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

Preliminaries

Nina Zumel and John Mount September 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.

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

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)
d['xc'] = ['level_' + str(5*numpy.round(yi/5, 1)) for yi in d['y']]
d['x2'] = numpy.random.normal(size=d.shape)
d['x3'] = 1
d.loc[d['xc']=='level_-1.0', 'xc'] = numpy.nan # introduce a nan level
return d

d = make_data(500)

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x y xc x2 x3
0 0.0 -0.104856 level_-0.0 0.367093 1
1 0.1 0.148332 level_0.0 -0.690937 1
2 0.2 0.280450 level_0.5 -0.256927 1
3 0.3 0.504849 level_0.5 0.188184 1
4 0.4 0.358950 level_0.5 0.619167 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_-0.5',
nan, 'level_1.5'], dtype=object)
d['xc'].value_counts(dropna=False)
level_-0.5    128
level_1.0     122
level_0.5      98
level_0.0      41
level_-0.0     40
NaN            36
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_
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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_-0.5 xc indicator_code False True NaN NaN True 7.0
5 xc_lev_level_1.0 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).

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y xc_is_bad x x2 xc_prevalence_code xc_lev_level_-0.5 xc_lev_level_1.0 xc_lev_level_0.5 xc_lev_level_0.0 xc_lev_level_-0.0 xc_lev__NA_ xc_lev_level_1.5
0 -0.104856 0.0 0.0 0.367093 0.080 0.0 0.0 0.0 0.0 1.0 0.0 0.0
1 0.148332 0.0 0.1 -0.690937 0.082 0.0 0.0 0.0 1.0 0.0 0.0 0.0
2 0.280450 0.0 0.2 -0.256927 0.196 0.0 0.0 1.0 0.0 0.0 0.0 0.0
3 0.504849 0.0 0.3 0.188184 0.196 0.0 0.0 1.0 0.0 0.0 0.0 0.0
4 0.358950 0.0 0.4 0.619167 0.196 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))}
0.26687361134312826

'x': 0.0012639910538561326,
'x2': 0.001609517233713642,
'xc_prevalence_code': -0.0044801038835988755,
'xc_lev_level_-0.5': -0.8087257353814689,
'xc_lev_level_1.0': 0.7247440547156317,
'xc_lev_level_0.5': 0.2180424429835109,
'xc_lev_level_0.0': -0.17839488726269243,
'xc_lev_level_-0.0': -0.43704784362522275,
'xc_lev__NA_': -0.5623566778416543,
'xc_lev_level_1.5': 1.0437386464118965}
# 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}

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
level_-0.5    0.256
level_1.0     0.244
level_0.5     0.196
level_0.0     0.082
level_-0.0    0.080
NaN           0.072
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
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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_-0.5 xc indicator_code False True NaN NaN True 2.0
5 xc_lev_level_1.0 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_
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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_-0.5 xc indicator_code False True NaN NaN True 7.0
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_0.0 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:

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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