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

Preliminaries

Nina Zumel and John Mount November 2019

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

Load modules/packages.

import pkg_resources
import pandas
import numpy
import numpy.random
import seaborn
import matplotlib.pyplot as plt
import vtreat
import vtreat.util
import wvpy.util

numpy.random.seed(2019)

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
def make_data(nrows):
    d = pandas.DataFrame({'x':[0.1*i for i in range(500)]})
    d['y'] = numpy.sin(d['x']) + 0.01*d['x'] +  0.1*numpy.random.normal(size=d.shape[0])
    d['xc'] = ['level_' + str(5*numpy.round(yi/5, 1)) for yi in d['y']]
    d['x2'] = numpy.random.normal(size=d.shape[0])
    d['x3'] = 1
    d.loc[d['xc']=='level_-1.0', 'xc'] = numpy.nan # introduce a nan level
    return d

d = make_data(500)

d.head()
x y xc x2 x3
0 0.0 -0.021768 level_-0.0 -0.704278 1
1 0.1 0.182979 level_0.0 1.508747 1
2 0.2 0.348797 level_0.5 0.048117 1
3 0.3 0.431707 level_0.5 -1.445366 1
4 0.4 0.357232 level_0.5 -0.037443 1

Some quick data exploration

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

d['xc'].unique()
array(['level_-0.0', 'level_0.0', 'level_0.5', 'level_1.0', 'level_1.5',
       'level_-0.5', nan], dtype=object)

d['xc'].value_counts(dropna=False)
level_1.0     127
level_-0.5    125
level_0.5      86
level_0.0      50
level_-0.0     39
NaN            38
level_1.5      35
Name: xc, dtype: int64

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.UnsupervisedTreatment(
     cols_to_copy = ['y'],          # columns to "carry along" but not treat as input variables
)

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

d_prepared = transform.fit_transform(d)

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.

transform.score_frame_
variable orig_variable treatment y_aware has_range PearsonR significance recommended vcount
0 xc_is_bad xc missing_indicator False True NaN NaN True 1.0
1 x x clean_copy False True NaN NaN True 2.0
2 x2 x2 clean_copy False True NaN NaN True 2.0
3 xc_prevalence_code xc prevalence_code False True NaN NaN True 1.0
4 xc_lev_level_1_0 xc indicator_code False True NaN NaN True 7.0
5 xc_lev_level_-0_5 xc indicator_code False True NaN NaN True 7.0
6 xc_lev_level_0_5 xc indicator_code False True NaN NaN True 7.0
7 xc_lev_level_0_0 xc indicator_code False True NaN NaN True 7.0
8 xc_lev_level_-0_0 xc indicator_code False True NaN NaN True 7.0
9 xc_lev__NA_ xc indicator_code False True NaN NaN True 7.0
10 xc_lev_level_1_5 xc indicator_code False True NaN NaN True 7.0

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

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

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()
y xc_is_bad x x2 xc_prevalence_code xc_lev_level_1_0 xc_lev_level_-0_5 xc_lev_level_0_5 xc_lev_level_0_0 xc_lev_level_-0_0 xc_lev__NA_ xc_lev_level_1_5
0 -0.021768 0.0 0.0 -0.704278 0.078 0.0 0.0 0.0 0.0 1.0 0.0 0.0
1 0.182979 0.0 0.1 1.508747 0.100 0.0 0.0 0.0 1.0 0.0 0.0 0.0
2 0.348797 0.0 0.2 0.048117 0.172 0.0 0.0 1.0 0.0 0.0 0.0 0.0
3 0.431707 0.0 0.3 -1.445366 0.172 0.0 0.0 1.0 0.0 0.0 0.0 0.0
4 0.357232 0.0 0.4 -0.037443 0.172 0.0 0.0 1.0 0.0 0.0 0.0 0.0

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 = ['y']
model_vars = [v for v in d_prepared.columns if v not in set(not_variables)]

import sklearn.cluster

d_prepared['clusterID'] = sklearn.cluster.KMeans(n_clusters = 5).fit_predict(d_prepared[model_vars])
d_prepared.clusterID

# colorbrewer Dark2 palette
mypalette = ['#1b9e77', '#d95f02', '#7570b3', '#e7298a', '#66a61e']
ax = seaborn.scatterplot(x = "x", y = "y", hue="clusterID", 
                    data = d_prepared, 
                    palette=mypalette, 
                    legend=False)
ax.set_title("y as a function of x, points colored by (unsupervised) clusterID")
plt.show()

png

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.

import sklearn.linear_model
import seaborn
import sklearn.metrics
import matplotlib.pyplot

not_variables = ['y', 'prediction', 'clusterID']
model_vars = [v for v in d_prepared.columns if v not in set(not_variables)]
fitter = sklearn.linear_model.LinearRegression()
fitter.fit(d_prepared[model_vars], d_prepared['y'])
print(fitter.intercept_)
{model_vars[i]: fitter.coef_[i] for i in range(len(model_vars))}
0.2663584367410492





{'xc_is_bad': -0.572594870933189,
 'x': 0.0012979680156703158,
 'x2': 0.0003944391214526676,
 'xc_prevalence_code': -0.00443433454624302,
 'xc_lev_level_1_0': 0.7171318997544217,
 'xc_lev_level_-0_5': -0.8133266363407927,
 'xc_lev_level_0_5': 0.21813583211202284,
 'xc_lev_level_0_0': -0.18317399739579526,
 'xc_lev_level_-0_0': -0.4133594109584141,
 'xc_lev__NA_': -0.5725948709331848,
 'xc_lev_level_1_5': 1.047187183761745}

# now predict
d_prepared['prediction'] = fitter.predict(d_prepared[model_vars])

# get R-squared
r2 = sklearn.metrics.r2_score(y_true=d_prepared.y, y_pred=d_prepared.prediction)

title = 'Prediction vs. outcome (training data); R-sqr = {:04.2f}'.format(r2)

# compare the predictions to the outcome (on the training data)
ax = seaborn.scatterplot(x='prediction', y='y', data=d_prepared)
matplotlib.pyplot.plot(d_prepared.prediction, d_prepared.prediction, color="darkgray")
ax.set_title(title)
plt.show()

png

Now apply the model to new data.

# create the new data
dtest = make_data(450)

# prepare the new data with vtreat
dtest_prepared = transform.transform(dtest)

# apply the model to the prepared data
dtest_prepared['prediction'] = fitter.predict(dtest_prepared[model_vars])

# get R-squared
r2 = sklearn.metrics.r2_score(y_true=dtest_prepared.y, y_pred=dtest_prepared.prediction)

title = 'Prediction vs. outcome (test data); R-sqr = {:04.2f}'.format(r2)

# compare the predictions to the outcome (on the training data)
ax = seaborn.scatterplot(x='prediction', y='y', data=dtest_prepared)
matplotlib.pyplot.plot(dtest_prepared.prediction, dtest_prepared.prediction, color="darkgray")
ax.set_title(title)
plt.show()

png

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': {'clean_copy',
  'indicator_code',
  'missing_indicator',
  'prevalence_code'},
 'indicator_min_fraction': 0.0,
 'indicator_max_levels': 1000,
 'user_transforms': [],
 'sparse_indicators': False,
 'missingness_imputation': <function numpy.mean(a, axis=None, dtype=None, out=None, keepdims=<no value>, *, where=<no value>)>,
 'tunable_params': ['indicator_min_fraction', 'indicator_max_levels']}

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

indicator_max_levels: The maximum nuber of indicator variables that UnsupervisedTreatment will produce. Indicator variables are sorted by decreasing prevalence and then level name before the cutoff is applied. The default is 1000. See the Example below.

indicator_min_fraction: A value between 0 and 1. By default, UnsupervisedTreatment creates indicators for all possible levels up to indicator_max_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. 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.

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

Example: Restrict the number of indicator variables

In unsupervised situations, it's generally most desirable to create indicators for all possible levels. However, in some situations this may result in an unworkably large number of variables. (for example, when using ZIP code as a variable). The indicator_max_levels and indicator_min_fraction parameters allow the data scientist to restrict the number of levels to be considered, either by count or by a prevalence limit.

# calculate the prevalence of each level by hand
d['xc'].value_counts(dropna=False)/d.shape[0]
level_1.0     0.254
level_-0.5    0.250
level_0.5     0.172
level_0.0     0.100
level_-0.0    0.078
NaN           0.076
level_1.5     0.070
Name: xc, dtype: float64

Restrict to exactly the four most prevalent levels

transform_common = vtreat.UnsupervisedTreatment(
    cols_to_copy = ['y'],          # columns to "carry along" but not treat as input variables
    params = vtreat.unsupervised_parameters({
        'indicator_max_levels': 4 # only make indicators for the four most prevalent levels
    })
)  

transform_common.fit_transform(d) # fit the transform
transform_common.score_frame_     # examine the score frame
variable orig_variable treatment y_aware has_range PearsonR significance recommended vcount
0 xc_is_bad xc missing_indicator False True NaN NaN True 1.0
1 x x clean_copy False True NaN NaN True 2.0
2 x2 x2 clean_copy False True NaN NaN True 2.0
3 xc_prevalence_code xc prevalence_code False True NaN NaN True 1.0
4 xc_lev_level_1_0 xc indicator_code False True NaN NaN True 4.0
5 xc_lev_level_-0_5 xc indicator_code False True NaN NaN True 4.0
6 xc_lev_level_0_5 xc indicator_code False True NaN NaN True 4.0
7 xc_lev_level_0_0 xc indicator_code False True NaN NaN True 4.0

Restrict levels by prevalence threshold

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
variable orig_variable treatment y_aware has_range PearsonR significance recommended vcount
0 xc_is_bad xc missing_indicator False True NaN NaN True 1.0
1 x x clean_copy False True NaN NaN True 2.0
2 x2 x2 clean_copy False True NaN NaN True 2.0
3 xc_prevalence_code xc prevalence_code False True NaN NaN True 1.0
4 xc_lev_level_1_0 xc indicator_code False True NaN NaN True 2.0
5 xc_lev_level_-0_5 xc indicator_code False True NaN NaN True 2.0

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.

Types of prepared variables

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

indicator_code: Produced from categorical variables, one for each level: for each level of the variable, indicates if that level was "on"

prevalence_code: Produced from categorical variables: indicates how often each level of the variable was "on"

missing_indicator: 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_copy, missing_indicator, and indicator_code), and no prevalence_code variables.

transform_thin = vtreat.UnsupervisedTreatment(
    cols_to_copy = ['y'],          # columns to "carry along" but not treat as input variables
    params = vtreat.unsupervised_parameters({
         'coders': {'clean_copy',
                    'missing_indicator',
                    'indicator_code',
                   }
    })
)  

transform_thin.fit_transform(d) # fit the transform
transform_thin.score_frame_
variable orig_variable treatment y_aware has_range PearsonR significance recommended vcount
0 xc_is_bad xc missing_indicator False True NaN NaN True 1.0
1 x x clean_copy False True NaN NaN True 2.0
2 x2 x2 clean_copy False True NaN NaN True 2.0
3 xc_lev_level_1_0 xc indicator_code False True NaN NaN True 7.0
4 xc_lev_level_-0_5 xc indicator_code False True NaN NaN True 7.0
5 xc_lev_level_0_5 xc indicator_code False True NaN NaN True 7.0
6 xc_lev_level_0_0 xc indicator_code False True NaN NaN True 7.0
7 xc_lev_level_-0_0 xc indicator_code False True NaN NaN True 7.0
8 xc_lev__NA_ xc indicator_code False True NaN NaN True 7.0
9 xc_lev_level_1_5 xc indicator_code False True NaN NaN True 7.0

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:

Some vtreat common capabilities are documented here:

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.