Wine quality example

[fortisil]

I am trying to SGD for classification of a huge dataset and wanted first to try it on the example you provided about the wine quality. But with the wine quality, something doesn't work for me. When I am trying to predict using the sgd.theta all the results are false and don't predict the quality at all.

Here is the code:

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Wine quality (Cortez et al., 2009): Logistic regression

set.seed(42)

data("winequality")

dat <- winequality

dat <- read.csv("../Data/winequality-red.csv", header = TRUE, sep = ";", stringsAsFactors = FALSE) dat$quality <- as.numeric(dat$quality > 5) # transform to binary test.set <- sample(1:nrow(dat), size=nrow(dat)/8, replace=FALSE) dat.test <- dat[test.set, ] dat <- dat[-test.set, ] sgd.theta <- sgd(quality ~ ., data=dat, model="glm", model.control=binomial(link="logit"), sgd.control=list(reltol=1e-5, npasses=200), lr.control=c(scale=1, gamma=1, alpha=30, c=1)) sgd.theta sprintf("Mean squared error: %0.3f", mean((theta - as.numeric(sgd.theta$coefficients))^2))

sum(dat[190,]*sgd.theta$coefficients)

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Output>

sgd.theta [,1] [1,] -0.21988224003 [2,] -0.14012303981 [3,] -0.70007323510 [4,] 0.24427708544 [5,] -0.27235118177 [6,] -0.06525874448 [7,] 0.07980364712 [8,] -0.04987978826 [9,] -0.21990837019 [10,] -0.74766256961 [11,] 0.24841101887 [12,] 0.55420888771 sprintf("Mean squared error: %0.3f", mean((theta - as.numeric(sgd.theta$coefficients))^2)) [1] "Mean squared error: 26.214"

sum(dat[190,]*sgd.theta$coefficients) [1] 4.761156998

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Maybe am I missing something?

[ptoulis]

SGD seems to be comparable to full GLM here:

theta.glm = glm(quality ~ ., data=dat, family = binomial)  # runs full logistic regression.

Xtest = as.matrix(dat.test[, -ncol(dat.test)])
Xtest = cbind(rep(1, nrow(Xtest)), Xtest)  # test features, add bias
Ytest = dat.test[, ncol(dat.test)]  # test outcome

# predict outcomes from SGD and GLM
expit = function(x) exp(x) / (1 + exp(x))
y_sgd = as.numeric(predict(sgd.theta, Xtest) > 0.5) 
y_glm = as.numeric(expit(predict(theta.glm, newdata =dat.test[, -ncol(dat.test)])) > 0.5)

# confusion tables
M_glm = table(y_glm, Ytest) 
M_sgd = table(y_sgd, Ytest)
print(M_glm)
print(M_sgd)

# Print accuracy
print(sprintf("GLM accuracy = %.2f -- SGD accuracy = %.2f", 
              sum(diag(M_glm)) / sum(M_glm), sum(diag(M_sgd)) / sum(M_sgd)))

I get

GLM accuracy = 0.71 -- SGD accuracy = 0.66

[fortisil]

What would be the criterias to use SGD for classification on others classification methods?

[ptoulis]

Note that SGD is not a classification method per se. It is a method to fit models, including classification models. However, it is a noisy method and in many cases it will perform worse than a deterministic method, such as maximum likelihood (the glm() output is the maximum likelihood estimate in the example above). That said, SGD may the only choice when you have a large model or dataset to fit.

So, in the example above you wouldn't want to use SGD because it is small enough to use glm(). However, in your application you might have, say, 200 features to train on, and then you might want to use SGD.