# Introduction

Xgboost is short for eXtreme Gradient Boosting package.

The purpose of this Vignette is to show you how to use Xgboost to build a model and make predictions.

It is an efficient and scalable implementation of gradient boosting framework by @friedman2000additive and @friedman2001greedy. Two solvers are included:

- linear model ;
- tree learning algorithm.

It supports various objective functions, including regression, classification and ranking. The package is made to be extendible, so that users are also allowed to define their own objective functions easily.

It has been used to win several Kaggle competitions.

It has several features:

- Speed: it can automatically do parallel computation on Windows and Linux, with OpenMP. It is generally over 10 times faster than the classical `gbm`.
- Input Type: it takes several types of input data:
  - Dense Matrix: R's dense matrix, i.e. `matrix` ;
  - Sparse Matrix: R's sparse matrix, i.e. `Matrix::dgCMatrix` ;
  - Data File: local data files ;
  - `xgb.DMatrix`: its own class (recommended).
- Sparsity: it accepts sparse input for both tree booster and linear booster, and is optimized for sparse input ;
- Customization: it supports customized objective functions and evaluation functions.

# Installation

## Github version

For up-to-date version (highly recommended), install from Github:

    devtools::install_github('dmlc/xgboost', subdir='R-package')

> Windows user will need to install RTools first.

## Cran version

As of 2015-03-13, ‘xgboost’ was removed from the CRAN repository.

Formerly available versions can be obtained from the CRAN archive

# Learning

For the purpose of this tutorial we will load Xgboost package.

    require(xgboost)

## Dataset presentation

In this example, we are aiming to predict whether a mushroom can be eaten or not (like in many tutorials, example data are the the same as you will use on in your every day life :-).

Mushroom data is cited from UCI Machine Learning Repository. @Bache+Lichman:2013.

## Dataset loading

We will load the `agaricus` datasets embedded with the package and will link them to variables.

The datasets are already split in:

- `train`: will be used to build the model ;
- `test`: will be used to assess the quality of our model.

Why split the dataset in two parts?

In the first part we will build our model. In the second part we will want to test it and assess its quality. Without dividing the dataset we would test the model on the data which the algorithm have already seen.

    data(agaricus.train, package='xgboost')
    data(agaricus.test, package='xgboost')
    train <- agaricus.train
    test <- agaricus.test

> In the real world, it would be up to you to make this division between `train` and `test` data. The way to do it is out of the purpose of this article, however `caret` package may help.

Each variable is a `list` containing two things, `label` and `data`:

    str(train)

    ## List of 2
    ##  $ data :Formal class 'dgCMatrix' [package "Matrix"] with 6 slots
    ##   .. ..@ i       : int [1:143286] 2 6 8 11 18 20 21 24 28 32 ...
    ##   .. ..@ p       : int [1:127] 0 369 372 3306 5845 6489 6513 8380 8384 10991 ...
    ##   .. ..@ Dim     : int [1:2] 6513 126
    ##   .. ..@ Dimnames:List of 2
    ##   .. .. ..$ : NULL
    ##   .. .. ..$ : chr [1:126] "cap-shape=bell" "cap-shape=conical" "cap-shape=convex" "cap-shape=flat" ...
    ##   .. ..@ x       : num [1:143286] 1 1 1 1 1 1 1 1 1 1 ...
    ##   .. ..@ factors : list()
    ##  $ label: num [1:6513] 1 0 0 1 0 0 0 1 0 0 ...

`label` is the outcome of our dataset meaning it is the binary classification we will try to predict.

Let's discover the dimensionality of our datasets.

    dim(train$data)

    ## [1] 6513  126

    dim(test$data)

    ## [1] 1611  126

This dataset is very small to not make the R package too heavy, however Xgboost is built to manage huge dataset very efficiently.

As seen below, the `data` are stored in a `dgCMatrix` which is a sparse matrix and `label` vector is a `numeric` vector (`{0,1}`):

    class(train$data)[1]

    ## [1] "dgCMatrix"

    class(train$label)

    ## [1] "numeric"

## Basic Training using Xgboost

This step is the most critical part of the process for the quality of our model.

### Basic training

We are using the `train` data. As explained above, both `data` and `label` are stored in a `list`.

In a sparse matrix, cells containing `0` are not stored in memory. Therefore, in a dataset mainly made of `0`, memory size is reduced. It is very usual to have such dataset.

We will train decision tree model using the following parameters:

- `objective = "binary:logistic"`: we will train a binary classification model ;
- `max.deph = 2`: the trees won't be deep, because our case is very simple ;
- `nthread = 2`: the number of cpu threads we are going to use;
- `nround = 2`: there will be two passes on the data, the second one will enhance the model by further reducing the difference between ground truth and prediction.

    bstSparse <- xgboost(data = train$data, label = train$label, max.depth = 2, eta = 1, nthread = 2, nround = 2, objective = "binary:logistic")

    ## [0]  train-error:0.046522
    ## [1]  train-error:0.022263

> More complex the relationship between your features and your `label` is, more passes you need.

### Parameter variations

#### Dense matrix

Alternatively, you can put your dataset in a dense matrix, i.e. a basic R matrix.

    bstDense <- xgboost(data = as.matrix(train$data), label = train$label, max.depth = 2, eta = 1, nthread = 2, nround = 2, objective = "binary:logistic")

    ## [0]  train-error:0.046522
    ## [1]  train-error:0.022263

#### xgb.DMatrix

Xgboost offers a way to group them in a `xgb.DMatrix`. You can even add other meta data in it. It will be usefull for the most advanced features we will discover later.

    dtrain <- xgb.DMatrix(data = train$data, label = train$label)
    bstDMatrix <- xgboost(data = dtrain, max.depth = 2, eta = 1, nthread = 2, nround = 2, objective = "binary:logistic")

    ## [0]  train-error:0.046522
    ## [1]  train-error:0.022263

#### Verbose option

Xgboost has severa features to help you to view how the learning progress internally. The purpose is to help you to set the best parameters, which is the key of your model quality.

One of the simplest way to see the training progress is to set the `verbose` option (see below for more advanced technics).

    # verbose = 0, no message
    bst <- xgboost(data = dtrain, max.depth = 2, eta = 1, nthread = 2, nround = 2, objective = "binary:logistic", verbose = 0)

    # verbose = 1, print evaluation metric
    bst <- xgboost(data = dtrain, max.depth = 2, eta = 1, nthread = 2, nround = 2, objective = "binary:logistic", verbose = 1)

    ## [0]  train-error:0.046522
    ## [1]  train-error:0.022263

    # verbose = 2, also print information about tree
    bst <- xgboost(data = dtrain, max.depth = 2, eta = 1, nthread = 2, nround = 2, objective = "binary:logistic", verbose = 2)

    ## tree prunning end, 1 roots, 6 extra nodes, 0 pruned nodes ,max_depth=2
    ## [0]  train-error:0.046522
    ## tree prunning end, 1 roots, 4 extra nodes, 0 pruned nodes ,max_depth=2
    ## [1]  train-error:0.022263

# Basic prediction using Xgboost

## Perform the prediction

The pupose of the model we have built is to classify new data. As explained before, we will use the `test` dataset for this step.

    pred <- predict(bst, test$data)

    # size of the prediction vector
    print(length(pred))

    ## [1] 1611

    # limit display of predictions to the first 10
    print(head(pred))

    ## [1] 0.28583017 0.92392391 0.28583017 0.28583017 0.05169873 0.92392391

These numbers doesn't look like binary classification `{0,1}`. We need to perform a simple transformation before being able to use these results.

## Transform the regression in a binary classification

The only thing that Xgboost does is a regression. Xgboost is using `label` vector to build its regression model.

How can we use a regression model to perform a binary classification?

If we think about the meaning of a regression applied to our data, the numbers we get are probabilities that a datum will be classified as `1`. Therefore, we will set the rule that if this probability for a specific datum is `> 0.5` then the observation is classified as `1` (or `0` otherwise).

    prediction <- as.numeric(pred > 0.5)
    print(head(prediction))

    ## [1] 0 1 0 0 0 1

## Measuring model performance

To measure the model performance, we will compute a simple metric, the average error.

    err <- mean(as.numeric(pred > 0.5) != test$label)
    print(paste("test-error=", err))

    ## [1] "test-error= 0.0217256362507759"

> Note that the algorithm has not seen the `test` data during the model construction.

Steps explanation:

1. `as.numeric(pred > 0.5)` applies our rule that when the probability (<=> regression <=> prediction) is `> 0.5` the observation is classified as `1` and `0` otherwise ;
2. `probabilityVectorPreviouslyComputed != test$label` computes the vector of error between true data and computed probabilities ;
3. `mean(vectorOfErrors)` computes the average error itself.

The most important thing to remember is that to do a classification, you just do a regression to the `label` and then apply a threshold.

Multiclass classification works in a similar way.

This metric is 0.02 and is pretty low: our yummly mushroom model works well!

# Advanced features

Most of the features below have been implemented to help you to improve your model by offering a better understanding of its content.

## Dataset preparation

For the following advanced features, we need to put data in `xgb.DMatrix` as explained above.

    dtrain <- xgb.DMatrix(data = train$data, label=train$label)
    dtest <- xgb.DMatrix(data = test$data, label=test$label)

## Measure learning progress with xgb.train

Both `xgboost` (simple) and `xgb.train` (advanced) functions train models.

One of the special feature of `xgb.train` is the capacity to follow the progress of the learning after each round. Because of the way boosting works, there is a time when having too many rounds lead to an overfitting. You can see this feature as a cousin of cross-validation method. The following technics will help you to avoid overfitting or optimizing the learning time in stopping it as soon as possible.

One way to measure progress in learning of a model is to provide to Xgboost a second dataset already classified. Therefore it can learn on the first dataset and test its model on the second one. Some metrics are measured after each round during the learning.

> in some way it is similar to what we have done above with the average error. The main difference is that below it was after building the model, and now it is during the construction that we measure errors.

For the purpose of this example, we use `watchlist` parameter. It is a list of `xgb.DMatrix`, each of them tagged with a name.

    watchlist <- list(train=dtrain, test=dtest)

    bst <- xgb.train(data=dtrain, max.depth=2, eta=1, nthread = 2, nround=2, watchlist=watchlist, objective = "binary:logistic")

    ## [0]  train-error:0.046522    test-error:0.042831
    ## [1]  train-error:0.022263    test-error:0.021726

Xgboost has computed at each round the same average error metric than seen above (we set `nround` to 2, that is why we have two lines). Obviously, the `train-error` number is related to the training dataset (the one the algorithm learns from) and the `test-error` number to the test dataset.

Both training and test error related metrics are very similar, and in some way, it makes sense: what we have learned from the training dataset matches the observations from the test dataset.

If with your own dataset you have not such results, you should think about how you did to divide your dataset in training and test. May be there is something to fix. Again, `caret` package may help.

For a better understanding of the learning progression, you may want to have some specific metric or even use multiple evaluation metrics.

    bst <- xgb.train(data=dtrain, max.depth=2, eta=1, nthread = 2, nround=2, watchlist=watchlist, eval.metric = "error", eval.metric = "logloss", objective = "binary:logistic")

    ## [0]  train-error:0.046522    train-logloss:0.233366  test-error:0.042831 test-logloss:0.226687
    ## [1]  train-error:0.022263    train-logloss:0.136656  test-error:0.021726 test-logloss:0.137875

> `eval.metric` allows us to monitor two new metrics for each round, `logloss` and `error`.

## Linear boosting

Until know, all the learnings we have performed were based on boosting trees. Xgboost implements a second algorithm, based on linear boosting. The only difference with previous command is `booster = "gblinear"` parameter (and removing `eta` parameter).

    bst <- xgb.train(data=dtrain, booster = "gblinear", max.depth=2, nthread = 2, nround=2, watchlist=watchlist, eval.metric = "error", eval.metric = "logloss", objective = "binary:logistic")

    ## [0]  train-error:0.024259    train-logloss:0.183142  test-error:0.017381 test-logloss:0.181439
    ## [1]  train-error:0.004146    train-logloss:0.069416  test-error:0.003724 test-logloss:0.067254

In this specific case, linear boosting gets sligtly better performance metrics than decision trees based algorithm.

In simple cases, it will happem because there is nothing better than a linear algorithm to catch a linear link. However, decision trees are much better to catch a non linear link between predictors and outcome. Because there is no silver bullet, we advise you to check both algorithms with your own datasets to have an idea of what to use.

## Manipulating xgb.DMatrix

### Save / Load

Like saving models, `xgb.DMatrix` object (which groups both dataset and outcome) can also be saved using `xgb.DMatrix.save` function.

    xgb.DMatrix.save(dtrain, "dtrain.buffer")

    ## 6513x126 matrix with 143286 entries is saved to dtrain.buffer

    ## [1] TRUE

    # to load it in, simply call xgb.DMatrix
    dtrain2 <- xgb.DMatrix("dtrain.buffer")

    ## 6513x126 matrix with 143286 entries is loaded from dtrain.buffer

    bst <- xgb.train(data=dtrain2, max.depth=2, eta=1, nthread = 2, nround=2, watchlist=watchlist, objective = "binary:logistic")

    ## [0]  train-error:0.046522    test-error:0.042831
    ## [1]  train-error:0.022263    test-error:0.021726

### Information extraction

Information can be extracted from `xgb.DMatrix` using `getinfo` function. Hereafter we will extract `label` data.

    label = getinfo(dtest, "label")
    pred <- predict(bst, dtest)
    err <- as.numeric(sum(as.integer(pred > 0.5) != label))/length(label)
    print(paste("test-error=", err))

    ## [1] "test-error= 0.0217256362507759"

## View feature importance/influence from the learnt model

Feature importance is similar to R gbm package's relative influence (rel.inf).

    importance_matrix <- xgb.importance(model = bst)
    print(importance_matrix)
    xgb.plot.importance(importance_matrix)

## View the trees from a model

You can dump the tree you learned using `xgb.dump` into a text file.

    xgb.dump(bst, with.stats = T)

    ##  [1] "booster[0]"
    ##  [2] "0:[f28<-1.00136e-05] yes=1,no=2,missing=1,gain=4000.53,cover=1628.25"
    ##  [3] "1:[f55<-1.00136e-05] yes=3,no=4,missing=3,gain=1158.21,cover=924.5"
    ##  [4] "3:leaf=1.71218,cover=812"
    ##  [5] "4:leaf=-1.70044,cover=112.5"
    ##  [6] "2:[f108<-1.00136e-05] yes=5,no=6,missing=5,gain=198.174,cover=703.75"
    ##  [7] "5:leaf=-1.94071,cover=690.5"
    ##  [8] "6:leaf=1.85965,cover=13.25"
    ##  [9] "booster[1]"
    ## [10] "0:[f59<-1.00136e-05] yes=1,no=2,missing=1,gain=832.545,cover=788.852"
    ## [11] "1:[f28<-1.00136e-05] yes=3,no=4,missing=3,gain=569.725,cover=768.39"
    ## [12] "3:leaf=0.784718,cover=458.937"
    ## [13] "4:leaf=-0.96853,cover=309.453"
    ## [14] "2:leaf=-6.23624,cover=20.4624"

You can plot the trees from your model using `xgb.plot.tree`

    xgb.plot.tree(model = bst)

> if you provide a path to `fname` parameter you can save the trees to your hard drive.

## Save and load models

May be your dataset is big, and it takes time to train a model on it? May be you are not a big fan of loosing time in redoing the same task again and again? In these very rare cases, you will want to save your model and load it when required.

Hopefully for you, Xgboost implements such functions.

    # save model to binary local file
    xgb.save(bst, "xgboost.model")

    ## [1] TRUE

> `xgb.save` function should return TRUE if everything goes well and crashes otherwise.

An interesting test to see how identic is our saved model with the original one would be to compare the two predictions.

    # load binary model to R
    bst2 <- xgb.load("xgboost.model")
    pred2 <- predict(bst2, test$data)

    # And now the test
    print(paste("sum(abs(pred2-pred))=", sum(abs(pred2-pred))))

    ## [1] "sum(abs(pred2-pred))= 0"

> result is `0`? We are good!

In some very specific cases, like when you want to pilot Xgboost from `caret` package, you will want to save the model as a R binary vector. See below how to do it.

    # save model to R's raw vector
    rawVec <- xgb.save.raw(bst)

    # print class
    print(class(rawVec))

    ## [1] "raw"

    # load binary model to R
    bst3 <- xgb.load(rawVec)
    pred3 <- predict(bst3, test$data)

    # pred2 should be identical to pred
    print(paste("sum(abs(pred3-pred))=", sum(abs(pred2-pred))))

    ## [1] "sum(abs(pred3-pred))= 0"

> Again `0`? It seems that `Xgboost` works pretty well!

# References