Unsupervised.md

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()

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))}

0.2663584367410494





{'xc_is_bad': -0.5725948709331847,
 'x': 0.0012979680156703069,
 'x2': 0.0003944391214530679,
 'xc_prevalence_code': -0.004434334546243255,
 'xc_lev_level_1_0': 0.717131899754422,
 'xc_lev_level_-0_5': -0.8133266363407938,
 'xc_lev_level_0_5': 0.21813583211202345,
 'xc_lev_level_0_0': -0.1831739973957961,
 'xc_lev_level_-0_0': -0.4133594109584157,
 'xc_lev__NA_': -0.5725948709331844,
 'xc_lev_level_1_5': 1.0471871837617448}

# 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()

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()

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,
 'user_transforms': [],
 'sparse_indicators': True,
 'missingness_imputation': <function numpy.mean(a, axis=None, dtype=None, out=None, keepdims=<no value>)>}

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.

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

# 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

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.

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_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:

• Regression: Python regression example, R regression example, fit/prepare interface, R regression example, design/prepare/experiment interface.
• Classification: Python classification example, R classification example, fit/prepare interface, R classification example, design/prepare/experiment interface.
• Unsupervised tasks: Python unsupervised example, R unsupervised example, fit/prepare interface, R unsupervised example, design/prepare/experiment interface.
• Multinomial classification: Python multinomial classification example, R multinomial classification example, fit/prepare interface, R multinomial classification example, design/prepare/experiment interface.

Some vtreat common capabilities are documented here:

• Score Frame score_frame_, using the score_frame_ information.
• Cross Validation Customized Cross Plans, controlling the cross validation plan.

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.