Classification.Rmd

---
title: "Classification"
output: github_document
---

# Using [vtreat](https://github.com/WinVector/vtreat) with Classification Problems

Nina Zumel and John Mount

updated February 2020

Note this is a description of the [`R` version of `vtreat`](https://github.com/WinVector/vtreat), the same example for the [`Python` version of `vtreat`](https://github.com/WinVector/pyvtreat) can be found [here](https://github.com/WinVector/pyvtreat/blob/master/Examples/Classification/Classification.md).

## Preliminaries


Load modules/packages.

```{r}
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. 
* Input `xc` is a categorical variable that represents a discretization of `y`, along some `NA`s
* Input `x2` is a pure noise variable with no relationship to the output

```{r}
set.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(.)
```


### Some quick data exploration


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

```{r}
unique(d['xc'])
```

```{r}
table(d$xc, useNA = 'always')
```

Find the mean value of `yc`

```{r}
mean(d[['yc']])
```


Plot of `yc` versus `x`.

```{r}
ggplot(d, aes(x=x, y=as.numeric(yc))) + 
  geom_line()
```

## Build a transform appropriate for classification problems.

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 transform design object, in this case a treatment for a binomial classification problem.

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

```{r}
unpack[
  transform = treatments,
  d_prepared = crossFrame
  ] <- vtreat::mkCrossFrameCExperiment(
    dframe = d,                                    # data to learn transform from
    varlist = setdiff(colnames(d), c('y', 'yc')),  # columns to transform
    outcomename = 'yc',                            # outcome variable
    outcometarget = TRUE                           # outcome of interest
  )
```

Notice that `d_prepared` now only includes derived variables and the outcome `yc`. The derived variables will be discussed below.

```{r}
d_prepared %.>%
  head(.) %.>%
  knitr::kable(.)
```

Note that for the training data `d`: `crossFrame` is **not** the same as `prepare(transform, d)`; the second call can lead to nested model bias in some situations, and is **not** recommended. For other, later data, not seen during transform design `transform.preprare(o)` is an appropriate step.

`vtreat` version `1.5.1` and newer issue a warning if you call the incorrect transform pattern on your original training data:

```{r}
d_prepared_wrong <- prepare(transform, d)
```

### The Score Frame

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.

```{r}
score_frame <- transform$scoreFrame

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: 

* an indicator variable for each possible level, plus `NA` (`xc_lev_*`)
* the value of a (cross-validated) one-variable model for `yc` as a function of `xc` (`xc_catB`)
* a variable that returns how prevalent this particular value of `xc` is in the training data (`xc_catP`)

The variable `x` has been converted to two new variables:

* a clean version of `x` that has no missing values or `NaN`s
* a variable indicating when `x` 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 smaller than `default_threshold`. See the section *Deriving the Default Thresholds* below for the reasoning behind such a default threshold. 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:

```{r}
# recommended variables
score_frame[score_frame[['recommended']], 'varName', drop = FALSE]  %.>%
  knitr::kable(.)
```

```{r}
# not recommended variables
score_frame[!score_frame[['recommended']], 'varName', drop = FALSE] %.>%
  knitr::kable(.)
```


## A Closer Look at `catB` variables

Variables 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:

```{r}
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.

```{r}
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.

## Using the Prepared Data in a Model

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`.

```{r}
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.

```{r}
# create the new data
dtest <- make_data(450)

# prepare the new data with vtreat
dtest_prepared = prepare(transform, dtest)
# dtest %.>% transform is an alias for prepare(transform, 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')
```

## Parameters for `BinomialOutcomeTreatment`

We've tried to set the defaults for all parameters so that `vtreat` is usable out of the box for most applications.

```{r}
suppressPackageStartupMessages(library(printr))
args("mkCrossFrameCExperiment")
```

Some parameters of note include:

**codeRestriction**: The types of synthetic variables that `vtreat` will (potentially) produce. By default, all possible applicable types will be produced. See *Types of prepared variables* below.

**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. 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](https://github.com/WinVector/vtreat/blob/master/Examples/Imputation/Imputation.md).

**customCoders**: For passing in user-defined transforms for custom data preparation. Won't be needed in most situations, but see [here](http://www.win-vector.com/blog/2017/09/custom-level-coding-in-vtreat/) for an example of applying a GAM transform to input variables.


## Types of prepared 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: for each level of the variable, 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](https://winvector.github.io/vtreat/articles/vtreatVariableTypes.html).

### 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 `catB` or `prevalence_code` variables.

```{r}
unpack[
  transform_thin = treatments,
  d_prepared_thin = crossFrame
  ] <- vtreat::mkCrossFrameCExperiment(
    dframe = d,                                    # data to learn transform from
    varlist = setdiff(colnames(d), c('y', 'yc')),  # columns to transform
    outcomename = 'yc',                            # outcome variable
    outcometarget = TRUE,                          # outcome of interest
    codeRestriction = c('lev',                     # transforms we want
                        'clean',
                        'isBAD')
  )

score_frame_thin <- transform_thin$scoreFrame

# no catB or catP
d_prepared_thin %.>%
  head(.) %.>%
  knitr::kable(.)
```

```{r}
# no catB or catP
knitr::kable(score_frame_thin[,cols])
```


## Deriving the Default Thresholds

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](http://www.win-vector.com/blog/2014/02/bad-bayes-an-example-of-why-you-need-hold-out-testing/) 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.

## 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**: [`R` regression example, fit/prepare interface](https://github.com/WinVector/vtreat/blob/master/Examples/Regression/Regression_FP.md), [`R` regression example, design/prepare/experiment interface](https://github.com/WinVector/vtreat/blob/master/Examples/Regression/Regression.md), [`Python` regression example](https://github.com/WinVector/pyvtreat/blob/master/Examples/Regression/Regression.md).
 * **Classification**: [`R` classification example, fit/prepare interface](https://github.com/WinVector/vtreat/blob/master/Examples/Classification/Classification_FP.md), [`R` classification example, design/prepare/experiment interface](https://github.com/WinVector/vtreat/blob/master/Examples/Classification/Classification.md), [`Python` classification  example](https://github.com/WinVector/pyvtreat/blob/master/Examples/Classification/Classification.md).
 * **Unsupervised tasks**: [`R` unsupervised example, fit/prepare interface](https://github.com/WinVector/vtreat/blob/master/Examples/Unsupervised/Unsupervised_FP.md), [`R` unsupervised example, design/prepare/experiment interface](https://github.com/WinVector/vtreat/blob/master/Examples/Unsupervised/Unsupervised.md), [`Python` unsupervised example](https://github.com/WinVector/pyvtreat/blob/master/Examples/Unsupervised/Unsupervised.md).
 * **Multinomial classification**: [`R` multinomial classification example, fit/prepare interface](https://github.com/WinVector/vtreat/blob/master/Examples/Multinomial/MultinomialExample_FP.md), [`R` multinomial classification example, design/prepare/experiment interface](https://github.com/WinVector/vtreat/blob/master/Examples/Multinomial/MultinomialExample.md), [`Python` multinomial classification example](https://github.com/WinVector/pyvtreat/blob/master/Examples/Multinomial/MultinomialExample.md).

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.