# vtreat v1.6.2

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## A Statistically Sound 'data.frame' Processor/Conditioner

A 'data.frame' processor/conditioner that prepares real-world data for predictive modeling in a statistically sound manner.
'vtreat' prepares variables so that data has fewer exceptional cases, making
it easier to safely use models in production. Common problems 'vtreat' defends
against: 'Inf', 'NA', too many categorical levels, rare categorical levels, and new
categorical levels (levels seen during application, but not during training). Reference:
"'vtreat': a data.frame Processor for Predictive Modeling", Zumel, Mount, 2016, <DOI:10.5281/zenodo.1173313>.

## Readme

`vtreat`

is a `data.frame`

processor/conditioner (available for
`R`

, and for
`Python`

) that prepares
real-world data for supervised machine learning or predictive modeling
in a statistically sound manner.

A nice video lecture on what sorts of problems `vtreat`

solves can be
found here.

`vtreat`

takes an input `data.frame`

that has a specified column called
“the outcome variable” (or “y”) that is the quantity to be predicted
(and must not have missing values). Other input columns are possible
explanatory variables (typically numeric or categorical/string-valued,
these columns may have missing values) that the user later wants to use
to predict “y”. In practice such an input `data.frame`

may not be
immediately suitable for machine learning procedures that often expect
only numeric explanatory variables, and may not tolerate missing values.

To solve this, `vtreat`

builds a transformed `data.frame`

where all
explanatory variable columns have been transformed into a number of
numeric explanatory variable columns, without missing values. The
`vtreat`

implementation produces derived numeric columns that capture
most of the information relating the explanatory columns to the
specified “y” or dependent/outcome column through a number of numeric
transforms (indicator variables, impact codes, prevalence codes, and
more). This transformed `data.frame`

is suitable for a wide range of
supervised learning methods from linear regression, through gradient
boosted machines.

The idea is: you can take a `data.frame`

of messy real world data and
easily, faithfully, reliably, and repeatably prepare it for machine
learning using documented methods using `vtreat`

. Incorporating `vtreat`

into your machine learning workflow lets you quickly work with very
diverse structured data.

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**:`R`

regression example, fit/prepare interface,`R`

regression example, design/prepare/experiment interface,`Python`

regression example.**Classification**:`R`

classification example, fit/prepare interface,`R`

classification example, design/prepare/experiment interface,`Python`

classification example.**Unsupervised tasks**:`R`

unsupervised example, fit/prepare interface,`R`

unsupervised example, design/prepare/experiment interface,`Python`

unsupervised example.**Multinomial classification**:`R`

multinomial classification example, fit/prepare interface,`R`

multinomial classification example, design/prepare/experiment interface,`Python`

multinomial classification example.

In all cases: variable preparation is intended to be a “one liner.”

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.

For more detail please see here: arXiv:1611.09477
stat.AP (the documentation describes
the `R`

version, however all of the examples can be found worked in
`Python`

here).

`vtreat`

is available as an `R`

package, and also as a
`Python`

/`Pandas`

package.

(logo: Julie Mount, source: “The Harvest” by Boris Kustodiev 1914)

Even with modern machine learning techniques (random forests, support
vector machines, neural nets, gradient boosted trees, and so on) or
standard statistical methods (regression, generalized regression,
generalized additive models) there are *common* data issues that can
cause modeling to fail. vtreat deals with a number of these in a
principled and automated fashion.

In particular vtreat emphasizes a concept called “y-aware pre-processing” and implements:

- Treatment of missing values through safe replacement plus indicator column (a simple but very powerful method when combined with downstream machine learning algorithms).
- Treatment of novel levels (new values of categorical variable seen during test or application, but not seen during training) through sub-models (or impact/effects coding of pooled rare events).
- Explicit coding of categorical variable levels as new indicator variables (with optional suppression of non-significant indicators).
- Treatment of categorical variables with very large numbers of levels through sub-models (again impact/effects coding).
- (optional) User specified significance pruning on levels coded into effects/impact sub-models.
- Correct treatment of nested models or sub-models through data split (see here) or through the generation of “cross validated” data frames (see here); these are issues similar to what is required to build statistically efficient stacked models or super-learners).
- Safe processing of “wide data” (data with very many variables, often driving common machine learning algorithms to over-fit) through out of sample per-variable significance estimates and user controllable pruning (something we have lectured on previously here and here).
- Collaring/Winsorizing of unexpected out of range numeric inputs.
- (optional) Conversion of all variables into effects (or “y-scale”)
units (through the optional
`scale`

argument to`vtreat::prepare()`

, using some of the ideas discussed here). This allows correct/sensible application of principal component analysis pre-processing in a machine learning context. - Joining in additional training distribution data (which can be useful in analysis, called “catP” and “catD”).

The idea is: even with a sophisticated machine learning algorithm there
are *many* ways messy real world data can defeat the modeling process,
and vtreat helps with at least ten of them. We emphasize: these problems
are already in your data, you simply build better and more reliable
models if you attempt to mitigate them. Automated processing is no
substitute for actually looking at the data, but vtreat supplies
efficient, reliable, documented, and tested implementations of many of
the commonly needed transforms.

To help explain the methods we have prepared some documentation:

- The vtreat package overall.
- Preparing data for analysis using R white-paper
- The types of new variables introduced by vtreat processing (including how to limit down to domain appropriate variable types).
- Statistically sound treatment of the nested modeling issue introduced by any sort of pre-processing (such as vtreat itself): nested over-fit issues and a general cross-frame solution.
- Principled ways to pick significance based pruning levels.

Data treatments are “y-aware” (use distribution relations between
independent variables and the dependent variable). For binary
classification use `designTreatmentsC()`

and for numeric regression use
`designTreatmentsN()`

.

After the design step, `prepare()`

should be used as you would use
model.matrix. `prepare()`

treated variables are all numeric and never
take the value NA or +-Inf (so are very safe to use in modeling).

In application we suggest splitting your data into three sets: one for building vtreat encodings, one for training models using these encodings, and one for test and model evaluation.

The purpose of `vtreat`

library is to reliably prepare data for
supervised machine learning. We try to leave as much as possible to the
machine learning algorithms themselves, but cover most of the truly
necessary typically ignored precautions. The library is designed to
produce a `data.frame`

that is entirely numeric and takes common
precautions to guard against the following real world data issues:

Categorical variables with very many levels.

We re-encode such variables as a family of indicator or dummy variables for common levels plus an additional impact code (also called “effects coded”). This allows principled use (including smoothing) of huge categorical variables (like zip-codes) when building models. This is critical for some libraries (such as

`randomForest`

, which has hard limits on the number of allowed levels).Rare categorical levels.

Levels that do not occur often during training tend not to have reliable effect estimates and contribute to over-fit. vtreat helps with 2 precautions in this case. First the

`rareLevel`

argument suppresses levels with this count our below from modeling, except possibly through a grouped contribution. Also with enough data vtreat attempts to estimate out of sample performance of derived variables. Finally we suggest users reserve a portion of data for vtreat design, separate from any data used in additional training, calibration, or testing.Novel categorical levels.

A common problem in deploying a classifier to production is: new levels (levels not seen during training) encountered during model application. We deal with this by encoding categorical variables in a possibly redundant manner: reserving a dummy variable for all levels (not the more common all but a reference level scheme). This is in fact the correct representation for regularized modeling techniques and lets us code novel levels as all dummies simultaneously zero (which is a reasonable thing to try). This encoding while limited is cheaper than the fully Bayesian solution of computing a weighted sum over previously seen levels during model application.

Missing/invalid values NA, NaN, +-Inf.

Variables with these issues are re-coded as two columns. The first column is clean copy of the variable (with missing/invalid values replaced with either zero or the grand mean, depending on the user chose of the

`scale`

parameter). The second column is a dummy or indicator that marks if the replacement has been performed. This is simpler than imputation of missing values, and allows the downstream model to attempt to use missingness as a useful signal (which it often is in industrial data).Extreme values.

Variables can be restricted to stay in ranges seen during training. This can defend against some run-away classifier issues during model application.

Constant and near-constant variables.

Variables that “don’t vary” or “nearly don’t vary” are suppressed.

Need for estimated single-variable model effect sizes and significances.

It is a dirty secret that even popular machine learning techniques need some variable pruning (when exposed to very wide data frames, see here and here). We make the necessary effect size estimates and significances easily available and supply initial variable pruning.

The above are all awful things that often lurk in real world data.
Automating these steps ensures they are easy enough that you actually
perform them and leaves the analyst time to look for additional data
issues. For example this allowed us to essentially automate a number of
the steps taught in chapters 4 and 6 of *Practical Data Science with R*
(Zumel, Mount; Manning
2014) into a
very short
worksheet (though
we think for understanding it is *essential* to work all the steps by
hand as we did in the book). The 2nd edition of *Practical Data Science
with R* covers using `vtreat`

in `R`

in chapter 8 “Advanced Data
Preparation.”

The idea is: `data.frame`

s prepared with the `vtreat`

library are
somewhat safe to train on as some precaution has been taken against all
of the above issues. Also of interest are the `vtreat`

variable
significances (help in initial variable pruning, a necessity when there
are a large number of columns) and `vtreat::prepare(scale=TRUE)`

which
re-encodes all variables into effect units making them suitable for
y-aware dimension reduction (variable clustering, or principal component
analysis) and for geometry sensitive machine learning techniques
(k-means, knn, linear SVM, and more). You may want to do more than the
`vtreat`

library does (such as Bayesian imputation, variable clustering,
and more) but you certainly do not want to do less.

There have been a number of recent substantial improvements to the library, including:

- Out of sample scoring.
- Ability to use
`parallel`

. - More general calculation of effect sizes and significances.

Some of our related articles (which should make clear some of our motivations, and design decisions):

- Modeling trick: impact coding of categorical variables with many levels
- A bit more on impact coding
- vtreat: designing a package for variable treatment
- A comment on preparing data for classifiers
- Nina Zumel presenting on vtreat
- What is new in the vtreat library?
- How do you know if your data has signal?

Examples of current best practice using `vtreat`

(variable coding,
train, test split) can be found
here
and here.

Some small examples:

We attach our packages.

```
library("vtreat")
# Loading required package: wrapr
packageVersion("vtreat")
# [1] '1.6.1'
citation('vtreat')
#
# To cite package 'vtreat' in publications use:
#
# John Mount and Nina Zumel (2020). vtreat: A Statistically Sound
# 'data.frame' Processor/Conditioner.
# https://github.com/WinVector/vtreat/,
# https://winvector.github.io/vtreat/.
#
# A BibTeX entry for LaTeX users is
#
# @Manual{,
# title = {vtreat: A Statistically Sound 'data.frame' Processor/Conditioner},
# author = {John Mount and Nina Zumel},
# year = {2020},
# note = {https://github.com/WinVector/vtreat/, https://winvector.github.io/vtreat/},
# }
```

A small categorical example.

```
# categorical example
set.seed(23525)
# we set up our raw training and application data
dTrainC <- data.frame(
x = c('a', 'a', 'a', 'b', 'b', NA, NA),
z = c(1, 2, 3, 4, NA, 6, NA),
y = c(FALSE, FALSE, TRUE, FALSE, TRUE, TRUE, TRUE))
dTestC <- data.frame(
x = c('a', 'b', 'c', NA),
z = c(10, 20, 30, NA))
# we perform a vtreat cross frame experiment
# and unpack the results into treatmentsC
# and dTrainCTreated
unpack[
treatmentsC = treatments,
dTrainCTreated = crossFrame
] <- mkCrossFrameCExperiment(
dframe = dTrainC,
varlist = setdiff(colnames(dTrainC), 'y'),
outcomename = 'y',
outcometarget = TRUE,
verbose = FALSE)
# the treatments include a score frame relating new
# derived variables to original columns
treatmentsC$scoreFrame[, c('origName', 'varName', 'code', 'rsq', 'sig', 'extraModelDegrees', 'recommended')] %.>%
knitr::kable(.)
```

origName | varName | code | rsq | sig | extraModelDegrees | recommended |
---|---|---|---|---|---|---|

x | x_catP | catP | 0.1669568 | 0.2064389 | 2 | FALSE |

x | x_catB | catB | 0.2547883 | 0.1185814 | 2 | TRUE |

z | z | clean | 0.2376018 | 0.1317602 | 0 | TRUE |

z | z_isBAD | isBAD | 0.2960654 | 0.0924840 | 0 | TRUE |

x | x_lev_NA | lev | 0.2960654 | 0.0924840 | 0 | FALSE |

x | x_lev_x_a | lev | 0.1300057 | 0.2649038 | 0 | FALSE |

x | x_lev_x_b | lev | 0.0060673 | 0.8096724 | 0 | FALSE |

```
# the treated frame is a "cross frame" which
# is a transform of the training data built
# as if the treatment were learned on a different
# disjoint training set to avoid nested model
# bias and over-fit.
dTrainCTreated %.>%
head(.) %.>%
knitr::kable(.)
```

x_catP | x_catB | z | z_isBAD | x_lev_NA | x_lev_x_a | x_lev_x_b | y |
---|---|---|---|---|---|---|---|

0.50 | 0.0000000 | 1 | 0 | 0 | 1 | 0 | FALSE |

0.40 | -0.4054484 | 2 | 0 | 0 | 1 | 0 | FALSE |

0.40 | -10.3089860 | 3 | 0 | 0 | 1 | 0 | TRUE |

0.20 | 8.8049919 | 4 | 0 | 0 | 0 | 1 | FALSE |

0.25 | -9.2104404 | 3 | 1 | 0 | 0 | 1 | TRUE |

0.25 | 9.2104404 | 6 | 0 | 1 | 0 | 0 | TRUE |

```
# Any future application data is prepared with
# the prepare method.
dTestCTreated <- prepare(treatmentsC, dTestC, pruneSig=NULL)
dTestCTreated %.>%
head(.) %.>%
knitr::kable(.)
```

x_catP | x_catB | z | z_isBAD | x_lev_NA | x_lev_x_a | x_lev_x_b |
---|---|---|---|---|---|---|

0.4285714 | -0.9807709 | 10.0 | 0 | 0 | 1 | 0 |

0.2857143 | -0.2876737 | 20.0 | 0 | 0 | 0 | 1 |

0.0714286 | 0.0000000 | 30.0 | 0 | 0 | 0 | 0 |

0.2857143 | 9.6158638 | 3.2 | 1 | 1 | 0 | 0 |

A small numeric example.

```
# numeric example
set.seed(23525)
# we set up our raw training and application data
dTrainN <- data.frame(
x = c('a', 'a', 'a', 'a', 'b', 'b', NA, NA),
z = c(1, 2, 3, 4, 5, NA, 7, NA),
y = c(0, 0, 0, 1, 0, 1, 1, 1))
dTestN <- data.frame(
x = c('a', 'b', 'c', NA),
z = c(10, 20, 30, NA))
# we perform a vtreat cross frame experiment
# and unpack the results into treatmentsN
# and dTrainNTreated
unpack[
treatmentsN = treatments,
dTrainNTreated = crossFrame
] <- mkCrossFrameNExperiment(
dframe = dTrainN,
varlist = setdiff(colnames(dTrainN), 'y'),
outcomename = 'y',
verbose = FALSE)
# the treatments include a score frame relating new
# derived variables to original columns
treatmentsN$scoreFrame[, c('origName', 'varName', 'code', 'rsq', 'sig', 'extraModelDegrees')] %.>%
knitr::kable(.)
```

origName | varName | code | rsq | sig | extraModelDegrees |
---|---|---|---|---|---|

x | x_catP | catP | 0.4047085 | 0.0899406 | 2 |

x | x_catN | catN | 0.2822908 | 0.1753958 | 2 |

x | x_catD | catD | 0.0209693 | 0.7322571 | 2 |

z | z | clean | 0.2880952 | 0.1701892 | 0 |

z | z_isBAD | isBAD | 0.3333333 | 0.1339746 | 0 |

x | x_lev_NA | lev | 0.3333333 | 0.1339746 | 0 |

x | x_lev_x_a | lev | 0.2500000 | 0.2070312 | 0 |

x | x_lev_x_b | lev | 0.0000000 | 1.0000000 | 0 |

```
# the treated frame is a "cross frame" which
# is a transform of the training data built
# as if the treatment were learned on a different
# disjoint training set to avoid nested model
# bias and over-fit.
dTrainNTreated %.>%
head(.) %.>%
knitr::kable(.)
```

x_catN | x_catD | z | z_isBAD | x_lev_NA | x_lev_x_a | x_lev_x_b | x_catP | y |
---|---|---|---|---|---|---|---|---|

-0.2666667 | 0.5000000 | 1 | 0 | 0 | 1 | 0 | 0.6 | 0 |

-0.5000000 | 0.0000000 | 2 | 0 | 0 | 1 | 0 | 0.5 | 0 |

-0.0666667 | 0.5000000 | 3 | 0 | 0 | 1 | 0 | 0.6 | 0 |

-0.5000000 | 0.0000000 | 4 | 0 | 0 | 1 | 0 | 0.5 | 1 |

0.4000000 | 0.7071068 | 5 | 0 | 0 | 0 | 1 | 0.2 | 0 |

-0.4000000 | 0.7071068 | 3 | 1 | 0 | 0 | 1 | 0.2 | 1 |

```
# Any future application data is prepared with
# the prepare method.
dTestNTreated <- prepare(treatmentsN, dTestN, pruneSig=NULL)
dTestNTreated %.>%
head(.) %.>%
knitr::kable(.)
```

x_catP | x_catN | x_catD | z | z_isBAD | x_lev_NA | x_lev_x_a | x_lev_x_b |
---|---|---|---|---|---|---|---|

0.5000 | -0.25 | 0.5000000 | 10.000000 | 0 | 0 | 1 | 0 |

0.2500 | 0.00 | 0.7071068 | 20.000000 | 0 | 0 | 0 | 1 |

0.0625 | 0.00 | 0.7071068 | 30.000000 | 0 | 0 | 0 | 0 |

0.2500 | 0.50 | 0.0000000 | 3.666667 | 1 | 1 | 0 | 0 |

Related work:

- Cohen J, Cohen P (1983). Applied Multiple Regression/Correlation Analysis For The Behavioral Sciences. 2 edition. Lawrence Erlbaum Associates, Inc. ISBN 0-89859-268-2.
- “A preprocessing scheme for high-cardinality categorical attributes in classification and prediction problems” Daniele Micci-Barreca; ACM SIGKDD Explorations, Volume 3 Issue 1, July 2001 Pages 27-32.
- “Modeling Trick: Impact Coding of Categorical Variables with Many Levels” Nina Zumel; Win-Vector blog, 2012.
- “Big Learning Made Easy – with Counts!”, Misha Bilenko, Cortana Intelligence and Machine Learning Blog, 2015.

## Installation

To install, from inside `R`

please run:

```
install.packages("vtreat")
```

## Note

Notes on controlling `vtreat`

’s cross-validation plans can be found
here.

Note: `vtreat`

is meant only for “tame names”, that is: variables and
column names that are also valid *simple* (without quotes) `R`

variables
names.

## Functions in vtreat

Name | Description | |

fit_transform | Fit and transform in a cross-validated manner. | |

fit | Fit first arguemnt to data in second argument. | |

kWayStratifiedY | k-fold cross validation stratified on y, a splitFunction in the sense of vtreat::buildEvalSets | |

fit_prepare | Fit and prepare in a cross-validated manner. | |

kWayStratifiedYReplace | k-fold cross validation stratified with replacement on y, a splitFunction in the sense of vtreat::buildEvalSets . | |

UnsupervisedTreatment | Stateful object for designing and applying unsupervised treatments. | |

ppCoderC | Solve a categorical partial pooling problem. | |

ppCoderN | Solve a numeric partial pooling problem. | |

format.vtreatment | Display treatment plan. | |

makekWayCrossValidationGroupedByColumn | Build a k-fold cross validation splitter, respecting (never splitting) groupingColumn. | |

oneWayHoldout | One way holdout, a splitFunction in the sense of vtreat::buildEvalSets. | |

mkCrossFrameCExperiment | Run categorical cross-frame experiment. | |

getSplitPlanAppLabels | read application labels off a split plan. | |

patch_columns_into_frame | Patch columns into data.frame. | |

prepare.treatmentplan | Apply treatments and restrict to useful variables. | |

design_missingness_treatment | Design a simple treatment plan to indicate missingingness and perform simple imputation. | |

print.multinomial_plan | Print treatmentplan. | |

flatten_fn_list | Flatten a list of functions onto d. | |

designTreatmentsZ | Design variable treatments with no outcome variable. | |

designTreatmentsN | build all treatments for a data frame to predict a numeric outcome | |

kWayCrossValidation | k-fold cross validation, a splitFunction in the sense of vtreat::buildEvalSets | |

get_transform | Return underlying transform from vps. | |

multinomial_parameters | vtreat multinomial parameters. | |

pre_comp_xval | Pre-computed cross-plan (so same split happens each time). | |

square_window | Build a square windows variable, numeric target. | |

novel_value_summary | Report new/novel appearances of character values. | |

prepare.simple_plan | Prepare a simple treatment. | |

prepare.multinomial_plan | Function to apply mkCrossFrameMExperiment treatemnts. | |

print.simple_plan | Print treatmentplan. | |

print.treatmentplan | Print treatmentplan. | |

.wmean | Compute weighted mean | |

unsupervised_parameters | vtreat unsupervised parameters. | |

square_windowc | Build a square windows variable, categorical target. | |

track_values | Track unique character values for variables. | |

vnames | New treated variable names from a treatmentplan$treatment item. | |

variable_values | Return variable evaluations. | |

vorig | Original variable name from a treatmentplan$treatment item. | |

rquery_prepare | Materialize a treated data frame remotely. | |

solveIsotone | Solve for best single-direction (non-decreasing or non-increasing) fit. | |

vtreat | vtreat: A Statistically Sound 'data.frame' Processor/Conditioner | |

makeCustomCoderNum | Make a numeric input custom coder. | |

makeCustomCoderCat | Make a categorical input custom coder. | |

get_feature_names | Return feasible feature names. | |

rqdatatable_prepare | Apply a treatment plan using rqdatatable. | |

mkCrossFrameNExperiment | Run a numeric cross frame experiment. | |

regression_parameters | vtreat regression parameters. | |

mkCrossFrameMExperiment | Function to build multi-outcome vtreat cross frame and treatment plan. | |

solveNonDecreasing | Solve for best non-decreasing fit using isotone regression (from the "isotone" package https://CRAN.R-project.org/package=isotone). | |

prepare | Apply treatments and restrict to useful variables. | |

get_score_frame | Return score frame from vps. | |

solveNonIncreasing | Solve for best non-increasing fit. | |

solve_piecewise | Solve as piecewise linear problem, numeric target. | |

value_variables_N | Value variables for prediction a numeric outcome. | |

solve_piecewisec | Solve as piecewise logit problem, categorical target. | |

value_variables_C | Value variables for prediction a categorical outcome. | |

problemAppPlan | check if appPlan is a good carve-up of 1:nRows into nSplits groups | |

spline_variable | Spline variable numeric target. | |

print.vtreatment | Print treatmentplan. | |

spline_variablec | Spline variable categorical target. | |

center_scale | Center and scale a set of variables. | |

buildEvalSets | Build set carve-up for out-of sample evaluation. | |

apply_transform | Transform second argument by first. | |

NumericOutcomeTreatment | Stateful object for designing and applying numeric outcome treatments. | |

BinomialOutcomeTreatment | Stateful object for designing and applying binomial outcome treatments. | |

classification_parameters | vtreat classification parameters. | |

as_rquery_plan | Convert vtreatment plans into a sequence of rquery operations. | |

designTreatmentsC | Build all treatments for a data frame to predict a categorical outcome. | |

MultinomialOutcomeTreatment | Stateful object for designing and applying multinomial outcome treatments. | |

No Results! |

## Vignettes of vtreat

## Last month downloads

## Details

Type | Package |

Date | 2020-10-17 |

URL | https://github.com/WinVector/vtreat/, https://winvector.github.io/vtreat/ |

BugReports | https://github.com/WinVector/vtreat/issues |

License | GPL-2 | GPL-3 |

LazyData | true |

VignetteBuilder | knitr, R.rsp |

RoxygenNote | 7.1.1 |

ByteCompile | true |

NeedsCompilation | no |

Packaged | 2020-10-17 15:12:10 UTC; johnmount |

Repository | CRAN |

Date/Publication | 2020-10-17 15:40:02 UTC |

suggests | data.table (>= 1.12.2) , datasets , DBI , isotone , knitr , lme4 , parallel , R.rsp , rmarkdown , rqdatatable (>= 1.2.8) , rquery (>= 1.4.5) , RSQLite , tinytest |

imports | digest , stats |

depends | R (>= 3.4.0) , wrapr (>= 2.0.2) |

Contributors | Nina Zumel, Win-Vector LLC |

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