multi-class logistic regression

multi_class_logistic_regression.Rmd

Multiclass classifier
----

```{r, include=FALSE}
knitr::opts_chunk$set(
  comment = "#>",
  collapse = TRUE,
  cache = TRUE,
  echo = FALSE,
  out.width = "70%",
  fig.align = "center",
  fig.width = 6,
  fig.asp = 0.618,
  fig.show = "hold"
)

library(tidyverse)
library(arm)
`%>%` <- magrittr::`%>%`
`%<>%` <- magrittr::`%<>%`
```

One-vs-all:  
Run three separate logistic regressions.  
Pick the model that is most confident on a given prediction.  
```{r, warning = FALSE}
cyl_levels <- levels(factor(mtcars$cyl))

# plot helper
plot_by_cyl <- function(cyl_level, ...) {
  with(mtcars,
  plot( mpg, disp,
        col = ifelse(cyl == cyl_levels[cyl_level], 1, 2),
        pch = ifelse(cyl == cyl_levels[cyl_level], 1, 2),
        ...
  ))
}

# dummy vars
mtcars %<>% mutate(i = 1, cyl_str = str_c('cyl', cyl)) %>% spread(cyl_str, i, fill = 0)

# model helpers
fit_model <- partial(arm::bayesglm, data = mtcars, family = binomial)
pred <- partial(predict, type = "link")
fit_and_pred <- compose(pred, fit_model)

# 4 cyl
plot_by_cyl(1, main = "4 cyl")
p.1 <- fit_and_pred(cyl4 ~ mpg + disp)

# 6 cyl
plot_by_cyl(2, main = "6 cyl")
p.2 <- fit_and_pred(cyl6 ~ mpg + disp)

# 8 cyl
plot_by_cyl(3, main = "8 cyl")
p.3 <- fit_and_pred(cyl8 ~ mpg + disp)

# Results
ll <- Reduce(cbind, list(as.numeric(factor(mtcars$cyl)), p.1, p.2, p.3))

results <- cbind(ll[, 1], apply(ll[,-1], 1, which.max)) 

caret::confusionMatrix(factor(results[, 1], levels = 1:3),
                       factor(results[, 2], levels = 1:3))
```