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Classification

Using vtreat with Classification Problems

Nina Zumel and John Mount

updated February 2020

Note this is a description of the R version of vtreat, the same example for the Python version of vtreat can be found here.

Preliminaries

Load modules/packages.

library(rqdatatable)
## Loading required package: wrapr

## Loading required package: rquery

library(vtreat)
packageVersion('vtreat')
## [1] '1.6.0'

suppressPackageStartupMessages(library(ggplot2))
library(WVPlots)

Generate example data.

  • y is a noisy sinusoidal function of the variable x
  • yc is the output to be predicted: whether y is > 0.5.
  • Input xc is a categorical variable that represents a discretization of y, along some NAs
  • Input x2 is a pure noise variable with no relationship to the output
set.seed(2020)

make_data <- function(nrows) {
    d <- data.frame(x = 5*rnorm(nrows))
    d['y'] = sin(d['x']) + 0.1*rnorm(n = nrows)
    d[4:10, 'x'] = NA                  # introduce NAs
    d['xc'] = paste0('level_', 5*round(d$y/5, 1))
    d['x2'] = rnorm(n = nrows)
    d[d['xc']=='level_-1', 'xc'] = NA  # introduce a NA level
    d['yc'] = d[['y']]>0.5
    return(d)
}

d = make_data(500)

d %.>%
  head(.) %.>%
  knitr::kable(.)
x y xc x2 yc
1.884861 1.0717646 level_1 0.0046504 TRUE
1.507742 0.9958029 level_1 -1.2287497 TRUE
-5.490116 0.8315705 level_1 -0.1405980 TRUE
NA 0.6007655 level_0.5 -0.2073270 TRUE
NA -0.8339836 NA -0.9215306 FALSE
NA -0.5329006 level_-0.5 0.3604742 FALSE

Some quick data exploration

Check how many levels xc has, and their distribution (including NA)

unique(d['xc'])
##             xc
## 1      level_1
## 4    level_0.5
## 5         <NA>
## 6   level_-0.5
## 27     level_0
## 269 level_-1.5

table(d$xc, useNA = 'always')
## 
## level_-0.5 level_-1.5    level_0  level_0.5    level_1       <NA> 
##         94          1         85         98        103        119

Find the mean value of yc

mean(d[['yc']])
## [1] 0.324

Plot of yc versus x.

ggplot(d, aes(x=x, y=as.numeric(yc))) + 
  geom_line()
## Warning: Removed 7 rows containing missing values (geom_path).

Build a transform appropriate for classification problems.

Now that we have the data, we want to treat it prior to modeling: we want training data where all the input variables are numeric and have no missing values or NAs.

First create the data treatment transform design object, in this case a treatment for a binomial classification problem.

We use the training data d to fit the transform and return a treated training set: completely numeric, with no missing values.

unpack[
  transform = treatments,
  d_prepared = crossFrame
  ] <- vtreat::mkCrossFrameCExperiment(
    dframe = d,                                    # data to learn transform from
    varlist = setdiff(colnames(d), c('y', 'yc')),  # columns to transform
    outcomename = 'yc',                            # outcome variable
    outcometarget = TRUE                           # outcome of interest
  )
## [1] "vtreat 1.6.0 start initial treatment design Wed Mar 11 16:28:39 2020"
## [1] " start cross frame work Wed Mar 11 16:28:40 2020"
## [1] " vtreat::mkCrossFrameCExperiment done Wed Mar 11 16:28:40 2020"

Notice that d_prepared now only includes derived variables and the outcome yc. The derived variables will be discussed below.

d_prepared %.>%
  head(.) %.>%
  knitr::kable(.)
x x_isBAD xc_catP xc_catB x2 xc_lev_NA xc_lev_x_level_minus_0_5 xc_lev_x_level_0 xc_lev_x_level_0_5 xc_lev_x_level_1 yc
1.8848606 0 0.2102102 14.206543 0.0046504 0 0 0 0 1 TRUE
1.5077419 0 0.2005988 14.139786 -1.2287497 0 0 0 0 1 TRUE
-5.4901159 0 0.2005988 14.139786 -0.1405980 0 0 0 0 1 TRUE
-0.1276897 1 0.1891892 1.219475 -0.2073270 0 0 0 1 0 TRUE
-0.3929879 1 0.2402402 -12.844663 -0.9215306 1 0 0 0 0 FALSE
-0.2908461 1 0.1766467 -12.563128 0.3604742 0 1 0 0 0 FALSE

Note that for the training data d: crossFrame is not the same as prepare(transform, d); the second call can lead to nested model bias in some situations, and is not recommended. For other, later data, not seen during transform design transform.preprare(o) is an appropriate step.

vtreat version 1.5.1 and newer issue a warning if you call the incorrect transform pattern on your original training data:

d_prepared_wrong <- prepare(transform, d)
## Warning in prepare.treatmentplan(transform, d): possibly called prepare() on
## same data frame as designTreatments*()/mkCrossFrame*Experiment(), this can lead
## to over-fit. To avoid this, please use mkCrossFrame*Experiment$crossFrame.

The Score Frame

Now examine the score frame, which gives information about each new variable, including its type, which original variable it is derived from, its (cross-validated) significance as a one-variable linear model for the outcome,and the (cross-validated) R-squared of its corresponding linear model.

score_frame <- transform$scoreFrame

cols = c("varName", "origName", "code", "rsq", "sig", "varMoves", "default_threshold", "recommended")
knitr::kable(score_frame[,cols])
varName origName code rsq sig varMoves default_threshold recommended
x x clean 0.0005756 0.5470919 TRUE 0.10 FALSE
x_isBAD x isBAD 0.0000771 0.8255885 TRUE 0.20 FALSE
xc_catP xc catP 0.0008468 0.4652101 TRUE 0.20 FALSE
xc_catB xc catB 0.7883578 0.0000000 TRUE 0.20 TRUE
x2 x2 clean 0.0026075 0.2000083 TRUE 0.10 FALSE
xc_lev_NA xc lev 0.1750095 0.0000000 TRUE 0.04 TRUE
xc_lev_x_level_minus_0_5 xc lev 0.1328708 0.0000000 TRUE 0.04 TRUE
xc_lev_x_level_0 xc lev 0.1185254 0.0000000 TRUE 0.04 TRUE
xc_lev_x_level_0_5 xc lev 0.0644178 0.0000000 TRUE 0.04 TRUE
xc_lev_x_level_1 xc lev 0.4701626 0.0000000 TRUE 0.04 TRUE

Note that the variable xc has been converted to multiple variables:

  • an indicator variable for each possible level, plus NA (xc_lev_*)
  • the value of a (cross-validated) one-variable model for yc as a function of xc (xc_catB)
  • a variable that returns how prevalent this particular value of xc is in the training data (xc_catP)

The variable x has been converted to two new variables:

  • a clean version of x that has no missing values or NaNs
  • a variable indicating when x was NA in the original data (x_isBAD).

Any or all of these new variables are available for downstream modeling.

The recommended column indicates which variables are non constant (varMoves == TRUE) and have a significance value smaller than default_threshold. See the section Deriving the Default Thresholds below for the reasoning behind such a default threshold. Recommended columns are intended as advice about which variables appear to be most likely to be useful in a downstream model. This advice attempts to be conservative, to reduce the possibility of mistakenly eliminating variables that may in fact be useful (although, obviously, it can still mistakenly eliminate variables that have a real but non-linear relationship to the output, as is the case with x, in our example).

Let’s look at the variables that are and are not recommended:

# recommended variables
score_frame[score_frame[['recommended']], 'varName', drop = FALSE]  %.>%
  knitr::kable(.)
varName
4 xc_catB
6 xc_lev_NA
7 xc_lev_x_level_minus_0_5
8 xc_lev_x_level_0
9 xc_lev_x_level_0_5
10 xc_lev_x_level_1 
# not recommended variables
score_frame[!score_frame[['recommended']], 'varName', drop = FALSE] %.>%
  knitr::kable(.)
varName
1 x
2 x_isBAD
3 xc_catP
5 x2

A Closer Look at catB variables

Variables of type catB are the outputs of a one-variable regularized logistic regression of a categorical variable (in our example, xc) against the centered output on the (cross-validated) treated training data.

Let’s see whether xc_catB makes a good one-variable model for yc. It has a large AUC:

WVPlots::ROCPlot(
  frame = d_prepared,
  xvar = 'xc_catB',
  truthVar = 'yc',
  truthTarget = TRUE,
  title = 'performance of xc_catB variable')

This indicates that xc_catB is strongly predictive of the outcome. Negative values of xc_catB correspond strongly to negative outcomes, and positive values correspond strongly to positive outcomes.

WVPlots::DoubleDensityPlot(
  frame = d_prepared,
  xvar = 'xc_catB',
  truthVar = 'yc',
  title = 'performance of xc_catB variable')

The values of xc_catB are in “link space”.

Variables of type catB are useful when dealing with categorical variables with a very large number of possible levels. For example, a categorical variable with 10,000 possible values potentially converts to 10,000 indicator variables, which may be unwieldy for some modeling methods. Using a single numerical variable of type catB may be a preferable alternative.

Using the Prepared Data in a Model

Of course, what we really want to do with the prepared training data is to fit a model jointly with all the (recommended) variables. Let’s try fitting a logistic regression model to d_prepared.

model_vars <- score_frame$varName[score_frame$recommended]
# to use all the variables:
# model_vars <- score_frame$varName

f <- wrapr::mk_formula('yc', model_vars, outcome_target = TRUE)

model = glm(f, data = d_prepared)

# now predict
d_prepared['prediction'] = predict(
  model,
  newdata = d_prepared, 
  type = 'response')

# look at the ROC curve (on the training data)
WVPlots::ROCPlot(
  frame = d_prepared,
  xvar = 'prediction',
  truthVar = 'yc',
  truthTarget = TRUE,
  title = 'Performance of logistic regression model on training data')

Now apply the model to new data.

# create the new data
dtest <- make_data(450)

# prepare the new data with vtreat
dtest_prepared = prepare(transform, dtest)
# dtest %.>% transform is an alias for prepare(transform, dtest)

# apply the model to the prepared data
dtest_prepared['prediction'] = predict(
  model,
  newdata = dtest_prepared,
  type = 'response')

WVPlots::ROCPlot(
  frame = dtest_prepared,
  xvar = 'prediction',
  truthVar = 'yc',
  truthTarget = TRUE,
  title = 'Performance of logistic regression model on test data')

Parameters for BinomialOutcomeTreatment

We’ve tried to set the defaults for all parameters so that vtreat is usable out of the box for most applications.

suppressPackageStartupMessages(library(printr))
args("mkCrossFrameCExperiment")
## function (dframe, varlist, outcomename, outcometarget, ..., weights = c(), 
##     minFraction = 0.02, smFactor = 0, rareCount = 0, rareSig = 1, 
##     collarProb = 0, codeRestriction = NULL, customCoders = NULL, 
##     scale = FALSE, doCollar = FALSE, splitFunction = NULL, ncross = 3, 
##     forceSplit = FALSE, catScaling = TRUE, verbose = TRUE, parallelCluster = NULL, 
##     use_parallel = TRUE, missingness_imputation = NULL, imputation_map = NULL) 
## NULL

Some parameters of note include:

codeRestriction: The types of synthetic variables that vtreat will (potentially) produce. By default, all possible applicable types will be produced. See Types of prepared variables below.

minFraction (default: 0.02): For categorical variables, indicator variables (type lev) are only produced for levels that are present at least minFraction of the time. A consequence of this is that 1/minFraction is the maximum number of indicators that will be produced for a given categorical variable. To make sure that all possible indicator variables are produced, set minFraction = 0

splitFunction: The cross validation method used by vtreat. Most people won’t have to change this.

ncross (default: 3): The number of folds to use for cross-validation

missingness_imputation: The function or value that vtreat uses to impute or “fill in” missing numerical values. The default is mean. To change the imputation function or use different functions/values for different columns, see the Imputation example.

customCoders: For passing in user-defined transforms for custom data preparation. Won’t be needed in most situations, but see here for an example of applying a GAM transform to input variables.

Types of prepared variables

clean: Produced from numerical variables: a clean numerical variable with no NAs or missing values

lev: Produced from categorical variables, one for each (common) level: for each level of the variable, indicates if that level was “on”

catP: Produced from categorical variables: indicates how often each level of the variable was “on” (its prevalence)

catB: Produced from categorical variables: score from a one-dimensional model of the centered output as a function of the variable

isBAD: Produced for numerical variables: an indicator variable that marks when the original variable was missing or NaN.

More on the coding types can be found here.

Example: Produce only a subset of variable types

In this example, suppose you only want to use indicators and continuous variables in your model; in other words, you only want to use variables of types (clean_copy, missing_indicator, and indicator_code), and no catB or prevalence_code variables.

unpack[
  transform_thin = treatments,
  d_prepared_thin = crossFrame
  ] <- vtreat::mkCrossFrameCExperiment(
    dframe = d,                                    # data to learn transform from
    varlist = setdiff(colnames(d), c('y', 'yc')),  # columns to transform
    outcomename = 'yc',                            # outcome variable
    outcometarget = TRUE,                          # outcome of interest
    codeRestriction = c('lev',                     # transforms we want
                        'clean',
                        'isBAD')
  )
## [1] "vtreat 1.6.0 start initial treatment design Wed Mar 11 16:28:42 2020"
## [1] " start cross frame work Wed Mar 11 16:28:42 2020"
## [1] " vtreat::mkCrossFrameCExperiment done Wed Mar 11 16:28:42 2020"

score_frame_thin <- transform_thin$scoreFrame

# no catB or catP
d_prepared_thin %.>%
  head(.) %.>%
  knitr::kable(.)
x x_isBAD x2 xc_lev_NA xc_lev_x_level_minus_0_5 xc_lev_x_level_0 xc_lev_x_level_0_5 xc_lev_x_level_1 yc
1.8848606 0 0.0046504 0 0 0 0 1 TRUE
1.5077419 0 -1.2287497 0 0 0 0 1 TRUE
-5.4901159 0 -0.1405980 0 0 0 0 1 TRUE
-0.0453530 1 -0.2073270 0 0 0 1 0 TRUE
-0.0453530 1 -0.9215306 1 0 0 0 0 FALSE
-0.4926751 1 0.3604742 0 1 0 0 0 FALSE 
# no catB or catP
knitr::kable(score_frame_thin[,cols])
varName origName code rsq sig varMoves default_threshold recommended
x x clean 0.0005756 0.5470919 TRUE 0.16666667 FALSE
x_isBAD x isBAD 0.0000771 0.8255885 TRUE 0.33333333 FALSE
x2 x2 clean 0.0026075 0.2000083 TRUE 0.16666667 FALSE
xc_lev_NA xc lev 0.1750095 0.0000000 TRUE 0.06666667 TRUE
xc_lev_x_level_minus_0_5 xc lev 0.1328708 0.0000000 TRUE 0.06666667 TRUE
xc_lev_x_level_0 xc lev 0.1185254 0.0000000 TRUE 0.06666667 TRUE
xc_lev_x_level_0_5 xc lev 0.0644178 0.0000000 TRUE 0.06666667 TRUE
xc_lev_x_level_1 xc lev 0.4701626 0.0000000 TRUE 0.06666667 TRUE

Deriving the Default Thresholds

While machine learning algorithms are generally tolerant to a reasonable number of irrelevant or noise variables, too many irrelevant variables can lead to serious overfit; see this article for an extreme example, one we call “Bad Bayes”. The default threshold is an attempt to eliminate obviously irrelevant variables early.

Imagine that you have a pure noise dataset, where none of the n inputs are related to the output. If you treat each variable as a one-variable model for the output, and look at the significances of each model, these significance-values will be uniformly distributed in the range [0:1]. You want to pick a weakest possible significance threshold that eliminates as many noise variables as possible. A moment’s thought should convince you that a threshold of 1/n allows only one variable through, in expectation.

This leads to the general-case heuristic that a significance threshold of 1/n on your variables should allow only one irrelevant variable through, in expectation (along with all the relevant variables). Hence, 1/n used to be our recommended threshold, when we originally developed the R version of vtreat.

We noticed, however, that this biases the filtering against numerical variables, since there are at most two derived variables (of types clean and is_BAD) for every numerical variable in the original data. Categorical variables, on the other hand, are expanded to many derived variables: several indicators (one for every common level), plus a catB and a catP. So we now reweight the thresholds.

Suppose you have a (treated) data set with ntreat different types of vtreat variables (clean, lev, etc). There are nT variables of type T. Then the default threshold for all the variables of type T is 1/(ntreat nT). This reweighting helps to reduce the bias against any particular type of variable. The heuristic is still that the set of recommended variables will allow at most one noise variable into the set of candidate variables.

As noted above, because vtreat estimates variable significances using linear methods by default, some variables with a non-linear relationship to the output may fail to pass the threshold. In this case, you may not wish to filter the variables to be used in the models to only recommended variables (as we did in the main example above), but instead use all the variables, or select the variables to use by your own criteria.

Conclusion

In all cases (classification, regression, unsupervised, and multinomial classification) the intent is that vtreat transforms are essentially one liners.

The preparation commands are organized as follows:

These current revisions of the examples are designed to be small, yet complete. So as a set they have some overlap, but the user can rely mostly on a single example for a single task type.