Nina Zumel and John Mount February 2020
This article documents vtreat
's "fit_prepare" variation for classification problems.
This API was inspired by the pyvtreat
API, which was in turn based on the .fit()
, .transform()
, .fit_transform()
workflow of scikit-learn
in Python
.
The same example in the original R
vtreat
notation can be found here.
The same example in the Python
version of vtreat
can be found here.
Load modules/packages.
library(rqdatatable) library(vtreat) packageVersion('vtreat') 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. xc
is a categorical variable that represents a discretization of y
, along some NA
sx2
is a pure noise variable with no relationship to the outputset.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$y/5, 1)) d['x2'] = rnorm(n = nrows) d[d['xc']=='level_-1', 'xc'] = NA # introduce a NA level d['yc'] = d[['y']]>0.5 return(d) } d = make_data(500) d %.>% head(.) %.>% knitr::kable(.)
Check how many levels xc
has, and their distribution (including NA
)
unique(d['xc'])
table(d$xc, useNA = 'always')
Find the mean value of yc
mean(d[['yc']])
Plot of yc
versus x
.
ggplot(d, aes(x=x, y=as.numeric(yc))) + geom_line()
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 NA
s.
First create the data treatment object, in this case a treatment for a binomial classification problem.
transform_spec <- vtreat::BinomialOutcomeTreatment( var_list = setdiff(colnames(d), c('y', 'yc')), # columns to transform outcome_name = 'yc', # outcome variable outcome_target = TRUE # outcome of interest )
Now call the fit_prepare()
function with the training data d
to fit the transform and also return a treated training set. The fit_prepare()
function returns the fitted data treatment object (as treatments
) and a
statistically correct treated training set (as cross_frame
) for training the model. The cross_frame
is guaranteed to be completely numeric, with no missing values.
# the unpack notation is a multiassignment operator # see https://winvector.github.io/wrapr/articles/unpack_multiple_assignment.html # for more details unpack[ treatment_plan = treatments, d_prepared = cross_frame ] <- fit_prepare(transform_spec, d) # list the derived variables get_feature_names(treatment_plan)
Notice that d_prepared
only includes derived variables and the outcome yc
:
d_prepared %.>% head(.) %.>% knitr::kable(.)
As we will see below, the prepare()
function applies the fitted data treatments to future data, prior to calling your model on the data.
Note that for the training data d
: fit_prepare(transform_spec, d)
is not the same as
fit(transform_spec, d) %.>% prepare(., d)
; the second call can lead to nested model bias in some
situations, and is not recommended. In other words, it is a bad idea to call prepare()
on your original training data.
For future application data df
that is not seen during transform design, prepare(treatment_plan, df)
is the 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(treatment_plan, d)
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.
# get statistics on the variables score_frame <- get_score_frame(treatment_plan) # only print a subset of the columns cols = c("varName", "origName", "code", "rsq", "sig", "varMoves", "default_threshold", "recommended") knitr::kable(score_frame[,cols])
Note that the variable xc
has been converted to multiple variables:
NA
(xc_lev_*
)yc
as a function of xc
(xc_catB
)xc
is in the training data (xc_catP
)The variable x
has been converted to two new variables:
x
that has no missing values or NaN
sx
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 (sig
) smaller than default_threshold
. See the section Deriving the Default Thresholds below for the reasoning behind the default thresholds. 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(.)
# not recommended variables score_frame[!score_frame[['recommended']], 'varName', drop = FALSE] %.>% knitr::kable(.)
catB
variablesVariables 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.
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
.
# only use the recommended variables to fit the model 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(treatment_plan, 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')
BinomialOutcomeTreatment
We've tried to set the defaults for all parameters so that vtreat
is usable out of the box for most applications.
classification_parameters()
Some parameters of note include:
codeRestriction (default: NULL): the types of synthetic variables that vtreat
will (potentially) produce. See Types of prepared variables below. By default, produces all applicable variable types.
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 (by default, 2% 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.
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: a 0/1 indicator variable that 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.
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 catB
or catP
variables.
# create a new set of parameters, overriding # the default for codeRestriction newparams = classification_parameters( list( codeRestriction = c('clean', 'isBAD', 'lev') )) thin_spec <- vtreat::BinomialOutcomeTreatment( var_list = setdiff(colnames(d), c('y', 'yc')), # columns to transform outcome_name = 'yc', # outcome variable outcome_target = TRUE, # outcome of interest params = newparams # set the parameters ) unpack[ thin_plan = treatments, thin_frame = cross_frame ] <- fit_prepare(thin_spec, d) # examine the new prepared training data # no catB or catP knitr::kable(head(thin_frame)) # examine the score frame for the new treatment plan # no catB or catP knitr::kable(get_score_frame(thin_plan)[,cols])
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.
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:
R
regression example, fit/prepare interface, R
regression example, design/prepare/experiment interface, Python
regression example.R
classification example, fit/prepare interface, R
classification example, design/prepare/experiment interface, Python
classification example.R
unsupervised example, fit/prepare interface, R
unsupervised example, design/prepare/experiment interface, Python
unsupervised example.R
multinomial classification example, fit/prepare interface, R
multinomial classification example, design/prepare/experiment interface, Python
multinomial classification example.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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