Variable Types

‘vtreat’ is a package that prepares arbitrary data frames into clean data frames that are ready for analysis (usually supervised learning). A clean data frame:

To effect this encoding ‘vtreat’ replaces original variables or columns with new derived variables. In this note we will use variables and columns as interchangeable concepts. This note describes the current family of ‘vtreat’ derived variable types.

In all cases vtreat variable names are built by appending a notation onto the original user supplied column name. In all cases the easiest way to examine the derived variables is to look at the scoreFrame component of the returned treatment plan.

When the target to predict is categorical

An example categorical variable treatment is demonstrated below:

library(vtreat)
dTrainC <- data.frame(x=c('a','a','a','b','b',NA),
   z=c(1,2,3,4,NA,6),y=c(FALSE,FALSE,TRUE,FALSE,TRUE,TRUE),
   stringsAsFactors = FALSE)
treatmentsC <- designTreatmentsC(dTrainC,colnames(dTrainC),'y',TRUE)

## [1] "desigining treatments Thu Apr 13 17:41:18 2017"
## [1] "designing treatments Thu Apr 13 17:41:18 2017"
## [1] " have level statistics Thu Apr 13 17:41:18 2017"
## [1] "design var x Thu Apr 13 17:41:18 2017"
## [1] "design var z Thu Apr 13 17:41:18 2017"
## [1] " scoring treatments Thu Apr 13 17:41:18 2017"
## [1] "have treatment plan Thu Apr 13 17:41:18 2017"
## [1] "rescoring complex variables Thu Apr 13 17:41:18 2017"
## [1] "done rescoring complex variables Thu Apr 13 17:41:18 2017"

scoreColsToPrint <- c('origName','varName','code','rsq','sig','extraModelDegrees')
print(treatmentsC$scoreFrame[,scoreColsToPrint])

##   origName   varName  code        rsq        sig extraModelDegrees
## 1        x  x_lev_NA   lev 0.19087450 0.20766228                 0
## 2        x x_lev_x.a   lev 0.08170417 0.40972582                 0
## 3        x x_lev_x.b   lev 0.00000000 1.00000000                 0
## 4        x    x_catP  catP 0.15582050 0.25493078                 2
## 5        x    x_catB  catB 0.49618022 0.04220134                 2
## 6        z   z_clean clean 0.25792985 0.14299775                 0
## 7        z   z_isBAD isBAD 0.19087450 0.20766228                 0

For each user supplied variable or column (in this case x and z) ‘vtreat’ proposes derived or treated variables (in this case x_lev_x.a, x_lev_x.b, x_catP, x_catB, z_clean, and z_isBAD). The mapping from original variable name to derived variable name is given by comparing the columns origName and varName. One can map facts about the new variables back to the original variables as follows:

# Build a map from vtreat names back to reasonable display names
vmap <- as.list(treatmentsC$scoreFrame$origName)
names(vmap) <- treatmentsC$scoreFrame$varName
print(vmap['x_catB'])

## $x_catB
## [1] "x"

# Map significances back to original variables
aggregate(sig~origName,data=treatmentsC$scoreFrame,FUN=min)

##   origName        sig
## 1        x 0.04220134
## 2        z 0.14299775

In the scoreFrame the sig column is the significance of the single variable logistic regression using the named variable (plus a constant term), and the rsq column is the “pseudo-rsquared” or portion of deviance explained (please see here for some notes).

Essentially a derived variable name is built by concatenating an original variable name and a treatment type (also recorded in the code column for convenience). The codes give the different ‘vtreat’ variable types (or really meanings, as all derived variables are numeric).

For categorical targets the possible variable types are as follows:

clean : a numeric variable passed through with all NA/NaN/infinite values replaced with either zero or mean value of the non-NA/NaN/infinite examples of the variable.
is_Bad : a companion to the ‘clean’ treatment. ‘is_Bad’ is an indicator that indicates a value replacement has occurred. For many noisy datasets this column can be more informative than the clean column!
lev : a 0/1 indicator indicating a particular value of a categorical variable was present. For example x_lev_x.a is 1 when the original x variable had a value of “a”. These indicators are essentially variables representing explicit encoding of levels as dummy variables. In some cases a special level code is used to represent pooled rare values.
cat_B : a single variable Bayesian model of the changine in logit-odds in outcome from mean distribution conditioned on the observed value of the original variable. In our example: x_catB = logit(P[y==target|x]) - logit(P[y==target]). This encoding is especially useful for categorical variables that have a large number of levels, but be aware it can obscure degrees of freedom if not used properly.
cat_P : a “prevalence fact” about a categorical level. Tells us if the original level was rare or common. Probably not good for direct use in a model, but possibly useful for meta-analysis on the variable.

When the target to predict is numeric

An example numeric variable treatment is demonstrated below:

library(vtreat)
dTrainN <- data.frame(x=c('a','a','a','b','b',NA),
   z=c(1,2,3,4,NA,6),y=as.numeric(c(FALSE,FALSE,TRUE,FALSE,TRUE,TRUE)),
   stringsAsFactors = FALSE)
treatmentsN <- designTreatmentsN(dTrainN,colnames(dTrainN),'y')

## [1] "desigining treatments Thu Apr 13 17:41:18 2017"
## [1] "designing treatments Thu Apr 13 17:41:18 2017"
## [1] " have level statistics Thu Apr 13 17:41:18 2017"
## [1] "design var x Thu Apr 13 17:41:18 2017"
## [1] "design var z Thu Apr 13 17:41:18 2017"
## [1] " scoring treatments Thu Apr 13 17:41:18 2017"
## [1] "have treatment plan Thu Apr 13 17:41:18 2017"
## [1] "rescoring complex variables Thu Apr 13 17:41:18 2017"
## [1] "done rescoring complex variables Thu Apr 13 17:41:18 2017"

print(treatmentsN$scoreFrame[,scoreColsToPrint])

##   origName   varName  code        rsq       sig extraModelDegrees
## 1        x  x_lev_NA   lev 0.20000000 0.3739010                 0
## 2        x x_lev_x.a   lev 0.11111111 0.5185185                 0
## 3        x x_lev_x.b   lev 0.00000000 1.0000000                 0
## 4        x    x_catP  catP 0.20000000 0.3739010                 2
## 5        x    x_catN  catN 0.37878788 0.1933777                 2
## 6        x    x_catD  catD 0.08834559 0.5672847                 2
## 7        z   z_clean clean 0.30450450 0.2562868                 0
## 8        z   z_isBAD isBAD 0.20000000 0.3739010                 0

The treatment of numeric targets is similar to that of categorical targets. In the numeric case the possible derived variable types are:

clean : a numeric variable passed through with all NA/NaN/infinite values replaced with either zero or mean value of the non-NA/NaN/infinite examples of the variable.
is_Bad : a companion to the ‘clean’ treatment. ‘is_Bad’ is an indicator that indicates a value replacement has occurred. For many noisy datasets this column can be more informative than the clean column!
lev : a 0/1 indicator indicating a particular value of a categorical variable was present. For example x_lev_x.a is 1 when the original x variable had a value of “a”. These indicators are essentially variables representing explicit encoding of levels as dummy variables. In some cases a special level code is used to represent pooled rare values.
cat_N : a single variable regression model of the difference in outcome expectation conditioned on the observed value of the original variable. In our example: x_catN = E[y|x] - E[y]. This encoding is especially useful for categorical variables that have a large number of levels, but be aware it can obscure degrees of freedom if not used properly.
cat_P : a “prevalence fact” about a categorical level. Tells us if the original level was rare or common. Tells us if the original level was rare or common. Probably not good for direct use in a model, but possibly useful for metanalysis on the variable.
cat_D : a “deviation fact” about a categorical level tells us if ‘y’ is concentrated or diffuse when conditioned on the observed level of the original categorical variable. Probably not good for direct use in a model, but possibly useful for metanalysis on the variable.

Note: for categorical targets we don’t need cat\_D variables as this information is already encoded in cat\_B variables.

In the scoreFrame the sig column is the significance of the single variable linear regression using the named variable (plus a constant term), and the rsq column is the “rsquared” or portion of variance explained (please see here) for some notes).

When there is no supplied target to predict

An example “no target” variable treatment is demonstrated below:

library(vtreat)
dTrainZ <- data.frame(x=c('a','a','a','b','b',NA),
   z=c(1,2,3,4,NA,6),
   stringsAsFactors = FALSE)
treatmentsZ <- designTreatmentsZ(dTrainZ,colnames(dTrainZ))

## [1] "desigining treatments Thu Apr 13 17:41:18 2017"
## [1] "designing treatments Thu Apr 13 17:41:18 2017"
## [1] " have level statistics Thu Apr 13 17:41:18 2017"
## [1] "design var x Thu Apr 13 17:41:18 2017"
## [1] "design var z Thu Apr 13 17:41:18 2017"
## [1] " scoring treatments Thu Apr 13 17:41:18 2017"
## [1] "have treatment plan Thu Apr 13 17:41:18 2017"

print(treatmentsZ$scoreFrame[, c('origName','varName','code','extraModelDegrees')])

##   origName   varName  code extraModelDegrees
## 1        x  x_lev_NA   lev                 0
## 2        x x_lev_x.a   lev                 0
## 3        x x_lev_x.b   lev                 0
## 4        x    x_catP  catP                 2
## 5        z   z_clean clean                 0
## 6        z   z_isBAD isBAD                 0

Note: because there is no user supplied target the scoreFrame significance columns are not meaningful, and are populated only for regularity of code interface. Also indicator variables are only formed by designTreatmentsZ for vtreat 0.5.28 or newer. Beyond that the no-target treatments are similar to the earlier treatments. Possible derived variable types in this case are:

clean : a numeric variable passed through with all NA/NaN/infinite values replaced with either zero or mean value of the non-NA/NaN/infinite examples of the variable.
is_Bad : a companion to the ‘clean’ treatment. ‘is_Bad’ is an indicator that indicates a value replacement has occurred. For many noisy datasets this column can be more informative than the clean column!
lev : a 0/1 indicator indicating a particular value of a categorical variable was present. For example x_lev_x.a is 1 when the original x variable had a value of “a”. These indicators are essentially variables representing explicit encoding of levels as dummy variables. In some cases a special level code is used to represent pooled rare values.
cat_P : a “prevalence fact” about a categorical level. Tells us if the original level was rare or common. Probably not good for direct use in a model, but possibly useful for metanalysis on the variable.

Overall

Variables that “do not move” (don’t take on at least two values during treatment design) or don’t achieve at least a minimal significance are suppressed. The catB/catN variables are essentially single variable models and are very useful for re-encoding categorical variables that take on a very large number of values (such as zip-codes).

The intended use of ‘vtreat’ is as follows:

Data is split into three non-overlapping portions
One portion is used to “design treatments” (we sometime informally call this calibration).
Another portion is used to train a model.
The remaining portion is used to evaluate the model.

‘vtreat’ attempts to compute “out of sample” significances for each variable effect ( the sig column in scoreFrame) through cross-validation techniques.

‘vtreat’ is primarily intended to be “y-aware” processing. Of particular interest is using vtreat::prepare() with scale=TRUE which tries to put most columns in ‘y-effect’ units. This can be an important pre-processing step before attempting dimension reduction (such as principal components methods).

The vtreat user should pick which sorts of variables they are want and also filter on estimated significance. Doing this looks like the following:

dTrainN <- data.frame(x=c('a','a','a','b','b',NA),
   z=c(1,2,3,4,NA,6),y=as.numeric(c(FALSE,FALSE,TRUE,FALSE,TRUE,TRUE)),
   stringsAsFactors = FALSE)
treatmentsN <- designTreatmentsN(dTrainN,colnames(dTrainN),'y')

## [1] "desigining treatments Thu Apr 13 17:41:19 2017"
## [1] "designing treatments Thu Apr 13 17:41:19 2017"
## [1] " have level statistics Thu Apr 13 17:41:19 2017"
## [1] "design var x Thu Apr 13 17:41:19 2017"
## [1] "design var z Thu Apr 13 17:41:19 2017"
## [1] " scoring treatments Thu Apr 13 17:41:19 2017"
## [1] "have treatment plan Thu Apr 13 17:41:19 2017"
## [1] "rescoring complex variables Thu Apr 13 17:41:19 2017"
## [1] "done rescoring complex variables Thu Apr 13 17:41:19 2017"

print(treatmentsN$scoreFrame[,scoreColsToPrint])

##   origName   varName  code        rsq       sig extraModelDegrees
## 1        x  x_lev_NA   lev 0.20000000 0.3739010                 0
## 2        x x_lev_x.a   lev 0.11111111 0.5185185                 0
## 3        x x_lev_x.b   lev 0.00000000 1.0000000                 0
## 4        x    x_catP  catP 0.20000000 0.3739010                 2
## 5        x    x_catN  catN 0.37878788 0.1933777                 2
## 6        x    x_catD  catD 0.08834559 0.5672847                 2
## 7        z   z_clean clean 0.30450450 0.2562868                 0
## 8        z   z_isBAD isBAD 0.20000000 0.3739010                 0

pruneSig <- 1.0 # don't filter on significance for this tiny example
vScoreFrame <- treatmentsN$scoreFrame
varsToUse <- vScoreFrame$varName[(vScoreFrame$sig<=pruneSig) &
                                   vScoreFrame$code %in% c('lev','catN','clean','isBad')]
print(varsToUse)

## [1] "x_lev_NA"  "x_lev_x.a" "x_lev_x.b" "x_catN"    "z_clean"

origVarNames <- sort(unique(vScoreFrame$origName[vScoreFrame$varName %in% varsToUse]))
print(origVarNames)

## [1] "x" "z"

We strongly suggest using the standard variables coded as ‘lev’, ‘clean’, and ‘isBad’; and the “y aware” variables coded as ‘catN’ and ‘catB’. The non sub-model variables (‘catP’ and ‘catD’) can be useful (possibly as interactions or guards on the corresponding ‘catN’ and ‘catB’ variables) but also encode distributional facts about the data that may or may not be appropriate depending on your problem domain.

When displaying variables to end users we suggest using the original names and the min significance seen on any derived variable:

origVarNames <- sort(unique(vScoreFrame$origName[vScoreFrame$varName %in% varsToUse]))
print(origVarNames)

## [1] "x" "z"

origVarSigs <- vScoreFrame[vScoreFrame$varName %in% varsToUse,]
aggregate(sig~origName,data=origVarSigs,FUN=min)

##   origName       sig
## 1        x 0.1933777
## 2        z 0.2562868

Variable Types

Win-Vector LLC

2017-04-13

When the target to predict is categorical

When the target to predict is numeric

When there is no supplied target to predict

Overall

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