---
title: "vtreat Rare Levels"
author: "John Mount"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{vtreat Rare Levels}
  %\VignetteEngine{knitr::rmarkdown}
  \usepackage[utf8]{inputenc}
---

For some categorical variables rarity can reflect structural features.  For
instance with United States Zip codes rare zip codes often represent low 
population density regions.

When this is the case it can make sense to pool the rare levels into a new
re-coded level called ``rare.''  If this new level is statistically significant 
it can be a usable modeling feature.  This sort of pooling is only potentially useful
if below a given training count behave similarly.

This capability was more of an experimental demonstration of possible extensions of `vtreat`
to have more inference capabilities about rare level than a commonly useful 
feature.  Most of this power has since been captured in the more useful `catP` feature
(also demonstrated here).  Even more power is found in using an interaction of `catN` or `catB`
with `catP`.

An example of the rare level feature using `vtreat` is given below.

First we set up some data by defining a set of population centers (`populationFrame`)
and code to observe individuals (with replacement) uniformly from the combined population with
a rare condition (`inClass`) that has elevated occurrence in observations coming
from the small population centers (`rareCodes`).

```{r}
library('vtreat')
library('ggplot2')

set.seed(2325)
populationFrame <- data.frame(
   popsize = round(rlnorm(100,meanlog=log(4000),sdlog=1)),
   stringsAsFactors = FALSE)
populationFrame$code <- paste0('z',formatC(sample.int(100000,
                                              size=nrow(populationFrame),
                                              replace=FALSE),width=5,flag='0'))
rareCodes <- populationFrame$code[populationFrame$popsize<1000]

# Draw individuals from code-regions proportional to size of code region
# (or uniformly over all individuals labeled by code region).
# Also add the outcome which has altered conditional probability for rareCodes.
drawIndividualsAndReturnCodes <- function(n) {
  ords <- sort(sample.int(sum(populationFrame$popsize),size=n,replace=TRUE))
  cs <- cumsum(populationFrame$popsize)
  indexes <- findInterval(ords,cs)+1
  indexes <- indexes[sample.int(n,size=n,replace=FALSE)]
  samp <- data.frame(code=populationFrame$code[indexes],
                     stringsAsFactors = FALSE)
  samp$inClass <- runif(n) < ifelse(samp$code %in% rareCodes,0.3,0.01)
  samp
}
```

We then draw a sample we want to make some observations on.

```{r}
testSet <- drawIndividualsAndReturnCodes(2000)
table(generatedAsRare=testSet$code %in% rareCodes,inClass=testSet$inClass)
```

Notice that in the sample we can observe the elevated rate of `inClass==TRUE`
conditioned on coming from a `code` that is one of the `rareCodes`.

We could try to learn this relation using `vtreat`.  To do this we 
set up another sample (`designSet`) to work on, so we are not inferring
from `testSet` (where we will evaluate results).

```{r}
designSet <- drawIndividualsAndReturnCodes(2000)
treatments <- vtreat::designTreatmentsC(designSet,'code','inClass',TRUE,
                                        rareCount=5,rareSig=NULL,
                                        verbose=FALSE)
treatments$scoreFrame[,c('varName','sig'),drop=FALSE]
```

We see in `treatments$scoreFrame` we have a level called `code_lev_rare`,
which is where a number of rare levels are re-coding.
We can also confirm levels that occur `rareCount` or fewer times are eligible to 
code to to `code_lev_rare`.

```{r}
designSetTreated <-  vtreat::prepare(treatments,designSet,pruneSig=0.5)
designSetTreated$code <- designSet$code
summary(as.numeric(table(designSetTreated$code[designSetTreated$code_lev_rare==1])))
summary(as.numeric(table(designSetTreated$code[designSetTreated$code_lev_rare!=1])))
```



We can now apply this treatment to `testSet` to see how this inferred
rare level performs.  Notice also the `code_catP` which directly encodes
prevalence or frequency of the level during training also gives usable 
estimate of size (likely a more useful one then the rare-level code itself).

As we can see below the `code_lev_rare` correlates with the condition, and
usefully re-codes novel levels (levels in `testSet` that were not seen in `designSet`)
to rare.

```{r, fig.width=6}
testSetTreated <- vtreat::prepare(treatments,testSet,pruneSig=0.5)
testSetTreated$code <- testSet$code
testSetTreated$newCode <- !(testSetTreated$code %in% unique(designSet$code))
testSetTreated$generatedAsRareCode <- testSetTreated$code %in% rareCodes

# Show code_lev_rare==1 corresponds to a subset of rows with elevated inClass==TRUE rate.
table(code_lev_rare=testSetTreated$code_lev_rare,
      inClass=testSetTreated$inClass)

# Show newCodes get coded with code_level_rare==1.

table(newCode=testSetTreated$newCode,code_lev_rare=testSetTreated$code_lev_rare)

# Show newCodes tend to come from defined rareCodes.
table(newCode=testSetTreated$newCode,
      generatedAsRare=testSetTreated$generatedAsRareCode)
```

```{r, fig.width=6}
# Show code_catP's behavior on rare and novel levels.
summary(testSetTreated$code_catP)
ggplot(data=testSetTreated,aes(x=code_catP)) + geom_density()

summary(testSetTreated$code_catP[testSetTreated$code_lev_rare==1])
ggplot(data=testSetTreated,aes(x=code_catP,color=as.factor(testSetTreated$code_lev_rare))) + 
  geom_density() + theme(legend.position="bottom")

summary(testSetTreated$code_catP[testSetTreated$newCode])

summary(testSetTreated$code_catP[testSetTreated$generatedAsRareCode])
ggplot(data=testSetTreated,aes(x=code_catP,color=as.factor(testSetTreated$generatedAsRareCode))) + 
  geom_density() + theme(legend.position="bottom")
```

