUE)
data2$B <- scale(data2$B, scale = TRUE)
data2$A2 <- data2$A^2
data2$B2 <- data2$B^2

# train a binomial glm model
model.glm2 <- train(Type ~ ., data=data2, method="glm")

# train a binomial glmnet model with ridge regularization (alpha = 0)
model.glmnet2 <- train(Type ~ ., data=data2, method="glmnet", 
                       tuneGrid=expand.grid(alpha=0, 
                                            lambda=c(0, 0.0001, 0.01, 0.1, 1, 10)))

From these:

> getTrainPerf(model.glm2)
  TrainAccuracy TrainKappa method
1             1          1    glm
> getTrainPerf(model.glmnet2)
  TrainAccuracy TrainKappa method
1             1          1 glmnet

Max

Upvotes: 1

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