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Unsupervised.Rmd

Using vtreat with Unsupervised Problems and Non-Y-aware data treatment

Nina Zumel and John Mount September 2019

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(vtreat)
suppressPackageStartupMessages(library(ggplot2))
library(WVPlots)
library(rqdatatable)
## Loading required package: rquery

Generate example data.

  • y is a noisy sinusoidal plus linear function of the variable x
  • Input xc is a categorical variable that represents a discretization of y, along with some NaNs
  • Input x2 is a pure noise variable with no relationship to the output
  • Input x3 is a constant variable
make_data <- function(nrows) {
    d <- data.frame(x = 5*rnorm(nrows))
    d['y'] = sin(d[['x']]) + 0.01*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['x3'] = 1
    d[d['xc']=='level_-1', 'xc'] = NA  # introduce a NA level
    return(d)
}

d = make_data(500)

d %.>%
  head(.) %.>%
  knitr::kable(.)
x y xc x2 x3
2.869921 0.2050366 level_0 -2.1165106 1
-7.800579 -1.0655070 NA 0.8836485 1
-3.987771 0.9476780 level_1 1.9157663 1
NA -0.2492630 level_0 0.9493477 1
NA -0.6926920 level_-0.5 0.4461547 1
NA 0.2191380 level_0 -1.1675057 1

Some quick data exploration

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

unique(d['xc'])
##           xc
## 1    level_0
## 2       <NA>
## 3    level_1
## 5 level_-0.5
## 9  level_0.5
table(d$xc, useNA = 'always')
## 
## level_-0.5    level_0  level_0.5    level_1       <NA> 
##         98         72         89        115        126

Build a transform appropriate for unsupervised (or non-y-aware) problems.

The vtreat package is primarily intended for data treatment prior to supervised learning, as detailed in the Classification and Regression examples. In these situations, vtreat specifically uses the relationship between the inputs and the outcomes in the training data to create certain types of synthetic variables. We call these more complex synthetic variables y-aware variables.

However, you may also want to use vtreat for basic data treatment for unsupervised problems, when there is no outcome variable. Or, you may not want to create any y-aware variables when preparing the data for supervised modeling. For these applications, vtreat is a convenient alternative to: pandas.get_dummies() or sklearn.preprocessing.OneHotEncoder().

In any case, we still want training data where all the input variables are numeric and have no missing values or NaNs.

First create the data treatment transform object, in this case a treatment for an unsupervised problem.

transform = vtreat::designTreatmentsZ(
    dframe = d,                              # data to learn transform from
    varlist = setdiff(colnames(d), c('y'))   # columns to transform
)
## [1] "vtreat 1.4.7 inspecting inputs Tue Oct  1 10:35:37 2019"
## [1] "designing treatments Tue Oct  1 10:35:37 2019"
## [1] " have initial level statistics Tue Oct  1 10:35:37 2019"
## [1] " scoring treatments Tue Oct  1 10:35:37 2019"
## [1] "have treatment plan Tue Oct  1 10:35:37 2019"
score_frame = transform$scoreFrame

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

d_prepared = prepare(transform, d)
d_prepared$y = d$y

Now examine the score frame, which gives information about each new variable, including its type and which original variable it is derived from. Some of the columns of the score frame (y_aware, PearsonR, significance and recommended) are not relevant to the unsupervised case; those columns are used by the Regression and Classification transforms.

knitr::kable(score_frame)
varName varMoves rsq sig needsSplit extraModelDegrees origName code
x TRUE 0 1 FALSE 0 x clean
x_isBAD TRUE 0 1 FALSE 0 x isBAD
xc_catP TRUE 0 1 TRUE 4 xc catP
x2 TRUE 0 1 FALSE 0 x2 clean
xc_lev_NA TRUE 0 1 FALSE 0 xc lev
xc_lev_x_level_minus_0_5 TRUE 0 1 FALSE 0 xc lev
xc_lev_x_level_0 TRUE 0 1 FALSE 0 xc lev
xc_lev_x_level_0_5 TRUE 0 1 FALSE 0 xc lev
xc_lev_x_level_1 TRUE 0 1 FALSE 0 xc lev

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

  • an indicator variable for each possible level, including NA or missing (xc_lev*)
  • a variable indicating when xc was NaN in the original data (xd_isBAD)
  • a variable that returns how prevalent this particular value of xc is in the training data (xc_catP)

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

Also note that the variable x3 did not show up in the score frame, as it had no range (didn’t vary), so the unsupervised treatment dropped it.

Let’s look at the top of d_prepared, which includes all the new variables, plus y (and excluding x3).

d_prepared %.>%
  head(.) %.>%
  knitr::kable(.)
x x_isBAD xc_catP 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 y
2.8699211 0 0.144 -2.1165106 0 0 1 0 0 0.2050366
-7.8005789 0 0.252 0.8836485 1 0 0 0 0 -1.0655070
-3.9877706 0 0.230 1.9157663 0 0 0 0 1 0.9476780
-0.3877845 1 0.144 0.9493477 0 0 1 0 0 -0.2492630
-0.3877845 1 0.196 0.4461547 0 1 0 0 0 -0.6926920
-0.3877845 1 0.144 -1.1675057 0 0 1 0 0 0.2191380

Using the Prepared Data to Model

Of course, what we really want to do with the prepared training data is to model.

K-means clustering

Let’s start with an unsupervised analysis: clustering.

# don't use y to cluster
not_variables <- c('y')
model_vars <- setdiff(colnames(d_prepared), not_variables)

clusters = kmeans(d_prepared[, model_vars, drop = FALSE], centers = 5)

d_prepared['clusterID'] <- clusters$cluster
head(d_prepared$clusterID)
## [1] 1 3 4 2 2 2
ggplot(data = d_prepared, aes(x=x, y=y, color=as.character(clusterID))) +
  geom_point() +
  ggtitle('y as a function of x, points colored by (unsupervised) clusterID') +
  theme(legend.position="none") +
  scale_colour_brewer(palette = "Dark2")

Supervised modeling with non-y-aware variables

Since in this case we have an outcome variable, y, we can try fitting a linear regression model to d_prepared.

f <- wrapr::mk_formula('y', model_vars)

model = lm(f, data = d_prepared)

# now predict
d_prepared['prediction'] = predict(
  model,
  newdata = d_prepared)
## Warning in predict.lm(model, newdata = d_prepared): prediction from a rank-
## deficient fit may be misleading
# look at the fit (on the training data)
WVPlots::ScatterHist(
  d_prepared, 
  xvar = 'prediction',
  yvar = 'y',
  smoothmethod = 'identity',
  estimate_sig = TRUE,
  title = 'Relationship between prediction and y')

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_prepared$y = dtest$y

# apply the model to the prepared data
dtest_prepared['prediction'] = predict(
  model,
  newdata = dtest_prepared)
## Warning in predict.lm(model, newdata = dtest_prepared): prediction from a
## rank-deficient fit may be misleading
# compare the predictions to the outcome (on the test data)
WVPlots::ScatterHist(
  dtest_prepared, 
  xvar = 'prediction',
  yvar = 'y',
  smoothmethod = 'identity',
  estimate_sig = TRUE,
  title = 'Relationship between prediction and y')

# get r-squared
sigr::wrapFTest(dtest_prepared, 
                predictionColumnName = 'prediction',
                yColumnName = 'y',
                nParameters = length(model_vars) + 1)
## [1] "F Test summary: (R2=0.965, F(10,439)=1212, p<1e-05)."

Parameters for UnsupervisedTreatment

We’ve tried to set the defaults for all parameters so that vtreat is usable out of the box for most applications. Notice that the parameter object for unsupervised treatment defines a different set of parameters than the parameter object for supervised treatments (vtreat.vtreat_parameters).

vtreat.unsupervised_parameters()

coders: The types of synthetic variables that vtreat will (potentially) produce. See Types of prepared variables below.

indicator_min_fraction: By default, UnsupervisedTreatment creates indicators for all possible levels (indicator_min_fraction=0). If indicator_min_fraction > 0, then indicator variables (type indicator_code) are only produced for levels that are present at least indicator_min_fraction of the time. A consequence of this is that 1/indicator_min_fraction is the maximum number of indicators that will be produced for a given categorical variable. See the Example below.

user_transforms: 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.

sparse_indicators: When True, use a (Pandas) sparse representation for indicator variables. This representation is compatible with sklearn; however, it may not be compatible with other modeling packages. When False, use a dense representation.

Example: Restrict the number of indicator variables

# calculate the prevalence of each level by hand
d['xc'].value_counts(dropna=False)/d.shape[0]

transform_common = vtreat.UnsupervisedTreatment(
    cols_to_copy = ['y'],          # columns to "carry along" but not treat as input variables
    params = vtreat.unsupervised_parameters({
        'indicator_min_fraction': 0.2 # only make indicators for levels that show up more than 20% of the time
    })
)  

transform_common.fit_transform(d) # fit the transform
transform_common.score_frame_     # examine the score frame

In this case, the unsupervised treatment only created levels for the two most common levels, which are both present more than 20% of the time.

In unsupervised situations, this may only be desirable when there are an unworkably large number of possible levels (for example, when using ZIP code as a variable). It is more useful in conjunction with the y-aware variables produced by NumericOutputTreatment, BinomialOutcomeTreatment, or MultinomialOutcomeTreatment.

Types of prepared variables

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

lev: Produced from categorical variables, one for each 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”

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

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, isBAD, and lev), and no catP variables.

transform_thin = vtreat::designTreatmentsZ(
    dframe = d,                              # data to learn transform from
    varlist = setdiff(colnames(d), c('y')),  # columns to transform
    codeRestriction = c('clean', 'lev', 'isBAD'))
## [1] "vtreat 1.4.7 inspecting inputs Tue Oct  1 10:35:40 2019"
## [1] "designing treatments Tue Oct  1 10:35:40 2019"
## [1] " have initial level statistics Tue Oct  1 10:35:40 2019"
## [1] " scoring treatments Tue Oct  1 10:35:40 2019"
## [1] "have treatment plan Tue Oct  1 10:35:40 2019"
score_frame_thin = transform_thin$scoreFrame
knitr::kable(score_frame_thin)
varName varMoves rsq sig needsSplit extraModelDegrees origName code
x TRUE 0 1 FALSE 0 x clean
x_isBAD TRUE 0 1 FALSE 0 x isBAD
x2 TRUE 0 1 FALSE 0 x2 clean
xc_lev_NA TRUE 0 1 FALSE 0 xc lev
xc_lev_x_level_minus_0_5 TRUE 0 1 FALSE 0 xc lev
xc_lev_x_level_0 TRUE 0 1 FALSE 0 xc lev
xc_lev_x_level_0_5 TRUE 0 1 FALSE 0 xc lev
xc_lev_x_level_1 TRUE 0 1 FALSE 0 xc lev

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.

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